V107 4 2016 S IN INSI I NINS 189 ISSN 1991-1696 … · 190 S IN INSI I NINS V107 4 2016 ... frequently in chemical processes and fault detection processes (dynamics). [21] further

Vol.107 (4) December 2016 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 189

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Africa Research JournalISSN 1991-1696

Research Journal of the South African Institute of Electrical EngineersIncorporating the SAIEE Transactions

Vol.107 (4) December 2016SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS190

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ISSN 1991-1696

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SPECIALIST EDITORSCommunications and Signal Processing:Prof. L.P. Linde, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SA Prof. S. Maharaj, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SADr O. Holland, Centre for Telecommunications Research, London, UKProf. F. Takawira, School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, SAProf. A.J. Han Vinck, University of Duisburg-Essen, GermanyDr E. Golovins, DCLF Laboratory, National Metrology Institute of South Africa (NMISA), Pretoria, SAComputer, Information Systems and Software Engineering:Dr M. Weststrate, Newco Holdings, Pretoria, SAProf. A. van der Merwe, Department of Infomatics, University of Pretoria, SA Dr C. van der Walt, Modelling and Digital Science, Council for Scientific and Industrial Research, Pretoria, SAProf. B. Dwolatzky, Joburg Centre for Software Engineering, University of the Witwatersrand, Johannesburg, SAControl and Automation:Prof K. Uren, School of Electrical, Electronic and Computer Engineering, North-West University, S.ADr J.T. Valliarampath, freelancer, S.ADr B. Yuksel, Advanced Technology R&D Centre, Mitsubishi Electric Corporation, JapanProf. T. van Niekerk, Dept. of Mechatronics,Nelson Mandela Metropolitan University, Port Elizabeth, SAElectromagnetics and Antennas:Prof. J.H. Cloete, Dept. of Electrical and Electronic Engineering, Stellenbosch University, SA Prof. T.J.O. Afullo, School of Electrical, Electronic and Computer Engineering, University of KwaZulu-Natal, Durban, SA Prof. R. Geschke, Dept. of Electrical and Electronic Engineering, University of Cape Town, SADr B. Jokanović, Institute of Physics, Belgrade, SerbiaElectron Devices and Circuits:Dr M. Božanić, Azoteq (Pty) Ltd, Pretoria, SAProf. M. du Plessis, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SADr D. Foty, Gilgamesh Associates, LLC, Vermont, USAEnergy and Power Systems:Prof. M. Delimar, Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia Engineering and Technology Management:Prof. J-H. Pretorius, Faculty of Engineering and the Built Environment, University of Johannesburg, SA

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VOL 107 No 4December 2016

SAIEE Africa Research Journal

Observer design for a bilinear model of a continuous countercurrent ion exchange process . .....................192N.M. Dube and R.T. Tzoneva

Power Pool Transfer Limits: Standardised Process . ..................215J. Lavagna and A.L. Marnewick

BER Performance of a Hierarchical APSK UEP System over Nakagami-m fading . ..............................................230T. Quazi and H. Xu

Secure Signal and Space Alamouti Scheme . ..............................237P.O. Akuon and H. Xu

SAIEE AFRICA RESEARCH JOURNAL EDITORIAL STAFF ...................... IFC


OBSERVER DESIGN FOR A BILINEAR MODEL OF A CONTINUOUS COUNTERCURRENT ION EXCHANGE PROCESS.

N.M. Dube* and R.T. Tzoneva**

* Dept. of Electrical Engineering (Bellville), Cape Peninsula University of Technology, Robert Sobukwe Rd/Symphony Way, Bellville, Western Cape, 7535, South Africa, email: [email protected] ** Dept. of Electrical Engineering (Belllville), Cape Peninsula University of Technology, Robert Sobukwe Rd/Symphony Way, Bellville, Western Cape, 7535, South Africa, email: [email protected]

Abstract: The paper describes a method and proposes an algorithm for a bilinear observer design as part of a state estimation solution for a Continuous Countercurrent Ion Exchange (CCIX) process used for desalination of water. The aim of the design is to determine immeasurable process state variables using real CCIX measurement data obtained from a different study. The solution requires determination of the observer gain matrix and it is formulated on the basis of the pole placement method. The contribution of the paper is in the developed bilinear dynamic models of the process and the observer and in the extending of the pole placement method for the special matrices of the bilinear observer. An analytical procedure is developed and implemented for calculation of the characteristic equation of the observer as part of calculation of the observer gain matrix. Matlab and SIMULINK software programs for determining the estimated states are developed. Investigation of the performance of the bilinear observer and the closed loop system under various constant values of the control input and different state initial conditions is performed. The results are presented and discussed.

Key words: linear systems, nonlinear systems, state estimation, observer design, bilinear model, ion exchange, pole placement.

1. INTRODUCTION AND BACKGROUND

A bilinear model of a Continuous Countercurrent Ion Exchange (CCIX) process described in [1–3] has been developed with the overall objective to be applicable to optimal control design of the process [4, 5]. Generally, in developing a model, more especially for the purpose of monitoring and optimal control of a process based on feedback controller design [6], some components of the process state are not known, and or cannot be measured directly from the process due to a lack of a suitable sensor or due to the nature of the plant [6–11]. This necessitates the need for developing a method for determining such states before application of the designed optimal control of the process [12]. [13] suggests that the state estimation problem in bilinear systems is a very important part of designing controllers in these systems. [14] considered the feedback property of the observer. [15] state that a lot of ground was covered in design of observers in determining the importance of observers in feedback control. In designing the observer, generally, two conditions must be met, 1) minimization of the error difference between the model states and the observer estimated states, and 2) keeping error dynamics and its rate at zero or close to zero under changing input or state variables [6, 7]. The observer methods for design can be divided into two main approaches: 1) for linear or 2) nonlinear systems. Unfortunately, a linear state observer is not adequate to reconstruct states of a nonlinear system

and this suggests the need for the design of nonlinear observers [6, 13, 16]. Unlike in the linear case [9, 12, 16–20], where the error dynamics are known to be independent of the input signal and the present value of the state; in the nonlinear or bilinear case, the error dynamics are not totally independent of the input signal and the state due to the bilinear dependence between these two variables [6, 13, 20]. With a lot of work in the (1980s) based on physical systems, which are mainly nonlinear or bilinear, the result was a lot of effort directed on linearization of the nonlinear systems [12, 16, 21, 22]. Different observer types are considered in [23]. [12, 21, 24] suggest that the common approach to solving observer design problem for nonlinear systems is to extend the linear Luenberger observer, the linear Kalman filter design approach or the pseudo-linearization techniques to the nonlinear systems. According to [23] these techniques are also valid only for small ranges around the operating point; and if applied in real time applications, they have an extensive computational requirement. A number of authors considered the nonlinear systems to be of Lipschitz typein designing their nonlinear observers [16, 23, 25, 26]. [23] gives the full description of the local and global Lipschitz systems. According to [8, 27, 28] research in nonlinear state observer design resulted in the following techniques, by which the above mentioned solutions can be categorized under: extended linearization, feedback linearization, variable structure, high-gain observer


design, extended Kalman filter and its family, Lyapunov-based techniques and state-dependent Riccati equation–based techniques. According to [13, 29] bilinear systems can be considered as a special class of nonlinear systems, and can also be considered good approximations to the nonlinear systems. Bilinear systems appear naturally as models for physical systems. [13] describes the bilinear systems as a special class of nonlinear systems where the control input appears both additive and multiplicative in the system model. [13, 29, 30] suggest that bilinear systems occur frequently in chemical processes and fault detection processes (dynamics). [21] further suggests that there are a number of reasons for studying bilinear systems, as a class of the nonlinear systems, such as, 1) these systems closely resemble linear systems (which already has a well-developed theory), 2) bilinear systems arise in variety in many physical and practically implementable processes [13, 16]. A lot of work on observer design for bilinear systems (models) appears in the literature [6, 7, 29–34]. In the mid 1970’s work on the design of bilinear observers started appearing in the literature and this attracted a lot of interest towards the end of the 1970’s to the early 1980’s. During this period a lot of significant successes and milestones were reached in estimating unknown state variables for bilinear systems [15, 29, 32–34, 35]. [13, 20] proposed an observer for nonlinear systems where the estimation error decays to zero irrespective of the input. These authors further gave an analysis of observability of nonlinear systems in comparison to that of linear ones. A number of authors propose the design of asymptotic observers [11, 12, 20]. [11] presented the problem of obtaining an asymptotic estimate of the state of a bilinear system given input and output measurements. [20] proposed an asymptotic observer that is capable of estimating state variables for all initialization of the observer. The initialization of the observer plays an important part in bioprocesses since initial conditions are not measured. Many authors considered stability, observability and controllability and associated necessary conditions for the existence of these properties in their design of observers, including analysis of observability of nonlinear systems [12, 13, 36]. [11, 12] generated necessary and sufficient conditions for the observability of a general system of bilinear and nonlinear equations. [14] discussed reducibility of a bilinear system to a canonical controllability form as a criterion for uniform for observability. [37] generated sufficient conditions for the existence of a stable observer. [12] considered necessary and sufficient conditions for the existence of a special observable form. [8, 30] work showed that the use of Lyapunov framework facilitates and proves asymptotic stabilization of observation errors. [23] gave a procedure for obtaining the observer gain such that there is quadratic stabilization of the error dynamics based on condition of existence of a certain Lyapunov function. [10] presented a design of an exponential observer based on Lyapunov method. [8, 30, 34] consider the Lyapunov stabilization procedure and convergence conditions in the

observer design. The work of [10, 28, 31] includes solving a Lyapunov equation in determining the state estimator. [20] proved convergence of their design using classical Lyapunov functions. [38] proposed an stable observer design based on Lyapunov stability for bilinear systems. This work considers a state observer with the error that may depend on the system input signal. The pole placement method is often used to design the state observer matrix [39–42]. It is applicable in the cases of the discrete time implementation of the controller and the state observer of the closed loop system. This approach is applied to various processes in the industry, but till now it has not been applied to the case of the countercurrent ion exchange process. This process, due to the nature of construction of its columns allows measurement only of the output variable and of the input disturbance. All states are not measurable and the proper control of the process requires corresponding state observer equations. There is no described algorithm for design on an observer for the countercurrent ion exchange process till now in the existing literature. This problem of design of the gain matrix of a bilinear observer is considered in the paper. The aim of the paper is to develop a method and an algorithm of designing an observer for a bilinear system for the case of the Continuous Countercurrent Ion Exchange (CCIX) process – to estimate the unknown states of the system that cannot be directly measured from the CCIX plant. The paper presents an observer design which is an extension of a Luenberger-type observer for bilinear systems. The observer design method developed proposes a solution where the disturbance is assumed constant for a long period of time. The input signal stays constant throughout the operational sampling period in some constrained region. This is a more realistic approach since it is a true reflection of the plant’s behaviour. The solution of the problem is developed using pole placement stability requirement of the characteristic equation of the observer. The special structure of the state space matrices of the process model makes the derivation of the calculation algorithm of the pole placement method very difficult. The paper proposes an extension of the existing algorithm based on the analytical derivation of the characteristic equation of the bilinear state observes. Further, the behaviour of the state observer and of the process closed loop system dynamics are investigated for various values of the control input and of the initial states of the observer. The observer matrix is calculated with data acquired from an existing counter current Ion Exchange process. The simulation results given here are for a constant input signal over the full plant trajectory. Though assumed constant over the process trajectory, different input signal values have been considered and are presented in the result section of the paper. The contributions of the paper are as follows:

1) Development of a pole placement method and algorithm for the design of the matrix of a bilinear observer of the ion exchange states in the case of constant values of the input control signal using


the observer characteristic equation stability analysis and the pole placement based approach.

2) Mathematical derivation of the characteristic equation of the observer and the process for the higher dimensional case and special structure of the Ion Exchange process.

3) Development of Matlab/Simulink software for use of the data from the ion exchange process for the design of the observer matrix and the simulation of the system closed loop consisting of a controller, the observer, and the process model.

4) The behavior of the observer and its convergence towards the process model states are investigated for various values of the constant control input and various initial conditions of the estimated states.

5) The behavior of the closed loop system is investigated for various values of the constant control input and various initial conditions of the estimated state.

The significance of the developments described in the paper is the transformation of the ion exchange process in a dynamic state space bilinear model, formulation of the Luenberg type of a state observer, its design through the extension of the pole placement method and the verification of the design by simulation, which is novel in the existing literature. There are no publications which consider the dynamic behavior of the ion exchange process and the connected to it state observers. The paper is organized as follows: in Section 2, the continuous countercurrent ion exchange (CCIX) process is described. Section 3 covers the model development of a bilinear multistage CCIX process based on component balances in the process column stages, and the formulation of the state estimation problem is discussed. In Section 4, the design of the proposed observer is presented. Section 5 presents the pole placement procedure applied to solve the stability problem for the unknown observer matrix, and in turn find the matrix entries using the observer characteristic equation. In Section 6 software for the observer design and simulation is presented. In Section 7, the observer design data are presented and the application of the data in the design of the observer is illustrated. Further, simulation results are given to demonstrate the effectiveness of the design; and this is followed by the conclusion section.

2. PROCESS DESCRIPTION

According to [43] an ion exchange process is a reversible chemical process where ions with similar polarities are exchanged between solids and an electrolyte solution if the two are contacted. The interaction of the ions happens at different levels, there is ion exchange in the solid phase to the liquid phase and also diffusion of ions within the solid phase [44–46]. The ion exchange process is a very convenient chemical process for wastewater desalination [1, 2, 5]. In water desalination application, ion exchange resins form the solid phase, and water being treated forms the liquid phase. Resins are charged beads of micrometers in diameters that are coated with replacement ions +H

(hydrogen ions) or −OH (hydroxide ions) depending on their ionic form (cation or anion). Hydrogen ions are used in the cation resins and hydroxide ions are used in the anion resins. In the cation phase the +H ions will exchange with Na (sodium) ions from sodium chloride ( NaCl ) in the water being processed. During the anion phase the −Cl (chloride) ions exchange with −OH ions from the acidic output stream from the cation phase (Figure 1). Figure 1 also shows the pilot plant as built in the Chemical Engineering Department of Cape Peninsula University of Technology [1, 2, 4, 5]. The basic ion exchange countercurrent configuration consists of four columns, two for each phase of the process. The system has a cation load column and a cation regeneration column for the cation phase, and an anion load column and an anion regeneration column for the anion phase. The columns operate in a multistage fashion with primary and secondary cycles. During the cation load primary cycle, NaCl is extracted from feed water, resulting in an acidic output stream; and during the primary cycle of the anion load, this acidic stream from the cation load column is split to produce product water. The secondary columns are for regeneration of partially exhausted resins back to their refreshed form using either an acid solution or a base solution for each phase respectively. This is one of the greatest advantages of the ion exchange process; resins are reusable for a number of years, depending on their type [1, 3, 4, 43 ,44, 46]. The considered ion exchange process is a countercurrent process with the solid and liquid phases flowing inopposite directions. The exchange is said to be countercurrent in that the moving resin bed and liquid move in opposite directions. The resins are in a packed bed form and they move from column to column in a cyclic form. This cyclic operation has three distinct periods for each of the two main cycles mentioned above in each phase, the primary and secondary cycles. Each cycle has three periodic flows for moving liquid streams and moving resin beds, 1) an up-flow period, 2) the settle time and 3) the pulldown period. During the primary cycle of the cation phase, liquid to be treated is pumped up the load column through a packed bed of resin to fluidize the resin beds held by each stage of the column and this is referred to as an up-flow period. After a certain predetermined period, resin beds are allowed to settle by stopping the up-flow stream. This is known as the settle time. And then finally, the resin bed at the bottom stage is pulled out to prepare it for regeneration; this period is referred to as pulldown period. Before pulldown can be initiated there must be enough resins to fill up a stage in the top holding vessels (Figure 1). During the secondary cycles of the regeneration columns, resin beds of specific amounts are intermittently moved from the top stage of the regeneration column down to the bottom stage in a controlled fashion [1, 2, 4, 46].


3. MODEL DEVELOPMENT AND PROBLEM FORMULATION

In the considered countercurrent ion exchange process the change in concentration of the feed flow at the first stage of the column is considered a disturbance to the system, and it needs to be modelled accordingly. The process is run under a global aim of the optimization. The optimization strategy of the process is to ensure that for a given desalination level, maximum purified water output is obtained with the minimum usage of the regenerant chemicals [1, 2, 3, 44, 46].

Figure 1: Continuous countercurrent ion exchange (CCIX) process as built at Chemical Engineering

Department of Cape Peninsula University of Technology

Technically, this aim can be formulated as an optimization problem using concentration of salt in the product water as a process output and the resin flow rate into the column as the control action for the process on the basis of the steady state balance [4, 5]:

)()()(

tThdtFtu R == (1)

Where

=)(tu the control input to the process, =)(tFR the moving resin bed flow rate in the cation load

column, considered as a control input, =)(tT the upflow period for the cation load column,

=h the resin holdups and =d the liquid-resin fractional balance constant

defining the fraction of the resin hold up which is moved from one stage to another and 3/2=d

The observed column behavior requires the developed mathematical process model to predict liquid and resin composition in each stage for every process cycle. The model design is developed on the basis of the steady state balance between the principal operating parameters of the ion exchange, the liquid flow rate )(tFL and the resin flow rate )(tFR . Up-flow cycle time )(tT determines the control action for the plant [1, 2, 4, 5], as given by equation (1). There are some models developed in the literature for the same process [44–46], however, these models are very complex and could not be used for the purposes of optimization and real-time control based on the intended overall control strategy. These models are more suitable for chemical engineering or analytical chemistry type analysis. The process model in the paper is developed for the purpose of control, and calculations in the model derivation are based on equilibrium and kinetic data, resin and liquid flow rates.

Figure 2: Countercurrent flows of liquid and resin in a single stage of a multistage column of a CCIX

process

These calculations are performed from the bottom to the top column stages, as the changes in the lower stage(s) states affect the following upper stage(s) states. Model equations are developed on the basis of the input and output rates of the mass balances for every process stage, Figure 2, based on the following assumptions [1, 2, 44]: (1) there is equal volume and amount of liquid and resin holdups just before the resin transfer from one stage to the other, (2) there is perfectly mixed fluidized phase in each stage and no back mixing occurs, (3) the process is in a steady state (electro-neutrality is maintained), and (4) a linear equilibrium exists between the liquid and resin phases. In Figure 2, )(, tx na is the mole fraction of sodium ( Na ) in the liquid phase )(, tF nL , )(' , tx nb is the

V19

V7

Carbonation Columns

Reg

ener

atio

n Co

lum

n

Load

Col

umn

1

2

3

4

5

6

7

8

pH

K

Product

L2 L4

L3 L1

Rotameters

V1 V2

V4

V3

V5

V6

V13

V8

V12

V9

V11

V10

1

2

3

4

5

6

7

8

Spent Regenerant

From waste feed tank

Rinse water

V14 V15

V16

V18

V17

No

Regenaration feed

Liquid flow into stage n

Resin flow out of stage n

Liquid flow out of stage n

Resin flow into stage n

stage n(Hn(t), hn(t))

)()( ,, tFtx nLna ⋅

)()( 1,1, tFtx nLna −− ⋅ )()( ,, tFtx nRnb ⋅′

)()( 1,1, tFtx nRnb ++ ⋅′


mole fraction of Na in the resin phase )(, tF nR , )(tH n is the liquid hold up, and hn(t) is the resin hold up for the n -th stage [1, 2, 4, 5, 44]. The ion exchange model is obtained based on the thi component mass balance on stage n with N representing the total number of stages in the process columns, Figure 1 [4, 5]. The component mass law of material balance based on rate of accumulation and rate of materials formation can be expressed as:

[ ][ ] NntxtFtxtF

txtFtxtFdt

txthddt

txtHd

nbnRnanL

nbnRnanL

nbnnan

,1 ,)(')()()(

)(')()()(

))(')(())()((

,,,,

1,1,1,1,

,,

=⋅+⋅−

−⋅+⋅=

=+

++−− (2)

Where

=)(, tF nL the molar flow rate of the liquid, =)(, tF nR the molar flow rate of the resin,

=⋅ −− )()( 1,1, txtF nanL the rate of material input with liquid coming from stage 1−n ,

=⋅ ++ )(')( 1,1, txtF nbnR the rate of material input with resin coming from stage 1+n ,

=⋅ )()( ,, txtF nanL the rate of material output with liquid leaving plate n for plate 1+n ,

=⋅ )(')( ,, txtF nbnR the rate of material output with resin leaving plate n for 1−n ,

=dt

txtHd nn ))()(( the rate of accumulation of sodium

specie in the liquid phase on plate n , and

=dt

txthd nbn ))(')(( , the rate of accumulation of sodium

specie in the resin phase on plate n .

Based on assumptions made, the liquid and resin holdups and flow rates are considered constants, i.e., HHn = ,

hhn = , RnR FtF =)(, , and LnL FtF =)(, . The equilibrium between the liquid and the resin fractions is assumed to be linear to maintain electroneutrality, and the relationship between the exchanging cations is given by [1, 2]

nnannb btxatx += )()(' ,, (3)

Where

=nn ba , the coefficients of the rate of the ion exchange reaction.

After substituting the conditions for the linear equilibrium (3), the component mass law of material balance, based

on the rate of accumulation and the rate of materials formation, the model (2) can be expressed as:

[ ][ ]nnannananR

nanaLnxa

nna

btxabtxaF

txtxFdt

tdha

dttdx

H

+−++

+−=+

+++

−

)())((

)()()()(

,1,1

,1,,,

,

Nn ,1= . (4)

The model (4) can be further simplified to,

+

+

+

+

−

−

+

−

+

=

++

−

Rnan

nRna

n

n

nan

Lna

n

Lna

FtxhaH

aFtx

haHa

txhaH

Ftx

haHF

dttdx

)()(

)()(

)()(

)()(

)(

1,1

,

,1,,

NnFhaH

bbR

n

nn ,1 ,)(

1 =

+

−+ + (5)

After selecting )()()( 01, txtxtx fna ==− , for 1=n as the

column input flow concentration, )()( , txty Na= as the output of the system,

[ ]TNnna txtxtxtxtxtx )(),..,(),..,(),()()( 21, == as the state space vector, and )()( tutFR = as the control input, the state space model of the ion exchange process (5) can be written as

)()(

)()()()()()(1

tCxty

tWxtBututxBtAxdt

tdxf

=

+++=, 0)0( xx =

(6)

Where

+−

+

+−

+

+−

+

+−

=

−−

haHF

haHF

haHF

haHF

haHF

haHF

haHF

A

N

L

N

L

N

L

N

L

LL

L

...00

000...............

0...0

0...00

11

22

1

+−

++−

++−++

−

=

−−

−

haHa

...

haHa

haHa

...............

...haH

ahaH

a

...haH

ahaH

a

B

N

N

N

N

N

N

000

000

00

00

11

1

2

3

2

2

1

2

1

1

1


+

+−

+−+−

=−

haHb

haHbb

haHbb

haHbb

B

N

N

n

NN )(

)(

)(

1

2

23

1

12

M ,

+

=

00...0

1haHF

W

L

,

T

C

=

10

00

M

The model matrices are:

=∈ ×NNRA the matrix of the state, =∈ ×NNRB1 the matrix of bilinear term of the state and

input control signal =∈ ×1NRB the matrix of the input signal =∈ ×1NRW the matrix of the disturbance, =∈ ×NRC 1 the matrix of the output signal.

The model variables are

=∈ ×11)( Rtu the control signal,

=∈ ×1)( NRtx the state vector and

=∈=∈ ×× 110,

11)( RxRtx af the disturbance to the system,

=∈ ×11)( Rty the output of the system.

The disturbance is considered as the change of liquid concentration that enters the first stage (the most bottom stage) of the cation column in the continuous countercurrent ion exchange process. Once the model has been developed and before using it for real time optimal control, one needs to estimate the unknown parameters. In the same breath, in this presentation, the liquid concentration of the CCIX plant cannot be measured inall the stages of the column except for the first and the last stages, one needs to estimate liquid concentration of all other stages using state estimation techniques. The aim is to develop a new algorithm for solving state estimation problem given that the system is nonlinear in terms of variables but linear in terms of parameters. The proposed solution is presented in the next section.

4. DESIGN OF THE OBSERVER

Consider the model of a bilinear system given by (6) above; the objective is to design a full-order observer to be able to identify all the unknown states. The proposed observer is constructed in the analogy of a Luenberger type of observer for linear time–invariant systems. The observer equation for the model (6) is expressed so as to correspond to the structure of the bilinear system, as follows:

)(ˆ)(ˆ

)()()()()(ˆ)(ˆ)(ˆ4321

txCty

tLytxLtuLtutxLtxLdt

txdf

=

++++= (7)

Where

=∈ ×1)(ˆ NRtx the estimated state vector,

=∈ ×11)(ˆ Rty the estimated system output based on estimated states,

=∈ ×NNRL1 the observer state matrix,

=∈ ×NNRL2 the bilinear term matrix of the observer,

=∈ ×13

NRL the observer control input matrix, and

=∈ ×1NRL the output (the observation) matrix.

The main aim of the observer is to minimize the error between the process states )(tx and the estimated states

)(ˆ tx and to be convergent, i.e., asymptotically stable. In order to achieve this aim, the design of the observer is based on fulfillment of two conditions: 1) for the value of the error and 2) for the rate of change of the errorbetween the real and estimated states. The first condition states that 0)( →te for ∞→t and this is presented by the error equation,

0)(ˆ)()( →−= txtxte (8)

This means that the estimated state vector is defined by )()()(ˆ tetxtx −= . Based on the condition for the error rate dynamics of the observed process and the observer states, the second condition is for the minimum error rate value and is expressed by

0)(ˆ)()( ≅

−=

dttxd

dttdx

dttde (9).

The error rate dynamic equation can therefore be expressed as

[ ][ ])()()()()(ˆ)(ˆ

)()()()()()(

4321

1

tLytxLtuLtutxLtxL

tWxtBututxBtAxdt

tde

f

f

++++−

−+++=(10)

From the output process equation, the error rate can be expressed using the output and state variables,

)()( tCxty = . This equation is used to incorporate the measured data )(ty into the equation (11) as a requirement for one of the inputs to the observer before producing the estimates. The error rate equation then becomes:

[ ][ ]))(()()()()(ˆ)(ˆ

)()()()()()(

4321

1

tCxLtxLtuLtutxLtxL

tWxtBututxBtAxdt

tde

f

f

++++−

−+++=(11)


The process of observer design involves determining the matrices 1L , 2L , 3L , and L in such a way that the two minimization error requirements for the error difference are met: the 1) minimization of the error between the process state and the estimated state

0)(ˆ)()( →−= txtxte ; and 2) keeping error rate at zero

or close to zero, 0)( =dt

tde . From this requirement it is

important to note that )(tx and )(tu cannot be zero in this case for the condition to hold. The mathematical derivation of the matrices of the observer is done following the steps below:

1) The error equation (12) is rewritten in the form:

[ ] )()()()()()(ˆ)(

)(ˆ)()()(

4321

1

txLWtuLBtutxLtxB

txLtxLCAdt

tde

f−+−+−+

+−−=

(12)

2) Condition 1 requirements are considered to be fulfilled: if → 0)( =te or )(ˆ)( txtx = . Then, the equation (12) can be rewritten in the following manner

)()()()(

)()()()()()(

43

211

txLWtuLB

tutxLBtxLLCAdt

tde

f−+−+

+−+−−= (13)

In order for dt

tde )( to approach zero, and since 0)( ≠tx ,

0)( ≠tu , 0)( ≠tx f , ∞→t the matrices in front of these variables have to be equal to zero. The following expressions can be generated from this condition

01 =−− LLCA and LCAL −=∴ 1 021 =− LB and 12 BL =∴

03 =− LB and BL =∴ 3 04 =− LW and WL =∴ 4 (14)

According to equation (14) the observer matrices 2L , 3Land 4L are determined.

3) Condition 2 requirements are such that:

The observer matrix 1L is not determined at this moment. This can be done through fulfillment of the second requirement mentioned above after back substitution of

1L , 3L and 4L obtained in equation (14). The error rate equation then becomes

[ ]

[ ] 0)()( )()()()(

)())(ˆ)(())(ˆ)(()(

1

1

1

→+−=+−=

−+−−=

tetuBLCAtuteBteLCA

tutxtxBtxtxLCAdt

tde

(15)

The design of the observer is to find a method for calculation of the observer matrix L in such a way that the rate of the error )(te between the process model state and the observer state is minimized and 0)( →te when

∞→t under some assumptions about the control input )(tu . The above requirement fulfillment means that the

system to be observed is detectable, which means if it cannot be observed, it is still asymptotically stable and the observer to be designed should converge to the real system. The control signal can be considered to be unconstrained or known and fixed. The second case is considered in the paper. In this case, the methods for observer design of linear time invariant linear systems can be applied. Using equation (15) it becomes possible to determine the L matrix using the second requirement. For (15) to converge to zero, the requirement is that the term [ ])()( 1 tuBLCA +− must be a stable matrix. From this requirement, the entries for the observer matrix L can be determined. If the value of the control input is fixed and constrained , the values of L can be determined from the matrix ][ LCA − , where )]([ 1 tuBAA += and the observed behavior is as of a linear system. [13] suggested that if the proper choice of the gain matrix L is made, then the error will go to zero with arbitrary exponential decay. From these interpretations, the observer design problem can be summarized as a problem of choosing or selecting the observer gain matrix L such that the error rate dynamics goes to zero. The pole placement method is used to calculate the observer matrix L .

5. POLE PLACEMENT METHOD FOR DESIGN OF THE OBSERVER MATRIX

5.1 Procedure for design of the observer gain matrix L

The procedure for the design of the matrix L is built on the basis of the pole placement method. The solution for the procedure is given for the case where the input is assumed constant for the entire process time trajectory, or for the case when the matrix L is calculated at every time in the sampling period in which the control is considered constant. The solution is derived from the stability requirement of the error rate dynamics, equation (15). This requirement translates to the pole placement procedure for system stability, i.e., the real parts of the poles of the characteristic equation of the observer must be on the negative side of the Cartesian plane, but not far from the imaginary line in order for the observer to have fast dynamics, faster than the process ones. This is another


reason why the solution is considered to be based on the pole placement method. This method can be used for calculation of the Matrix L coefficients at every sampling period, and in real time if the values of the input signal are changing at every sampling period. Two characteristic equations of the observer are needed for the solution, one is an equation (16) for the determinant of the observer error rate equation and the other is the desired one, determined by the equation (17) for the determinant of the desired observer error rate equation.

[ ])()(det 1 tuBLCAsIsobs +−−= (16)

0)()(det

),)...()(()(det 21

=+=

+++=N

des

Ndes

pss

orpspspss (17)

Where

=s the Laplace variable, [ ] 1

21 ... ×∈= NTN RlllL ,

=Nppp ..., , , 21 the desired poles for every stage of the process and

=p the desired pole that has the same value for all stages of the process.

The coefficients of the observer gain matrix for the given value of the control input are determined by equalization of the two determinants, as follows:

)(det)(det ss desobs = (18)

5.2 Algorithm of the pole placement method for determination of the L matrix

The algorithm for the solving the pole placement problem is given by: 1) Give a trajectory of ftttu ,0),( = , 2) Select the input signal )(tuut = – for a given time

fttt ,0, =

3) Form the determinant of the observer ,det obs with unknown observer gain matrix L ,

[ ]TN tltltltL )(),...,(),()( 21= , 4) Form the desired determinant desdet , 5) Compare the two determinants and calculate the gain

matrix elements, Ni tli ,1),( =The solution to step 5) can be obtained numerically or analytically, e.g., using fsolve functions in Matlab software program provides a numerical solution. The paper proposes an analytical technique of back substitution between the two characteristic equations. The derivation is explained in section 5.3.

5.3 Derivation of the determinant detobs equations

The observer characteristic equation formed from the equation (16) is derived for the considered case of the ion exchange process as follows:

[ ] [ ]

−−

−−

×+

+×−

−

−

−−

−

−

−

=

66

5655

2322

1211

621

6665

3332

2221

11

0.........0......0

0...0000...0000...0

)(

1...00...

.........000......00...000......00.........0

......0000000...0000...0

det

)(det

bbb

bbbb

tu

lll

aa

aaaa

a

s

ss

s

T

obs

O

O

O

O

(19)

Where the elements of the observer matrix L are unknown. In evaluating (19), the resulting simplified expression of the )(det sobs is a 66×R matrix given by (20),

[ ]{ } 66det)(det ×∈= RAs obsobs (20)

Where

+−+−+

−−+−

−+−−+

=

)(0000)(000

000000000

6666665

565

443

334333332

223222221

1121111

lgasagl

lalggasalggasalggas

Aobs

OO

OO

Where

== iiii btug )( the product of control input and b

coefficients of the bilinear term, 6,1=i== ijij btug )( the product of control input and

coefficients of the bilinear term for 5,1=i and 6,2=j .


The mathematical derivation of the characteristic equation from the determinant obsA is very complex because of the higher dimension of the matrix obsA . In order to simplify the calculations the resulting determinant is presented as a sum of sub-determinants which further aids in simplifying the calculation. The sub-determinants are derived from the first row obsA

)(det)(det)(det)(det 621 ssssobs ++= (21)

Where

)(000)(00

0000

)(det

6666665

556

443

334333332

2232222

11111

lgasalg

lalggasalggas

gas

+−+−+

−−+−

−+

×

×−+=

OO

OO

(22)

)(000)(00

00000

)(det

6666665

556

445444443

3343333

22321

122

lgasalg

lggasalggaslga

gs

+−+−+

−+−−+

−

×

×−=

OO

(23)

65

555554

45444443

34333332

23222221

16

0000000

000000

)(det

agasa

ggasaggasa

ggasals

−−+−

−+−−+−

−+−

×

×−=

(24)

Equations (20) – (24) are determined for every sampling period if the control vector is not constant. Using the same approach the sub-determinants )(det1 s , )(det 2 s , and )(det6 s are presented by their sub-determinants, (25) – (27)

[ ])(det)(det)(det)()()(det

1621223112222

11111

slsgsgasgass

+−−+××−+=

(25)

[ ])(det)(det)(det )(det

2622223212112

2

slsgsags

+−=

(26)

[ ])(det)(det)()(det)(det

63236222226121

16

sgsgassals

+−+−−××−=

(27).

The procedure above is followed for all new sub-determinants until their mathematical expressions are derived and the characteristic equation of the observer is obtained, written according to the power of the Laplace variable s . The desired characteristic equation is calculated for a real negative desired pole 5−=ip ,

Ni ,1= . Determination of its equation is via a Matlab software system function, simplify( ) and expand( ) functions,

= )( ))^+((s =

ceexpandNpsimplifyce

ssyms

θ (28)

Where ce stands for characteristic equation.

After evaluating both characteristic equations, the resulting simplified equations are equated to determine values of Nili ,1, = , as follows:

6,1 );(det

1562518759375250037530

)(det23456

=

=++++++

=

il

ssssss

s

iobs

des

(29)

The algorithm for calculation of the observer gain matrix is based on the derivations in point 5. It is shown in Figure 3 and Figure 4.

6. SOFTWARE FOR DESIGN AND SIMULATION

The solution of the observer gain matrix is obtained by the development of a Matlab/Simulink software program. The software program is written according to the proposed algorithm in Figure 3 using the Simulink part as described in Figure 4. The algorithm and the developed software have two parts:

1) Matrix calculation. The first part is used to calculate the model parameters based on the experimental data; then the observer gain matrix L is calculated based on theobserver and the observer desired characteristic equations. 2) Verification of the observer gain matrix. Once the observer parameters are determined, the second part of the program is to simulate the system error based on various specified constant control input and initial conditions for the states of the observer for the full trajectory of the system until the error and error rate requirements are met. If these requirements are not met, then new desired poles are generated and the calculation of the observer gain matrix is calculated again, and so on. Simulink environment, Figure 4 is used for this part. The results from the simulations in this part of the program provide means to evaluate, for which area of constant values of the control input the proposed algorithm will be applicable. The same is done for the initial conditions of the estimated states.


Figure 3: Algorithm for the design process

The proposed algorithm for design can be used for real-time control too, when the control action is changing, but having constant values in the sampling periods for the calculation of the observer gain matrix. In this case the algorithm will be run for every new value of the control signal and the obtained value of L will be directly used for calculation of the estimated state values. These values will be used for calculation of the control action. The structure of the algorithm is similar as in Figure 3, but the difference is that the real-time system replaces the Simulink block, Figure 3, and the calculated observer gain matrix is directly used to produce the real-time state estimates. No verification of the L values is performed in real-time.

Figure 4: Simulation diagram of the closed loop system

7. SIMULATION RESULTS AND DISCUSSION

The observer gain matrix entries are finally determined from Matlab using data obtained from the previous CCIX project [1, 2, 4, 5], Table I, and the error dynamics are observed through Simulink.

7.1 Description of the data

Concentration measurement data from [1, 2, 3] were used to estimate the state variables of the newly developed bilinear model of the continuous countercurrent ion exchange (CCIX) process. The results are based on normalized data of a six stages CCIX process column. Process parameters were calculated for the input flow rate

hmFL /2000 3= , the up-flow period of hT )60/17(= , resin liquid constant ratio 3/2=d , the liquid holdups

l809.42 and the resin holdups of l93.32 [1, 2, 4, 5]. The normalised original data measured from the University of Cape Town (UCT) project [1] is presented in Table I below.

TABLE I. CCIX DATA SHOWING CONCENTRATION IN EACH STAGE OF THE CATION COLUMN AS PER UCT

PROJECT

Stage H+ fractional change in liquid concentration using data obtained from UCT Project [Hendry, 1982b ,Vol. 4]

Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

0.221 0.000 0.000 0.000 0.000 0.000

0.577 0.140 0.040 0.000 0.000 0.000

Observer Model

CONTROLLER B

)(tx f

∫ C

L

C

)(2 txL

∫

3L

1L

A

1BProcess Model

)(tx )(ty)(tx&

)(ˆ ty

)(ˆ tx

[ (ˆ)( tytyL −)(ty

)(tu

)(tu

)(tu

)(ˆ tx )(ˆ tx&

–

)(tx

)(ˆ tx

W

+ +

++ +

Calculation of the model parameters

Calculation of the characteristic equation of

the observer

Calculation of the desired characteristic

equation

Initial values of the desired poles

State data Control data

Calculation of the Lmatrix

Verification of the observer for various constant control values, and

various initial conditions of the observer states in Simulink

Extraction and plotting the values of )(tx , )(ˆ tx , )(te

and )(te&

Is 1)( ε<te

and 2)( ε<te&

Select new desired poles

Desired poles

Terminate calculation

No

Yes


0.730 0.314 0.066 0.004 0.000 0.000

0.847 0.523 0.184 0.035 0.003 0.000

0.920 0.656 0.295 0.082 0.020 0.000

0.936 0.766 0.454 0.168 0.052 0.001

0.968 0.842 0.601 0.277 0.113 0.024

0.974 0.886 0.690 0.361 0.167 0.033

0.981 0.900 0.758 0.440 0.207 0.063

0.989 0.933 0.804 0.522 0.340 0.124

0.988 0.958 0.877 0.698 0.474 0.167

0.997 0.963 0.881 0.784 0.547 0.233

1.000 0.982 0.951 0.899 0.780 0.482

1.000 0.974 0.965 0.931 0.860 0.539

1.000 0.991 0.972 0.966 0.899 0.672

1.000 0.994 0.981 0.966 0.905 0.779

1.000 0.993 1.000 0.991 0.975 0.940

1.000 0.993 0.988 0.991 0.973 0.972

This data set shows the concentration in fractional change of sodium ions, +H as determined from the equation,

++

++

−−=

initialfinal

initialnn FIHFI

HFIHFIFC....

.... (30)

Where

=nFC the fractional change [2]

=+nHFI .. the ionic fraction of +H ions of the current

measurement from the step change moment [2], =+

initialHFI .. the initial ionic fraction of the +H ions in stage [2],

=+finalHFI .. the final ion fraction of the +H ions in the

stage [2].

7.2 Calculation of model matrices

Matlab software programs were run using the data from Table I above to determine the unknown process parameters. The matrices of the process model were calculated to be:

−−

−−

−−

=

382.43382.4300000959.37959.3700000726.35726.3500000966.31966.3100000921.28921.2800000406.26

A

−−

−−

−−

=

002.000000002.0006.0000000054.0007.000000006.0010.000000009.0012.000000011.0013.0

1B

=

3500.00500.01000.01000.00500.00400.0

B ,

=

000004065.26

W ,

T

C

=

100000

The observer gain matrix evaluated with the constant input signal value and model parameters from the above model matrices is shown in equation (31).

[ ]TL 0016.0020.0024.0235.1975.1782.0101 5×= (31)

7.3 Experiments for validation of the observer gain matrix and closed loop system performance

Multiple simulation runs were performed with different input signal values, initial conditions for the observer and the same initial conditions for the process, as per Table II below. A selected sample of the runs is presented here. The steps followed in the simulation procedure are also presented. The initial values of the estimated states are the same for every stage of the column. The simulation programs are run according to values in Table II until the dynamic error rate reaches zero.

TABLE II. THE VALUES USED FOR VALIDATION OFTHE OBSERVER PERFORMANCE

Experiments performed Run 1 Run 2 Run 3 Run 4 Run 5

Input value

)(ku0.0 1.0 5.0 10.0 20.0

Process Init. Cond. 1.0 1.0 1.0 1.0 1.0

Observer Init. Cond.

Set 1 – 1.0 – 1.0 – 1.0 – 1.0 – 1.0 Set 2 0.0 0.0 0.0 0.0 0.0


Set 3 0.5 0.5 0.5 0.5 0.5 Set 4 1.0 1.0 1.0 1.0 1.0 Set 5 10.0 10.0 10.0 10.0 10.0 Set 6 20.0 20.0 20.0 20.0 20.0

7.4 Graphs and results of the simulation process

The following graphs (Figures 5–22) show the behaviour of the process states (from the model) versus that of the estimated states (observer) based on Simulink simulation runs with a constant input signal of 1.0 and constant

initial conditions of the states at 1.0 based on the number of upflow cycles. The different runs are based on the changing observer (estimated) states initial conditions of -1.0, 0, 1/2, 1.0, 5.0 and 10.0; these initial conditions are the same for every stage per each run, i.e., for

621 ˆ,...,ˆ,ˆ xxx . On the graphs the estimated states are

represented by nx~ , 6,1=n . The error and error rate display (Figures 5–21) colour coding matches that of the process and the observer.

Figure 5:Model states and estimated states for observer initial conditions of –1.0 and model initial conditions of 1.0 using a constant control input of 1.0.

Figure 6: Error between process states and estimated states for observer initial conditions of –1.0 and model initial conditions of 1.0 using a constant control input of 1.0.


Figure 7: Rate of change of the error for observer initial conditions of –1.0 and model initial conditions of 1.0 using a constant control input of 1.0.

Figure 8: Model states and estimated states for observer initial conditions of 0.0 and model initial conditions of 1.0 using a constant control input of 1.0.


Figure 9: Error between process states and estimated states for observer initial conditions of 0.0 and model initial conditions of 1.0 using a constant control input of 1.0.

Figure 10: Rate of change of the error for observer initial conditions of 0.0 and model initial conditions of 1.0 using a constant control input of 1.0.


Figure 11: Model states and estimated states for observer initial conditions of 0.5 and model initial conditions of 1.0 using a constant control input of 1.0.




Figure 14: Model states and estimated states for initial conditions of 1.0 for both the observer and model using a constant input signal of 1.0.

In Figure 14, in the same fashion for 11 ~xx = , 22 ~xx = , etc., 44 ~xx = and 55 ~xx = .





Figure 17: Model states and estimated states for observer initial conditions of 5.0 and model initial conditions of 1.0 using a constant input signal of 1.0.




Figure 20: Model states and estimated states for observer initial conditions of 10.0 and model initial conditions of 1.0 using a constant input signal of 1.0.




These results are based on a system with constant observer gain matrix L . It can be clearly seen from the Figures 5–22 that the observer fully tracks the system and converges at a relatively short time period, the 30th cycle for the last stage. Each cycle is 17min. In general, the process of ion exchange is a slow process. In the case where the observer and the system have the same initial conditions, the observer converges even at a shorter period, just before the 20th cycle. This case also shows that the observer is stable. These results further show that the observer is performing very well. At higher observer initial conditions, compared to that of the system (Figure

20), the observer seems to be not smooth in its tracking, but does converge in time compared to other cases where the initial conditions are not far from that of the system. The process system response times have also been examined over various constant control signals and different initial conditions, and these cases are presented by Table III and Table IV. The system responses considered are the rise time ( Tr ), delay time ( Td ) and settle time ( Ts ) for the first, the third and the sixth stages of the ion exchange process column. Both the model and the observer (estimated) system responses are presented in Table III – Table IV.


TABLE III. RISE TIME VS OBSERVER CHANGING INITIAL CONDITION

Process Rise Time vs. Observer Changing Initial Conditions

Input Signal 0)( =ku

State x1 State x3 State x6 Observer Init.

Cond. 1x 1x̂ 3x 3x̂ 6x 6x̂

-1 9.319 9.319 9.170 9.170 11.42 1.622 0 8.846 0 8.940 0 11.42 #NA

0.5 8.079 8.079 8.993 8.993 11.42 1.622 1 4.061 4.061 4.625 4.625 4.237 4.237

Input Signal 1)( =ku-1 9.351 9.290 9.331 9.015 11.56 1.624 0 8.870 8.814 9.100 10.22 11.57 #NA

0.5 8.111 7.138 9.130 9.264 11.53 8.831 1 4.078 4.078 4.693 4.693 4.294 4.294


0.5 8.238 8.380 9.847 11.43 12.08 9.550 1 4.145 4.145 4.964 6.309 6.300 6.309


0.5 8.413 8.850 11.47 #NA 12.96 10.75 1 4.231 4.231 5.400 5.400 6.728 6.724

Input Signal 20)( =ku-1 10.04 8.863 #NA 7.731 18.56 1.667 0 9.783 8.947 #NA 10.89 18.21 #NA

0.5 8.723 10.30 13.26 12.86 17.95 17.10 1 4.407 4.407 20.96 20.96 20.96 20.96

TABLE IV. SETTLE TIME VS OBSERVER CHANGING INITIAL CONDITION

Process Settle Time vs. Observer Changing Initial Conditions

Input Signal 0)( =ku

State x1 State x3 State x6 Observer Init. Con.

1x 1x̂ 3x 3x̂ 6x 6x̂

-1 16.00 16.00 23.00 22.90 26.50 28.50 0 28.20 16.40 40.00 21.00 45.00 42.00

0.5 14.30 14.40 19.20 21.20 27.70 36.00 1 11.00 16.00 22.00 22.00 0.000 0.000

Input Signal 1)( =ku-1 16.20 15.90 24.00 22.50 29.80 28.80 0 31.50 21.30 39.70 42.80 46.50 59.00

0.5 14.50 14.50 22.30 20.30 27.20 28.00 1 11.50 11.50 14.60 14.60 25.50 29.10

Input Signal 5)( =ku-1 17.00 15.20 32.00 26.00 36.00 32.00 0 39.00 37.50 47.50 38.50 54.00 48.00

0.5 15.55 19.30 21.10 21.50 30.40 29.70 1 12.00 12.00 21.00 21.00 28.00 28.00

Input Signal 10)( =ku-1 16.00 13.40 23.50 18.20 29.80 28.30 0 37.50 37.50 41.50 36.00 59.00 59.00

0.5 17.74 27.50 21.88 21.60 28.40 35.00 1 15.50 15.50 25.60 25.60 26.00 26.00

Input Signal 20)( =ku-1 16.00 16.10 23.00 17.80 29.30 28.00 0 31.50 25.00 41.50 35.00 58.00 51.00

0.5 22.00 14.50 21.70 22.00 35.00 29.80 1 11.75 11.75 13.30 13.30 30.00 25.30

7.5 Discussion

The observer has shown that it converges within a reasonable time and maintains the error rate close to zero for the rest of the observed period, Figure 5 – Figure 22. The observer has also shown to be sensitive to the input signal. The input signal values should also be kept within normalized values (0–1.0), otherwise overshoot will be experienced in some process stages. The observer gain matrix values tend to be very high; this could be associated with the determinant calculation that involves a very large number of computational values. Error results showed the success of the observer. The error tracked the difference between estimated and measured states correctly as expected. The error rate showed fairly fast tracking capabilities, thus confirming a well designed observer.

8. CONCLUSION

The observer design for a bilinear model of the Continuous Countercurrent Ion Exchange (CCIX) process has been developed. The observer design has been developed based on real data of the ion exchange process obtained from experiments conducted previously in an ion exchange process of the same type. The data have been normalized for this exercise and simulation results from Simulink and Matlab showed the design to be competently conclusive. The observer converges even if different initial conditions are applied (see Figures 5–22). The results show that the bilinear type observer is applicable in this type of a bilinear process models. The influence of the process initial conditions in comparison to the observer initial conditions has been presented through system responses as indicated by the figures and the tables, Tables III – IV.

9. ACKNOWLEDGMENT

The authors would like to thank Mr. BA. Henry and Mr. K. Raqowa both of Chemical Engineering Department of Cape Peninsula University of Technology (Bellville) for the help with the process technology and knowledge about the ion exchange process. The project is funded under NRF (National Research Foundation) THRIP grant TP2011061100004.


10. REFERENCES

[1]. B.A. Hendry: “Continuous countercurrent ion exchange for desalination and tertiary treatment of effluents and other brackish waters”, Water Science Technology, Vol. 14, No. 6-7, pp. 535 – 352, 1982.

[2]. B.A. Hendry: “Ion exchange for desalination and tertiary treatment of effluents”, Department of Chemical Engineering, University of Cape Town(UCT), Vol. 1–5, December 1982.

[3]. E.W. Randall: 1984. “A microprocessor-based data monitoring and control system for a continuous ion exchange plant”, Desalination, 49, pp. 169–184.

[4]. N.M. Dube; “Modelling and optimal control of ion exchange process”, MTech Dissertation, Department of Electrical Engineering, Peninsula Tech., Bellville, 2001, pp. 139–162.

[5]. N.M. Dube and R. Tzoneva: “Method for optimal control of ion exchange process for desalination of water”, The Third International Conference on Control and Automation (ICCA ’01), pp. 579–583, December 2001.

[6]. Z. Wang, and H. Zhang: “Design of bilinear observer for singular bilinear systems”, Journal of Control Theory and Applications, Vol. 4, 2006, pp. 413–417.

[7]. S. Hara, and K. Furuta: “Minimal order state observers for bilinear systems”, International Journal of Control, 1976, Vol. 24, No. 5, pp. 705–718.

[8]. N. Kazantzis, and C. Kravaris: “Nonlinear observer design Lyapunov’s auxiliary theorem”, Systems & Control Letters, 34, (1998), pp. 241–247.

[9]. D.G. Luenberger: “Observing the state of a linear system”, IEEE Transactions on Military Electronics, 1964, pp. 74–80.

[10]. B.L. Walcott, and S.H. Zak: “State observation of nonlinear uncertain dynamical systems”, IEEE Transactions on Automatic Control, Vol. AC-32, No. 2, February 1987, pp 166–170.

[11]. D. Williamson: “Observation of bilinear systems with application to biological control”, Automatica, Vol. 13, (1977), pp. 243–254.

[12]. A.J. Krener and W. Respondek: “Nonlinear observer with linearizable error dynamics”, SIAM Journal of Control & Optimization, Vol. 23, No. 2, 1985, pp. 197–216.

[13]. M. Saif: “A disturbance accommodating estimator for bilinear systems”, Proceedings of American Control Conference, San Francisco, California, 1993, Paper WP 11–16:30, pp. 945–949.

[14]. A. Behal, A.K. Jain, and K. Joshi: “ Observers for a special class of bilinear systems: Design and application,” IEEE Transactions on Automatic

Control, Vol. 51, No. 11, pp. 1854–1858, November 2006.

[15]. O.M. Grasselli, and A. Isidori: An existence theorem for observers of bilinear systems,” IEEE Transactions on Automatic Control, 1981, Vol. 27, No. 6, pp. 1299–1300.

[16]. J.P. Gauthier, H. Hammouri, and S. Othman: “A simple observer for nonlinear systems applications to bioreactors,” IEEE Transactions on Automatic Control, Vol. 37, No. 6, pp. 875–880, June 1992.

[17]. D.G. Luenberger: “An introduction to observers”, IEEE Transactions on Automatic Control, Vol. AC-16, No. 6, pp. 596–602, December 1971.

[18]. A.F. Lynch and S.A. Bortoff: “Nonlinear observer design by approximate error linearization”, Systems & Control Letters, 32, (1997), pp. 161–172.

[19]. M.-Q. Xiao: “A direct construction of nonlinear discrete-time observer with linearizable error dynamics”, Proceedings in: 2005 American Control Conference, 2005, Portland, OR, USA. , June 8–10

[20]. D. Atroune: “Nonlinear observers for continuous fermentation processes,” Applied Mathematics Letters, Vol. 1, No. 4, (1988), pp 321–325.

[21]. E.B. Braiek, and F. Rotella: “State observer design for analytical nonlinear systems”, Proceedings of IEEE International Conference on Systems, Man, & Cybernetics, 1994, Vol. 3, pp. 2045–2050.

[22]. M.R. James and J.S. Baras: 2006. “An observer design for nonlinear control systems”, In: Analysis and Optimization of Systems, (Eds) A. Bensoussan and JL. Lions, Series: Lecture Notes in Control andInformation Sciences, Vol. 111, Heidelberg: Springer-Verlag, pp. 170–180.

[23]. Raghavan, and J.K. Hedrik: “Observer design for a class of nonlinear systems”, International Journal of Control, Vol. 59, No. 2, 1994, pp. 515–528.

[24]. K.K. Busawon, and M. Saif: “A State observer for nonlinear systems”, IEEE Transactions on Automatic Control, Vol. 44, No. 11, pp. 2098–2103, November 1999.

[25]. M.-S. Chen and C.-C. Chen: “Robust nonlinear observer for Lipschitz nonlinear systems subject to disturbances”, IEEE Transactions on Automatic Control, Vol. 52, No. 12, December 2007, pp. 2365–2369.

[26]. A. Zemouche, and M. Boutayeb: “On LMI conditions to design observers for Lipschitz nonlinear systems”, Automatica, 49, (2013), pp. 585–591.

[27]. X. Hu: “On state observers for nonlinear systems”, Systems & Control Letters, 17, (1991), pp. 465–473.

[28]. E.E. Yaz, C.S. Jeong, A. Bahakeem, and Y.I. Yaz: “Discrete-time nonlinear observer design with


general criteria”, Journal of the Franklin Institute, 344, (2007) pp. 918–928.

[29]. H. Souley Ali, H. Rafaralahy, M. Zasadzinski, S. Halabi and M. Darouach: “Observer design for a class of stochastic bilinear systems with multiplicative noise”, FrA07.6, (2005) American Control Conference, Portland, OR, USA, pp. 3641–3642, June 8-10, 2005.

[30]. K. Joshi, A. Behal, A.K. Jain, and R. Sadagopan: “Observers for a special class of bilinear systems: Design, analysis, and application,” 2005 American Control Conference, Portland, OR, USA, FrC08.3, pp. 4808–4813, June 8–10, 2005.

[31]. B. Tibken, and E.P. Hofer: “Systematic observer design for bilinear systems,” IEEE. ISCAS '89, IEEE International Symposium on Circuits & Systems,Vol. 4, pp. 1611–1616.

[32]. C.S. Hsu, and U.B. Desai: “Approximate reduced-order observers of bilinear systems,” Proceedings of 23rd Conference on Decision & Control, Las Vegas, NV, pp. 798–799, December 1984.

[33]. T. Taniguchi, L. Eciolaza, and M. Sugeno: “Full-order state observer design for nonlinear systems based on piecewise bilinear models,” International Journal of Modeling and Optimization, Vol. 4, No. 2, April 2014, pp. 120–125.

[34]. M.A. Hammami, and H. Jerbi: “Separation principle for nonlinear systems using a bilinear approximation,” Kybernetika, Vol. 37, (2001), No. 5, pp. 565–573.

[35]. D. Vries, K.J. Keesman, and H. Zwart: “A Luenberger observer for an infinite dimensional bilinear system: a UV disinfection example”, Preprints of the 3rd IFAC Symposium on System, Structure & Control, SSSC07, Foz do Iguassu, Brazil, October 17-19th, 2007.

[36]. V. Sundarapandian: General observers for nonlinear systems, Mathematical & Computer Modelling, 39, (2004), pp. 97–105.

[37]. O.I. Goncharov: “Observer design for bilinear systems of a special form,” Differential Equations, 2012, Vol. 48, No. 12, pp. 1596–1606, Pleiades Publishing, Ltd., 2012.

[38]. Y. Funahashi: 1979. An observable canonical form of discrete-time bilinear systems, IEEE Transactions on Automatic Control, 24, No. 5, pp. 802–803.

[39]. M.Q. Phan, F.Vicario, R.W. Longman, and R. Betti: 2015. Observers for bilinear state-space models by interaction matrices, Columbia University Academic Commons, http://dx.doi.org/10.7916/D8W37VKR.

[40]. P.A. Ioannou and J. Sun: 2012. Robust adaptive control (Dover Books on Electrical Engineering). Dover edition, Mineola, New York (United States): Dover Publications.

[41]. K. Rothenhagen, and F. W. Fuchs: 2009. “Current sensor fault detection by bilinear observer for a doubly fed induction generator”, IEEE Transactions on Industrial Electronics, Vol. 56, No. 10, October 2009, pp. 4239–4245.

[42]. H. Rafaralahy, M. Zasadzinski, M. Boutayeb, M. Darouach: 1996 “Comments on ‘State observation of a fixed-bed reactor based on reduced bilinear models’” International Journal of Systems Science, Taylor & Francis, 1996, Vol. 27, No. 3, pp. 349–351. <hal-00098272>

[43]. R.E. Treybal: 1980. Mass transfer operations, 3rd Ed. International Edition Singapore: McGraw-Hill.

[44]. R. Dodds, P.I. Hudson, L. Kershenbaum, and M. Streat: “The operation and modelling of a periodic countercurrent solid-liquid reactor”, Chemical Engineering Science, Vol. 28, No. 6, 1973, pp. 1233–1248.

[45]. F.J.M. Horn: 1967. Periodic countercurrent processes, I and EC Process Design and Development, Vol. 6, No.1, pp. 30–35.

[46]. M.J. Slater: 1974. Continuous ion exchange in fluidized beds. The Canadian Journal of Chemical Engineering, Vol. 52, No. 1, pp. 43–51, February 1974.


POWER POOL TRANSFER LIMITS: STANDARDISED PROCESS

J. Lavagna* and A.L. Marnewick** * Eskom, Simmerpan, Germiston, 1401, Johannesburg, South Africa Email: [email protected] ** Postgraduate School of Engineering Management, University of Johannesburg, Auckland Park, 2006, South Africa Email: [email protected] Abstract: The Southern African Power Pool (SAPP) is a pool of interconnected electrical utilities in southern Africa. The SAPP hosts a workshop annually between all its constituents to determine the power transfer limits for the interconnected network for the following year. These limits ensure that the power pool remains stable and does not experience a blackout. Consistent processes have led to accurate and consistent results; therefore the aim of this research was to identify the gaps in the SAPP transfer limits studies process compared to international best practice processes. The inconsistencies identified translate to the identified potential process improvements that can be made to the consistency of the SAPP process and therefore the accuracy of the results produced. Key words: Transfer limits studies, transfer limits, Southern African Power Pool (SAPP), electrical system stability, case study.

1. INTRODUCTION There are two elements of electrical supply that are important to customers: price and security of supply. For electrical utilities to remain popular among their customers, they are required to supply electrical energy at low cost with maximum levels of reliability [1]–[7]. The security of electrical supply is directly dependent on the stability of the electrical system from which it is supplied. System stability can be described as the condition in which an electrical power network is able to sufficiently supply all the loads connected to it, even under the worst system contingency conditions, i.e. if there is a fault or disturbance on the network [1], [3], [7]–[14]. If a system becomes unstable after all stability resources of the network have been exhausted, a blackout will occur. A blackout is the situation where an electrical network collapses and all load and generation connected to the network are lost [1], [7], [10], [15]. This happened in Canada and Italy in 2003 [1], [16]. A method of increasing system stability is to form an electrically interconnected power pool between neighbouring utilities. This provides additional resources to all the utilities connected, benefiting from the concept of pooled resources. In southern Africa there is a power pool between the neighbouring countries, each of which has its own national electrical utility. This power pool, as any power pool in the world, is operated within certain stability limits. The stability limits referred to in this research are the power transfer limits implemented on the interconnecting electrical transmission lines between the utilities. Figure 1 indicates the geographical layout of the SAPP as well as the encircled interconnecting transmission

(tie) lines to which the SAPP transfer limits studies results apply.

Figure 1: SAPP and tie lines highlighted from the Eskom Transmission Spatial Information System

(TxSIS)

A process is required to determine the transfer limits between the utilities. The exercise of determining the transfer limits is conducted annually in the SAPP and these transfer limits are then used to trade electrical power for the rest of the year [17]–[19]. The SAPP consists of the interconnected national utilities of Zimbabwe (Zimbabwe Electricity Supply Authority – ZESA), Namibia (Namibia Power – NamPower), Botswana (Botswana Power Corporation – BCP), Mozambique (Electricidade de Moçambique – EdM), Zambia (Zambia Electricity Supply Corporation – ZESCO), Swaziland (Swaziland Electricity Company – SEC), Lesotho (Lesotho Electricity Company – LEC) and South Africa (Eskom) [17]–[21]. The consequences of inaccurate transfer limits can be devastating; the security of all the utilities connected to the power pool would be at risk [6], [9], [10], [15], [20], [22]–[26], particularly in southern Africa, where


there are still-developing world infrastructure and processes and no strong neighbouring sources of electrical power; thus it could take up to a few weeks to black start (restore the power supply). The socioeconomic implications of a large population (southern Africa) without electrical power for a few weeks would include industries closing, mass loss of data, communication links down, extensive food spoilage, lack of transportation and lack of sewerage or water supply services to meet basic human needs [9], [15]. If a transfer limit is under-estimated, the interconnected utilities could become unstable and the entire network lost [23]. If the transfer limits are over-estimated, the profits between the utilities in the process of buying and selling electrical power are not maximised, or future network expansion plans initiated to increase system stability are rendered redundant [24], [27]. The purpose of determining transfer limits in a power pool is to ensure that the power pool remains stable even under contingency conditions. The undesirable effect of a system blackout points towards the importance of accurately calculated transfer limits. Research indicates that consistent processes will lead to more consistent and accurate results; thus the results of the SAPP transfer limits studies process could have improved consistency and accuracy as a result of a consistent process followed. One of the challenges in this research was to establish the best way to accurately describe the execution of the transfer limits process best practice (internationally) and in the SAPP. This was so that the comparison between the two processes would be valid, producing reliable results for this research. The first challenge was overcome through a thorough investigation of a number of methodologies employed throughout interconnected utilities all over the world and consolidated into a single process that could be compared to the process described by the SAPP. The way in which the challenge in establishing the SAPP process was overcome was by using a case study research methodology with which to represent the execution of the SAPP transfer limits studies process (stemming from a number of data sources) and finalising the SAPP transfer limits studies process from the empirical data collected. Rival hypotheses were developed in arguing the contrary view that a consistent process leads to more accurate results and these were tested once all data had been collected and analysed. This research is directed at the SAPP and other power pools that conduct transfer limits studies. Implementing the findings from this research both in the international standard process of transfer limits and the actions that can be taken by the SAPP could lead to improved transfer limits studies results. The stability of the interconnected power pool has an effect on every electricity consumer within the power pool, in this case in southern Africa. More consistent transfer limits studies results could minimise the probability of the devastating socioeconomic consequences of a power

pool blackout that affects every electricity consumer in the region. It would also ensure maximum profits for the electrically connected utilities buying and selling power from one another. This paper is structured into three parts: first, the compilation of the literature best practice transfer limits studies process, second, the case study research methodology revealing the SAPP transfer limits studies process, and finally, the identification of the gaps between the processes through results analysis. These gaps reveal the relevant recommendations applicable to the SAPP, concluding the research aim. The gaps revealed also point towards additional research that could be conducted in the field.

2. LITERATURE

System security has been improved in many ways in the electrical industry. One such method, implemented worldwide, is the establishment of power pools – interconnected electrical utilities [1], [7], [10], [15], [23]. The interconnection of the utilities adds system stability to the overall power pool by pooling resources. The power pool can provide: Excess generation when needed; Excess load for frequency balancing; Inertia for additional dynamic security; Fault ride through assistance; and Blackstart facilities to provide for a blackout due

to the system becoming unstable. Stability in a network is defined by thermal, voltage and dynamic stability. Thermal and voltage stability are taken in this research as the limiting factors that power pools consider when determining the stability limits through power transfer. Thus these are the two factors to consider as defining stability when determining transfer limits [6], [7], [22]–[24], [27]–[33]. The stability of a network is also dependent on the network topology and the loading and generation in each of the interconnected networks in the power pool. Figures 2 and 3 describe thermal and voltage stability concepts, respectively.

Figure 2: Thermal stability transfer limit

Line

FLow (M

W)

Level of Power Transfer (MW)

Thermal Stability

Line Rating

Low Transfer

High Transfer

Transfer Limit


Thermal stability is dependent on the power flow on the line with regard to its physical components and terminal equipment power ratings [1], [8], [10], [14], [19]. The thermal transfer limit is the limiting power flow (incrementally increasing in the figure) that the transmission line can carry before damage occurs to any of the equipment through which it flows. The transfer limit point, as indicated by the arrow in Figure 2, is the transfer limit for thermal stability of a network [7], [20]. The concept of voltage stability on an electrical network is illustrated in Figure 3. Figure 3 is post-contingency as the network is required to be N-1 stable [7], [20]. The figure indicates the slow decline in voltage of the network as the incremental power transfer between two interconnected utilities is increased. The first point on the graph is the 95% voltage transfer limit. This is the point at which a busbar in the network reached the minimum operating voltage in pu (0.95 pu). In some networks busbars are operated below the minimum 0.95 pu mark. In these examples or under more serious contingency conditions, the decline in voltage as the transfer is increased can surpass the 95% transfer limit and the busbar voltage tends towards voltage collapse. Voltage collapse is the point at which the electrical network is rendered unstable and blacks out [6], [7], [23]. Thus the voltage collapse transfer limit for a network is taken at 95% of the power transfer at this point to ensure that there is always a 5% safety margin with which to operate in a network.

Figure 3: Voltage collapse and 95% safety margin transfer limits

Understanding thermal and voltage stability is imperative in determining transfer limits. This is because the power flows for which thermal or voltage stability points are reached on a network are the points within which the network has to be operated to maintain system stability in preparation for the next worst contingency [3], [23], [30]. A process has to be

followed by the utilities to establish the operating limits specified above [6], [22]–[24], [31]. The literature describes a process as a means of creating outputs from specified inputs under the restrictions of certain standards or guidelines (controls) [34]–[37]. These standards or guidelines are used to ensure the reliability of the outputs achieved. Literature indicates three phases of transfer limits studies: the planning and design phase, the execution phase and the monitoring and evaluation phase [5]–[7], [20], [22]–[24], [26], [30], [31], [33], [38]–[40]. Each of these phases has the necessary inputs that are processed to produce useful outputs contributing towards the setup, execution and continuous improvement of the transfer limits studies process. Figure 4 is a summarised process, derived from literature, of the international best practice transfer limits studies [4]–[7], [22]–[24], [26], [31]–[33], [38], [41].

Figure 4: Process of transfer limits studies 2.1 Planning and Design Phase The planning and design phase prepares all the elements required in the execution phase to produce the actual transfer limits for the network [33], [40]. Governance documentation is required to stipulate the various operating guidelines required for the power pool in question [19], [33]. The output from the governance documentation in the planning and design phase is creating a standardised knowledge base from which the transfer limits studies can be conducted [19], [33]. The main output produced from the planning and design phase is the range of contingency base cases. Each network configuration (topology) has to be studied and the transfer limits determined for each one, so that the worst case scenario can be taken as the limiting factor for the interconnection [5]–[7], [10], [20], [22]–[24], [26], [30], [31], [33], [38]–[40]. In the planning and design phase of the overall transfer limits studies process, an accurate network model would have to be obtained [6]. An accurate representation of the physical network would best

Volta

ge (V

)

Incremental Transfer (MW)

AC‐Based Transfer Limits

Low Voltage Limit

Planning and Design Phase

• Governance documentation ‐ developing and implementing• Real network parameters ‐ network modelling• Real‐time network data ‐ specific base case process• Simulation inputs ‐ contingency case file setup• Engineers ‐ representative, experienced and trained

Execution Phase

• Execution procedure ‐ standardised• Common understanding ‐ theoretical and procedural• Results presentation ‐ standardised • All possible configurations ‐ all cases taken into account• Finalised compilation report ‐ for relevant distribution

Monitoring and Evaluation Phase

• Output of studies ‐ SAPP transfer limits ‐ evaluated through peer review

• Results of studies ‐ implementation on power pool‐ improvement on process:

tools/efficiency ‐ sustainability

95% Low Voltage Transfer Limit

Voltage Collapse Transfer Limit

Voltage Collapse Point


represent real-life scenarios and therefore offer the most realistic results [10]. Standardisation should be ensured in this phase: the software package used to model the interconnected networks (from each utility) should be the same and the respective engineers should be familiar with it [42], [43]. Different network configurations will change the transfer limits of the system [5]–[7], [20], [23], [39]. The engineers should similarly be skilled in executing the overall process; consistency is introduced when their understanding of the method of executing the transfer limits studies is the same [7], [19], [33]. Figure 5 represents the overall process in creating the necessary contingency base cases [5]–[7], [10], [20], [22]–[24], [26], [30], [31], [33], [38]–[40]. The software package simulation network is often known as a case file. These resulting case files would be used to determine the transfer limits between utilities in a power pool in the execution phase. To create an accurate base case, the process begins with the requirement of an accurate transmission network model represented on the simulation package (case file) [10]. The specific loading and generation scenario of the network to which the transfer limits are meant to apply (worst case) then needs to be modelled [7], [23]. This entails the active and reactive power flows on the transmission network in a specific season or on a specific day, under the relevant network configuration [7], [20], [23], [38].

Figure 5: Contingency base case process

This base case or case file represents the system healthy network condition: all the voltages and transmission path flows are within voltage and thermal limits [23], [38], [39]. The relevant contingency (plant out of service) that causes a limitation to the transfer limits between the utilities in the power pool should then be selected and the contingency taken out of service. This process continues until all contingencies that limit the transfer between interconnected utilities are considered [33]. If there is a voltage or thermal violation in the system healthy base case, the load flow has to be changed so that the power transfer is reduced, ensuring that the network is operated within limits [23], [33], [38]. A

number of base cases have to be simulated to ensure that all threatening network conditions for transfer limits are addressed [23]. These inputs ensure that the most accurate contingency base cases are set up to represent real network conditions, revealing results as close to realistic network reactions as possible [1], [3], [6], [23]. The final requirement of the planning and design phase of transfer limits studies as indicated by international best practice is the consistent experience of the engineers required to perform the studies. These engineers have to appropriately represent all areas of the power pool and should be knowledgeable in the theory, tools used and processes of transfer limits studies [7], [19], [33], [42], [43]. 2.2 Execution Phase The execution phase of the overall process identifies the output of the process: the transfer limits for the power pool. This requires a standard procedure and common understanding of the engineers regarding thermal and voltage stability and identifying the relevant transfer limits on the simulation package outputs. The results from this process are compiled into a single report, in a standard format, that is distributed to the relevant stakeholders. A step-by-step indication of the transfer limits studies as indicated in international best practice is presented below [5]–[7], [20], [22]–[24], [26], [30], [31], [33], [38]–[40]:

Step 1: Determine the load to be incrementally increased and the rate of increase (in MW): This involves establishing the corridor for which the transfer limits are going to be determined and defining the relevant loads that are going to be scaled to detect where the thermal or voltage stability limits lie [5]–[7], [20], [22]–[24], [26], [30], [31], [33], [38]–[40]. Step 2: Increase the identified load by the step increase: Continual power flow simulation tools are used to conduct this process automatically using linear solving techniques [5]–[7], [22]–[24], [26], [33], [38]. However, the process can be conducted manually [23], [38]. Step 3: Observe the electrically interconnected networks for voltage or thermal violations: The limit ensures that once a disturbance has occurred on the network and the disturbance on the network settles, the network remains in a stable state [7]. Step 4: If there are no system violations, repeat steps 2 and 3; if there is a violation, switch back the next worst contingency and record the transfer limit: System stability, as has been mentioned, refers to the sustainability of network stability even under the next worst contingency on the network. Therefore the network must be operated within the limits of the next worst contingency. It is therefore important to take a

Step 1: Represent transmission network on software package

Step 2: Select time of year for simulated network (case file) representing worst case scenario loading conditions

Step 3: Determine accurate active and reactive power flowing on transmission lines in case file

Step 4: Simulate worst case scenario generation dispatch

Step 5: Select relevant contingency

Step 6: Solve case file, save as specific contingency base case

Iterate until all

contingency base cases are saved


pre-contingency transfer limit to ensure the stability of the network even after the next worst contingency occurs on the network [30]–[33], [40]. This process is repeated for each contingency case file to find the corresponding transfer limit for each possible contingency pair on the network [5]–[7], [20], [22]–[24], [26], [30], [31], [33], [38]–[40]. In most studies, the worst case contingency is used as the transfer limit, i.e. the lowest power transfer, to eliminate the need to conduct the transfer limits studies on a regular basis every time the network configuration changes [32]. The outputs of the transfer limits process, whether conducted automatically or manually, can be tabulated or represented on a power voltage (PV) curve or plot. International best practice suggests that a way in which consistency can be introduced into the process is through monitoring and re-evaluating the process on a regular basis. This also provides for continual process improvement. 2.3 Monitoring and Evaluation Phase The monitoring and evaluation phase attempts to increase the reliability of the process. Methods such as peer reviews, investigations into more powerful simulation tools and training of the engineers could be used [1], [7], [10], [23]. Sustainability is introduced to the process by training younger engineers. In this way there is a clear knowledge path and sufficient experience in the theoretical background, processes and required tools in annual transfer limits studies. The consolidation of the literature available on the topic of transfer limits studies processes internationally revealed the best practice process implemented as well as the methods by which the processes are governed and standardised. As a result, a process with inputs, processes and outputs was constructed in tabular format (see appendix, Table 6). This table was pattern matched against the empirically collected data describing the process followed by the SAPP. 2.4 SAPP – Southern African Power Pool This research was centred on the Southern African Power Pool, a power pool that comprises neighbouring national utilities in southern Africa. Involved are the national utilities of South Africa, Namibia, Botswana, Lesotho, Swaziland, Zimbabwe and Mozambique [17]–[19]. The South African utility is the largest with the most interconnections. It is therefore split up into different grids, each with an assigned network operations engineer. There are generally 18 people

present at the SAPP transfer limits studies workshop on an annual basis. The engineers that study the grids interconnecting to neighbouring utilities participate in these studies with each corresponding network operations engineer – forming sub-workgroups [17]–[19], [44]. The workshop forms part of the SAPP transfer limits study process [17]–[19], [44]. The SAPP process aims to achieve reliable outputs from the various inputs into the process, which is governed by guidelines and standards [17]–[19]. This process was compared to international best practice so that discrepancies could be identified and the overall process improved.

3. METHODOLOGY The method in determining the way in which the empirical data should be collected had to be reliable and valid. As a result of the research aim, the focus on a contemporary problem and the resources available, a case study research methodology was selected [45]–[48]. This was also motivated by access to the relevant resources available and respondents for a questionnaire adequately representing the annual workshop participants. In this way the data collected from the respondents was representative of the workshop (case study). Thus the conclusions drawn from this data, combined with the documentation available, as well as the participant observation views from the researcher who participated in the workshop before, can be taken as accurately representing the process followed during the SAPP transfer limits studies. Further motivation of reliable and valid data according to the case study methodology was the formulation and subsequent rejection of rival hypotheses in the case [45]–[48]. Figure 6 is an illustration of the overall case study research methodology, compiled in an effort to ensure there was construct validity in the process, leading to accurate empirical data conclusions [45]. The case study was set up to represent the annual SAPP transfer limits studies workshop in which the transfer limits are determined for the rest of the year for trading and system security in the SAPP. The more sources of data for a case study research methodology, the more reliable and valid the results of the research will be [45], [46], [49]. Thus the case study consisted of four types of data collection, as shown in Figure 6: A questionnaire completed by engineers that had

participated in the workshops in the past and had experience in the field;

The SAPP documentation relevant to the transfer limits studies – governance and procedural documentation;


Figure 6: SAPP transfer limits case study methodology The SAPP archival records – previous reports on

SAPP transfer limits studies results; and The participant observation views from the

researcher – who had also participated in the workshop previously.

The most important element in collecting empirical data from which to draw conclusions is to ensure that once the data analysis exercise has been conducted, the conclusions can be considered relevant, valid and reliable [45], [46], [49]. From the figure it is clear that the ways in which the empirical data was collected were decided upon before the data collection process began in a clear research trail that could be followed, thus discouraging any research bias [45], [46], [48]. This aimed to increase the validity and reliability of the research results. Hence, the findings in the research process could contribute to the relevant field of knowledge. The empirical data collection methods and analysis aimed to: 1. Find conclusive data that provides direct answers

to the research questions; and 2. Reject the rival hypotheses based on the research

questions. From Figure 6 the questions to be asked in the questionnaire were developed by testing the theoretical and process knowledge of the respondents regarding the SAPP transfer limits studies. Rival hypotheses were formulated as a validity check for the research results from the questionnaires [45], [46]: if conclusions found from the empirical data answered the research question but also sufficiently rejected the rival hypothesis

relevant to a particular element in the overall process, the results from the analysis could be concluded as reliable. The results of the questions asked are revealed in the data analysis section. These results were summarised in tabular format (using Table 6 in the appendix as a basis) according to the process identified from the literature so that a triangulation exercise could be conducted on all the empirically collected arrangements of data to form a single empirically collected data conclusion. This final conclusion was used as a comparison to the international best practice process from which to identify possible gaps in the process. The documentation used for data analysis was from the SAPP, relevant to the process of transfer limits studies. This documentation was analysed within the same tabular format so that the relevant conclusions could be drawn. The researcher has had the opportunity to participate in the SAPP transfer limits studies. It was thus important that all the preparation for the research and the analysis of the research were done so that the opinion of the researcher did not skew the data [45]–[47]. The observations of the participant observation data from the researcher were not viewed as concrete as the raw empirical data collected from the respondents to the questionnaires, nor the documentation from the SAPP [45]–[47]; thus the results from the studies were only enhanced from the participant observation views of the researcher. The final observation in Figure 6 relevant to this research is the triangulation process required of all the collected data to ensure internal validity of the results in forming overall report research conclusions [45], [46], [48]. The multiple sources used to devise the case study were triangulated and then used as an overall


empirical data collection case study view. This, in turn, was used for pattern matching comparison to the study processes discovered from international best practice.

4. RESULTS In this section the results from the various empirical data sources are described. It is important for research to ensure that its sources are valid and reliable. Before this research could be analysed and conclusions drawn from it, validations were required for the data sources used. In order to use the information from the questionnaire, respondents had to represent elements of the workshop conducted by the SAPP to determine the transfer limits. The profile of the respondents that completed the questionnaire is indicated in Table 1.

Table 1: Relationship between study experience and professional working field

Study experience

Professional field

Tota

l

Network operations

Expansion planning Other

Electrical engineering degree

8 1 1 10

Other engineering degree

1 0 0 1

Total 9 1 1 11 The results analysis from the questionnaires distributed to engineers was seen as reliable and valid, because the 11 respondents (out of a full workshop of 17 less the researcher) represented three utilities and the SAPP. Thus, the engineers were found to have enough experience in the relevant fields to represent the workshop and could be used to draw accurate conclusions. From Table 1 it is clear that the respondents from different utilities in the SAPP all had engineering degrees, with the vast majority holding electrical engineering degrees and with experience in network operations. The analysis of the documentation from the SAPP was conducted with reference to Figure 7, which is linked directly to Figure 4 from the literature. The background described in the documentation proves that the information observed from the documentation is an accurate representation of the SAPP transfer limits process. Thus conclusions drawn from the SAPP documentation will be applicable to conclusions drawn overall about the empirically collected data for the case study.

Figure 7: Inputs, processes and outputs of the SAPP transfer limits studies process

There was a possibility that the views of the researcher as a participant in previous studies could introduce bias in the results. These views were therefore only used to reinforce conclusions drawn from the triangulation of the above resources. Data analysis was conducted in accordance with the three phases of transfer limits as indicated by the literature. The following findings were revealed: 4.1 Planning and Design Phase Theoretical, Tools and Procedural Training for Engineers: Results from the questions in the questionnaire that tested the knowledge of the respondents in the field of thermal and voltage stability reveal that the respondents’ understanding of stability was not sufficient. Respondents were asked to identify the thermal and voltage transfer limits (0.95% and voltage collapse) as illustrated in Figures 2 and 3. 82% of the respondents were able to accurately display the thermal transfer limit, but as seen in Figure 8, the superimposed answers reveal that the engineers did not convincingly identify the correct positions of A – the voltage collapse point, B – the 0.95 pu voltage transfer limit and C – the voltage collapse transfer limit (taken at 95% of the collapse point). The randomised collection of responses from the individuals indicated in Figure 8 clearly illustrates that there are problems in the understanding of voltage stability in the context of transfer limits studies by the engineers required to conduct the studies. Information from the documentation analysed indicated that all the correct procedures and theoretical explanations are present in the governance and procedural documentation applicable to the SAPP. This therefore further suggests that either this documentation is not implemented correctly or the understanding of the engineers conducting the studies is lacking.

Inputs:• Governance

procedures• Real network

parameters• Real-time

network data• Simulation

inputs• Engineering

skills, knowledge and experience

Studies Execution:• Standard

procedure• Common

understanding• Case file setup• Standard

results presentation

• All network configurations

• Finalised report

Outputs:• Transfer

limits• Format of

report• Peer review• Sustainability• Recommend-

ed actions for improvement


Figure 8: Voltage stability question results

Step-by-Step Documentation Instructions: Table 2 presents the results of the questions posed to the respondents on the SAPP governance documentation applicable to the transfer limits studies. The results indicate that the documents containing the SAPP transfer limits study information (governance and procedural documents) were known and available to the respondents. However, of the 11 respondents to which the execution of the available process was applicable, 67% indicated that they followed the process available, but 70% did not think that the process was adequately available in the execution phase of the transfer limits studies. The contradicting information in the results of Table 2, combined with the clear uncommon understanding of thermal and voltage stability limits from the results analysis above, indicates that the process followed by the SAPP is faulty. It is also clear from Table 2 that the respondents felt they required training for the studies, which does not indicate confidence in their abilities to accurately conduct the studies, and therefore produce accurate results.

Table 2: Question results on SAPP governance

Category Yes No Awareness of document 11 0 Able to access document 10 1 Follow prescribed process 6 3 Process adequately available 3 7 Training required 10 0

The SAPP documentation indicates sufficient guidelines on how to set up the inputs and conduct the studies. However, there are no specific step processes that indicate how the studies should be conducted, especially in the necessary software package. Standard Process in Compiling the Base Case and Individual Contingency Base Cases: The questions in the questionnaire also attempted to test the process knowledge of the respondents with reference to the

SAPP transfer limits studies. These questions were derived from voltage and thermal stability as well as transfer limits studies literature. The engineers were required to order the steps required in compiling a contingency base case – as indicated in Figure 5. Table 3 below indicates the responses compared to international best practice. The correctly identified process steps are indicated unshaded, faulty processes where there were faults in shaded and completely incorrect answers in black. The arrows on the figure indicate the correct identification of the iteration in the process. White represents a correct answer; light grey a partially correct answer and dark grey a completely incorrect or absent answer.

Table 3: Base case set up process Feedback Step in the process Correct sequence according to literature 1 5 3 2 6 4

Respon

dents

1 1 5 3 6 2 4 2 1 5 2 3 6 4 3 1 5 2 3 6 4 4 1 2 5 3 6 4 5 1 3 6 4 5 2 6 1 5 2 3 6 4 7 1 5 2 3 6 4 8 1 5 3 2 6 4 9 1 5 2 6 3 4

10 5 2 1 6 3 4 11 "All processes are iterative"

Each of the differing methodologies identified by the respondents in Table 3 indicates that the base cases are set up differently in each of the sub-workgroups required to complete the transfer limits studies between the relevant utilities. This introduces a clear inconsistency in the results from the overall transfer limits studies process. It is also clear from the poor understanding in the process of compiling the base cases that training is required by the respondents. 4.2 Execution Phase Standard Execution Phase Process: The process knowledge of the respondents was further tested in a question requiring the organisation of the steps involved in executing the transfer limits studies process in the correct order. Table 4 below indicates the responses compared to international best practice. The correctly identified process steps are shaded lightly and completely incorrect answers in black.

Volta

ge (V

)

Incremental Transfer (MW)

AC‐Based Transfer Limits

Low Voltage Limit

A

B

C

A

B

C

No ResponseA B C A C

??

C

A B

C

A

BC BC

A

B

C

A

B

B

A

B

A

A

A

B

C

A

B

C


Table 4: Execution phase process

Feedback Step in the process Correct sequence

according to literature 4 2 3 1

Respon

dents

1 4 2 3 1 2 4 1 3 2 3 4 2 3 1 4 4 2 3 1 5 4 2 3 1 6 4 2 3 1 7 4 2 3 1 8 4 2 3 1 9 4 2 3 1 10 4 2 3 1 11 "Depends"

4.3 Execution process of the transfer limits studies Table 4 is well understood by the engineers in determining the transfer limits. However, with inconsistent base cases (Table 3), the results from the studies were inconsistent nonetheless. In the execution phase, the knowledge of the engineers fell short once again, with their inability to determine the points at which the transfer limits should be identified when voltage collapse occurs on the network or when the busbars (as stipulated in the governance documents as a requirement for SAPP transfer limits) operate below 0.95 pu (Figure 8). This finding was emphasised by the responses to a question on iteration exceeded in the relevant software package, which translates to voltage collapse in the case file, but was correctly identified by only 27% of the respondents.

Standard Study Results Format (software package included): From the questionnaire: 7/11 respondents (64%) preferred recording the

transfer limits in a table including the corresponding conditions;

2/11 respondents (18%) preferred recording the transfer limits on PV curves and pointers; and

2/11 respondents (18%) liked both options of displaying the results.

Table 5: Cross-tabulation of software package

preferences

Package Reason for package preferences

Userfriendly

Experience/ case setup Accuracy Applic

Tools Total

PSS/E 5 2 3 4 14 DIgSILENT 2 1 2 3 8 VSAT 1 0 0 1 2 Total 8 3 5 8 24

As seen from the statistics above as well as the information in Table 5, the way in which the transfer limits studies results are recorded is not consistent. This information also indicates that the preference for and

experience in software packages used by the respondents is not consistent. This is part of the process of the transfer limits studies. The SAPP documentation required results to be presented in PV curves, but in the results documentation analysed, the results appear in a variety of formats, including PV curves with or without explanations or even tables of the transfer limits with or without explanations. This is a clear indication of incorrect and inconsistent execution of the studies from the governance documentation. 4.4 Monitoring and Evaluation Phase Implementation of Better Analysis Tools: The information in the SAPP guidelines documentation sourced indicates that transient (dynamic) studies are required for transfer limits studies to assess the overall health of the system. This is not evident in the reports from the studies conducted and introduces more inconsistency concerns into the overall SAPP transfer limits process. Often the guidelines documentation on the transfer limits studies process is consistent with international best practice, but the execution of those processes indicated in the guidelines is not followed through. This is concluded by the absence of the results in the reports from the studies conducted. A further indication that dynamic studies are not conducted is that this is a recommendation from one of the respondents as a method to improve the overall SAPP transfer limits studies. Introduce Measures of Sustainability and Process Improvement: Neither the questionnaire results analysis nor the documentation from the SAPP revealed measures of sustainability or process improvement in the overall process of the SAPP transfer limits studies.

5. DISCUSSION The results from the data analysis were triangulated and a pattern matching exercise conducted with the international best practice process (Table 6) in an attempt to determine if gaps exist between the processes. The rejection of the rival hypotheses formulated ensured that all possible conclusions from the empirical research were addressed. The analysis revealed that the process followed by the SAPP could be compared to the process developed from the literature as international best practice. The gaps between these two processes from the pattern-matching exercise identified the areas in which the SAPP transfer limits process could be improved. Thus, recommendations were created for the SAPP in standardising the process used to determine the transfer limits studies results to improve their consistency.


5.1 Planning and Design Phase From the results in terms of Theoretical, Tools and Procedural Training for Engineers, a major finding of this research is that the engineers required to conduct the studies on which the power pool operates do not understand the process to be followed in setting up the relevant inputs (case files, networks, etc.) to be used in the execution phase of the transfer limits studies producing the actual MW transfer limits. This is despite the procedures present in the SAPP documentation on the process. Therefore the following action is recommended to be taken by the SAPP: The engineers that participate in the SAPP transfer

limits studies should be trained, specifically targeting the theoretical background and methodology of the studies to be conducted.

The SAPP documentation (final reports of the studies) should include a short section on the competency or experience of the engineers that participate in the studies to determine the international transfer limits.

From the information gathered in Step-by-Step Documentation Instructions, the process in which the base cases are set up from both sets of empirically collected data indicates inconsistency between the individual workgroups. Therefore: The SAPP needs to create a procedural step-by-

step document on setting up and conducting transfer limits studies (specific to the SAPP) in the appropriate software. This recorded process would also introduce consistency from one year to the next and provide opportunities for continuous improvement.

From the information gathered in Standard Process in Compiling the Base Case and Individual Contingency Base Cases, it is evident that the engineers do not follow a standardised process in compiling the base cases upon which to conduct the studies. Thus: All SAPP sub-workgroups performing the SAPP

transfer limits studies must follow the same process in compiling the base case for their interconnection as well as the same setup parameters and processes in determining the individual contingency base cases.

5.2 Execution phase From the results relating to Standard Execution Phase Process, the processes available to the engineers to follow from the SAPP documentation are clearly not executed. Thus: The engineers should be required to follow the

standardised step-by-step procedure documented

by the SAPP for the duration of the SAPP transfer limits studies process.

From the results pertaining to Standard Study Results Format (software package included) according to the SAPP guidelines, the results should be reported in the form of PV curves from the software package used to conduct the studies. However, the results documentation indicates a number of inconsistent methods in presenting the data. From the questionnaire data, there were a number of different preferences among the respondents in how they present the results from the studies. Therefore the recommendation is: Consistency should be maintained in the standard

study results format for recording the SAPP transfer limits. This also pertains to the training required of the engineers so that all engineers are capable of using the required software package tools.

5.3 Monitoring and Evaluation Phase From results in Implementation of Better Analysis Tools and Introduce Measures of Sustainability and Process Improvement, it would be advisable for the SAPP to introduce: The dynamic (transient) stability limits of the

system included in the studies and the report; Human resource sustainability through young

engineers participating in the training conducted and transfer limits studies process;

Improved development of the overall process by observing international best practice methods and incorporating suggested tools into the process;

Investigations conducted into other software packages, such as VSAT, that could conduct the studies more accurately and efficiently.

The final recommendation, as is implemented in international best practice, which was also brought up by one of the respondents, is as follows:

The SAPP should strive to achieve online transfer limits, i.e. real-time studies conducted by background software onto transmission energy management systems.

5.4 Rival Hypotheses All rival hypotheses, bar one, were rejected based on the results of the research. This was an inconclusive finding regarding the frequency with which the transfer limits studies should be conducted for the most accurate network representations to reveal the most accurate results. The information from the questionnaire was not strong enough to draw a valid conclusion. Thus additional research on this topic could be conducted to contribute to the field of knowledge.


However, the rest of the rejections indicate from the case study methodology that all of the alternative hypotheses were addressed in the overall empirical data collection. The comparison of this data to the international best practice process can be confirmed as complete and conclusive. 5.5 Overall Overall, the process of the SAPP transfer limits studies follows the same structure as a general process: converting supplied inputs to valid, reliable outputs through a series of actions that are controlled by certain rules or guidelines (controls). The documentation available for the SAPP transfer limits studies indicates that valid, reliable processes are in place to ensure the validity and reliability of the results achieved each year after the annual workshop is conducted by the relevant engineers. The overall conclusion of the research through the analysis of the questionnaire data, the documentation data and the participant observations (triangulated) is that when matched to theoretical international best practice, the process is not consistent and therefore the results for the studies are also not consistent or accurate.

6. CONCLUSION

The research aimed at determining the gaps between the SAPP transfer limits studies process and international best practice. It can be concluded through the gaps identified that not only is the process of transfer limits studies conducted by the SAPP inconsistent, but also the results produced from the process. The gaps identified, however, also reveal the actions that can be taken by the SAPP to improve the process of transfer limits studies conducted in producing more reliable results to ensure overall network security. Actions include training the engineers that are required to conduct the studies in the theory behind transfer limits and the process to be followed to determine them. It would also be beneficial for the organisation to investigate other software tools that might streamline the process of transfer limits determination in the SAPP. Actions of continuous improvement after the execution of the process are important to maintain a high quality process and these will need to be implemented by the SAPP. The overall conclusion to this research is as follows: A standardised method of the execution of the SAPP transfer limits studies process can improve the consistency of the transfer limits obtained each year. The training of the engineers in transfer limits studies will not only benefit the power pool and the countries that rely on its electricity supply, but also the engineers themselves in that they will develop more skills and understanding of the stability and appropriate operation of the network. This recommendation promotes

individual growth of the utilities and the representative engineers. The increased consistency in the process of conducting the SAPP transfer limits studies is an indication to power pools all over the world of the importance of consistency in engineering processes that produce operating guidelines on an interconnected power pool, as the consequences of instability are drastic. Additional research opportunities lie in other methods of increasing the overall stability of a power pool, such as dynamic system studies and how these processes can be created and implemented. It should also be noted that the sustainability issues addressed in the recommendations above would promote a process of monitoring and continual improvement for the SAPP transfer limits and therefore for the accuracy of the results of the studies. As mentioned above, this could even involve the incorporation of new tools or software, used internationally, to conduct these studies. Future studies on a similar topic, unknown to this research, could investigate whether:

The effects of dynamic system stability in interconnected power pools have a major influence on the transfer limits.

The studies take into consideration each network portion’s worst case scenario setup in establishing the contingency base case.

Human resource sustainability exists within the overall SAPP transfer limits studies process.

The SAPP transfer limits studies process takes into account worst case contingency case file setup consistently in all sub-workgroups.

The consistency of the results of SAPP transfer limits studies improves with more regular workshops.

The SAPP is growing fast and reliability in the operation of the power pool is imperative. The implementation of the actions listed above could ensure added system security for the operation of the SAPP providing power for Africa.

7. REFERENCES [1] Union for the Co-ordination of Transmission of

Electricity (UCTE), “UCTE Report: Final report of the investigation committee on the 28 September 2003 blackout in Italy,” 2004.

[2] X. Bai, S. M. Shahidehpour, V. C. Ramesh, and E. Yu, “Transmission analysis by nash game method,” IEEE Transactions on Power Systems, Vol. 12, No. 3, pp. 1046–1052, 1997.

[3] L. Meeus, K. Purchala, and R. Belmans, “Development of the internal electricity market in Europe,” Electricity Journal, Vol. 18, No. 6, pp. 25–35, 2005.

[4] C. Chengaiah and R. V. S. Satyanarayana,


“Power flow assessment in transmission lines using Simulink,” International Conference on Computing, Electronics and Electrical Technologies, pp. 151–155, 2012.

[5] R. J. Marceau, F. D. Galiana, and R. Mailhot, “Stability transfer limit calculation in a power transmission network (US Patent),” 5566085, 1996.

[6] M. V. Venkatasubramanian and R. Goddard, “Report on: Coordination of transmission line transfer capabilities,” Washington, 2002.

[7] D. M. S. R. Murthy and D. C. Radhakrishna, “Training program for Ceylon electricity engineers on power system analysis and operation,” in Training for Transmission System Engineers - Ceylon Electricity Board, 2010, no. 386.

[8] B. Christison, “System operator security guideline,” Germiston, Johannesburg, 2014.

[9] J. Mclinn, “Major power outages in the US, and around the world,” IEEE Reliability Society 2009 Annual Technology Report, pp. 1–5, 2009.

[10] North American Electricity Reliability Corporation (NERC), “Report to the NERC Board of Trustees: Technical analysis of the August 14, 2003, blackout: what happened, why, and what did we learn?,” Princeton, 2004.

[11] M. K. Elfayoumy, R. R. Tapia, and R. Clayton, “Merchant transmission and the reliability of the New York State Bulk Power System (NYSBPS). Part I. Thermal transfer limit analysis,” IEEE PES Power Systems Conference and Exposition, 2004, 2004.

[12] S. Grijalva and P. W. Sauer, “A necessary condition for power flow Jacobian singularity based on branch complex flows,” IEEETransactions on Circuits and Systems I: Regular Papers, Vol. 52, No. 7, pp. 1406–1413, 2005.

[13] R. Gorini de Oliveira and M. T. Tolmasquim, “Regulatory performance analysis case study: Britain’s electricity industry,” Energy Policy, Vol. 32, No. 11, pp. 1261–1276, 2004.

[14] National Energy Regulator of South Africa (NERSA), “The South African grid code - The system operation code,” 2010.

[15] E. Agneholm, “The restoration process following a major breakdown in a power system,” Final Doctorial Thesis, Chalmers University of Technology, 1996.

[16] U.S.-Canada power system outage task force, “Final report on the August 14, 2003 blackout in the United States and Canada: causes and recommendations,” 2004.

[17] SAPP Transmission Planning Working Group, “SAPP transfer limit studies for 2014,” Germiston, Johannesburg, 2014.

[18] SAPP Power System Study Task Team, “SAPP transfer limit study for 2015 in the Eskom

control area,” Germiston, Johannesburg, 2015. [19] SAPP Operating Sub Committee, “Southern

African Power Pool operating guidelines,” Southern Africa, 2013.

[20] M. C. Coetzee, “Improvement of power transfer in an existing power system by means of series and shunt compensation,” Final Dissertation, University of Johannesburg, 2008.

[21] M. Nene, “Eskom-Nampower meeting feedback report No. 342-12.” System Operator, Eskom, Germiston, Johannesburg, 2011.

[22] P. Marannino, P. Bresesti, A. Garavaglia, F. Zanellini, R. Vailati, and I. Elettrica, “Assessing the transmission transfer capability sensitivity to power system parameters,” in 14th Power Systems Computation Conference, 2002, Vol. Session 23, No. Paper 4, pp. 1 – 7.

[23] I. Dobson, S. Greene, R. Rajaraman, C. L. DeMarco, F. L. Alvarado, M. Glavic, J. Zhang, and R. Zimmerman, “Electric power transfer capability: concepts, applications, sensitivity and uncertainty,” Power Systems Engineering Research Centre Publication, Vol. 01, No. 34, p. 98 pp., 2001.

[24] X. Dong, C. Wang, J. Liang, X. Han, F. Zhang, H. Sun, M. Wang, and J. Ren, “Calculation of power transfer limit considering electro-thermal coupling of overhead transmission line,” IEEE Transactions on Power Systems, Vol. 29, No. 4, pp. 1503–1511, 2014.

[25] M. Larsson, C. Rehtanz, and J. Bertsch, “Corporate ABB Report: Real-time voltage stability assessment of transmission corridors,” Switzerland, 2003.

[26] B. S. Gisin, M.V. Obessis, and J. V. Mitsche, “Practical methods for transfer limit analysis in the power industry deregulated environment,” Proc 21st 1999 IEEE International Conference Power Industry Computer Applications (PICA), pp. 261–266, 1999.

[27] T. De la Torre, J. W. Feltes, T. Gomez San Roman, and H. M. Merrill, “Deregulation, privatization, and competition: transmission planning under uncertainty,” IEEE Transactions on Power Systems, Vol. 14, No. 2, pp. 460–465, 1999.

[28] D. Gan, X. Luo, D. V. Bourcier, and R. J. Thomas, “Min-max transfer capabilities of transmission interfaces,” International Journal of Electrical Power and Energy System, Vol. 25, No. 5, pp. 347–353, 2003.

[29] K. P. Basu, “Power transfer capability of transmission line limited by voltage stability: simple analytical expressions,” IEEE Power Engineering Review, Vol. 8, No. 5, pp. 6–7, 2000.

[30] A. Khursheed, M. Azad, and A. Singh, “Recent available transfer capability calculation methods: a review,” International Journal of Advanced in Engineering & Technology, Vol.


8, No. 2, pp. 134 – 142, 2015. [31] G. C. Ejebe, J. Tong, J. G. Waight, J. G. Frame,

X. Wang, and W. F. Tinney, “Available transfer capability calculations,” IEEE Transactions on Power Systems, Vol. 13, No. 4, pp. 1521–1527, 1998.

[32] M. Hojabri and H. Hizam, “Available transfer capability calculation,” Applications of MATLAB in Science and Engineering, pp. 143–164, 2011.

[33] North American Electric Reliability Corporation (NERC), “Available transfer capability definitions and determination,” 1996.

[34] S. Hanson, “Change Management and Organizational Effectiveness for the HR Professional,” Cornell HR Review, pp. 1–8, 2012.

[35] M. Mangram, “MAM Baby Products - Strategic Planning and Leadership Analyses,” International Journal of Management Cases, 2013.

[36] K. K. Movassaghi, “Project management — A managerial approach,” European Journal of Operational Research, Vol. 45, No. 2–3. pp. 372–373, 1990.

[37] C. Booth, “Knowledge management and decision support for electric power utilities,” Knowledge and Process Management, Vol. 8, No. 4, pp. 207–216, 2001.

[38] PowerWorld Corporation, “Available transfer capability,” in Steady-State Power System Security Analysis with PowerWorld Simulator, 2001, Vol. 1, No. 217, pp. 1–56.

[39] M. Ilić, F. Galiana, L. Fink, A. Bose, P. Mallet, and H. Othman, “Transmission capacity in power networks,” International Journal of Electrical Power & Energy Systems, Vol. 20, No. 2, pp. 99–110, 1998.

[40] Y. Ou and C. Singh, “Assessment of available transfer capability and margins,” IEEE Transactions on Power Systems, Vol. 17, No. 2, pp. 463–468, 2002.

[41] Y. O. Y. Ou and C. S. C. Singh, “Improvement of total transfer capability using TCSC and SVC,” 2001 Power Engineering Society Summer Meeting Conference Proceedings (Cat No01CH37262), Vol. 2, No. C, pp. 944–948, 2001.

[42] B. Watkins and R. Lewis, “Winning With Apps: A Case Study of the Current Branding Strategies Employed on Professional Sport Teams’ Mobile Apps,” International Journal of Sport Communication, Vol. 7, No. 3, pp. 399–416, Sep. 2014.

[43] M. Skibniewski and G. Vecino, “Web-based project management framework for dredging projects,” Journal of Management in Engineering, No. April, pp. 127–139, 2011.

[44] Southern African Power Pool Workgroup, “SAPP 2014 Transfer Limits Summary Report

- Updated 15 JAN 2014.” . [45] R. K. Yin, Case Study Research Design and

Methods, 4th ed. California: Sage Publications Inc., 2009.

[46] J. D. Farquhar, Case Study Research for Business. London: Sage Publications Ltd, 2012.

[47] J. Gill and P. Johnson, Research methods for managers, 3rd ed. London: Sage Publications Ltd, 2002.

[48] D. E. Perry, S. E. Sim, and S. Easterbrook, “Case Studies for Software Engineers,” in NASA SW Engineering Workshop 2005 Tutoria, 2005, pp. 1–64.

[49] D. E. Gray, Doing Research in the Real World, 3rd ed. London: Sage Publications Ltd, 2014.

[50] S. Horowitz, A. G. Phadke, and B. Renz, “The future of power transmission,” IEEE Power and Energy Magazine, Vol. 8, No. 2, pp. 34–40, 2010.

[51] C. Moloney, “‘Understanding understanding’ across the disciplines: towards strategies for sustainable engineering education for the 21st century,” Transforming Engineering Education: Creating Interdisciplinary Skills for Complex Global Environments, 2010 IEEE, 2010.

[52] P. Carrillo, H. Robinson, and F. Hartman, “Knowledge management strategies: learning from other sectors,” Bridges, Vol. 44, No. 0, pp. 1–9, 2003.

[53] R. D. Malmgren, J. M. Ottino, and L. A. Nunes Amaral, “The role of mentorship in protégé performance,” Nature, Vol. 465, No. 7298, pp. 622–6, Jun. 2010.

[54] Y. Mansour, E. Vaahedi, and A. Y. Change, “Method of on-line transient stability assessment of electrical power system (US Patent),” 5638297, 1997.

[55] F. Wu and P. Varaiya, “Coordinated multilateral trades for electric power networks: theory and implementation.,” International Journal of Electrical Power & Energy Systems, Vol. 21, No. 2, pp. 75–102, 1999.


8.A

PPEN

DIX

Tabl

e 6:

Sum

mar

y of

the

trans

fer l

imits

stud

ies p

roce

ss

Sum

mar

y ta

ble

of th

e tra

nsfe

r lim

its p

roce

ss in

a p

ower

poo

l

Phas

e In

puts

Pr

oces

s O

utpu

ts

Planning and Design [33], [40]

Gov

erna

nce

docu

men

tatio

n [1

9], [

33]

Proc

edur

es a

nd p

roce

sses

use

d to

con

duct

tran

sfer

lim

its st

udie

s Tr

ansf

er li

mits

stud

ies

Stan

dard

kno

wle

dge

base

to u

se fo

r tra

nsfe

r lim

its st

udie

s

Rea

l net

wor

k pa

ram

eter

s [6]

, [1

0]

Acc

urat

e m

odel

led

netw

ork

case

file

with

all

inte

rcon

nect

ed n

etw

orks

repr

esen

ted

Net

wor

k m

odel

ling

– co

rrec

t tra

nsm

issi

on li

ne

para

met

ers o

r tra

nsfo

rmer

mod

els t

o re

pres

ent t

he

netw

ork

in re

al li

fe e

tc.

Acc

urat

e vo

ltage

and

ther

mal

vi

olat

ions

iden

tifie

d

Rea

l-tim

e ne

twor

k da

ta

Cor

rect

net

wor

k co

nfig

urat

ion

[5]–

[7],

[20]

, [23

], [3

9]

Wor

st c

ase

scen

ario

bas

e ca

se se

tup

Mos

t acc

urat

e ba

se c

ase

set u

p to

re

pres

ent r

eal n

etw

ork

cond

ition

s, re

veal

ing

real

istic

net

wor

k re

actio

n re

sults

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50]

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1

BER Performance of a Hierarchical APSK UEP System over Nakagami-m fading T. Quazi* and H. Xu** * School of Engineering, Dept. of Electrical, Electronic & Computer Engineering, King George V Avenue, Durban 4041, University of KwaZulu-Natal, South Africa, E-mail: [email protected] ** School of Engineering, Dept. of Electrical, Electronic & Computer Engineering, King George V Avenue, Durban 4041, University of KwaZulu-Natal, South Africa, E-mail: [email protected] Abstract—Bit error rate (BER) performance studies of amplitude phase shift keying (APSK) have not looked at the unequal error protection (UEP) facility provided by such a modulation scheme. In this paper hierarchical 16-APSK is studied using a bit allocation mechanism that allows for UEP for two classes of multimedia traffic. Theoretical BER expressions are derived for two UEP bit streams using the nearest neighbourhood method in additive white Gaussian noise (AWGN) and Nakagami-m fading channels. Simulation results are then used to validate the accuracy of the theoretical expressions. A low complexity maximum likelihood (ML) detection for hierarchical 16-APSK is also proposed and simulation results show that the proposed low complexity ML detector achieves the same BER performance as the optimum ML detector. Keywords: Hierarchical modulation, unequal error protection, multimedia transmission.

1. INTRODUCTION The demand for high quality multimedia communications has led to the requirement for highly efficient modulation schemes. The modulation scheme considered for this purpose in the DVB-S2 framework for satellite communications is amplitude phase shift keying (APSK) [1]. The setup of the constellation in APSK leads to a lower Peak-to-Average Power (PAPR) when compared to square or rectangular modulation schemes such as M-ary quadrature amplitude modulation (MQAM). This is because APSK uses a smaller number of amplitude levels in comparison to a MQAM constellation with the same modulation parameter M. A low PAPR is not only useful in satellite communications where high power amplifiers are utilized, but also in handheld mobile devices in which energy conservation is a major concern. Hierarchical modulation (HM) has been proposed as an energy efficient methodology for increasing the transmission rate in a broadcast scenario. HM schemes use the concept of superposition coding where the available energy is shared among several bit streams which are then transmitted simultaneously [2]. HM has also been used widely for providing unequal error protection (UEP) in the transmission of multimedia traffic [3-6]. The UEP mechanism allows for the simultaneous transmission of multiple classes of traffic with different error protection requirements, and has been utilized in systems transmitting traffic with varying quality of service (QoS) and for increasing capacity and coverage in video broadcast systems transmitting layered video. However all of the schemes proposed for enabling UEP use hierarchical MQAM (H-MQAM), which being MQAM based, have a higher PAPR when compared to APSK based schemes. The system in [2] was the first to consider hierarchical APSK (H-APSK), however the objective of the proposed scheme was to increase the rate

of transmissions, and it did not consider UEP in its formulation. The focus of this paper is the application of hierarchical APSK for facilitating UEP. More specifically hierarchical 16-APSK is used to provide UEP for the simultaneous transmission of two classes of multimedia traffic. A bit-to-symbol allocation scheme is considered for hierarchical 16-APSK for the purpose of UEP, and the bit error rate (BER) performance of the high and low priority bit streams in additive white Gaussian noise (AWGN) and Nakagami-m fading channels is presented. Furthermore, in order to increase the energy efficiency of the proposed system, a low complexity detection algorithm is proposed that uses significantly reduced computations as compared to the optimum Maximum Likelihood (ML) detection algorithm but achieves the same BER performance. In related work, hierarchical APSK has been studied for satellite broadband communications in [7] and for land mobile systems in [8]. Symbol error rate (SER) performance of APSK has been studied in [9-11] but none of these consider the hierarchical case, especially from the perspective of facilitating UEP for multimedia traffic transmission, which is the focus of the study in this paper. A low complexity detection algorithm for 16-APSK has been studied in [12], however it has been proposed for a coded system unlike the proposed detector in this paper which is for an un-coded system. Also the hierarchical case is not considered in [12]. The rest of the paper is organized as follows. Section II details the design of the hierarchical APSK constellation for the purposes of UEP. Section III presents the theoretical and simulation BER performance of the system in AWGN and Nakagami-m channels. The low complexity ML detection algorithm is presented in Section IV. Finally, Section V concludes the paper.


2

2. HIERARCHICAL APSK CONSTELLATION DESIGN

The constellation structure for the hierarchical 16-APSK proposed in [2] is shown in Figure 1. This is the same structure chosen for the DVB-S2 standard [1] with 4 symbols uniformly spaced on the inner ring with radius 𝑅𝑅1 while 12 symbols are placed on the outer ring with radius 𝑅𝑅2. There are two design parameters in the modulation scheme [2]: (1) The ratio between the outer and inner concentric circles, 𝛼𝛼 = 𝑅𝑅2

𝑅𝑅1, and (2) the angle 𝜃𝜃 between

the constellation points on the outer ring in each quadrant. This angle determines how close the symbols in the outer ring are to each other.

R1

R2

s1

s2

s3

s4

s5

s6

s7

s8

s9

s10

s11

s12

s13

s14

s15

s16

θ

θ

Figure 1: Hierarchical 16-APSK Constellation

Structure [2]

The bit-to-symbol allocation for the hierarchical 16-APSK is shown in Figure 2.

0011

0001

0000

0010

0111

0110

0100

0101

1111

1101

1100

1110

1011

1001

1000

1010

Figure 2: Bit-to-Symbol allocation for Hierarchical 16-

APSK modulation

In the bit allocation for hierarchical 16-APSK, the first two bits of each symbol determine the quadrant in which it falls, while the remaining two bits identify the symbol within the quadrant. As can be seen, the Hamming distance between each symbol on the outer ring in a quadrant is 1. This allocation scheme will allow for two streams of unequally protected data, with the high priority (HP) data stream bits being assigned to the first two bits of a symbol while the low priority (LP) data stream bits

being assigned to the 3rd and 4th bits of the symbol. The level of hierarchy can be varied by the use of the constellation parameters 𝛼𝛼 and 𝜃𝜃 which determine how clustered the points are between the quadrants and within the quadrants. This in turn will determine the level of relative error protection for the HP bit stream as compared to the LP bit stream. The bit allocation shown in Figure 2 can be compared to that which is shown in Figure 1(a) of [9]. The bit allocation in [9] is such that the last two bits of each symbol in a quadrant are identical while the first two bits differ. Thus this is the swapped version of the allocation shown in Figure 2 and can be used for the same purpose, namely to provide UEP for two classes of traffic. However the work in [9] did not mention any explicit objective in the design of the bit allocation unlike the proposed allocation in this paper. Also, as mentioned in Section 1, it did not consider the hierarchical case in the performance analysis.

3. BER PERFORMANCE ANALYSIS In this section we first derive SER using the union bound approach, and then derive BER for the two streams of data from the pairwise error probability (PEP). The SER of an M-ary modulation is given by

𝑃𝑃𝑠𝑠(𝑒𝑒) = 1𝑀𝑀∑𝑃𝑃(𝑒𝑒|𝑠𝑠𝑖𝑖)

𝑀𝑀

𝑖𝑖=1 (1)

where, is 𝑃𝑃(𝑒𝑒|𝑠𝑠𝑖𝑖) the probability an error will occur if symbol 𝑠𝑠𝑖𝑖 is transmitted. This is further given by

𝑃𝑃𝑠𝑠(𝑒𝑒) ≤ 1𝑀𝑀∑ ∑ 𝑃𝑃(𝑠𝑠𝑖𝑖 → 𝑠𝑠𝑗𝑗)

𝑀𝑀

𝑖𝑖=1,𝑗𝑗≠𝑖𝑖

𝑀𝑀

𝑖𝑖=1 (2)

where, 𝑃𝑃(𝑠𝑠𝑖𝑖 → 𝑠𝑠𝑗𝑗) is the PEP that 𝑠𝑠𝑖𝑖 is transmitted and 𝑠𝑠𝑗𝑗 is detected. 3.1 BER in Additive White Gaussian Noise (AWGN) In order to calculate the BER, the SER expression is modified to take into account the number of bits that will be in error for each PEP in (2). Thus the BER is given by

𝑃𝑃𝑠𝑠(𝑒𝑒) ≤ 1𝑙𝑙𝑙𝑙𝑙𝑙2𝑀𝑀

(1𝑀𝑀∑ ∑ 𝑁𝑁(𝑠𝑠𝑖𝑖 , 𝑠𝑠𝑗𝑗)𝑃𝑃(𝑠𝑠𝑖𝑖 → 𝑠𝑠𝑗𝑗)

𝑀𝑀

𝑖𝑖=1,𝑗𝑗≠𝑖𝑖

𝑀𝑀

𝑖𝑖=1) (3)

where, 𝑁𝑁(𝑠𝑠𝑖𝑖 , 𝑠𝑠𝑗𝑗) is the number of bits in error from symbol 𝑠𝑠𝑖𝑖 to 𝑠𝑠𝑗𝑗. Given the bit-to-symbol allocation shown in Figure 2, the two HP bits, which are allocated to the first two bits of a symbol, will be in error if the detected symbol is in either the adjacent or diagonal quadrant of the quadrant of the transmitted symbol. To determine the likelihood of this, it


3

is important to consider the geometry of the hierarchical 16-APSK constellation structure shown in Figure 2. The parameter which affects the constellation structure most is 𝛼𝛼, and the DVB-S2 standard specifies that 𝛼𝛼 should be set between 2.57 and 3.15 [1]. The implication of choosing 𝛼𝛼 in this range while keeping 𝜃𝜃 relatively small is that the distance between the inter-quadrant symbols on the outer ring is far greater than the distance between the corresponding quadrant inner ring symbols. Thus only symbols on the inner ring are considered for the BER calculation of the HP bits. Then using (3), assuming 𝑠𝑠1 is transmitted, the HP BER can be approximated as

𝑃𝑃𝐻𝐻𝐻𝐻 ≈14 (𝑃𝑃(𝑠𝑠1 → 𝑠𝑠5) + 𝑃𝑃(𝑠𝑠1 → 𝑠𝑠13)) (4)

In the AWGN channel model, the received signal, assuming that symbol 𝑠𝑠 is transmitted, is given by 𝑟𝑟 =𝑠𝑠 + 𝑛𝑛. 𝐸𝐸[|𝑠𝑠|2] = 1, 𝐸𝐸 being the expectation. 𝑛𝑛 is independent and identically distributed (i.i.d) according to the complex Gaussian distribution 𝐶𝐶𝐶𝐶(0,𝜎𝜎2) where 𝜎𝜎2 =𝜌𝜌−1. 𝜌𝜌 is the symbol based signal-to-noise ratio (SNR). The PEP for this channel can be calculated using the Gaussian Q-function and the Euclidean distance between the transmitted and detected symbols. Thus BER for the HP bits can be expressed as

𝑃𝑃𝐻𝐻𝐻𝐻(𝑒𝑒|𝜌𝜌) = 14(𝑄𝑄(√

𝑑𝑑1,5�̅�𝐸𝑠𝑠

𝜌𝜌) + 𝑄𝑄(√𝑑𝑑1,13�̅�𝐸𝑠𝑠

𝜌𝜌)) (5)

where, 𝑄𝑄(∙) is the is the Gaussian function which is given as 𝑄𝑄(𝑥𝑥) = 1

2𝜋𝜋 ∫ 𝑒𝑒𝑥𝑥𝑒𝑒 (− 𝑢𝑢2

2 )∞𝑥𝑥 𝑑𝑑𝑑𝑑, 𝑑𝑑𝑖𝑖,𝑗𝑗 is the Euclidean

distance between 𝑠𝑠𝑖𝑖 and 𝑠𝑠𝑗𝑗 given by 𝑑𝑑𝑖𝑖,𝑗𝑗 = |𝑠𝑠𝑖𝑖 − 𝑠𝑠𝑗𝑗|2, and

�̅�𝐸𝑠𝑠 is the average symbol energy for 16-APSK constellation, given as

�̅�𝐸𝑠𝑠 = (𝑅𝑅12 + 2𝑅𝑅22)/4 (6) A similar approach to that used to calculate the BER of the HP bits is used to calculate the BER of the LP bits. Given the bit-to-symbol arrangement shown in Figure 2, these two bits will only be in error if the transmitted and detected symbol pairs are within a quadrant. Using the nearest neighbourhood method and considering the inter symbol distances between the symbols on the inner and outer ring, with the specified range for 𝛼𝛼 (2.57 ≤ 𝛼𝛼 ≤3.15) and 𝜃𝜃 relatively small, only the 3 symbols on the outer ring in each quadrant are considered for the LP BER calculation. Thus, assuming that 𝑠𝑠2 is transmitted, the LP BER in AWGN is given as

𝑃𝑃𝐿𝐿𝐻𝐻(𝑒𝑒|𝜌𝜌) = 14𝑄𝑄(√


𝜌𝜌) + 12𝑄𝑄(√


𝜌𝜌) (7)

The theoretical BER bounds (5) and (7) for the HP and LP bits respectively are plotted in Figure 3 with 𝛼𝛼 = 3 and 𝜃𝜃 = 𝜋𝜋/18. The simulation results are also presented for comparison. As can be seen in Figure 3, there is a good match between the analytical bounds and the simulation results, especially for 𝑆𝑆𝐶𝐶𝑅𝑅 ≥ 3 dB for HP bits and 𝑆𝑆𝐶𝐶𝑅𝑅 ≥ 5 dB for LP bits. The BER for the HP and LP bits depends on the smallest Euclidean distance between the constellation symbols. Given the geometry of the proposed hierarchical 16-APSK constellation, only the symbols on the inner ring in adjacent quadrants are considered for the BER of the HP bits and only the symbols on the outer ring within a quadrant are considered for the BER of the LP bits. The simulations results justify this formulation as the simulation curves in Figure 3 closely match the theoretical BER expressions.

Figure 3: BER of hierarchical 16-APSK in AWGN

3.2 BER in Nakagami-m fading In the Nakagami-m fading channel model, the received signal, assuming that symbol 𝑠𝑠 is transmitted, is given by 𝑟𝑟 = ℎ𝑠𝑠 + 𝑛𝑛, where ℎ is the fading channel coefficient, and the probability density function (pdf) of the amplitude of the fading channel is the Nakagami-m distribution which is given by 𝑒𝑒𝜗𝜗(𝜗𝜗) =2

Γ(𝑚𝑚) (𝑚𝑚Ω)

𝑚𝑚𝜗𝜗2𝑚𝑚−1𝑒𝑒𝑥𝑥𝑒𝑒 (−𝑚𝑚

Ω 𝜗𝜗2), where 𝑚𝑚 is the

Nakagami-m fading parameter, Γ(𝑚𝑚) =∫ 𝑦𝑦𝑚𝑚−1exp (−𝑦𝑦)𝑑𝑑𝑦𝑦∞0 and Ω = E[|𝜗𝜗|2], E being the

expectation. 𝑛𝑛 is the AWGN component described in the previous subsection. If the received instantaneous SNR is defined as 𝛾𝛾 = |ℎ|2𝜌𝜌, the pdf of 𝛾𝛾 is given by [13]:

𝑒𝑒𝛾𝛾(𝛾𝛾) = (𝑚𝑚�̅�𝛾 )𝑚𝑚 𝛾𝛾𝑚𝑚−1𝑒𝑒𝑥𝑥𝑒𝑒 (−𝑚𝑚𝛾𝛾

�̅�𝛾 )Γ(𝑚𝑚) , 𝛾𝛾 ≥ 0 (8)

where, �̅�𝛾 = 𝐸𝐸[𝛾𝛾]. In the Nakagami-m fading channel model, given 𝛾𝛾, the BER for the HP and LP bit streams are given by

0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

SNR, dB

Bit E

rror R

ate

Theoretical BER LP bitsSimulation BER LP bitsTheoretical BER HP bitsSimulation BER HP bits


(16)

4

𝑃𝑃𝐻𝐻𝐻𝐻(𝑒𝑒|𝛾𝛾) = 14(𝑄𝑄(√


𝛾𝛾) + 𝑄𝑄(√𝑑𝑑1,13�̅�𝐸𝑠𝑠

𝛾𝛾)) (9)

𝑃𝑃𝐿𝐿𝐻𝐻(𝑒𝑒|𝛾𝛾) = 14𝑄𝑄(√


𝛾𝛾) + 12𝑄𝑄(√


𝛾𝛾) (10)

Then the average BER for the HP and LP bit streams using hierarchical 16-APSK in a Nakagami-m fading channel is derived by

𝑃𝑃𝐻𝐻𝐻𝐻(�̅�𝛾) = ∫ 𝑃𝑃𝐻𝐻𝐻𝐻(𝑒𝑒|𝛾𝛾)𝑝𝑝𝛾𝛾(𝛾𝛾)𝑑𝑑𝛾𝛾∞

0 (11)

𝑃𝑃𝐿𝐿𝐻𝐻(�̅�𝛾) = ∫ 𝑃𝑃𝐿𝐿𝐻𝐻(𝑒𝑒|𝛾𝛾)𝑝𝑝𝛾𝛾(𝛾𝛾)𝑑𝑑𝛾𝛾∞

0 (12)

where, 𝑃𝑃𝐻𝐻𝐻𝐻(𝑒𝑒|𝛾𝛾) and 𝑃𝑃𝐿𝐿𝐻𝐻(𝑒𝑒|𝛾𝛾) are given by (9) and (10), respectively. In order to evaluate (11) and (12), an alternative expression for the Q-function will need to be used. The 𝑄𝑄(𝑥𝑥) function is defined in [14] as

𝑄𝑄(𝑥𝑥) = 1𝜋𝜋∫ 𝑒𝑒𝑥𝑥𝑝𝑝 ( −𝑥𝑥2

2𝑠𝑠𝑠𝑠𝑠𝑠2𝜃𝜃)𝑑𝑑𝜃𝜃𝜋𝜋/2

0 (13)

Applying the trapezoidal rule for numerical integration to evaluate (13) leads to 𝑄𝑄(𝑥𝑥) =

12𝑠𝑠(

exp (−𝑥𝑥2

2 )2 + ∑𝑒𝑒𝑥𝑥𝑝𝑝 (− 𝑥𝑥2

2𝑠𝑠𝑠𝑠𝑠𝑠2(𝜃𝜃𝑘𝑘))𝑛𝑛−1

𝑘𝑘=1) (14)

where, 𝜃𝜃𝑘𝑘 = 𝑘𝑘𝜋𝜋

2𝑛𝑛. It is experimentally shown in [15] that choosing 𝑠𝑠 greater than 6 results in sufficient accuracy in the numerical integration. Defining the moment generating function (MGF) as 𝑀𝑀(𝑠𝑠) = ∫ 𝑒𝑒𝑥𝑥𝑝𝑝(𝑠𝑠𝛾𝛾)𝑓𝑓𝛾𝛾(𝛾𝛾)∞

0 𝑑𝑑𝛾𝛾, the MGF function for the Nakagami-m pdf is given as [14]

𝑀𝑀(𝑠𝑠) = ∫ 𝑒𝑒𝑥𝑥𝑝𝑝(−𝑠𝑠𝛾𝛾)𝑓𝑓𝛾𝛾(𝛾𝛾)𝑑𝑑𝛾𝛾 ∞

0

=( 11+𝑠𝑠�̅�𝛾/𝑚𝑚)

𝑚𝑚

(15)

Using (14) and (15), (11) and (12) can be derived as: 𝑃𝑃𝐻𝐻𝐻𝐻(�̅�𝛾) = (16)

18𝑠𝑠 (

12𝑀𝑀(𝑑𝑑1,5

2�̅�𝐸𝑠𝑠) + ∑𝑀𝑀( 1

2𝑠𝑠𝑠𝑠𝑠𝑠2(𝜃𝜃𝑘𝑘)𝑑𝑑1,5�̅�𝐸𝑠𝑠

)𝑛𝑛−1

𝑘𝑘=1)

+ 18𝑠𝑠 (


2�̅�𝐸𝑠𝑠) + ∑𝑀𝑀( 1


)𝑛𝑛−1

𝑘𝑘=1)

𝑃𝑃𝐿𝐿𝐻𝐻(�̅�𝛾) =

18𝑠𝑠 (


2�̅�𝐸𝑠𝑠) + ∑𝑀𝑀( 1


)𝑛𝑛−1

𝑘𝑘=1)

+ 14𝑠𝑠 (


2�̅�𝐸𝑠𝑠) + ∑𝑀𝑀( 1


)𝑛𝑛−1

𝑘𝑘=1)

(17)

where, in both (16) and (17), 𝑑𝑑𝑖𝑖,𝑗𝑗 is the Euclidean distance between symbol 𝑠𝑠 and 𝑗𝑗. The theoretical BER bounds (16) and (17) for the HP and LP bits over Nakagami-m, m=1 and m=2 channels are plotted in Figure 4. 𝛼𝛼 = 3, 𝜃𝜃 = 𝜋𝜋/18 and 𝛺𝛺 = 𝐸𝐸[|ℎ|2] =1. The system was simulated over the fading channels and the results are shown in Figure 4 for comparison. As graphs show, there is a good match between the analytical bounds and the simulation results, especially in the higher SNR regions. Since the BER is dependent on the smallest distances between the constellation points, only the symbols on the inner ring in adjacent quadrants are considered for the HP bit stream BER and only the symbols on the outer ring within a quadrant are considered for the LP bit stream BER. The closely matching simulation results justify this formulation, and the derived theoretical expressions can thus be used to accurately design UEP applications using the proposed hierarchical 16-APSK modulation scheme. The use of the UEP design parameters 𝛼𝛼 and 𝜃𝜃 leads to a geometry in the constellation in which the relative distance between the outer ring symbols between quadrants is much higher than the distance between outer ring symbols within the quadrants. The consequence of this is that, given the bit-to-symbol allocation of the proposed constellation, the distance between symbols that contribute to the HP bit stream BER is greater than the distance between the symbols that contribute to the LP bit stream BER. The greater relative distance between these symbols leads to a lower BER for the HP bits as compared to the LP bits, and this is shown in the curves in Figure 4. As an example for the relative UEP between the two bit streams, if a SNR of 30dB is considered for the system setup in Figure 4(a), the HP bits can be transmitted with a BER of 6x10-4 while simultaneously the LP bits can be transmitted with a BER of 7x10-3.


5

(a) Nakagami-m, m=1

(b) Nakagami-m, m=2

Figure 4: BER of hierarchical 16-APSK in Nakagami-m fading

4. LOW COMPLEXITY DETECTION ALGORITHM

The most optimum detection algorithm used for the detection of constellations with an irregular structure is the ML detector. Assuming a general fading channel, the ML criterion can be expressed as:

�̂�𝑠 = arg min𝑠𝑠𝑠𝑠𝑠𝑠

|𝑟𝑟 − ℎ𝑠𝑠|2 (18) where, �̂�𝑠 is the estimated transmitted symbol, 𝑠𝑠 is a symbol from the signal set 𝑆𝑆, 𝑟𝑟 is the received signal and ℎ is the fading channel coefficient. The disadvantage of the ML detector is that it is highly computationally expensive, especially when the signal set is large. This leads to inefficient power usage in systems that have limited power sources such as satellite and mobile handheld devices. There has been much effort in designing low complexity ML detectors. However most of these detectors are based on systems that use QAM modulation structures. The recent work in [16] presents a

low complex ML algorithm for un-coded MPSK modulation, but there is no such proposal for the un-coded APSK scheme. Motivated by the work in [16], a low complexity ML algorithm is proposed in this section for the hierarchical 16-APSK system. The algorithm, which is designed by exploiting the structure of the hierarchical 16-APSK constellation, achieves the same BER performance as the optimum detector but with significantly reduced computational complexity. The proposed low complexity ML (LC-ML) algorithm is as follows. Step 1: Determine the quadrant in which the received signal 𝑟𝑟 falls in. Step 2: Calculate the amplitude of 𝑟𝑟, i.e. compute |𝑟𝑟|2.

Step 3: If |𝑟𝑟|2 is less than (𝑅𝑅1+𝑅𝑅22 )2 then �̂�𝑠 is estimated to

be the symbol on the inner ring in the respective quadrant which was determined from Step 1. Assuming Step 1 results in the top right quadrant, the estimated symbol will be one of the following symbols, 𝑠𝑠1, 𝑠𝑠5, 𝑠𝑠9 or 𝑠𝑠13 as shown in Figure 5. Step 4: Else, �̂�𝑠 is estimated to be one of the three symbols on the outer ring in the respective quadrant. The symbol is selected by computing the angle of the received signal 𝑟𝑟 and comparing it to two angular boundaries as shown in Figure 5. Referring to this figure, assuming the top right quadrant is determined from Step 1, if the angle for the dashed line is 𝜑𝜑, then the estimated symbol will be 𝑠𝑠2 if 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑟𝑟) is less than 𝜑𝜑 − 𝜃𝜃

2; 𝑠𝑠4 if 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑟𝑟) is more than

𝜑𝜑 + 𝜃𝜃2; or 𝑠𝑠3 otherwise, where 𝜃𝜃 is the angle between the

constellation points on the outer ring as shown in Figure 1. It should be noted the procedure in this step is similar to the one used to determine received symbol angle in [16]. In the complexity analysis, the computation complexity is defined as the total number of real-valued multiplications required by an algorithm [16]. For the ML detection, the computation of |𝑟𝑟 − ℎ𝑠𝑠|2 requires 4 real-valued multiplications for the multiplication of ℎ and 𝑠𝑠, and 2 for the computing the square of the amplitude of 𝑟𝑟 − ℎ𝑠𝑠. Given there are 16 symbols that need to be tested for the hierarchical 16-APSK constellation, the ML detection process requires a total of 16 × (4 + 2) = 96 real-valued multiplications. The computation complexity for the proposed LC-ML algorithm is calculated as follows. Step 1 requires no real-valued multiplications as determining the quadrant in which the received signal 𝑟𝑟 falls in needs only comparisons which can be done using subtractions. Step 2 requires 2 real-valued multiplications in the computation of |𝑟𝑟|2. Step 3 requires no real-valued

multiplications as it is assumed that (𝑅𝑅1+𝑅𝑅22 )2can be pre-

calculated and used for the comparison.

0 5 10 15 20 25 30 35 4010

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101

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ate


0 5 10 15 20 25 30 35 4010

-5

10-4

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101

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rror R

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6

R1

R2

s1

s2

s3

s4

s5

s6

s7

s8

s9

s10

s11

s12

s13

s14

s15

s16

θ/2θ/2

Figure 5: Hierarchical 16-APSK Constellation with

angular boundaries for symbol detection Finally, the computation of the angle of 𝑟𝑟 in Step 4 requires 3 real-valued multiplications as specified in [16]. Thus the LC-ML algorithm requires a total of 2 + 3 = 5 real-valued multiplications. The efficiency of the proposed algorithm relative to the ML detection is 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸= 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐸𝐸𝐶𝐶𝐸𝐸𝐶𝐶𝐸𝐸 (𝑀𝑀𝑀𝑀) − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐸𝐸𝐶𝐶𝐸𝐸𝐶𝐶𝐸𝐸 (𝑀𝑀𝐶𝐶 − 𝑀𝑀𝑀𝑀)

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐸𝐸𝐶𝐶𝐸𝐸𝐶𝐶𝐸𝐸 (𝑀𝑀𝑀𝑀)

= 94.79% For a performance comparison, Figure 6 shows the BER performance of ML and LC-ML in both AWGN and Nakagami-m (m=1) with 𝛼𝛼 = 3 and 𝜃𝜃 = 𝜋𝜋/18. As is shown in the figure, the proposed LC-ML detector achieves the same error performance as the optimum ML detector.

(a) AWGN

(b) Nakagami-m, m=1

Figure 6: Error performance comparison of the proposed low complexity ML detector with the optimum ML

detector

5. CONCLUSION This paper presents a scheme which provides two parameters, namely the ratio between the outer and inner rings of the APSK constellation and the angle between the constellation points on the outer ring, which can be varied by a designer to facilitate relative UEP targets for two classes of traffic in a multimedia traffic transmission system. The theoretical BER expressions derived for the high and low priority bit streams are shown to be accurate by comparing the theoretical results with simulation results of the system in AWGN and Nakagami-m fading channels. Thus these expressions can be used to accurately model and design UEP applications using the proposed hierarchical 16-APSK scheme. A low complexity ML detector for the proposed modulation scheme is also proposed in this paper, and is shown to be as accurate as the optimum ML detector. In future work, the system will be extended to accommodate UEP for more than two classes of multimedia traffic.

REFERENCES

[1] ETSI EN 302 307 V1.2.1, “Digital video broadcasting (DVB); second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications,” April 2009.

[2] H. Meric, J. Lacan, F. Arnal, Lesthievent, G. and M.-

L. Boucheret: “Combining Adaptive Coding and Modulation With Hierarchical Modulation in Satcom Systems”, IEEE Transaction on Broadcasting, Vol. 59 No. 4, pp. 627-637, December 2013.

[3] J. Hossain, P.K. Vitthaladevuni, M.S. Alouini, V.K.

Bhargava and A.J. Goldsmith: “Adaptive hierarchical

0 5 10 15 20 25 3010

-6

10-5

10-4

10-3

10-2

10-1

100

SNR, dB

Bit E

rror R

ate

Optimum ML BER LP bitsOptimum ML BER HP bitsLow-Complexity ML BER LP bitsLow-Complexity ML BER HP bits

0 5 10 15 20 25 30 35 4010

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7

modulation for simultaneous voice and multiclass data transmission over fading channels”, IEEE Transactions on Vehicular Technology, Vol. 55 No. 4, pp. 1181-1194, July 2006.

[4] S.S. Arslan, P.C. Cosman and L.B. Milstein:

“Coded Hierarchical Modulation for Wireless Progressive Image Transmission”, IEEE Transactions on Vehicular Technology, Vol. 60 No. 9, pp. 4299-4313, November 2011.

[5] M. Ghandi, B. Barmada, E. Jones, and M. Ghanbari:

“Unequally error protected data partitioned video with combined hierarchical modulation and channel coding”, Proceeding of the IEEE International Conference on Acoustics, Speech Signal Processing, Toulouse, pp. II-529-II532, May 2006.

[6] Z. Hu and H.Liu: “A Low-Complexity LDPC

Decoding Algorithm for Hierarchical Broadcasting: Design and Implementation”, IEEE Transactions on Vehicular Technology, Vol. 62 No. 4, pp. 1843-1849, May 2013.

[7] R. De Gaudenzi, A. Guillen, I. Fabregas, A.

Martinez: “Performance analysis of turbo-coded APSK modulations over nonlinear satellite channels”, IEEE Transactions on Wireless Communications, Vol. 5 No. 9, pp. 2396-2407, September 2006.

[8] M. Baldi, F. Chiaraluce, A. de Angelis, R.

Marchesani and S. Schillaci: “Performance of APSK modulation in wireless tactical scenarios for land mobile systems”, Proceeding of the IEEE Symposium on Computers and Communications (ISCC), Sousse, pp. 591-569, July 2011.

[9] W. Sung, S. Kang, P. Kim, D-I. Chang and D-J.Shin:

“Performance analysis of APSK modulation for DVB-S2 transmission over nonlinear channels”, International Journal of Satellite Communications and Networking, Vol. 27 No. 6, pp. 295-311, December 2009.

[10] J. Lee, D. Yoon and S.K. Park: “Error Performance

Analysis for 4+12+16 APSK Signal over a Satellite Channel”, Proceeding of the 4th International Conference on Digital Communications, Colmar, pp. 93-95, July 2009.

[11] C-I. Oh, S-H. Choi, D.I. Chang and D-K. Oh: “An

analysis of Hierarchical APSK and PSK scheme and an Application to increase the transmission capacity of the S-DMIB”, Proceeding of the International Conference on Consumer Electronics, Las Vegas, pp. 1-2, January 2007.

[12] J. Lee and D. Yoon: “Soft-decision demapping

algorithm with low computational complexity for

coded 4+12 APSK”, International Journal of Satellite Communications and Networking, Vol. 31 No. 3, pp. 103-109, February 2013.

[13] M.S. Alouini and A.J. Goldsmith: “Adaptive

modulation over Nakagami fading channels”, Kluwer Journal on Wireless Communications, Vol. 13 No. 1, pp. 119-143, May 2000.

[14] M.K. Simon and M.S. Alouini: Digital

Communications over Fading Channels, Wiley & Sons, Inc., USA, second edition, January 2005.

[15] T. Quazi : “Cross-layer Design for the Transmission

of Multimedia Traffic over Fading Channels”, PhD Thesis, University of KwaZulu-Natal, December 2009.

[16] H. Men and M. Jin: “A Low Complexity ML

Detection Algorithm for Spatial Modulation Systems with MPSK Constellation”, IEEE Communications Letters, Vol. 18 No. 8, pp. 1375-1378, August 2014.


SECURE SIGNAL AND SPACE ALAMOUTI SCHEME P. O. Akuon* and H. Xu** * School of Engineering, University of Nairobi, P O Box 30197 – 00100, Nairobi, Kenya E-mail:[email protected], [email protected] ** School of Engineering, University of KwaZulu-Natal, King George V Avenue, Durban, 4041, South Africa, E-mail: [email protected] Abstract: A method is proposed that secures the conventional Alamouti space-time block code against an eavesdropper by use of both signal and space rotations. Signal rotation is realized by applying a random rotation angle to the conventional signal constellation. This is followed by a second random phase rotation of the Alamouti codeword. The received signal strength levels between legitimate users are used to exchange the secret key that produces the random rotations at the receiver. This is possible due to the availability of short-term reciprocity of the radio channel. Both signal and space rotation angles are chosen such that the peak-to-average ratio (PAR) of the transmit signal is not increased. Firstly, we show that the rotation of the codeword alone compromises system security under receive diversity, especially when the eavesdropper is close to the legitimate user. Then, through the analysis of mutual information rate and bit error rate, we show that by the addition of signal rotation, it is possible to reduce the capacity of the eavesdropper to zero, even when receive diversity is enhanced. Key words: Alamouti scheme, secure signal and space, secret key, wireless communications

1. INTRODUCTION

Securing information in wireless communication links is vital so as to allow only the intended users to retrieve the transmitted messages. Traditionally, information security is achieved via cryptographic approaches like the two-key public key cryptography (PKC) [1]. In the presence of a secure channel, any two users can exchange secret-key information that is required for further communication processes. Recent developments in the physical layer show that the knowledge of a random variable by two users can be exploited to pass this secret-key information [2]. In addition, it has been established that short-term reciprocity of the radio channel and the scenario in which the impulse response viewed by two legitimate users is about the same, can be utilized to achieve a similar result like PKC [3]. This invaluable phenomenon was improved by [4], where, in the first step, the rapid decorrelation of the phase response of the channel is probed and then the signal is modified to precompensate for phase rotation of the channel. It is this difference in channel properties between users and adversaries that secures the communication processes. Indeed, several security schemes have been developed with the assumption that the channel state information (CSI) is known at the transmitter. Furthermore, secret communication for multiple antenna elements is well studied in [5]. In [6], artificially-generated noise is added to the information signal in the null space of the channel matrix of the legitimate receiver. As a result, the channel of the eavesdropper will be degraded. Other forms of secrecy include maximal ratio transmission through

beamforming, which requires full CSI at the transmitter for best performance [7]. Finally, a cross-layer approach based on space-time block code (STBC) was introduced in [8], but it expands the signal constellation. In summary, it is desirable to devise a highly secure technique that does not expand the signal constellation and yet exploits the unique modulation properties of the wireless channel for exchanging the secret information. Therefore, the technique introduced by [9] is desirable because it is capable of providing secure communication for space-time systems, while degrading the diversity order of the eavesdropper to zero. The scheme in [9] employs STBC including the Alamouti code. In addition, the enhanced security is achieved without the knowledge of the CSI at the transmitter. However, we show in Section 3 that the message security is compromised if the eavesdropper knows one space angle and increases the number of receive antennas. As a result, we propose a diverse technique that retains the advantages of the scheme in [9] and yet achieves zero diversity for the eavesdropper even under enhanced receive diversity. The enhanced security is achieved due to the rotation of the signal constellation, which is only known to the legitimate user. As a result, even in the case that the eavesdropper decodes the transmitted message, he/she will still need to demap the intended message through a rotation phase angle of the signal constellation. For notations in this paper, matrices are denoted by bold upper case fonts, vectors are denoted by bold lower case fonts and ( ) represents the complex conjugate. denotes the Frobenius norm. denotes the expectation operator over all transmitted symbols.


2. SYSTEM MODEL

PhaseDecoderML Decision

AlamoutiSTBC Phase

rotation

Symbolrotation

v

sxqxm

Symbolrotation

rx' x'q s'

Figure 1: System Block Diagram

In the proposed system model, the Alamouti STBC is adopted to transmit digital messages to a legitimate receiver. However, two random set of rotations are applied at the transmitter before transmission is made. An illustration of the scheme is shown in Figure 1. In general, two modulated symbols , are selected from the conventional M-ary signal constellation and mapped to a new constellation through rotation by a random angle to form .

Then, the Alamouti STBC is applied to the new signal constellation to produce the codeword matrix denoted by whose elements are required for transmission by each transmit antenna for two time slots. The signal transmitted at each antenna is further rotated by a random phase angle . The rotations are applied at each transmit antenna (Alice) and therefore any eavesdropper (Eve) would require the knowledge of the two phase rotation angles in order to detect the message in each codeword and a further two signal constellation angles in order to demap the detected signals. Maximum-likelihood (ML) detector is employed by both legitimate user (Bob) and the eavesdropper (Eve) so as to obtain the transmitted symbols. Finally, based on the knowledge of the signal rotation angles at the receiver, the signals are then rotated into the conventional constellation.

In order to explore the possibility of the eavesdropper accessing the secure information, the following worst case assumptions are normally taken into account. That Eve: (1) knows that the transmitter uses secure Alamouti scheme with double rotations, whose rotation angles change with every STBC codeword; (2) knows the original signal constellation; (3) receives the transmitted signals with perfect receive CSI; (4) Bob is many wavelengths away from Eve; (5) channel is reciprocal between Bob and Alice for both probing and transmission processes. Therefore, channel reciprocity is exploited to pass the key that generates the rotation angles at the destination. In the proposed scheme, we add the fact that Eve knows the original signal constellation but not the new constellation after signal rotation.

In this paper, we exploit the channels for the eavesdropper and the legitimate receiver that fade independently. In order to enhance further security in the channel, it becomes necessary that the rate of transmission is made higher than the speed of the receiver

so that the channel is reciprocal for both the probing and transmission processes [4]. It is also well known that any adversary eavesdropping on both legitimate users will receive a different phase from either of them, as long as the adversary is many wavelengths away from the intended receiver. Therefore, blind deciphering of information by the eavesdropper is not possible due to this phase difference. However, the exchange of the secret key between legitimate users is required and the process can be achieved through their common receive signal strength indicator (RSSI) levels. 2.1 RSSI and channel reciprocity Each fading path is characterised by independent characteristics. This unique phenomenon can be exploited to pass secret key information. For example, by measuring the receive signal strength (RSS) levels between the source and the destination, different signal levels can be quantized to pass meaningful and secret information seed, which generates the random rotation angles between Alice and Bob. In the cognitive radio environment, the RSS can be measured as [10]

Where denotes the RSS of the th time from the th device denotes the sample size is the fading gain of the th device from the source denotes the transmission symbols from the source with symbol energy equal to accounts for the geographical distance between the th pair of devices is the attenuation constant, which is typically larger

than 2 and thus,

gives the pass-loss

denotes the on/off emission state since initial value is the random noise sample of the th time Following (1), it is clear that given that the legitimate destination and the eavesdropper observe the source with different fading gains, the RSS levels will be different. Therefore, the key can be passed securely to the legitimate receiver. However, if , which implies correlated channel and , which implies close proximity, then the security is compromised, since all other factors in (1) would lead to the same RSS level. Therefore, a method is required that provides security beyond the channel permeability. In the following text, we give a discussion on the secure space scheme, which is limited by the channel permeability. 2.2 Secure space encoding and transmission In order to achieve the secure signal transmission, the


rotation angles are chosen such that the PAR of the signal constellation is not changed. This is achieved by making sure that after the rotation is performed, the new signal constellation remains similar to the original one. For example, let us look at the signal constellation of quadrature phase shift-keying (QPSK). There are four symbols: . In the modulator, given any one of these symbols, any other three symbols can be generated by rotating the given symbol. For example, if is given then all four symbols , and can be generated by ,

,

and , respectively. Clearly, if we transmit a

symbol , where and

, then we can achieve secure communication.

The rotated information symbols are then transformed by the conventional Alamouti STBC scheme. However, the system security is limited by the number of random rotations that can be performed. Therefore, in order to maintain the same PAR, the rotation angles for the M-ary quadrature amplitude modulation (MQAM) takes on the values

. For M-ary phase-shift keying

(MPSK) modulation, rotation angles can be generated thus improving system security. In the secure signal scheme, for the kth Alamouti STBC codeword, the encoder transmits from antenna one and from antenna two at time slot one. At time slot two, the encoder transmits

from antenna one and from

antenna two, resulting in the following equivalent parameterized STBC [9, 11]

By assuming a single transmit antenna at the receiver, each equivalent received signal sample is given by

Where is the channel coefficient associated with transmit antenna i,

and are the noise samples. Noise samples and channel coefficients are modelled as circularly-symmetric independent and identically distributed (i.i.d.) complex-valued Gaussian random variables with zero mean and variance /2 and per dimension, respectively. is the double-sided noise spectral density. The channel whose coherence time spans over one STBC codeword is assumed to remain fixed.

Let , and , then (3) can be re-written as

Mainly, the secure space approach generates two random phases to form a modified random channel fading at Eve’s receiver, which is very difficult to estimate. Moreover, it is noticeable that the channel is a function of the rotation angle and the equivalent received signal is written as Where is the channel matrix, which is orthogonal and depends on and . Nonetheless, we previously discussed how the phase rotation angles needs to be conveyed secretly to Bob. The RSS between legitimate users is measured to serve as a secret key. The secret key serves as a seed to a random number generator. In fact, only most significant bits are kept from the generator output for possible values. For brevity, how the transmitter hands over the rotation angle information to Bob is well-addressed in [9]. The secure space system proposed in [9] utilizes random signal rotation at the transmitter to secure the channel between the legitimate users. However, we will demonstrate in the simulations, that channel security may be compromised when an eavesdropper deciphers one space angle and exploits more receive diversity to intercept multipath signals to retrieve information. We also observed from (1) that in the case that Eve is in the proximity of Bob or if the channels for Bob and Eve are correlated, Eve will decipher the channel key and breach the channel security. Even though, this scenario may seem highly unlikely, the secure space scheme assumes that the channel remains the same over the two transmissions. Therefore, there is a possibility that Eve will know the key under correlation conditions. Despite the low probability of detection of secured information, further investigations reveal that Eve will be able to decode the secured information under enhanced receive diversity. Therefore, we propose to combine the secure space with security provided by the signal constellation itself such that, the channel key alone is not a sufficient condition for network security. 2.3 Secure signal and space encoding and transmission In the proposed secure signal and space scheme, the exact information symbol in the conventional constellation diagram is first rotated by a signal phase angle . This step is then followed by a signal phase rotation through


, which is similar to the secure space scheme. Therefore, for the kth Alamouti STBC codeword, the encoder transmits from antenna one and from antenna two at time slot one. At time slot two, the encoder transmits

from antenna one and

from antenna two, resulting in the following equivalent parameterized STBC

Where are the information symbols [9, 11]. 2.3 Secure signal and space decoding The received signal for the kth Alamouti STBC codeword can be expressed as

At Bob’s receiver, all the rotation angles are known. Therefore, the equivalent received signals for the kth codeword can simply be given by the following matched filter, which is the typical Alamouti STBC detection scheme [11]

2.4 Eavesdropper’s ML detection Conventionally, Eve also receives a signal similar to Bob’s in (7), but with varying channel phases. In fact, Eve does not know the rotation angles for the signal constellation or the phase rotation angles. Therefore, Eve computes the ML estimates for the rotated symbols first by assuming the knowledge of to obtain the rotated symbol estimates. This is then followed by demapping of the symbols by assuming the knowledge of , where . Similar to Bob’s, the ML detection process for Eve can be expressed as follows Where denotes the estimated matrix of independent fading channel coefficients denotes the matrix of the estimated rotation angles.

Moreover, it is assumed that Eve has perfect receive CSI, but she has no knowledge of . However, using a maximum likelihood detector over all possible values of , the ML detector for Eve can be written as

Notably, the search over all the symbol alphabets and the two pair of angles greatly increases the receiver complexity for Eve. In the case that the phase angle is decoded by Eve, the signal rotation angles , will still be required, without which the transmitted information cannot be decoded/demapped.

3. SIMULATION RESULTS This section presents the simulation results for secure space scheme with receive diversity and the proposed secure signal and space scheme. For the two secure systems, the bit error rate (BER) is presented against signal-to-noise ratio (SNR). In the case of secure space system, since the rotation is known at Bob’s receiver, the transmitted symbol can easily be detected as the conventional MPSK/MQAM detection. However if is not known, the detection for the transmitted symbol is not possible through the Rayleigh fading channel. But since two transmit antennas are employed, there is a possibility that the eavesdropper may obtain the value for one angle. Therefore, in the case that one angle is known, the probability of error reduces for the eavesdropper. Figure 2 shows the BER plots for secure space system under receive diversity. In the event that one of the space rotations at the transmitter is known to the eavesdropper, the space secure scheme proposed in [9] suffers when the receive diversity is increased by having more receive antennas. For example, the legend ‘2x1 Alamouti QPSK without two rotations’, which implies two transmit and one receive antenna, shows that Eve cannot decode the transmitted information under the secure system that exploits the aforementioned assumptions. However, in reality and due to the stochastic nature of the fading channel, Eve could be in close proximity to Bob and could share the RSS levels, where the key is secretly submitted. In that case Eve will be able to generate at least one phase rotation angle of the channel and decode the message. Furthermore, “Without two rotations” in Figure 2 indicates the case where the two rotation angle for are not known. Furthermore, we see that with 2 receive antennas, the reliability of the eavesdropper improves. A further improvement is also observed with 3 receive antennas. In fact, with the knowledge of just one phase rotation angle and the use of 3 receive antennas; the reliability of Eve goes beyond the conventional Alamouti scheme. This is a very huge compromise on communications system security.


Figure 2: Space STBC BER for Bob and Eve

Figure 3: Signal and Space STBC BER for Bob and Eve

In the case of secure signal and space scheme, the knowledge of the angles for both the space and the signal rotations are required in order to detect and demap the messages correctly. In the event that no space rotation angle is known, then Eve cannot decode the message. In the event that two signal rotation angles are known, then a certain level of system security is achieved similar to the one in [9]. On the other hand, if it is the two space rotation angles that are known, then a different level of security is attained. Actually, Eve cannot decode the message. For example if the detected symbol is then the transmitted symbol could be ,

, or

. Readily, we see that the rotation of the signal

constellation promises tight security for the STBC system and the combination with space rotation at the transmitter promises even a better system. The security level is raised by a pre-assigned signal rotation angle between legitimate users. Since this information is not relayed to the intended receiver over the channel, Eve cannot decode the signal rotation angle. As a result, Eve won’t be able to demap the decoded information. Figure 3 shows the BER plots for the secure signal and space scheme under receive diversity. In summary, for the secure signal and space scheme, the knowledge of a

single is not sufficient for the eavesdropper to decode the message even under receive diversity. Thus, the result for this scheme is similar to the case of secure space scheme, where no phase rotation angle is known by the eavesdropper. Furthermore, “full CSI” refers to the assumption of the worst case scenario, where the eavesdropper is aware of the secret key by sharing the knowledge of the channel information or CSI at the transmitter, thus gaining the knowledge of .

4. DISCUSSION ON MUTUAL INFORMATION In order to theoretically support the validity of the simulations results obtained in the ML detection, we apply mutual information (MI) metric to show that the capacity for Eve degrades to zero, even in the case that all the channel rotation angles are known. It is well known that MI can be used to measure the amount of information rate or capacity. It is also straightforward that the information capacity for the secure space scheme differs from that of the secure signal and space scheme. Therefore, in the following text, the capacity analysis for each scheme is provided separately.

4.1 Mutual information for secure space scheme In the secure space scheme, the overall probability of error arises due to the probability of error in detecting the channel phase angle and the probability of error in the ML signal detector. Therefore, for both receivers (Bob and Eve), the overall symbol error probability (SEP) can be written as

Where denotes the error probability of signal detection denotes the error probability of the phase rotation angle for the kth codeword Essentially, is used in evaluating reliability of signal detector, while is used in evaluating the level of security. For the case of receive antennas and assuming that the transmitted symbols are equally probable at the receiver, is given by

Where is the vector of channel coefficients for all the receive antennas denotes the noise variance

0 2 4 6 8 10 12 14 16 18 2010-4

10-3

10-2

10-1

100

SNR (dB)

BER

2x1 Alamouti QPSKEve 2x1 Alamouti QPSK without two rotationsEve 2x1 Alamouti QOSK with 1 rotationEve 2x2 Alamouti QPSK with 1 rotationEve 2x3 Alamouti QPSK with 1 rotation

0 2 4 6 8 10 12 14 16 18 2010-4

10-3

10-2

10-1

100

SNR (dB)

BER

Enhanced Bob 2x1 Alamouti QPSKEnhanced Eve 2x1 with 1 Tx rotation and all symbol rotationEnhanced Eve 2x1 with full CSI Tx and 1 symbol rotationEnhanced Eve 2x3 with full CSI Tx and 1 symbol rotation


The legitimate user Bob has the information about the rotation angles, while Eve does not. It follows from (11) that for Bob, and , which is as shown in (12). Therefore, for Bob, there will only be uncertainty in the reliability of the transmitted symbols, but security is achieved. For Eve, since there are N unknown rotation angles ( for MPSK and for 4QAM), the probability of choosing correct rotation angles is

given by and therefore by substituting into (11), we obtain the new probability of error as Immediately (13) shows that if N is large, which is the case in selecting MPSK symbols, and , then tends to unity. For example, let and we assume that only one channel phase rotation angle is known i.e. , then Eve will detect the secure information albeit with a very high probability of error which is always above , i.e. It is also clear from (12) that decreases with the increase in and Eve can employ different angles at the receive antenna in order to increase the probability of choosing the correct channel phase angle. In the case that , the new overall can be obtained by substituting into (11) and by using (12), the new error rate is written as

Evidently, for the factor in (15) is smaller than , which is obtained in the case of a single receive antenna. Therefore, when Eve uses several receive antennas, the probability of error in detecting the channel phase angle could reduce significantly. This finding clearly supports the increased signal reliability, which is depicted in Figure 2, when 2 or 3 receive antennas are used together with the knowledge of one channel phase rotation angle. So far, we have clarified some features of the secure space scheme based on the probability of error. However, the in (11) varies according to the instantaneous channel . We therefore need to quantize the amount of secured information based on an average time period, and this can be achieved by evaluating the entropy of the observed system errors. Classical information theory, defines entropy as a measure of uncertainty that remains after receiving the

transmitted symbols at the receiver [12]. This may be written as

Consequently, the mutual information or capacity between the input and output can then be expressed as the maximum achievable rate minus the amount of uncertainty, thus Using the example given in (14), and (17), we observe that the mutual information for a single STBC codeword would fall below 0.25 bits/s/Hz. However, for we have , where is lower than . In this case, the information rate will improve to 0.5 bits/s/Hz. Generally, we observe that the information rate is increased by employing receive diversity in order to reduce both the probability of error for the symbol detection and the probability of error for the obtaining the channel phase angle, whenever different angles are used in various receive antennas per STBC codeword. 4.2 Mutual information for secure signal and space scheme In the proposed secure signal and space scheme, a further knowledge of is required in order to demap the detected message. Since signal detection and demapping are independent events, for both Bob and Eve, the overall may be expressed as

Similar to the secure space scheme, in the case of Bob, there is no error in knowing all the rotation angles and it follows that and . Therefore, for Bob, there will only be uncertainty in the reliability of the transmitted symbols, but security is achieved in both the space and the signal constellations. In the case of Eve, since there are unknown signal rotation angles, the probability of selecting the

correct signal rotation angles is given by . Thus we can write the overall error as

Where

.


Two secure system cases arise in the general equation given in (19). For example, firstly, if all signal rotation angles are known and only one space rotation angle is known, i.e. , then is given by (15), which is the case in [9]. Secondly, if no set of angles is known or if only one of the signal constellation rotation angles is known, then , even when is increased. For example, let then we obtain In summary, the results in (20) to (22) imply a near zero information rate for Eve under the secure signal and space scheme, and this supports the illustrations in Figure 3. This is possible because the demapping process for the symbols from the new constellation is independent of the transmission channel and the benefits of enhanced receive diversity.

5. CONCLUSION We have provided a secure signal and space Alamouti STBC scheme by performing a secret rotation of the signal constellation in order to block the eavesdropper’s intrusion. By the use of an analysis for mutual information, we have shown that the proposed scheme degrades mutual information for the eavesdropper to zero, even if the eavesdropper has knowledge of one channel phase rotation angle for the signal constellation. As a result, additional receive diversity cannot help to improve information rate. This condition implies that intrusion by the eavesdropper is most unlikely.

6. REFERENCES [1] R. L. Rivest, A. Shamir, and L. Adelman, “A method for obtaining

digital signatures and public key crypto-systems,” Commun., ACM21, no. 2 (1978), 120-126.

[2] U. M. Maurer, “Secret key agreement by public discussion from common information,” IEEE Trans. Inform. Theory, vol. 39, pp.733-742, 1993.

[3] A. A. Hassan, W. E. Stark, J. E. Hershey, and S. Chennakeshu,

“Key distribution for mobile radio systems,” in Proc. Japan-Canada Int. Workshop on Multimedia Wireless Communications and Computing, Victoria, BC, Canada, 1996.

[4] H. Koorapaty, A. A. Hassan, S. Chennakeshu, “Secure information transmission for mobile radio,” IEEE Trans. Communications Lettrs., vol. 4, N0. 2, pp. 52-55, Feb. 2000.

[5] A. E. Hero, “Secure space-time communication,” IEEE Trans. Information Theory, pp. 3235-3249, Dec. 2003.

[6] R. Negi, S. Goel, “Secret communication using artificial noise,” IEEE Vehicular Technology Conference, Fall 2005, vol. 3, pp. 1906 – 1910.

[7] A. Mukherjee and A. Swindlehurst, “Robust beamforming for security in MIMO wiretap channels with imperfect CSI,” IEEE Trans. Signal Processing, vol. 59, pp. 351-361, Jan. 2011.

[8] S. A. A. Fakoorian,; Jafarkhani, Hamid; Swindlehurst, A.L., "Secure space-time block coding via artificial noise alignment," Signals, Systems and Computers (ASILOMAR), Conference Record of the Forty Fifth Asilomar Conference on , pp.651-655, Nov. 2011

[9] T. Allen, J. Cheng, N. Al-Dhahir, “Secure space-time block coding without transmit CSI,” IEEE Wireless Commun. Letters, 2014 .DOI 10.1109/LWC.2014.2344666.

[10] J. Ma, G. Y. Li, and B. –H. Juang, “Signal processing in cognitive radio,” The Proceedings of IEEE, vol. 97, no.5, May 2009, pp. 805-823

[11] S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. on Select Areas in Communications, vol. 16, no. 8, pp. 1451-1458, Oct. 1998.

[12] C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., 27, pp. 379-423, Jul.-Oct. 1948.


NOTES


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