A Multi-opjective Solution Algorithm for Optimum Utilization of Smart Grid Infrastructure Twoards Social Welfare

8/9/2019 A Multi-opjective Solution Algorithm for Optimum Utilization of Smart Grid Infrastructure Twoards Social Welfare

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A multi-objective solution algorithm for optimum utilization of Smart

Grid infrastructure towards social welfare

Sandip Chanda a,, Abhinandan De b

a Department of Administration, Technique Polytechnic Institute, Hooghly, Indiab Department of Electrical Engineering, Bengal Engineering & Science University, Shibpur, India

a r t i c l e i n f o

Article history:

Received 31 July 2012

Received in revised form 15 August 2013

Accepted 11 January 2014

Keywords:

Smart GridState space

Demand response

Generation surplus

Jacobian

Load curtailment

a b s t r a c t

This paper proposes an optimization model to maximize social welfare by standardizing the operatingconditions with an overall improvement of dynamic stability of power markets endowed with Smart Grid

communication technology. The state space based model developed along with the proposed methodol-ogy maximizes load catering and simultaneously minimizes the operating standard constrained genera-tion cost to restore power market equilibrium even in the most inadvertent states of the Energy System

Network. For optimumutilization of smart metering facility, the model effectively involves resources likedemand response, generation surplus and an efficient methodology to optimize the Market Clearing Price

(MCP) as well as profit of the market participants by effective categorization. The power market dynamicprice equilibrium has been estimated by forming Jacobian of the sensitivity matrix to regulate the state

variables for the standardization of the quality of solution. A novel load curtailment strategy has alsobeen proposed to amalgamstability restoringshedding with profit retentive load cut. Themodel has been

tested in IEEE 30 bus system in comparison with standard curtailment based optimization technique toproduce encouraging results.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

The synergism of power system with information network hasemerged as Smart Grid to undertake the modern power network

issues like demand side management, standardization of operatingconditions and integration of renewable energy sources. Moreoverthe Smart Grid is inherently designed to be self-healing to improvereliability and to respond to natural disaster or malicious sabotage

[1]. Efficient deployment of information network augmented withSmart Grid can appear to be an invaluable resource to regulate theoperational condition of the system and to optimize the systemoperation to a prolific solution [2,3]. In the quest of optimizing

the utilization of these new resources, researchers in the recentpast have been proposing indigenous methodologies and solutionalgorithm. Though the power system planers heavily rely uponthe methodologies in [4,5] introduced a distinctive work where

operating conditions viz loss and voltage profiles were optimizedwith a coordination methodology of plug in vehicle charging. A hy-brid method has been enunciated in[6]for effective utilization ofSmart Grid data viz synchrophasor to improve grid reliability from

generation side. Ref.[7]portrayed a framework of future transmis-sion grid while [810] identified the challenges associated with theincorporation of Demand Response (DR) in distribution of theexisting grid. From this survey, it is quite evident that all the major

parts of the grid require extensive reformation for optimization ofSmart Grid resources summarized in [11]. All these alterations willlead to a grid capable of monitoring and control andfast responsivedevices are to be installed to retaliate almost instantaneously [12]

to locate disturbance and to minimize the same. The grid underconsideration must possess at least these attributes to negotiatematters like intermittent energy sources, up-gradation of operatingconditions and self-regularization. During the incorporation of

renewable energy sources the unprecedented intermittent natureand cost curve pose immense difficulty to system optimization.The challenges and possible solutions have been enunciated forthe power system networks of Europe in [13]. Refs. [1416]pro-

posed optimization methodologies to escalate the operational sta-tus of power grid subscribing a particular renewable energy source.Ref.[17]depicted a novel algorithm to regulate the system param-eters under multiple intermittent sources. The model optimized

the system operation by an energy hub concept but the implemen-tation of the same will require efficient infrastructure which maynot be available and the model moreover does not incorporate is-sues like line flow management and load curtailment. Ref. [18]

http://dx.doi.org/10.1016/j.ijepes.2014.01.029

0142-0615/2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +91 9836921589.

E-mail addresses: [email protected] (S. Chanda), abhinandan.de@

gmail.com(A. De).

Electrical Power and Energy Systems 58 (2014) 307318

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dealt with the integration of demand response with irregular en-ergy sources. The multi objective algorithm proposed minimized

cost and curtailment but could not maximize load catering policyof the system operator. In addition, issues like payment cost min-imization by involving maximum number of consumers as sug-gested in [1921] have not been considered. Apart fromtribulations associated with intermittent renewable energy

sources, Smart Grid has to efficiently employ demand side man-agement technique. The methods proposed in[2224]effectivelyutilize demand side bidding or auction strategy or multi-agent pol-icy but the price responsiveness of other available parameters have

not been considered. All these efforts concentrated only one of theprice responsive parameter and their objective was to minimizethe market clearing price rather than maximizing social welfareby catering optimum load at minimum cost. Refs. [25,26] intro-

duced social welfare as an objective but apply less emphasis onsustaining operating conditions of the system or the load sheddingtechnique. The contemporary load curtailment strategies havebeen illustrated in[27,28]whereas in[29,30]some new strategies

have been introduced. Most of these techniques are operating con-dition constraint Optimal Load Curtailment (OLC) programs couldnot assure customer a reliable supply with standard operating con-

ditions. In view of this above survey, the need of an algorithm canbe felt which can ensure a standard parametric operational condi-tion with an objective of minimizing the price of electricity withoptimal load catering without violating the price equilibrium ofthe market. The algorithm is required to be supported by a pricing

model, which not only integrates the demand response and gener-ation characteristics but also involves price sensitivity of voltageprofile, line loss, congestion and load curtailment. The existingprice forecasting models proposed in [3139] are optimistic in nat-

ure developed to offer solutions under specific operational con-straints and these models are only fertile for single objectivedomain. Moreover they do not consider the dynamic price equilib-rium as stated in [40] hence cannot provide an insight of the power

market stability. The endeavor of the work presented in this paper

has been to develop a state space model of a power system net-work endowed with smart metering facility not only to forecastprice, but also to minimize the same without compromising social

welfare, power market stability and thus ensuring sustenance ofprolific operating conditions. The convex nature of solution algo-rithm with nonlinear working surface was compelling in the selec-tion of a stochastic optimization technique like Particle Swarm

Optimization (PSO). For comparison of the solution obtained astandard Optimal Power Flow (OPF) [41] has been adopted. Thesimulations have been carried out in IEEE 30 bus system and theobtained results looked quite promising.

2. Market structure and functioning in Smart Grid

The Smart Grid is an eco-friendly optimization of the presentgrid endeavored to achieve operational excellence with high de-gree of reliability. The functional architecture proposed [2] and

implemented [10] are based on some basic modification of thepresent grid organization for proper management of distributedgeneration with renewable energy sources, improvement of sus-tainability with self healing activities like congestion, power qual-

ity management and encouragement of price responsive demandreduction. The profusion of these activities employs extensive bi-directional communication between wholesale markets/transmis-sion operation and retail markets/distribution operations. Fig. 1 de-

picts one such architecture enabling the system operator to notonly utilize the generator information, but is also to make itself

capable of incorporating the demand response of consumers aggre-gated by local entities like Regional Transmission Organization

(RTO), historical and forecasted data, Available TransmissionCapacity (ATC) margins etc.

Efficient employment with these new resources as wholesalemarket product, Independent System Operator (ISO) will be ableto reach the furthest corners of the network from generation toload end to maintain profound operating conditions under theworst possible states of the system. In this context ISO will be able

to identify the state variable creating imbalance in the power mar-ket to de-standardize its operations. The price responsiveness ofthe state variables of modern power markets has been elaboratedin the following section.

3. The proposed price responsive OPF model

3.1. Price sensitivity of demand

The price responsiveness of demand has become an incredibleinput to the OPF algorithms for their load peak shaving capability

in high price conditions[3]. Effective deployment of this resourcemay lead to the solutions of modern day power network tribula-tions like network congestion, voltage instability and perturbations

in dynamics in power market. The demand elasticity of price is,hence as depicted in [42]an important parameter to be consideredfor Optimal Power Flow. With the assistance of smart metering thisproduct can be incorporated in optimization to achieve distinctionin operating conditions and welfare of the market participants. As

shown inFig. 2, a demand with a marginal benefit above the mar-ginal price will lead to an expansion in consumption until the equi-librium is reached. InFig. 2a ABC represents the bid curve at aparticular hour, while XY its tangent. The price responsive de-

mand curve (Fig. 2b) shows the nature of the consumer towardsprice volatility corresponding to the bids. From the bid curve thewillingness to pay of the consumers can be determined as

willingness to pay tan hfd1 fd2

d1d2

b1b2d1d2

1

where d1, d2. . .etc. are the power demands and the bid curve isexpressedas a function of demand such asf(di). The Market ClearingPrice (MCP) corresponding to each point of the bid curve have been

plotted in Fig. 2a and b. In this figure it has been assumed thatb1= d1MCP1, b2= d2MCP2, b3= d3MCP3. Let us assume that thetwo curves are fitted with two different polynomials.k1x

2 + l1x+ m1represent the bid curve while k2x

2 + l2x+ m2 represent the price

responsive curve where k1, l 1, m1 are the coefficients of bid curveand k2, l2, m2 are the coefficients of price responsive curve. Nowmapping willingness to pay into price responsiveness of demand

tan hb2b1d2d1

d2MCP2d1MCP1

d2d1

d2k2d22l2d2m2 d1 k2d

21l2d2m2

d2d1

k2 d22d2d1d

21

l2d2d1 m2 2

The willingness to pay is as sensitive to bid curve as is to priceresponsive curve. Hence, inclusion of demand response or priceresponsive characteristics into OPF not only incorporates the pricedependent consumption characteristics but also involves the will-

ingness to pay of the consumers for a particular alteration in price.In the present work load demand is also scheduled like generation,the load curtailment becomes willingness to pay dependent andinvolves the consumer more into OPF. In every hour (or a specified

period) the consumer with the assistance of smart metering, willbe able to modify his stand in the power market enabling Indepen-

dent System Operator (ISO) to regulate curtailment depending onwillingness to pay of the consumers.

308 S. Chanda, A. De / Electrical Power and Energy Systems 58 (2014) 307318


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3.2. An alternative approach to price dependent load curtailment

In Demand Response (DR) scenario, the load demand is alsoconsidered to be following a predetermined schedule just like

generation schedule, the willingness to pay of individual consum-ers are available to the system operator. The operator under peak

load condition, for security limit violation, can curtail a part ofthe load according to consumers demand response curve but the

Fig. 1. Interaction of power market entities of Smart Grid. Note: Conceptualized architecture of modern power grid or Smart Grid to ensure optimumutilization of generation,

transmission and distribution resources.

Fig. 2. A andB: Mapping the price responsiveness of demand from Bidcurve. Note:Incorporationof this price responsive demand curve into optimal power flow ensures load

curtailment of consumers in accordance with their willingness to pay.

S. Chanda, A. De/ Electrical Power and Energy Systems 58 (2014) 307318 309
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process is entirely price dependant [28,29,43]. This process doesnot concern the revenue loss suffered by the Generation Compa-

nies (GENCOs). A more rational way of curtailment should haveconsidered not only the market price but also the generation sur-plus of the GENCOs. The generation surplus can be defined as thedifference between maximum generation available and load dis-patched. The present work proposes a novel curtailment strategy,

which not only adheres to consumer demand response curve, butalso equally shields the GENCOs against a foreseeable revenue loss.

In the proposed strategy, the ISO can set generation surplus Smaxfor the GENCOs above which the net curtailment would be zero to

protect GENCOs from further revenue loss, irrespective of pricecondition of the market. In demand response the minimum limitof demand is set by the consumer. To maintain reliability of supplyand to build consumers confidence for the least supply this mini-

mum dispatch has to be assured for all the time.

Smax Sum of maximum possible generation

Sum of minimum limit of requested demand

When surplus is maximum i.e.Smax, the ISO should stick to zerocurtailment policy conversely to maintain price equilibrium ISO

must also set a maximum limit for curtailmentPmaxwhen the sur-plus is minimumSmin.

The maximum curtailment limit Pmax can alternatively ex-pressed in the form of

Pmax Sum of maximum limit of requested demand

Sum of minimum limit of requested demand

For the rest of the cases ISO may choose the operating point

from the curtailment-surplus relationship, which can be approxi-mated by a straight-line relationship

P PmaxPmax SSmin

SmaxSmin3

where Srepresents generation surplus and Prepresent the corre-sponding upper limit of curtailment or ISO set limit of load curtail-ment. The proposed method utilizes Eq. (3) to determine themaximum allowable load curtailment at any given price equilib-

rium point or ISO set limit of curtailment.The proposed methodology with the assistance of PSO searches

for an optimal solution which can maximize the income of thegenerators by reducing generation surplus to minimum while lim-iting load curtailment to an optimum value by adjusting the de-mand of the consumers.

The price of electricity in modern power markets not only relieson demand response or load curtailment, but also includes gener-ator cost characteristics, congestion, voltage and loss profile man-agement costs [24,4446]. Optimum utilization of Smart Grid

infrastructure will be ensured only when all these influencing fac-tors are standardized with an objective to maximize the benefitsfor all the market participants.

4. State space modeling of the proposed system

For m numbers of generators and n numbers of loads the pricesensitive state variables of a power system network may be de-fined as follows:

X P1P2. . .PmL1L2. . .LnPcTLVminPlmaxT

4

wherePi= Generation ofith bus for a particular schedule, Lj= Loadcatered forjth bus for a particular load schedule Pc= load curtailed,

TL= Total line loss, Vmin= minimum bus voltage, Plmax= maximumline flow.

It is quite evident from the above discussion that the price ofelectricity is dependent on these state variables.

And hence price of electricity p=f(x), as the market playersare connected with ISO through smart metering, on receipt ofthe price information at the hth hour (a chosen time frame)the participants either alter or persist with their characteristics.With the objective of social welfare the ISO implements the

OPF and determines the price dependent state variablesx(h+ 1) at the (h+ 1)th hour based on the price of hth hour.Mathematically

xh 1 fp Axh Buh

Is a function of price of electricity 5

where A i s the sensitivity matrix of the order of (m+ n+ 4) (m+ n+ 4).

A

A11 . . . A1mn4

.

.

.

Amn41 . . . Amn4mm4

2664

3775

with the elementsAij bi;1bj;1

bi;1n1bi;1nbj;1n1bj;1n

, for linear approximation

about hth hour.B is the contingency or state modification matrix, which will

arise only when participant characteristics are altered by eitherdeliberately or inadvertently.

In an energy system or power system network the above mod-eling not only enables the ISO to determine stability of a particularoptimal solution in an hour but also makes the ISO capable of pre-dicting the most feasible optimal generation pattern and load sche-

dule for a specified operational standard.The ISO benefit function can be defined as

yh 1 Cxh

The demand cost benefit function

limit violation constraint generation cost

Cd Cglv

Social Welfare with desired operating conditions 6

where

Cd Xndj1

rjP2djsjPdj demand cost benefit function 7

d stand for demand, rj, sj are coefficients of cost benefit function,and

Cglv Xngi1

aiP2gi biPgi ci Pc P1 TL P2 Vmin P3 Plmax P4

!

Limit violation constrained generation cost

8

glv stands for generation cost with limit violation constraint.AndCis a 1 (m+ n+ 4) matrix with the following pattern of

cofactors

Cg1Cg2. . .Cgm CL1CL2. . . CLnCPcCTLCVminCPlmax

where Cgi= Cofactors of theith bus of generation, CLj= Cofactor tojth bus of load, CPc= Cofactor of the load curtailed, CTL= Cofactorof transmission loss, CVmin= Cofactor of the minimum bus voltage,CPlmax= Cofactor of maximum line flow, ai, bi, ci= Cost coefficientsof theith generator,Pgi= generation of theith generator,Pdj= Loadcatered to jth consumer, Vmin= minimum value of bus voltage, P1,P2,P3= Penalties for limit violation set by ISO.

Hence the objective function of the proposed optimization algo-rithm stands as



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MaximizeXndj1

rjP2djsjPdj

!

Xngi1

aiP2gibiPgiciPc P1TLP2VminP3PlmaxP4

!

9

Instead of traditional cost optimization the system operators

should prefer formulation of pareto-optimal objectives for cateringmaximum amount of load at standard operational constraints.

The objective function has been proposed in this literature asthe difference of consumer cost benefit function and the limit vio-

lation constrained generation cost. Maximization of this result inmaximization of cost benefit function or load catering as well asminimization of generation cost and constraint violations like loadcurtailment limit, transmission power loss limit, limit of minimumbus voltage and maximum line flow or congestion limit. For the

collection of higher revenue, the generator companies would wantoptimum utilization of available generation (also known as utilitymaximization) by proper load distribution. On the other hand, con-sumers or distribution companies (DISCO) would want low price

with higher reliability of supply. In between the transmission com-panies (TRANSCO) would like to maintain standard operation con-dition in terms low transmission loss, high value of minimum busvoltage and low level of line congestion. Thus the objective func-

tion causes welfare of all the stakeholders associated with energysystem under consideration.

In conventional power network optimization method, theobjective function is same as depicted in [47]. But in Smart Grid

scenario with the available communication facility, as enunciatedin [48], social welfare maximization should be the objective ofoptimization. The function expressed in (9) is the outcome of that

contemplation.For effective comparison of the proposed model, a standard OPF

model proposed in[28,40]has been utilized.Equality or power balance constraints for the present OPF are

PGiPDiViXbi1

VjGij cos hijBij sin hij 0 10

QGiQDiViXbi1

VjGij cos hijBij sin hij 0 11

where PGi= Active power injected in bus i, PDi= Active power de-

mand on busi, Vi= magnitude of voltage of busesi, Vj= magnitude

Fig. 4. The proposed optimization technique. Note: Proposed energy systems structure with smart metering facility which will assist the consumers to alter theirconsumption level by directly participating in optimization with their price responsive demand characteristics.

Fig. 3. Traditional optimization technique. Note: Conventional optimization tech-

nique based on generation cost and Market Clearing Price (MCP).

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of voltage of busj,Gij= Conductance of transmission line from busi

toj, Bij= Susceptance of transmission line frombus i toj, b= number

of buses.Inequality or generator output constraints

Pmingi Pgi Pmaxgi 12

Q

min

gi Qgi Q

max

gi 13

where, Pgi, Qgi = Active and reactive power of generator i respec-

tively, Pmingi , Qmin

gi Lower limit of active andreactive power of the

generators, Pmaxgi , Qmax

gi Upperlimit of active andreactive power

of thegenerators

Voltage constraint : Vmini Vi Vmaxi 14

Vmaxi ; Vmini are upper and lower limits ofVi

Transmission constraint : Pijmax Pij Pijmin 15

Pijmax, Pijminare the maximum and minimum line flow limits ofPij

Curtailment Constraint : 0 < Pc


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6. Implementation of the proposed method in IEEE 30 bus

system

The feasibility and effectiveness of the proposed algorithm hasbeen demonstrated in the modified IEEE 30 bus system shown inFig. B1 in the appendix. The summary of relevant data for the mod-

ified IEEE 30 bus system is presented in Tables B1B3 of the appen-

dix. All the simulations have been performed in PSO environment.A brief description of PSO based optimization technique has beenpresented in the appendix. The parameter setting of the same is gi-ven inTable 1.

A flowchart depicting implementation of the proposed methodin IEEE 30 bus system is presented inFig. 5. In the proposed meth-odology the swarm intelligence based optimizer generates randomsolution particles in the workspace bounded by the maximum and

minimum limit set by the generators and the consumers as de-scribed inTables B2andB3. In each step the optimizer generatesan optimum generation, load schedule with an objective of maxi-mizing social welfare (described in(9)). The global best solution

is selected as optimal solution for the given set of operatingconstraints.

6.1. Comparison of the proposed optimization technique with

traditional optimization

The examination of the feasibility and effectiveness of the algo-rithm proposed remains incomplete without testing its adoptabil-

ity in the worst possible scenarios of the network. Four differenttest-beds have been chosen to compare the proposed algorithmwith the traditional optimal load curtailment based OPF technique[41]. In all the four cases the MCP of traditional algorithm has

been maintained at same level that of proposed method by

performing a controlled OLC based load curtailment at bus no. 5and 2 (assumed to have least willingness to pay or the same has

gotten its turn in a rotational load curtailment strategy). In the1st test bed active loading stress has been increased on selectednumber of buses and the operating conditions have been kept un-der observation. Though the minimum bus voltage gets least af-fected with active power loading stress, Table 2 depicts a

significant improvement in the line loss profile and line flow dis-tribution compared to the traditional method. In the next step ofstudy, reactive loading stress has been applied on the weakestbus of the system (bus no 30). As discussed earlier that excess

requirement of reactive power not only degrades the operatingconditions of the system especially the voltage profile but also af-fects the price of electricity. For the same MCP, a tantalizingimprovement in bus voltage profile, line loss and line congestion

can be observed inTable 2for the proposed method. Line contin-gency is almost inevitable in modern and future grids working un-der heavy loading stress. Disruption resilience with self-healingshould be one of the most desirable attributes of the present

and future Smart Grid. It is imperative from Table 2that the pro-posed algorithm working in a Smart Grid scenario would delivermore excelling operating conditions especially in terms of conges-

tion management under single or multiple contingencies as com-pared to traditional optimization algorithms working in theenvironments which rely solely on forecasted demand with gener-ation cost optimization objective.

The calculations carried out in this comparison, mainly deter-

mines the operating state of the system under consideration for aparticular generation pattern and load schedule (Optimal scheduleas obtained from the PSO based methodology developed) in spec-ified solution space to maintain standards of operational condition

with high degree of reliability.

Table 2

Comparison of performance of traditional and proposed optimization technique with active, reactive loading stress and line contingency.

Observations MCP ($/

MWh)

Traditional optimization Proposed optimization

Line loss

(MW)

Max line flow

(MW)

Min bus voltage

(p.u)

Line loss

(MW)

Max line flow

(MW)

Min bus voltage

(p.u)

Under active loading stress

29% 3.3 11.8 125.18 0.9742 6.79 71.93 0.978232% 3.29 11.68 131.17 0.9743 8.03 84.22 0.9761

36% 3.29 12.71 130.27 0.9740 9.13 98.14 0.9800

40% 3.29 12.42 130.34 0.9740 9.42 97.07 0.9748

Under reactive loading stress

3.12% 3.22 13.62 131.36 0.9440 11.33 113 0.96007% 3.3 13.51 132.52 0.9046 13 125 0.9077

11% 3.28 14.6 130.37 0.8606 13.5 123 0.8667

42% 3.24 15.08 130.86 0.8089 13.65 117.08 0.8611

Under contingency

12 3.34 22.28 178.84 0.9687 10.61 115.96 0.9776

12, 24 3.35 22 177.07 0.9657 14.00 134.52 0.9706

12, 24, 2122 3.35 21.02 176.99 0.9660 13.50 131.22 0.972312, 24, 2122, 27

29

3.35 21.59 169.84 0.9123 14.61 134.26 0.9224

Test cases of comparison.

1. Active loading stress: The maximum loading is increased in different percentage of base case loading.

2. Reactive loading stress: The reactive loading stress is increased at different percentage of the base case reactive power loading at the weakest bus.

3. Under Contingency: (N 1), (N 2), (N 3),N 4) contingency cases have been studied for line outages.

Table 3

Forecasted percentage availability of intermittent sources.

Hour Generator1 (%) Generator2 (%) Generator3 (%) Generator4 (%) Generator5 (%) Generator6 (%)

h-1 100 100 100 100 100 100

h-2 100 100 60 90 100 50

h-3 100 100 40 90 100 30

h-4 100 100 20 90 100 10

Renewable energy sources may not be available in full capacity at every hour. Arbitrary shortages have been considered for different generating sources.

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6.2. Implementation of the proposed methodology with intermittent

energy sources

Promotion of distributed generation with renewable energy

sources as stated earlier is one of the nonnegotiable objectives of

the present and future grids. However, their intermittent genera-tion profile requires extensive load management for power marketequilibrium. With the intermittency of the generators as shown in

Table 3, the performance of the proposed algorithm has been ob-served to be remarkably superior in sustaining the operating con-ditions within safe limit (Table 4), owing to the fact that theproposed algorithm not only manages generation for an optimal

cost (as in case of traditional method) but also efficiently managesloads to cater maximum demand at minimum cost in the mostoptimal way maintaining all operating constraints.

The efficiency of the proposed algorithm to self heal under the

alterations of operating conditions particularly during peak peri-ods, when the available generation is less than requested demandis depicted inFig. 6, where the peak shaving attribute of the pro-

posed algorithm has been demonstrated at selected buses.

6.3. Conservative load curtailment attribute of the proposed

methodology

Fig. 7illustrates the comparison of load curtailment in the pro-

posed method with reference to the ISO set limit for the case

Fig. 7. Comparison of curtailment by proposed method against their corresponding ISO set limit. Note: The ISO set limit is proposed to be determined by consumer priceresponsiveness and maximum generation surplus. Load curtailment below this limit will benefit all the stakeholders.

Table 4

Performance comparison of traditional and proposed optimization technique during intermittency of generation.

Observations MCP ($/MW h) Traditional Optimization Proposed Optimization

Line loss (MW) Max line flow (MW) Min bus voltage (p.u) Line loss (MW) Max line flow (MW) Min bus voltage (p.u)

h-1 3.33 12.06 124.85 0.9740 6.75 71.91 0.9763

h-2 3.12 14.20 140.80 0.9741 13.26 129 0.9701

h-3 3.08 13.27 142.96 0.9746 12.50 105.13 0.9767h-4 2.75 18.14 121.28 0.9739 15.80 110.09 0.9900

During intermittency of generation at different hours, the operating conditions have been found to improve by the application of the proposed optimization technique.

Fig. 6. Peak shaving of Demand during intermittency of Generation. Note: During

intermittency or shortage of generation the price increases. In the proposed

methodology the demand peak is effectively shaved in accord with therequirement.



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studies conducted inTable 2and4. As discussed earlier, the cur-

tailment should not always be price dependent but ISO should alsomonitor the generation surplus in order to maintain a profitablecurtailment operation in the power market. The ISO is constrainedto perform selective curtailment in order to keep the price of elec-

tricity constant or in other words to balance generation and de-mand at particular MCP. The results shown in Fig. 7AD depictthat, the proposed algorithm is capable of curtailing load at a more

conservative margin, well below the limits set by ISO.

The load curtailment limit has not fall below the ISO set curtail-ment limit in any of the test cases as in Fig. 7. The formula pro-posed in Eq.(3)is the optimal allowable load curtailment limit in

accordance with minimum generation surplus and curtailmentpolicy of ISO. This limit not only minimizes the generation surplusfor the benefit of GENCOs but also retains the result within maxi-mum curtailment limit for the welfare of consumers. As the results

are the outcome of Particle Swarm Optimization within the limit oferror gradient, the result has been tested to be optimal. Thus theproposed methodology proves to maximize social welfare.

The claim of social welfare maximization may thus be assured

by the convergence of the objective function of optimization asshown inFig. 8.

7. Conclusion

The accessibility to smart metering infrastructure has brought

about radical changes in power grid operation and simultaneouslyhas thrown newer operational challenges for electric power systemoperators, where a departure from traditional operations planning,scheduling, and dispatch practices needs to be altered to take into

account tribulations like voltage instability, line congestion, lineloss intensification and payment cost minimization. In this pursuitthis paper presents a new state space based pricing model and amethodology to illustrate optimal and efficient operations of Smart

Grid. The model effectively identifies the state variables of MCPand regulates the same utilizing PSO to reach prolific solutions

negotiating with generator characteristics, demand response, volt-age stability, and congestion, curtailment and line loss limits. As

the market participants are aware of pricing signals, the proposed

model will enable them to regulate their consumption, productionor curtailment limits to cause an overall social welfare. The meth-odology determines the eigen values of the sensitivity matrix byforming Jacobian to ensure power market stability and deploys a

novel curtailment technique to ensure the dispatch of minimumpower demand requested by the consumer for maintaining a highdegree of reliability. Simulation results convincingly demonstrate

that the combined operations of the proposed model and the

methodology mitigate network constraints while catering higherdemand levels and reducing the energy costs even under worstpossible states of the system operation. In comparison with the

conventional system operation which is based on only Gencoscheduling between maximum and minimum possible generation,the proposed algorithm incorporates consumer scheduling with asmart communication facility where not only GENCOs but also

consumers can participate to change their stand for their ownand social benefit.

Appendix A. Overview of PSO

A brief overview of the PSO method is provided here which has

been used in this paper for solving the problem of maximization ofsocial welfare. Kennedy and Eberhart introduced the concept of

function Optimization by means of a particle swarm[49]. Supposethe global optimum of an N-dimentional function is to be located.The function may be mathematically represented as:

fx1;x2;x3;. . .xn fX A1

whereXis the search vector, which actually represents the set

of independent variables of the given function. The task is to findout such a X, that the function value f(X) is either a minimum ora maximum denoted by f* in the search range. If the componentsofXassume real values then the task is to locate a particular point

in the n-dimensional hyperspace which is a continuum of suchpoints.

PSO is a multi-agent parallel search technique. Particles are con-ceptual entities, which fly through the multidimentional search

Fig. 8. Convergence curve of maximization of the objective function.

http://-/?-http://-/?-


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space. At any particular instant, each particle has aposition andvelocity. The position vector of a particle with respect to the origin

of the search space represents a trial solution of the search prob-lem. At the beginning a population of particles is initialised with

random positions marked byx i!

and random velocitiesv i!

. The pop-ulation of such particles is called a Swarm S. A neighborhoodrelation N is defined in the swarm. N determines for any two par-

ticlespiwhether they are neighbors or not. Thus for any particle p,neighborhood can be assigned asN(p), containing all the neighborsof that particle. A popular version of PSO uses N= Sfor each parti-

cle. In this case, any particle has all the remaining particles in theswarm in its neighborhood. Each particle has two state variablesviz., its current position and velocity as stated earlier. It is alsoequiped with a small memory comprising its previous best posi-

tion (One yielding the highest value of the fitness function found

so far) pt!

that is personal best experience and the best pt!

of

p2 Np : gt!

that is the best position so far in the neighborhood

of the particle. When we set N(p) = S, gt!

is referred to as the

globally best particle in the entire swarm. The PSO scheme hasthe following algorithmic parameters:

Vmax or maximum velocity which restrictsvi!

within the interval[Vmax, Vmax]

An inertial weight factor x. Two uniformly distributed random numbers U1 and U2 that

respectively determine the influence of pt!

and gt!

on thevelocity update formula

Two constant multiplier terms c1 and c2 known as self-

confidence and swarm confidence, respectively.

Initially the settings for pt!

andgt!

arep0!

g0!

x0!

forall particles. Once the particles are initialized, an iterative optimi-zation process begins, where the positions and velocities of all

particles are altered by the following recursive equations. Theequations are presented for the dth dimension of the positionand velocity of theith particle.

midt 1 x vidt c1U1pidt xidt c2U2gidt xidt

A2

xidt 1 xidt vidt 1 A3

The first term in the velocity updating formula represents the

initial velocity of the particle. x is the inertia factor. Venter

and Sobeiski[50]termedc1as self confidence andc2as swarmconfidence. These terminologies provide an insight from asociological standpoint. Since the coefficient c1 has a contribution

towards self-exploration, we regard it as particles self-confidence.On the other hand the particle c2 has a contribution towardsmotion of the particles towards a global direction, which takes intoaccount the motion of all the particles in the preceding programiteration, naturally its definition, as Swarm Confidence is appar-

ent. U1 and U2 stand for a uniformly distributed random numberin the interval [0, 1] After having calculated the velocities andposition for the next stept+ 1, the first iteration of the algorithmis completed.

Appendix B. Description of the system with generator and

consumer cost characteristics

Descriptions of the system with its generator and consumer

cost characteristics are given in the following tables and the SingleLine Diagram (SLD) is portrayed inFig. B1(seeTables B1B3).

Table B1

Description of IEEE 30 bus system.

SL No IEEE 30 bus system

Variables Adopted system

1 Branches 41

2 Generators 6

3 Total demand (MW) 365 (In the base case)

All the case studies have been executed in this system.

Fig. B1. SLD of IEEE 30 bus system. Note:Single Line Diagram of the test system with positions of generations and loads.



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References

[1] Gang L, Debraj D, Wen-Zhan S. Smart Grid Lab: a laboratory-based smart gridtest bed. In: The 1st IEEE international conference on smart gridcommunications, 2010; Gaithersburg, USA; 2010. p. 1438.

[2]Farrokh R, Ali I. Demand response as a market resource under the smart gridparadigm. IEEE Trans Smart Grid 2010;1(1).

[3] Ali Ipakchi. Demand side and Distributed Resource Management atransactive solution, IEEE OATI Power and Energy, July 22nd, 2011.

[4] Natarajan Ramsamy. Computer-aided system analysis. New York,Basel: Marcel Dekkar INC.; 2002.

[5] Sara D, Amir S, Paul S, Moses S, Masoum Mohammad AS. Real-timecoordination of plug-in electric vehicle charging in smart grids to minimize

power losses and improve voltage profile. IEEE Trans Smart Grid 2011;2(3).[6] Yunzhi C, Wei-Jen L, Shun-H, Huang John A. Dynamic parameter identificationof generators for smart grid development. In: Power and energy societygeneral meeting, IEEE, 2429 July, 2011, San Diego; 2011. p. 17.

[7]Fangxing L, Wei Q, Hongbin S, Hui W, Jianhui W, Yan X. Smart transmissiongrid: vision and framework. IEEE Trans Smart Grid 2010;1(2).

[8]Jose M, Nelson M, Ilya R. Demand response and distribution grid operations:opportunities and challenges. IEEE Trans Smart Grid 2010;1(2).

[9] Amir-Hamed M, Wong Vincent WS, Juri J, Robert S, Alberto L. Autonomousdemand-side management based on game-theoretic energy consumptionscheduling for the future smart grid. IEEE Trans Smart Grid 2010;1(3) .

[10] Pouyan K, Hassan M, Hassan A. Load profile reformation through demandresponse programs using smart grid modern electric power systems 2010,Wroclaw, Poland MEPS10; 2010.

[11] David Sun, Laurent Schmitt. Advanced power system operations with smartgrid technologies, 2010 IEEE PES Panel Session; 2010.

[12] In-Ho C, Joung-Han Lee. Development of smart controller with demandresponse for AMI connection. In: International conference on control,automation and systems 2010 October, 2730, 2010, Korea; 2010. p. 7525.

[13] Hammons TJ. Integrating renewable energy sources into European grids. Int JElectr Power Energy Syst 2008;30(8):46275.

[14] Yann R, Seddik B, Franck B, Stephane P. Optimal power flow management forgrid connected PV systems with batteries. IEEE Trans Sustain Energy2011;2(3).

[15] Warsono, King DJ, zveren CS, Bradley DA. Economic load dispatchoptimization of renewable energy in power system using genetic algorithm,Power Tech; 2007.

[16] Wong YS, Lai LL, KT, Gao Shuang, Chau. Stationary and mobile battery energystorage systems for smart grids., Electric Utility Deregulation andRestructuring and Power Technologies (DRPT). In: 4th internationalconference on, 69 July, 2011, Weihai, Shandong; 2011. p. 16.

[17] Martin G, Gran A. Optimal power flow of multiple energy carriers. IEEE TransPower Syst 2007;22(1).

[18] Carlo C, Costantino C, Pierluigi S. Combined operations of renewable energysystems and responsive demand in a smart grid. IEEE Trans Sustain Energy2011;2(4).

[19] Kazem Zare, Sheikh-el-Eslami MK, Parsa Moghaddam Tarbiat M. Largeconsumer decision making to cost reduction in real time power market. In:42nd International conference on power engineering. UPEC; 2007. p. 8992.46 September.

[20] Satish S, Rohit B, Padhy NP, Gupta HO. Payment cost minimization auction inelectricity markets power and energy society general meeting, IEEE, 2429July, 2011, San Diego, CA; 2011. p. 16.

[21] Shahram J, Nahid A. Factoring the price elasticity of demand in the optimalpower flow. In: International power engineering conference, IPEC 2007,Singapore; 207. p. 127.

[22] Undan Jason Alfons. Optimisation of demand-side bidding. In: 45th annualconference, University of Auckland, Auckland, NewZealand, 2930 November,2010. p. 7281.

[23] BhuvaneswariR, Sanjeev KS, ChrisS, DavidA. Anintelligent auction scheme forsmart grid market using a hybrid immune algorithm. IEEE Trans IndustrElectron 2011;58(10).

[24] Centolella Paul, Ott Andrew. The integration of price responsive demand intoPJM wholesale power markets and system operations..

[25] Arman K, Anuradha A. The effect of a smart meter on congestion and stabilityin a power market. In: Proceedings of 49th IEEE conference on decision andcontrol, Atlanta, GA, USA, December 1517, 2010. p. 1949.

[26] Pedram S, Amir-Hamed M, Robert S, Wong Vincent WS, Jatskevich Juri.Optimal real-time pricing algorithm based on utility maximization for smartgrid. In: 1st IEEE international conference on smart grid communication,Gaithersburg, USA, 46 October, 2010.

[27] Sortomme E, El-Sharkawi. Optimal power flow for a system of micro-gridswith controllable loads and battery storage. In: Power systems conference andexposition, PSCE 09. p. 15.

[28] Majid O, Gerd B, Hasan S, Mohammad S. Market-based transmission expansionplanning. IEEE Trans Power Syst 2004;19(4).

[29] Fernandes Thelma SP, Lenzi JR, Mikilita Miguel A. Load shedding strategies

using optimal load flow with relaxation of restrictions. IEEE Trans Power Syst2008;23(2).

[30] Huang Garng M, Nair Nirmal-Kumar C. An OPF based algorithm to evaluateload curtailment incorporating voltage stability margin criterion..

[31] Kresen Kjetil F, Egil H. A joint state-space model for electricity spot andfutures prices, Norwegian Computing Center; 2002.

[32] Mihaela M. Energy futures prices: term structure models with kalman filterestimation. Taylor and Francis Group; 2010.

[33] Ofuji K, Kanemoto S. Price forecasting of japan electric power exchange usingtime-varyingAR model. In: Proceedings of the 14th internationalconferenceonintelligent system applications to power systems, ISAP 2007, November 48.

[34] Shiva S, Mehdi P, Mohsen S. Short-term electricity price forecasting inderegulated markets using artificial neural network. In: Proceedings ofinternational conference on industrial engineering and operationsmanagement, Kuala Lumpur, Malaysia, January 2224, 2011.

[35] Burgery Markus, Klarz Bernhard, Muller Alfred, Schindlmayry Gero. A spotmarket model for pricing derivatives in electricity markets. J Quant Finance2010;5(1).

[36] Alicia Mateo G, Antonio Muoz San R, Javier G. Modeling and forecastingelectricity prices with input/output hidden Markov models. IEEE Trans PowerSyst 2005;20(1).

[37] Ramteen S, Walter S. Evaluating the impacts of real-time pricing on the usageof wind generation. IEEE Trans Power Syst 2009;24(2).

[38] Manuela B, Brockwell Anthony E, Duane J. A dynamic supply-demand modelfor electricity prices. .

[39] Aggarwal SK, Saini LM, Kumar A. Electricity price forecasting in deregulatedmarkets: a review and evaluation. Int J Electr Power Energy Syst2009;31(1):1322.

[40]Florin C, Mevludin G, Damien E, Louis W. Interior-point based algorithms forthe solution of optimal power flow problems. Electric Power Syst Res2007:50817. Elsevier.

[41] Rueda-Medina AC, Padilha-Feltrin A. Pricing of reactive power supportprovided by distributed generators in transmission systems, 2011 IEEEPower Tech.

[42] Bomparda Ettore, Maa Yuchao, Napolia Roberto, Abrateb Graziano, RagazzibElena. The impacts of price responsiveness on strategic equilibrium in

competitive electricity markets. Int J Electr Power Energy Syst2007;29(5):397407.

Table B3

Coefficients of consumer cost benefit function.

Bus no Real power demand

limits in MW

Cost co-efficient

Min Max A (US$/MW2) B (US$/MW) C (US$)

2 21.7 31.7 0.1 87.2 03 2.4 5 0.15 90 0

4 7.6 10 0.25 85.5 0

5 94.2 110 0.2 87 07 22.8 40 0.075 70 0

8 30 45 0.1 90 0

10 5.8 10 0.2 70 0

12 11.2 15 0.1 50 0

14 6.2 12 0.15 80 0

15 8.2 10 0.15 60 0

16 3.5 10 0.15 70 017 9 15 0.05 65 0

18 3.2 5 0.1 90 0

19 9.5 12 0.25 68 0

20 2.2 5 0.25 90 0

21 17.5 20 0.2 80 0

23 3.2 6 0.1 60 0

24 8.7 10 0.2 80 0

26 3.5 5 0.3 90 0

29 2.4 4 0.4 95 0

30 10.6 15 0.2 95 0

Base case parameters of consumer cost benefit function.

Table B2

Generator cost coefficients.

Bus no Real power output limit

in MW

Cost co-efficient

Min Max A (US$/MW2) B (US$/MW) C (US$)

1 50 200 0.00375 2.00 0

2 20 80 0.01750 1.75 05 15 50 0.06250 1.00 0

8 10 35 0.00834 3.25 0

11 10 30 0.02500 3.00 0

13 12 40 0.02500 3.00 0

This is the base case generator characteristics and relevant parameters.

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[43] Losi Arturo. Trade curtailment schemes for security control of transmissionnetwork in a deregulated environment. Int J Electr Power Energy Syst2002;24(1):917.

[44] Juan Carlos M, Pablo Cuervo F. Transmission lossallocation through equivalentbilateral exchanges and economical analysis. IEEE Trans Power Syst2005;20(4).

[45] Tripathy M, Mishra S. Bacteria foraging-based solution to optimize both realpower loss and voltage stability limit. IEEE Trans Power Syst 2007;22(1).

[46] Sandip C, Abhinandan D. Improvement of economic aspect of power networkcongestion management by swarm intelligence based multi-objective

algorithm. Int J Eng Sci Technol 2011;3(5).

[47] Coelho LdSa, Lee C-Sb. Solving economic load dispatch problems in powersystems using chaotic and Gaussian particle swarm optimisation approaches.Int J Electr Power Energy Syst 2008;30(5):297307.

[48] Fanga Debin, Wua Jingfang, Tangb Dawei. A double auction model forcompetitive generators and large consumers considering power transmissioncost. Int J Electr Power Energy Syst 2012;43(1):8808.

[49] Kennedy J, Eberhart R. Particle swarm optimisation. In: The proceedings ofIEEE international conference on neural networks; 1995. p. 19428.

[50] Venter G, Sobieszczanski-Sobieski J. Particle swarm optimization. AIAA J2003;41(8):15839.

http://refhub.elsevier.com/S0142-0615(14)00042-8/h0215http://refhub.elsevier.com/S0142-0615(14)00042-8/h0215http://refhub.elsevier.com/S0142-0615(14)00042-8/h0215http://refhub.elsevier.com/S0142-0615(14)00042-8/h0220http://refhub.elsevier.com/S0142-0615(14)00042-8/h0220http://refhub.elsevier.com/S0142-0615(14)00042-8/h0220http://refhub.elsevier.com/S0142-0615(14)00042-8/h0225http://refhub.elsevier.com/S0142-0615(14)00042-8/h0225http://refhub.elsevier.com/S0142-0615(14)00042-8/h0225http://refhub.elsevier.com/S0142-0615(14)00042-8/h0230http://refhub.elsevier.com/S0142-0615(14)00042-8/h0230http://refhub.elsevier.com/S0142-0615(14)00042-8/h0230http://refhub.elsevier.com/S0142-0615(14)00042-8/h0235http://refhub.elsevier.com/S0142-0615(14)00042-8/h0235http://refhub.elsevier.com/S0142-0615(14)00042-8/h0235http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0250http://refhub.elsevier.com/S0142-0615(14)00042-8/h0250http://refhub.elsevier.com/S0142-0615(14)00042-8/h0250http://refhub.elsevier.com/S0142-0615(14)00042-8/h0250http://refhub.elsevier.com/S0142-0615(14)00042-8/h0250http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0240http://refhub.elsevier.com/S0142-0615(14)00042-8/h0235http://refhub.elsevier.com/S0142-0615(14)00042-8/h0235http://refhub.elsevier.com/S0142-0615(14)00042-8/h0235http://refhub.elsevier.com/S0142-0615(14)00042-8/h0230http://refhub.elsevier.com/S0142-0615(14)00042-8/h0230http://refhub.elsevier.com/S0142-0615(14)00042-8/h0230http://refhub.elsevier.com/S0142-0615(14)00042-8/h0225http://refhub.elsevier.com/S0142-0615(14)00042-8/h0225http://refhub.elsevier.com/S0142-0615(14)00042-8/h0220http://refhub.elsevier.com/S0142-0615(14)00042-8/h0220http://refhub.elsevier.com/S0142-0615(14)00042-8/h0220http://refhub.elsevier.com/S0142-0615(14)00042-8/h0215http://refhub.elsevier.com/S0142-0615(14)00042-8/h0215http://refhub.elsevier.com/S0142-0615(14)00042-8/h0215

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