Application of Particle Swarm Optimisation for Relieving Congestion in Deregulated Power System

Sandip Chanda Department of Electrical Engineering

Techno India Kolkata, India

sandipee1978@gmail.com

Abhinandan De Department of Electrical Engineering

Bengal Engineering. & Science University, Shibpur Howrah 711103, WB, India abhinandan.de@gmail.com

Abstract— This paper presents a Swarm intelligence based Optimization technique to manage congestion in power system networks with transmission line overload. To maintain all the power transaction requests, line congestion in deregulated systems is almost inevitable which may degrade the system stability, security and reliability by additional line outages. In practice System Operators (SO) charge additional price known as congestion management charge against line limit violation. Thus, restricting power flows within the safe limits is important from stability as well as economy point of view. The algorithm proposed in the present paper uses a standard congestion sensitivity Index to identify the congested lines in a large power network and optimizes ‘congestion management charge’ without any load curtailment and installation of FACTS devices. The operating conditions with the proposed methodology have been demonstrated to be subjected to an improvement with reference to conventional method. The applicability of the proposed methodology has been presented on IEEE 30 bus benchmark system.

Keywords-Congestion; ; Contingency; Congestion; Congestion Sensitivity index;

I. INTRODUCTION Transmission line congestion due to contingencies like line

or generator outage may lead to cascading failure of the system [1]. Hence congestion management is a challenging task for independent System Operator (ISO) for maintaining stability, security and reliability. A generation rescheduling method for alleviation of line overloads using PSO has been proposed in [2].The objective of the method is to minimize the rescheduling of generation to tackle line congestion, which may have a beneficiary impact from the economic considerations, but put less emphasis on the management of the congestion itself. A control method based on power flow tracing and generator re-dispatching has been proposed [3] but the adjustments of generators are not optimal. In [4], the authors have proposed a congestion constrained economic load dispatch using IPSO but the solution could only limit line congestions within the thermal limits of the lines rather than restricting line flows to a desired value. PSO based zonal congestion management with optimal rescheduling of real and reactive power of generators has been depicted in [5] but the contingent conditions and their impact on power flows have not been considered. Penalty based Security constrained optimal power flow (SCOPFs) have been proposed in [6] and [7] where rescheduling cost have been minimized without ascertaining maximum allowable line

flow or level of congestion. Moreover, the penalty method applied has to trace and calculate penalties for all the lines, the therefore time complexity of the algorithms may be very high at times. [8] and [9] proposed a voltage stability constrained Optimal Power Flow (OPF) to alleiavate congestion, but the proposed generation schedule could not maintain a particular level of congestion during contingencies. The line congestion can also be managed by employing FACTs devices and HVDC as cited in [10]- [12]. But the excess cost associated with these devices may prohibit their use in many existing systems. In [13], [14] load curtailment based congestion management has been proposed, but the value of lost load (VOLL) may restrict its practical implementation. In [15] a generator and load participation factor based congestion management technique has been proposed which curtails the specific loads contributing more to congestion. But sustained load curtailment may again be prohibitive in many systems. Dynamic control of congestion as reported in [16] may be too expensive and also require precise monitoring.

In the present work, the congestion zones in a power network are first identified using a ‘Congestion sensitivity index’ method described in section II. Tripping of one or more of these lines may lead to even greater level of congestion in the remaining lines. The objective of the present work is to relieve congestion in these lines by formulating a ‘congestion constrained OPF problem’ and solving the same using Particle Swarm Optimization (PSO) technique as described in section II. The OPF solution attempts to reschedule the generators in such a way that the individual line flows are brought down to a desired level, not exceeding their loadability limits with an optimum ‘congestion management charge’ without any load curtailment and installation of FACTS devices.

II. THEORY

A. Problem formulation Objective function in a conventional cost optimization

problem can be described as:

Minimize1

G

T

N

n

F C=

=∑ $/hr (1)

2i gi giC AP BP C= + + (2)

978-1-4244-9477-4/11/$26.00 ©2011 IEEE

837

where, GN =No of generators ,A, B, C = cost co-efficient of generators , giP = generation of ith generator in MW.

In the present work, the objective function is suitably modified to incorporate the proposed voltage, line loss and congestion penalties. The congestion management charge is the difference between the total generation cost for maintaining the aforesaid operating condition and without stipulating the same. The modified multi-objective OPF can be described as:

Minimize:

min max max1 1

1 2 3G G

T T

N N

l ijn n

F C p xV p xP p xP C= =

= + + + −∑ ∑ $/hr

(3)

1p =Penalty for voltage constraint violation, minV = Minimum bus voltage in p.u. to be allowed, 2p =Penalty for line loss limit violation, maxlP =Maximum limit of line loss to be allowed, 3p =Penalty for congestion limit violation,

maxijP =Maximum line flow to be allowed between ith and jth bus.

The constraints are common for both the objective functions and are described as follows:

1. Equality or power balance constraints:

1( cos sin ) 0

n

Gi Di i j ij ij ij iji

P P V V G Bθ θ=

− − + =∑ (4)

1( sin cos ) 0

n

Gi Di i j ij ij ij iji

P P V V G Bθ θ=

− − − =∑ (5)

Where, GiP =Active power injected in bus i, DiP =Active power demand on bus i, iV =magnitude of voltage of buses i, jV =

magnitude of voltage of buses j, ijG =Conductance of

transmission line from bus i to j, ijB = Susceptance of transmission line from bus i to j ,n = number of buses

2. Inequality or generator output constraints: min max

gi gi giP P P≤ ≤ (6)

min maxgi gi giQ Q Q≤ ≤ (7)

Where, giP , giQ = Active and reactive power of generator i

respectively, mingiP , min

giQ = Upper limit of active and reactive

power of the generators, maxgiP , max

giQ = lower limit of active and reactive power of the generators

3. Voltage constraint: min max

i i iV V V≤ ≤ (8)

maxiV , min

iV are upper and lower limit of iV

4. Transmission constraint:

max minij ij ijP P P≤ ≤ (9)

maxijP , minijP are the max and minimum line flow limits of Pij

B. Congestion Sensitivity Index: The loading limit of transmission lines are restricted by

several constraints. In many cases the transmission capacity is limited by thermal capacity of the lines. However, it has been established in [17] [18] that in case of long EHVAC lines the synchronous (Angular) and static voltage stability limits play more predominant role in restricting the power flow to the surge impedance loading (SIL) level. Hence in the present paper a “Congestion Sensitivity Index” has been proposed and formulated as

Congestion sensitivity index = ijPSIL

(10)

ijP = Line flow between ith and jth bus; SIL= surge impedance loading of the line

C. Step by step procedure followed in the proposed method: 1. Ac load flow analysis in the IEEE 30 bus system under study has been carried out using Newton-Raphson load flow method

2. Six most congested lines were identified based upon their congestion sensitivity indices

3. A multiobjective congestion constrained cost optimization algorithm has been developed using particle swarm optimization.

4. For outage of each of the six congested lines , according to the ranking table ac load flow has been carried out to determine the degree of congestion.

5. The constraints are set in PSO based OPF , each for maximum line flows ,.line losses and minimum bus voltage amplitudes.

6. The results of PSO are evaluated to determine constraint violation. The penalties are applied for violation of maximum line flow limits, minimum value of p.u. bus voltage and on actual value of the line losses.

7. PSO search algorithm now looks for the optimal generation pattern which minimizes the congestion management charge as in equation 3..

8. The search procedure repeats the following steps in accordance with the method proposed by Kennedy and Eberhart in 1995 [19], [20] for a given number of iterations.

i) Velocity of the particles with inertia weight have been found according to the following expression

11 1 2 2. (....) ( ) (....) ( )k k k k

i i i i iv wV cxrand x pbest x c xrand x gbest x+ = + − + − (11)

838

ii) The velocity is added with the previous iteration solution to obtain the new set of population following the equation:

1 1k k ki i ix x v+ += + (12)

Particle in this way changes its position with the knowledge of pbest and gbest . The pbest and gbest are computed as:

1

11 1

if (

if ( ) pbest

t t ti i it

i t t ti i i

pbest f x pbestpbest

x f x

++

+ +

⎧ ) >⎪=⎨<⎪⎩

(13)

1 1 1 1

1 2( , ............ )t t t ti Ngbest best pbest pbest pbest+ + + += (14)

iii) Ac power flow has been carried out and the fitness function is calculated as stated in step5.

iv) Fitness values are compared and gbest values are evaluated as best possible solution.

III. SIMULATION AND RESULT The feasibility and effectiveness of the proposed algorithm

has been demonstrated in the modified IEEE 30 bus system shown in Fig. 1. The summary of relevant data from the modified IEEE 30 bus system is presented in Table I.

TABLE I. GENERATOR COST CO-EFFICIENT OF IEEE 30 BUS SYSTEM

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 5000 2 20 80 0.01750 1.75 1000 5 15 50 0.06250 1.00 600 8 10 35 0.00834 3.25 300

11 10 30 0.02500 3.00 350 13 12 40 0.02500 3.00 400

Figure 1. The standard IEEE 30 bus system

A. Identification of most vulnerable lines in terms of congestion byCongestion sisitivity index For proper identification and assessment of the congestion

zone in the system, with the assistance of the proposed Congestion sensitivity index a ranking table depicting 10 lines(Among 41) with their respective indices has been

presented in Table III. It is obvious that the exclusion of these lines will represent worst possible contingencies of the system. The applicability of the proposed algorithm can be established if the level of congestion can be limited under these contingencies.

TABLE II. SELECTION OF VULNERABLE LINES BY LINE LOADING INDEX

Line connecting Bus Nos.

Power (MW)

Line Loading index

1-2 117.7962 0.818029 1-3 59.44315 0.4128 2-4 34.07481 0.236631 2-5 63.01612 0.437612 2-6 45.4126 0.315365 3-4 55.59228 0.386058 4-6 50.85563 0.353164

4-12 30.17419 0.209543 6-7 34.65778 0.240679 6-8 10.09864 0.070129

12-15 17.39429 0.120794

B. Relieving congestion by imposing Penalty : The objective of the proposed method is to optimize the

overall operational cost by minimizing the congestion management charge of the power generating system including the cost of generation as well as the penalty cost due to congestion considering voltage profile and total line losses. The table IV depicts the results of the case study where a comparison of line flows between the conventional method and the proposed method. The improvement of line congestion is observable with the proposed method with penalty for constraint violation

TABLE III. COMPARISON OF MAXIMUM LINE FLOW AND GENERATION COST OF IEEE 30 BUS SYSTEM

Tripped lines

Conventional Optimization without any Penalty

Optimization with voltage ,power loss and congestion

Penalty Genera-

tion cost($/hr)

Max line flow

(MW)

Generation cost($)

Max line flow

(MW) 1-2 8490 151.30 8560 71.99 2-5 8490 103.49 8910 50.59 1-3 8470 169.47 8560 71.98 3-4 8460 167.29 8550 71.99 4-6 8460 129.26 8510 71.94 2-6 8460 104.43 8490 69.66

C. Reduction in Power total line Losswith the proposed algorithm: Along with congestion management, the proposed

algorithm can cause a considerable reduction in total line loss . Fig 3 shows the comparison of total line losses of the network with the conventional and proposed algorithm. The performance of a network entirely relies on the total line loss in serving for all the requests of the region. Apart from managing line congestion the proposed algorithm is capable of effective reduction of the total line loss to improve the overall efficiency of the system. During the consideration of the of the additional congestion management cost , the cost of power losses and the corresponding saving need also to be accounted.

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Figure 2. Comparison of total line losses

1) Improvement in Voltage profilewith the proposed algorithm:

Another important feature of the proposed algorithms is the improvement in voltage profiles .Fig. 2 shows the comparison of voltage profiles between the proposed algorithm and the conventional cost optimization. It is evident that the voltage profile with penalty algorithm is better than the conventional cost optimization method. Improvement in voltage profile suggests an enhancement in stability margin of the system.

Figure 3. Comparison of Bus Voltage Profile.

IV. CONCLUSION For the optimization of congestion management charge, a

swarm intelligence based methodology has been proposed to restore the operating conditions of the system to a desired level but without any load curtailment and installation of FACTS devices. The PSO based search process has been directed to the optimum solution by introducing penalty in generation cost with the violation of each specified constraint. The improvement of line congestion. Successful implementation of the proposed methodology in the IEEE 30 bus benchmark system depicts that the proposed algorithm can develop a cost effective solution to the deviation of operating conditions viz degradation of voltage and loss profile in contingent state of the system. ISO can effectively utilize the benefits of this algorithm in deregulated power market for maintaining price equilibrium.

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