Improvement of Load Frequency Control With Fuzzy Gain Scheduled SMES Unit Considering Governor

Dead-Band and GRC M.R.I. Sheikh, S.M. Muyeen, R. Takahashi, Toshiaki Murata and Junji Tamura

Kitami Institute of Technology, 165 Koen-cho, Kitami, Hokkaido, 090-8507, Japan Email: sheikh@pullout.elec.kitami-it.ac.jp

Abstract - Since a Superconducting Magnetic Energy Storage (SMES) unit with a self-commutated converter is capable of controlling both the active and reactive power simultaneously and quickly, increasing attention has been focused recently on power system stabilization by SMES control. In this study, a fuzzy gain scheduled supplementary control scheme with SMES unit is proposed and applied to Automatic Generation Control (AGC) in power system for the improvement of Load Frequency Control (LFC). The performances of the system for load changes in the areas in the interconnected power system are studied. The computer simulation of the interconnected power system shows that SMES unit with the proposed gain scheduled supplementary controller can perform a more effective primary frequency control for multi area power system.

I. Introduction Automatic generation control is a very important subject in power system operation for supplying sufficient and reliable electric power with quality. Frequency variations in interconnected power systems can cause large-scale serious instability problems. LFC is one of control schemes to provide the stable and reliable operation in multi-area power systems. For stable operation, constant frequency and active power balance must be provided. To improve the stability of the power networks, it is necessary to design LFC systems that control the power generation and active power on tie-lines. In an interconnected power system, as the load demand varies randomly, the area frequency and tie-line power interchange also vary. The objective of LFC is to minimize the transient deviations in these variables and to ensure their steady state values to be zero. The LFC by only a governor control of synchronous generators imposes a limit on the degree to which the deviations in frequency and tie-line power exchange can be minimized. However, as the fundamental purpose of LFC is solving the problem of an instantaneous mismatch between the generation and demand of active power, the incorporation of a fast-acting energy storage device in the power system can improve the performance under such conditions. But fixed gain controllers based on classical control theories are presently used. They are not sufficient for the case with changing operating point during a daily cycle [1–4] and also not suitable for all operating conditions. Therefore, variable structure controller [5–7] has been proposed for AGC. For designing controllers based on these techniques, the perfect model is required which has to track the state variables and satisfy system constraints.

Therefore it is difficult to apply these adaptive control techniques to AGC in practical implementations. In multi area power system, if a load variation occurs at any one of the areas in the system, the frequency related with this area is affected first and then that of other areas are also affected from this perturbation through tie-lines. In this study, the same gain scheduled controller is used to implement AGC in the interconnected system having two areas including SMES units when a step load perturbation occurs in one or both areas. In the model system, each area in the interconnected system includes steam reheat turbines and generation rate constraints. We reported a work [8] for LFC by fuzzy gain scheduled SMES. However, in our previous study [8] the governor dead-band (DB) and generation rate constraints (GRC) were not considered. In the present work effect of boiler system and governor DB and GRC are also considered, by which the worst situation of power system can be considered. When a small load disturbance in any area of the interconnected system occurs, tie-line power deviations and power system frequency oscillations continue for a long duration. To damp out the oscillations in a short time, automatic generation control including a SMES unit with the proposed gain scheduled supplementary controller is used. The basic objective of the supplementary control is to restore balance between each area load and generation for a load disturbance. This is met when the control action maintains the frequency and the tie-line power interchange at the scheduled values. The supplementary controller with integral gain KIi is therefore made to act on area control error, which is a signal obtained from tie-line power flow deviation added to frequency deviation weighted by a bias factor .

nACE = P + fi tie, i j i ij=1

(1)

where the suffix i refer to the control area and j refer to the number of generator. Using fuzzy logic, the integrator gain (KIi) of supplementary controller is so scheduled that it compromise between fast transient recovery and low overshoot in dynamic response of the system. It is seen that with the addition of gain scheduled supplementary controller, a simple controller scheme for SMES is sufficient to improves effectively the damping of the oscillations after the load deviation in one or both of the areas in the interconnected system.

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II. Integration of SMES with Two-Area Power System

Figure 1 shows the two-area power system with SMES unit used in the analyses. Two areas are connected by a weak tie-line. When there is a sudden rise in power demand in a control area, the stored energy is almost immediately released by the SMES through its power conversion system (PCS). As the governor control mechanism starts working to set the power system to the new equilibrium condition, the SMES coil stores energy back to its nominal level. Similar action happens when there is a sudden decrease in load demand. Basically, the operation speed of governor-turbine system is slow compared with that of the excitation system. As a result, fluctuations in terminal voltage can be corrected by the excitation system very quickly, but fluctuations in generated power or frequency are corrected slowly. Since load frequency control is primarily concerned with the real power/frequency behavior, the excitation system model will not be required in the approximated analysis. This important simplification paves the way for constructing the simulation model shown in Fig. 1. All the governors have dead-band which affects the stability of the system and produces a continuous sinusoidal oscillation of natural period. So effects of governor dead-band are studied in relation to AGC. The limiting value of dead-band is specified as 0.06%. Also

in practical steam turbine, due to thermodynamic and mathematical constraints, there is a limit to the rate at which its output power (dPt/dt) can be changed. This limit is referred to as Generation rate constraint (GRC). In practice, there exists a maximum limit on the rate of change in the generating power of a steam plant. In the presence of GRC, the dynamic responses of the system experience larger overshoots and longer settling time compared to the case without considering the GRC. Hence, if the load change are too fast under transient conditions, then system nonlinearities will prevent its achievement. Moreover, if the parameters of the controller are not chosen properly, the system may become unstable. So considering these, the GRC is taken into account by adding a limiter to the turbine as shown in Fig. 2, with a value of 0.1 p.u. MW/min [9] as shown in eq.(2). This is a typical value up to 3.4 MW/second. All parameters are same as that used in [8].

P =0.1 p.u.MW/min=0.0017p.u.MW/sec=generation (2)

I1-Ks

G1

G1

K1+sT

T1

T1

K1+sT

1

1R

1

turbine

governor

supplementary control

function of eq.(1)

SMEScontroller

SMESdynamics

ZOH

ACE1

P*sm1

Psm1

p1

p1

K1+sT

PL1(s)

Equivalentgenerator

-

+

+ +

+

-

-

122 Ts

+

Tie-line

P12(s)Control area 1

function of eq.(1)

SMEScontroller

SMESdynamics

ZOH

P*sm2

Psm2

f2

-

I2-Ks

G2

G2

K1+sT

T2

T2

K1+sT

2

1R

2

turbine

governor

supplementarycontrol ACE2

p2

p2

K1+sT

PL2(s)

Equivalent generator

-

+

+-

+

-

Control area 2

-

Fig. 1 Simulation model for the two-area power system

f1

f1 f2

Pt1 Pt2

Pg1 Pg2

Fig. 2: A non-linear turbine model with GRC

1

Tt

1

s

Pg Pt

-+ -

22

III. Optimization of the Integral Gain, KI and Frequency Bias Factors, in Multi-Area

Power System

Figure 3 shows the frequency deviations for different values of KI for a specific load change. It is observed that a higher value of KI results in reduction of maximum deviation of the system frequency but the system oscillates for longer times. Decreasing the value of KIyields comparatively higher maximum frequency deviation at the beginning but provides very good damping in the later cycles. These initiate a variable KI,which can be determined from the frequency error and its derivative. Obviously higher values of KI is needed at the initial stage and then it should be changed gradually depending on the system frequency change.

Dynamic performance of the AGC system would obviously depend on the value of frequency bias factors,

1 = 2 =B and integral controller gain value, KI1=KI2=KI.In order to optimize B and KI the concept of maximum stability margin is used, evaluated by the eigen values of the closed loop control system [7]. For a fixed gain supplementary controller, the optimal values of KI and B are chosen, here, on the basis of a performance index (PI) given in eq.(3) for a specific load change. The Performance Index (PI) curves are shown in Fig. 4 with considering governor dead-band (DB) and generation rate constraints (GRC).

dtfwfwPP.I.40

0

222

211

2tie (3)

Where, w1 and w2 are the weight factors. The weight factors w1 and w2 both are chosen as 0.25 for the system under consideration. From Fig. 4, in the presence of DB & GRC it is observed that the value of integral controller gain, KI = 0.28 and frequency bias factors, B=0.15 which occurs at PI= 0.0363.

IV. Fuzzy Gain Scheduler PI Control (FGSPI)

Figure 5 shows the membership functions for PI control system with a fuzzy gain scheduler. The approach taken here is to exploit fuzzy rules and reasoning to generate controller parameters. The triangular membership functions for the proposed FGSPI controller of the three variables (et, cet , KIi) are shown in Fig. 5, where

frequency error (et) and change of frequency error ( cet )are used as the inputs of the fuzzy logic controller. KIi(i=1,2) is the output of fuzzy logic controller. Considering these two inputs, the output of gain KIi is determined. The use of two input and single output variables makes the design of the controller very straightforward. A membership value for the various linguistic variables is calculated by the rule given by μ e ,ce =min μ e ,μ cet t t t (4) The equation of the triangular membership function used to determine the grade of membership values in this work is as follows:

b-2 x-aA x =

b (5)

Where A(x) is the value of grade of membership, ‘b’ is the width and ‘a’ is the coordinate of the point at which the grade of membership is 1 and x is the value of the input variables. The control rules for the proposed strategy are very straightforward and have been developed from the viewpoint of practical system operation and by trial and error methods. The fuzzy rule base for the FGSPI controller is shown in Table I. The membership functions, knowledge base and method of defuzzification determine the performance of the FGSPI controller in a multi area power system as shown in eq. (6).

0 2 4 6 8 1 0 1 2-8

-6

-4

-2

0

2

4

6x

- 4

T i m e i n s e c o n d

Freq

uenc

y de

viat

ion

in p

u

Fig. 3 Frequency deviation step response for different values of KI

KI=0

KI=1

0.1 0.2 0.3 0.4 0.5 0.60.035

0.036

0.037

0.038

0.039

0.04

0.041

0.042

0.043

0.044

Integral Gain (KI)

Perf

orm

ance

Inde

x (P

I)

B=0.1B=0.15B=0.2B=0.25B=0.3B=0.35B=0.4B=0.45B=0.5

With GRC and Gov. Dead-bandK

I=0.28 and B=0.15 at P.I.=0.0363

Fig. 4 The optimal integral controller gain, KI and frequency bias factor, B with DB and GRC

33

nμ uj jj=1K = nIiμ jj=1

(6)

Table I Fuzzy Rule Base for FGSPI Controller

e ce

NB NS Z PS PB

NB PB PB PB PS Z NS PB PB PS Z Z Z NS NS Z NS NB PS Z Z NS PB NB PB Z NS NB NB NB

V. Control System of SMES The schematic diagram in Fig. 6 shows the configuration of a thyristor controlled SMES unit, which is incorporated in each control area of power system for LFC as shown in Fig. 7. The converter firing angle controls the DC voltage Vsm appearing across the inductor to be continuously varied between a wide range of positive and negative values. The inductor is initially charged to its rated current by applying a low positive voltage. Once the current reaches the rated value, it is maintained constant by reducing the voltage across the inductor to zero. Figure 8 outlines the proposed simple control scheme for SMES, which is incorporated in each control area to reduce the instantaneous mismatch between demand and generation. ACEi (i=1,2) in each control area is taken as the control input signal for SMES. It is desirable to restore the inductor current to its rated value as quickly as possible after a system disturbance, so that the SMES unit can respond properly to any subsequent disturbance. So inductor current deviation is sensed and used as negative

feedback signal in the SMES control loop to achieve quick restoration of current and SMES energy level.

VI. Simulation ResultsTo demonstrate the usefulness of the proposed controller, computer simulations were performed using the MATLAB environment under different operating conditions. The system performances with gain scheduled SMES and fixed gain SMES are shown in Fig. 9 through Fig. 14. Three cases studies are conducted.

Ism

ACEi

Vsm

Fig. 8 SMES control system in each area

Kp

dcsT11

Vsm

+-

Ksm

Ism0

Ism

Ism

Psm

+ +

+

+

Psm

Psm0

+

+ Psm

P*sm

1sL

3- AC from generator

terminal bus

Vsm

Fig. 6. SMES unit with 6-pulse bridge AC/DC thyristor controlled converter

Ism (DC current)

L sm

Supe

rcon

duct

ive

coil

1 3 5

4 6 2Y/

Transformer

[et(x)] NB NS Z PS PB

[det(x)/dt] NB NS Z PS PB

[KIi(x)] NB NS Z PS PB

Fig. 5 Membership functions for the fuzzy variables

-0.1 -0.05 0 0.05 0.1 et(x)

1 0.75 0.32 0.01 0.001 KIi(x)

-0.03 -0.15 0 0.15 0.03 det(x)/dtTie Line

SMESUnit

SMESUnit

PD1+ PD PD2+ PD

G11

G21

Gn1

G12

G22

Gn2

Area 1 Bus Area 2 Bus

Fig. 7 Configuration of SMES in a two-area power system

Load Load

1

1

1

44

Case I: a step load increase ( PL1=0.015 pu MW) in area1.In this case, it is seen from Fig. 9 that the tie-line power deviation are reduced with the proposed gain scheduled SMES controller and the deviations are negetive. Thus sensing the input signal ACEi in the control areas SMES provide sufficient compensation, and it is seen from Fig. 10 that SMES in area1 is discharging energy and SMES in area2 is charging energy to keep the frequency deviations in both areas minimum. From Fig. 10, it is also seen that FGSPI controller of the loaded area determines the integral gain KI to a scheduled value to resotore the frequency to its nominal value, and FGSPI controller of the unloaded area reamains unscheduled and selects the critical value as its integral gain. Finally it is seen that the damping of the system frequency is not satisfactory for the fixed gain controller. But the proposed gain scheduled supplementary controller significantly improves the system performances.

0 5-8

-6

-4

-2

0

2x 10

-3

Time in sec

Tie

pow

er d

evia

tion

Gain Scheduled SMES Fixed gain SMES

Case II: the same step load increase in both areas.

In this case, the same load increase, PL1= PL2= 0.01 p.u MW, is applied to both areas. It is seen from Fig. 11 that the tie-line power deviation is zero. Thus SMES compensation depends on fi in both areas. As the load change is same in both areas, the SMES in both areas provide same compensation. Finally it is seen from Fig.

13 that FGSPI controller of both the loaded areas determine the integral gain KIi (i=1,2) to a scheduled value to resotore the frequency to its nominal value. Due to this, the damping of the system frequency is also significantly improved with the proposed controller.

0 5 10 15-1

0

1

Time in sec

Tie

pow

er d

evia

tion

Gain Scheduled SMES Fixed gain SMES

Case III: the different step load increases are applied to each Area. In this case, as each area is loaded by the different increase, each area adjusts their own load. Figure 12 shows the tie power deviation but the magnitude is small. So the SMES controller in both areas dominated on fi.As PL1=0.01 p.u MW & PL2=0.015 p.u MW, it is seen from Fig. 14 that SMES in area2 provided more compensation than area1. Finally frequency deviations restore to its nominal value with the gain scheduled SMES controller.

0 5 10 15-1

0

1

2

3x 10

-3

Time in sec

Tie

pow

er d

evia

tion

Gain Scheduled SMESFixed gain SMES

G ain Scheduled SM ESFixed gain SM ES

G ain Scheduled SM ESFixed gain SM ES

Fig. 10: System performances for a step load change PL1= 0.015 p.u MW in area-1 only [Case I]

Fig. 9 Performance of tie power deviation [Case I]

Fig. 11 Performance of tie power deviation [Case II]

Fig. 12 Performance of tie power deviation [Case III]

55

G ain Scheduled SM ESF ixed gain SM ES

G ain Scheduled SM ESF ixed gain SM ES

G ain Scheduled SM ESFixed gain SM ES

G ain Scheduled SM ESFixed gain SM ES

VII. Conclusions The simulation studies are carried out on a two-area power system considering DB and GRC to investigate the impact of the proposed intelligently controlled SMES on the power system dynamic performance. The results show that the scheme is very powerful in reducing the frequency and tie-power deviations under a variety of load perturbations. On line adaptation of supplementary controller gain associated with SMES makes the proposed intelligent controllers more effective and are expected to perform optimally under different operating conditions.

References:[1] Benjamin NN, Chan WC.:“Multilevel Load-frequency Control of Inter-Connected Power Systems”, IEE Proceedings, Generation, Transmission and Distribution,1978; No.125: pp.521–526. [2] Nanda J, Kavi BL.:“Automatic Generation Control of Interconnected Power System”, IEE Proceedings, Generation, Transmission and Distribution, 1988; No.125(5): pp.385–390. [3] Das D, Nanda J, Kothari ML, Kothari DP.:“Automatic Generation Control of Hydrothermal System with New Area

Control Error Considering Generation Rate Constraint”, Electrical Machines and Power System 1990; 18:461–471. [4] Mairaj uddin Mufti, Shameem Ahmad Lone, Sheikh Javed Iqbal, Imran Mushtaq:“Improved Load Frequency Control with Superconducting Magnetic Energy Storage in Interconnected Power System”, IEEJ Transaction, 2007, vol. 2,pp. 387-397. [5] Benjamin NN, Chan WC.:”Variable Structure Control of Electric Power Generation”, IEEE Transactions on Power Apparatus and System 1982; 101(2):376–380. [6] Sivaramaksishana AY, Hariharan MV, Srisailam MC.:”Design of Variable Structure Load-Frequency Controller Using Pole Assignment Techniques”, International Journal of Control 1984; 40(3):437–498.[7] Tripathy SC, Juengst KP.:”Sampled Data Automatic Generation Control with Superconducting Magnetic Energy Storage”, IEEETransactions on Energy Conversion 1997; 12(2):187–192. [8] M.R.I. Sheikh, S.M. Muyeen, Rion Takahashi, Toshiaki Murata and Junji Tamura “Improvement of Load Frequency Control with Fuzzy Gain Scheduled Superconducting Magnetic Energy Storage Unit”, International Conference of Electrical Machine (ICEM, 08),Conference CD, Paper ID-1026, 06-09 September, 2008, Portugal. [9] C.T. Pan,C. M. Lian, “An Adaptive Controller For Power System Load-Frequency Control”, IEEE Transactions on Power System, Vol. 4, No. 1, February, 1988.

Fig. 13: System performances for a step load change PL1= PL2= 0.01 p.u MW in both areas [Case II]

Fig. 14: System performances for a step load change PL1=0.01 p.u MW in area1& PL2= 0.015 p.u MW in area2 [Case III]

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