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Congestion Management in a Deregulated Power System ... - IJETAE

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

Congestion Management in a Deregulated Power System

by Rescheduling Of Sensitive

Generators and load curtailment using PSO

Tulika Bhattacharjee 1 , Ajoy Kumar Chakraborty 2

1,2 Dept Of Electrical Engg, NIT Agartala,India

1 tulika4@gmail.com

2 akcalll@yahoo.co.in

Abstract—In a deregulated electricity market, CM is one of

the key functions of a System Operator (SO) as congestion

threatens system security and may cause rise in electricity

price resulting in market inefficiency. Rescheduling

generations and demands is an effective tool to relieve

congestion. This paper presents a congestion management

(CM) algorithm by optimal rescheduling of active powers of

generators and power consumption of load. In addition to the

rescheduling of real power generation, demand-side

participation through load curtailment has been considered to

manage congestion. Generator Sensitivity to the congested line

and the costs of generation and demand side adjustments are

considered while re-scheduling the generators and demands.

The re-dispatch of transactions for congestion management in

a pool model is formulated as an Optimal Power Flow (OPF)

problem. Particle Swarm Optimization (PSO) is employed to

solve the OPF problem formulated. The proposed method has

been tested on IEEE-30 bus System and the results show that

the proposed technique is effectively minimizing the cost of

CM in alleviating congestion in the transmission lines.

Keywords— deregulation; congestion management; optimal

power flow; demand side bidding; sensitivity

I. INTRODUCTION

Increased volumes of power trade happening due to the

deregulation of electric power industry has led to intensive

usage of transmission network, which in turn leads to more

frequent congestion. Thus, one of the most challenging

problems in the operation of restructured power systems is

congestion management. In a competitive power market,

the system is said to be congested when the producers and

consumers of electric energy desire to produce and

consume in amounts that would cause the transmission

system to operate at or beyond one or more transfer limits

[1].Congestion may result in preventing new contracts,

infeasibility in existing contracts, price spike in some

regions, market power abuse.

Congestion exists in both new and traditional systems

but CM is more complex in case of competitive power

markets due to the unbundled nature of the same, which

calls for more coordination. In the vertically integrated

structure ,generation, transmission and distribution being

managed by one utility ,managing congestion was

relatively easier. Approaches used to manage congestion

vary with market structures. Several techniques of

congestion management have been reported in [2].

Out of the various approaches used for CM, the most

widely used is generation rescheduling. Generators

participate in the congestion management market by

bidding for incrementing and decrementing their

production. Also, demands can bid as demand side bidding

(DSB) [3] for adjusting their loads. However, it is crucial

for SO to select the most sensitive generators to re-schedule

their optimal real powers for congestion management.The

CM problem has two parts. The first part of the power

dispatch problem is to find out the preferred schedule using

Optimal Power Flow (OPF) and the second part is

rescheduling the generation and demands for removing the

congestion. The traditional approach to OPF is to minimize

the costs subject to system security constraints. In the

deregulated market environment, the OPF problem aims at

maximizing social welfare based on generation costs and

the benefits to customers so as to achieve optimal dispatch

plan among operating units and satisfy the system load

demand in an economic and reliable manner while

respecting generator operation constraints and line flow

limits. The objective of the second part is to minimize total

rescheduling cost.

A literature survey on the application of various

evolutionary approaches to congestion management reveals

that researchers have not attempted so far to consider

Demand Side Bidding (DSB) to relieve congestion in the

overloaded line(s).Z.X. Chen et al. [4] introduced PSO for

solving Optimal Power Flow (OPF) which deals with

congestion management in pool market and proved using

IEEE 30 Bus system that congestion relief using PSO is

284


International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

effective in comparison with Interior Point Method and

Genetic Algorithm approach. J. Hazra and Sinha [5]

proposed cost efficient generation rescheduling and/or load

shedding approach for congestion management in

transmission grids using Multi Objective Particle Swarm

Optimization (MOPSO) method. S. Dutta and Singh [6]

proposed a technique for reducing the number of

participating generators and optimum rescheduling of their

outputs while managing congestion in a pool at minimum

rescheduling cost and explored the ability of PSO

technique in solving congestion management problem.

Reference [7] proposes an optimal congestion management

approach in a deregulated electricity market using particle

swarm optimization with time-varying acceleration

coefficients (PSO-TVAC). Venkaiah and D.M.Vinod

Kumar [8] proposed fuzzy adaptive bacterial foraging

(FABF) based congestion management (CM) by optimal

rescheduling of active powers of generators selected based

on the generator sensitivity to the congested line. None of

the models have taken care of the role of demand response

in congestion management in a deregulated environment.

So, the main objective of this paper is to propose a model

for congestion management in deregulated power sector,

with demand side participation and solve the same using

PSO.

In this paper, a model for congestion management that

dispatches the pool, with maximization of social benefit

with all system constraints, has been proposed. The bulk

loads as well as retailers are required to bid their maximum

demand and price. All generators are also required to bid

their supply price along with maximum generation. The

contribution of this paper is to relieve congestion by

rescheduling active power outputs of generators based upon

their sensitivity to line flows in the overloaded line(s).In

addition to generators, demands are so participated into the

congestion market that the total rescheduling cost is

minimum. The proposed method has two steps. The first

step is to solve the social welfare optimization problem to

find the status of transmission congestion under the

existing transmission system condition. The second step is

to reschedule generation and load in a manner that

congestion is mitigated. The proposed method has been

tested on IEEE 30-bus system.

II. PROBLEM FORMULATION

The CM problem can be divided into two parts. The first

part of the problem is to find out the preferred schedule

using Optimal Power Flow (OPF) and the second part is

rescheduling the generation and demands for removing the

congestion.

285

A. Part 1

The objective for the first part is maximization of social

benefit which can be mathematically stated as follows:

Where

N

d

C maximize(

d

C

g and

$/MWhr, respectively;

C

d

( P

d

) P

d

Ng


g

C g ( P g ) Pg

)

(1)

C

d

are supply and demand bids in

P

g and

power levels in MW, respectively.

Subject to

Where,

P

D

=Load Demand (MW)

P

L = Transmission loss (MW)

P

d

are supply and demand

Ng

P P 0

i 1 gi D

P L

P gi

= Power output of ith generator (MW)

Where,

P

Q

min

gi

min

gi

gi

max

gi

(2)

P P

(3)

Q Q

(4)

gi

max

gi

min

P gi =The lower bound on the active power output from

the i th generator.

max

P gi = The upper bound on the active power output from

the i th generator.

min

Q gi =The lower bounds on the reactive power output

from the i th generator.

max

Q gi = The upper bound on the reactive power output

from the i th generator.


Where,

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

P

l

P

l max

, l 1,2,...,

L (5)

P

l

=The power transmitted over line l (MW).

min min

Pg

P g P g

min

max

Pg

P g P g

max max

P g P g P g , g 1,2,...,N g (9)

P

l max

=The max limit of the transmissible power over line

l (MW).

L =The total number of lines.

Where,

min max

Vgi

V gi V gi (6)

min

V i

= lower voltage magnitude bounds for the i th bus.

max

V i

= upper voltage magnitude bounds for the i th bus.

B. Part 2

The objective of the second part is to minimize the

amount of rescheduling required, which can be

mathematically stated as follows:

Cc

Ng

N

'

d '

minimize( C g ( P g ) P g C ( P

d

) P

d

)

g

d

d

(7)

'

Where C

g

refers to the incremental and decremental

price bids submitted by the generator that are willing to

adjust their real power outputs,

C refers to the

decremental price bids submitted by the demands that are

willing to adjust their load(only power decreasing

adjustment is considered for loads in congestion

management), P is the real power adjustment done by

generator g and

demand d.

Subject to

g

is the load adjustment done by

Pd

'

d

Ng

P g F

k

F

k

k N

g

0 max

GS g ) )

, 1,2,3,....,

1 (( l

(8)

286

min

max

P

d

P

d

P

d

(10)

Ng Nd

P g P

P

0

g 1 d 1

d loss

(11)

0

F

k represents the power flow caused by all contracts

max

requesting the transmission service and F

k represents

the line flow limit of the line connecting buses i and j.

N =no. of participating generators. N =No. of lines ;

g

min

P

g

=Minimum limit of generator

max

output; P

g

=Maximum limit of generator output. Pg

is

the change in generator output; represents the

reduction in load; Ploss

represents the total change in

transmission loss due to the changed schedule post CM.

GS

g represents the sensitivity of the generator g to the

congested line. The generators in the system under

consideration have different sensitivities to the power flow

on the congested line. Mathematically, Generator Sensitivity

(GS) for line k can be written as [6]

P is the real power flow on the congested line-

ij

k, and

Where

GS

g

Pd

l

P

ij

(12)

P

G

g

P is the real power generated by generator g.

g

III. PARTICLE SWARM OPTIMIZATION

PSO(Particle Swarm Optimization) is a population based

stochastic optimization technique inspired by social

behavior of organisms such as bird flocking or fish

schooling, originally developed by Eberhat and Kennedy in

1995[9].It optimizes a problem by trying to improve a

population of candidate solutions over several generations.


International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

It provides a population based search procedure in which

individuals (or candidate solutions) dubbed as particle

change their position (state) with time. The movement of the

particles in the search space is guided by its own experience

and the experience of a neighboring particle, making use of

the best position found by itself and the entire swarm’s best

known position. The PSO algorithm is characterized by high

speed of convergence and has better exploration and

exploitation provided by the inherent combination of the

local and global search capabilities of the PSO algorithm.

PSO is initialized with a group of random particles

(candidate solutions) and then searches for optima by

updating the positions of these particles over generation. In

every generation, each particle is updated by following two

best values viz the best position(fitness) it has achieved so

far(pbest) and the best value obtained so far by any particle

in the population(called gbest or global best).

Based upon the knowledge of the two best values, the

particle updates its velocity and position, according to the

following equation:

k1

k

k

k

v

id

w

v

id

c

1

r

1pbest

id

x

id


c

2

r

2gbest

d

x

id


k1 k k1

x

id

x

id

v

id

(14)

where x x

, x ,..., x and v v

, v ,..., v

i i1

i2

iD i i1

i2

iD

represent the position and velocity of the ith particle,

respectively; d=1,2…,D where D is the dimension of the

search space; i=1,2,…,N where N is the size of the

population(swarm);w is the inertia weight used as a

parameter to control exploration and exploitation in the

search space;c1 and c2 are positive constant parameters

called acceleration coeffients;r1 and r2 are uniform random

numbers in [0,1].More details regarding PSO can be found

in [9].

IV. RESULTS

The IEEE 30-bus system has been used to show the

effectiveness of the proposed algorithm. The IEEE 30-bus

system consists of six generator buses and 24 load buses.

To stress the system and create congestion, the load at

every bus is increased up to 1.3 times of original load data.

Price bids of generators (excluding the slack bus)to adjust

their scheduled power production are given in Table I .

Increment and decrement bids are assumed equal in this

work. Price bids of loads to adjust their power consumption

are given in Table II.

TABLE I.

Bus No.

PRICE BIDS OF GENERATORS FOR POWER

ADJUSTMENTS

'

C

g

($/MWh)

2 13

5 12

8 11

11 11

13 12

Bus 1 is assigned as the reference bus. At first market

clearing happens based upon the objective of maximizing

social welfare. The generation and demand schedule

arrived at as a result of market clearing causes congestion

on certain transmission lines. The details of which are

shown in Table III. The Generator Sensitivities are

computed for the congested lines using (12).The GS values

of 6 generation units in the IEEE 30-bus system are shown

in Table IV. In the IEEE 30-bus system, it is observed that

the GS values of all 6 generators are close probably

because of the system being very small. In this case all the

sensitivities are negative which indicates increase in

generation. The fact that all generators show almost equal

influence on the congested lines necessitates that all the

generator buses are selected for the rescheduling to

alleviate the overload.

287


Bus No.

TABLE II.

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

PRICE BIDS OF LOADS FOR POWER

'

C

d ($/MWh)

ADJUSTMENTS

Bus No.

3 23 19 24

4 21 23 24

5 23 24 23

7 22 30 23

8 24

12 23

15 21

16 21

'

C

d ($/MWh)

It is observed that when the system is subjected to this

kind of stressed loading (1.3 times the base load) rescheduling

of generator active power outputs alone cannot

not relieve congestion in the lines completely.

However with simultaneous load adjustments congestion

is completely relieved. Thus demand response plays a vital

role to relieve the congestion in such a case.

The PSO algorithm is employed to optimally reschedule

the active power of the generators and power consumption

of the load for relieving congestion in the affected lines. For

a larger system, selected group of generators having the

largest GS values may be used to save the computational

effort. Table V depicts the cost of CM, power flows on the

congested line after rescheduling and the total transmission

loss. The generators and loads participating in congestion

management and their active power adjustments are

presented in Table VI.

TABLE V.

RESULTS

Approx. Cost Of CM($/hr) 632.1346 1107.7

Congested Line

TABLE III.

DETAILS OF CONGESTION

Power

Flow(MW)

Line

Limit(MW)

1-2 357.32 200

1-3 359.68 200

6-7 38.53 25

Power Flow on Previously Congested Line(1-2)

(MW)

Power Flow on Previously Congested Line(1-3)

(MW)

Power Flow on Previously Congested Line(6-7)

(MW)

191.17 190.19

194.10 195.22

24.14 135.95

Transmission Loss(MW) 14.8699 15.0328

TABLE IV.

Congested

line

GS VALUES FOR IEEE 30 BUS SYSTEM

GS Values

G2 G5 G8 G11 G13

1-2 -1.330 -0.754 -0.790 -0.881 -0.887

1-3 -0.307 -0.294 -0.308 -0.344 -0.346

6-7 -0.096 -0.165 -0.163 -0.139 -0.145

The following parameter setting is used for the proposed

PSO algorithm:

Population Size (N) = 50;

Initial inertia weight(w max )=0.9;

Final inertia weight(w min )=0.4;

Maximum Iterations = 100;

Acceleration Constants c 1 =2,c 2 =2;

The methodology adapted provides the minimum redispatch

cost of $632.1346/h.

288


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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

TABLE VI.

Generator Rescheduling

RESCHEDULING FOR CM

∆P 1(MW) 0

∆P 2(MW) 16.1181

∆P 5(MW) 1.3145

∆P 8(MW) 1.3770

∆P 11(MW) 9.0461

∆P 13(MW) -0.0189

Load Adjustments

∆P 3(MW) -0.0189

∆P 4(MW) -0.3120

∆P 5(MW) 0

∆P 7(MW) -5.5010

∆P 8(MW) -2.5649

∆P 12(MW) -1.1504

∆P 15(MW) -0.0617

∆P 16(MW) -1.0305

∆P 19(MW) 0

∆P 23(MW) -0.8341

∆P 24(MW) -0.2895

∆P 30(MW) -1.1310

Total Rescheduling(MW) 40.7686

DSB is considered during both market clearing and CM

phases. The problem of congestion is modeled as an

optimization problem and solved by particle swarm

optimization technique. The method has been tested on

IEEE 30-bus system successfully. Test results on the IEEE

30-bus system prove the efficacy of the proposed approach

in managing transmission congestion in a deregulated power

system.

REFERENCES

[1] R. Christie, B. Wollenberg, and I. Wangensteen, ―Transmission

management in the deregulated environment,‖ in Proc. of the IEEE,

vol. 88,no. 2, pp. 170–195, 2000.

[2] Druce Donald J,‖Modelling the transition from cost-based to bidbased

pricing in a deregulated electricity-market,‖ Appl Energy, vol.

84,no.12,pp.1210–25, 2007.

[3] Ashwani Kumar, S.C. Srivastava, S.N. Singh, Congestion

management in competitive power market: a bibliographical survey,

Electric Power Systems Research,vol. 76 ,pp.153–164, 2005.

[4] Z. X. Chen , L. Z. Zhang and J. Shu "Congestion management based

on particle swarm optimization", in Proc. 7th Int. Power Engineering

Conf., vol. 2, pp.1019 ,2005.

[5] J. Hazra, A.K. Sinha, ―Congestion management using multiobjective

particle swarm optimization,‖ IEEE Transactions on Power

Systems,vol. 22, no.4, pp.1726–1734, 2007.

[6] S. Dutta, S.P. Singh, ―Optimal rescheduling of generators for

congestion management based on particle swarm optimization,‖

IEEE Transactions on Power Systems,vol. 23,no.4, pp.1560–1569,

2008.

[7] P.Boonyaritdachochai, C.Boonchuay, W.Ongsakul,‖Optimal

congestion management in an electricity market using particle

swarm optimization with time-varying acceleration coefficients,‖

Computers and Mathematics with Applications ,vol.60,pp.1068–

1077,2010.

[8] C. Venkaiah, D.M. Vinod Kumar, ―Fuzzy adaptive bacterial

foraging congestion management using sensitivity based optimal

active power re-scheduling of generators,‖ Appl. Soft Comput. J.,

vol. 11, no.8,pp.4921-4930, 2011.

[9] A. Kennedy and R. Eberhart, ―Particle Swarm Optimization,‖ in

Proc.IEEE Int. Conf. Neural Networks, Nov. 29–Dec. 1 1995, vol.

IV, pp.1942–1948.

V. CONCLUSION

In this paper, the proposed congestion management

approach based on PSO is efficiently minimizing the

congestion management cost. Redispatched generators are

selected based on GS. The present paper focuses on

demonstrating the role of demand side participation in CM.

289

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