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

International Journal of Emerg**in**g Technology and Advanced Eng**in**eer**in**g

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

**Congestion** **Management** **in** a **Deregulated** **Power** **System**

by Reschedul**in**g Of Sensitive

Generators and load curtailment us**in**g 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 result**in**g **in** market **in**efficiency. Reschedul**in**g

generations and demands is an effective tool to relieve

congestion. This paper presents a congestion management

(CM) algorithm by optimal reschedul**in**g of active powers of

generators and power consumption of load. In addition to the

reschedul**in**g of real power generation, demand-side

participation through load curtailment has been considered to

manage congestion. Generator Sensitivity to the congested l**in**e

and the costs of generation and demand side adjustments are

considered while re-schedul**in**g 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 m**in**imiz**in**g the cost of

CM **in** alleviat**in**g congestion **in** the transmission l**in**es.

Keywords— deregulation; congestion management; optimal

power flow; demand side bidd**in**g; sensitivity

I. INTRODUCTION

Increased volumes of power trade happen**in**g due to the

deregulation of electric power **in**dustry has led to **in**tensive

usage of transmission network, which **in** turn leads to more

frequent congestion. Thus, one of the most challeng**in**g

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** prevent**in**g new contracts,

**in**feasibility **in** exist**in**g 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 coord**in**ation. In the vertically **in**tegrated

structure ,generation, transmission and distribution be**in**g

managed by one utility ,manag**in**g 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 reschedul**in**g. Generators

participate **in** the congestion management market by

bidd**in**g for **in**crement**in**g and decrement**in**g their

production. Also, demands can bid as demand side bidd**in**g

(DSB) [3] for adjust**in**g 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 f**in**d out the preferred schedule us**in**g

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

reschedul**in**g the generation and demands for remov**in**g the

congestion. The traditional approach to OPF is to m**in**imize

the costs subject to system security constra**in**ts. In the

deregulated market environment, the OPF problem aims at

maximiz**in**g social welfare based on generation costs and

the benefits to customers so as to achieve optimal dispatch

plan among operat**in**g units and satisfy the system load

demand **in** an economic and reliable manner while

respect**in**g generator operation constra**in**ts and l**in**e flow

limits. The objective of the second part is to m**in**imize total

reschedul**in**g 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 Bidd**in**g (DSB) to relieve congestion **in** the

overloaded l**in**e(s).Z.X. Chen et al. [4] **in**troduced PSO for

solv**in**g Optimal **Power** Flow (OPF) which deals with

congestion management **in** pool market and proved us**in**g

IEEE 30 Bus system that congestion relief us**in**g PSO is

284

International Journal of Emerg**in**g Technology and Advanced Eng**in**eer**in**g

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effective **in** comparison with Interior Po**in**t Method and

Genetic Algorithm approach. J. Hazra and S**in**ha [5]

proposed cost efficient generation reschedul**in**g and/or load

shedd**in**g approach for congestion management **in**

transmission grids us**in**g Multi Objective Particle Swarm

Optimization (MOPSO) method. S. Dutta and S**in**gh [6]

proposed a technique for reduc**in**g the number of

participat**in**g generators and optimum reschedul**in**g of their

outputs while manag**in**g congestion **in** a pool at m**in**imum

reschedul**in**g cost and explored the ability of PSO

technique **in** solv**in**g congestion management problem.

Reference [7] proposes an optimal congestion management

approach **in** a deregulated electricity market us**in**g particle

swarm optimization with time-vary**in**g acceleration

coefficients (PSO-TVAC). Venkaiah and D.M.V**in**od

Kumar [8] proposed fuzzy adaptive bacterial forag**in**g

(FABF) based congestion management (CM) by optimal

reschedul**in**g of active powers of generators selected based

on the generator sensitivity to the congested l**in**e. None of

the models have taken care of the role of demand response

**in** congestion management **in** a deregulated environment.

So, the ma**in** objective of this paper is to propose a model

for congestion management **in** deregulated power sector,

with demand side participation and solve the same us**in**g

PSO.

In this paper, a model for congestion management that

dispatches the pool, with maximization of social benefit

with all system constra**in**ts, 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

reschedul**in**g active power outputs of generators based upon

their sensitivity to l**in**e flows **in** the overloaded l**in**e(s).In

addition to generators, demands are so participated **in**to the

congestion market that the total reschedul**in**g cost is

m**in**imum. The proposed method has two steps. The first

step is to solve the social welfare optimization problem to

f**in**d the status of transmission congestion under the

exist**in**g 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 **in**to two parts. The first

part of the problem is to f**in**d out the preferred schedule

us**in**g Optimal **Power** Flow (OPF) and the second part is

reschedul**in**g the generation and demands for remov**in**g 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

m**in**

gi

m**in**

gi

gi

max

gi

(2)

P P

(3)

Q Q

(4)

gi

max

gi

m**in**

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.

m**in**

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 Emerg**in**g Technology and Advanced Eng**in**eer**in**g

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 l**in**e l (MW).

m**in** m**in**

Pg

P g P g

m**in**

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 l**in**e

l (MW).

L =The total number of l**in**es.

Where,

m**in** max

Vgi

V gi V gi (6)

m**in**

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 m**in**imize the

amount of reschedul**in**g required, which can be

mathematically stated as follows:

Cc

Ng

N

'

d '

m**in**imize( C g ( P g ) P g C ( P

d

) P

d

)

g

d

d

(7)

'

Where C

g

refers to the **in**cremental and decremental

price bids submitted by the generator that are will**in**g to

adjust their real power outputs,

C refers to the

decremental price bids submitted by the demands that are

will**in**g to adjust their load(only power decreas**in**g

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

m**in**

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

request**in**g the transmission service and F

k represents

the l**in**e flow limit of the l**in**e connect**in**g buses i and j.

N =no. of participat**in**g generators. N =No. of l**in**es ;

g

m**in**

P

g

=M**in**imum 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 l**in**e. The generators **in** the system under

consideration have different sensitivities to the power flow

on the congested l**in**e. Mathematically, Generator Sensitivity

(GS) for l**in**e k can be written as [6]

P is the real power flow on the congested l**in**e-

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 **in**spired by social

behavior of organisms such as bird flock**in**g or fish

school**in**g, orig**in**ally developed by Eberhat and Kennedy **in**

1995[9].It optimizes a problem by try**in**g to improve a

population of candidate solutions over several generations.

International Journal of Emerg**in**g Technology and Advanced Eng**in**eer**in**g

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

It provides a population based search procedure **in** which

**in**dividuals (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 neighbor**in**g particle, mak**in**g 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 **in**herent comb**in**ation of the

local and global search capabilities of the PSO algorithm.

PSO is **in**itialized with a group of random particles

(candidate solutions) and then searches for optima by

updat**in**g the positions of these particles over generation. In

every generation, each particle is updated by follow**in**g two

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

far(pbest) and the best value obta**in**ed 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, accord**in**g to the

follow**in**g 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 **in**ertia 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 regard**in**g 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 **in**creased up to 1.3 times of orig**in**al load data.

Price bids of generators (exclud**in**g 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

clear**in**g happens based upon the objective of maximiz**in**g

social welfare. The generation and demand schedule

arrived at as a result of market clear**in**g causes congestion

on certa**in** transmission l**in**es. The details of which are

shown **in** Table III. The Generator Sensitivities are

computed for the congested l**in**es us**in**g (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 be**in**g very small. In this case all the

sensitivities are negative which **in**dicates **in**crease **in**

generation. The fact that all generators show almost equal

**in**fluence on the congested l**in**es necessitates that all the

generator buses are selected for the reschedul**in**g to

alleviate the overload.

287

Bus No.

TABLE II.

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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

k**in**d of stressed load**in**g (1.3 times the base load) reschedul**in**g

of generator active power outputs alone cannot

not relieve congestion **in** the l**in**es 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 reliev**in**g congestion **in** the affected l**in**es. For

a larger system, selected group of generators hav**in**g the

largest GS values may be used to save the computational

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

congested l**in**e after reschedul**in**g and the total transmission

loss. The generators and loads participat**in**g **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 L**in**e

TABLE III.

DETAILS OF CONGESTION

**Power**

Flow(MW)

L**in**e

Limit(MW)

1-2 357.32 200

1-3 359.68 200

6-7 38.53 25

**Power** Flow on Previously Congested L**in**e(1-2)

(MW)

**Power** Flow on Previously Congested L**in**e(1-3)

(MW)

**Power** Flow on Previously Congested L**in**e(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

l**in**e

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 follow**in**g parameter sett**in**g is used for the proposed

PSO algorithm:

Population Size (N) = 50;

Initial **in**ertia weight(w max )=0.9;

F**in**al **in**ertia weight(w m**in** )=0.4;

Maximum Iterations = 100;

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

The methodology adapted provides the m**in**imum redispatch

cost of $632.1346/h.

288

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TABLE VI.

Generator Reschedul**in**g

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 Reschedul**in**g(MW) 40.7686

DSB is considered dur**in**g both market clear**in**g 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** manag**in**g transmission congestion **in** a deregulated power

system.

REFERENCES

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V. CONCLUSION

In this paper, the proposed congestion management

approach based on PSO is efficiently m**in**imiz**in**g the

congestion management cost. Redispatched generators are

selected based on GS. The present paper focuses on

demonstrat**in**g the role of demand side participation **in** CM.

289