2015 International Conference on Energy Systems and Applications (ICESA 2015) Dr. D. Y. Patil Institute of Engineering and Technology, Pune, India 30 Oct - 01 Nov, 2015
Generator Rescheduling for Congestion Management using Firefly Algorithm Sadhan Gope Assistant Professor Electrical Engineering Dept. Mizoram University Aizawl-796004
[email protected]
Prashant Kumar Tiwari Assistant Professor Electrical Engineering Dept. NIT Silchar Silchar, Assam-788010
[email protected]
Arup Kumar Goswami Assistant Professor Electrical Engineering Dept. NIT Silchar Silchar, Assam-788010
[email protected]
constraint fitness is satisfied and then optimal objective is determined. In [8] the concept of Relative Electrical Distance (RED) is utilized to reschedule all the generators for congestion management. The authors focused on the transmission losses and voltage profile based on the RED concept. Hydro- thermal generator combined operation for congestion management is presented in [9]. Recently Sen Transformer (ST), Thyristor Controlled Series Compensators (TCSC) and Unified Power Flow Controller (UPFC) are used for congestion management [10]-[11]. Congestion management with FACTS devices considering voltage stability as loadability limit is discussed in [12]. In [13], Real power rescheduling for congestion management with the application of Fuzzy adaptive bacterial foraging is presented, where generators are selected based on generator sensitivity. In paper [14] author considers the wind energy for congestion management. Line flow sensitivity factor based optimal location of DG’s is identified for congestion management with reduced losses and better voltage profile [15].
Abstract— In power system operation, congestion management has become more complicated with the increase of system complexity in deregulated environment. That is why, in present scenario of power system congestion management is a complex task of an independent system operator (ISO). In this paper, generator rescheduling is used as a congestion management technique. A recently developed meta heuristic algorithm known as Firefly Algorithm (FA) has been introduced in proposed work. The present work is two folded. Firstly, Generator sensitivity factor (GSF) is calculated to identify the generators participating in congestion management by rescheduling their output. Secondly, FA is introduced to find optimal rescheduling cost of participating generators. Present work is tested on IEEE 39 bus New England Test System. Keywords—Generator sensitivity factor, generator rescheduling, transmission congestion management, optimization techniques, firefly algorithm.
I.
INTRODUCTION
Power System congestion management issue is becoming more complex day by day as number of consumer is increasing. Transmission lines play as an interconnected medium between suppliers and consumers and maintain its thermal limits. Violation of thermal limits results in congestion in the lines which may further destroy some other lines or entire system. So, proper techniques must be taken to avoid congestion. So, one of the technique called generator rescheduling is adopted in present work to manage transmission congestion.
Present work is concentrated on generator rescheduling method for transmission congestion management. Firstly generator sensitivity factor (GSF)’s calculated and optimal selection of generators are done based on GSF values considering non-uniform and large magnitude of sensitivities values. The major contribution is presented secondly where exploration of recently developed meta heuristic algorithm known as Firefly Algorithm (FA) has been introduced in generator rescheduling technique for congestion management [16]-[17].
Major changes are done in power utility system after introduction of power system restructuring. Restructured electricity market and various congestion management techniques are discussed in [1-3]. Managing transmission congestion in a pool/ bilateral/ multilateral market with introduction of willingness to pay priority to avoid curtailment is presented in [4]. The reference [5] presents an approach for congestion management based on voltage stability. In [6], real and reactive power has been rescheduled based on the zonal congestion management technique. The generators lying in most sensitive zones are identified optimally to reschedule their outputs. Particle swarm optimization based generator rescheduling is presented in [7] where optimal selection of generators is done based on generator sensitivity. Binding
978-1-4673-6817-9/15/$31.00 ©2015 IEEE
Subhasish Deb Assistant Professor Electrical Engineering Dept. Mizoram University Aizawl-796004
[email protected]
II.
FIREFLY ALGORITHM
Firefly Algorithm is a metaheuristic algorithm which was introduced by Yang [16]-[17]. It was based on the following idealized behavior of the flashing characteristics of fireflies: ͌ Regardless of the sex, one firefly is attracted to other fireflies. ͌ Attractiveness is proportional to their brightness, the less bright firefly will move towards the brighter one. Both firefly decreases their brightness as their distance increases. It moves randomly, if no one is brighter than a particular firefly;
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The light intensity or brightness of a firefly is affected or determined by the landscape of the objective function to be optimized.
The detail derivations for GSF are discussed in [7].
wPij
GSFg
For a maximization problem, the brightness can simply be proportional to the objective function. The brightness can be defined in a similar way to the fitness function in genetic algorithms or the bacterial foraging algorithm (BFA).
wG i
.
wPij wG j wG i . wPGg wG j wPGg
(4)
Where,
wPij
D ij
ViV jYij sin(T ij G j G i )
wG i
(5)
Firefly Algorithm Objective function f(x), x = (x1, . . ., xd)T Initialize a population of fireflies xi(i = 1, 2, . . ., n) Define light absorption coefficient _ while (t < MaxGeneration) for i = 1: n all n fireflies for j = 1: i all n fireflies Brightness Ii at xi is determined by f(xi) if (Ij > Ii) Move firefly i towards j in all d dimensions end if Attractiveness changes with distance r via exp [-Ȗr2] Update brightness and evaluate new solutions end for j end for i Rank the fireflies and find the current best end while Post process results and visualization
x
x E0e
J rij2
t i
t j
( x x ) DH
t i
Ng
Minimize¦ C g ( 'Pg )'Pg
The solution of above equation i.e., rescheduling amount at each GENCO are be obtained so that the following constraints are satisfied. Subject to: GSF Constraint:
(1)
Ng
¦ ((GSF )'P ) F g
g
0
k
d Fkmax
k 1, 2,...........n1
(8)
g 1
Ramp Limit: Pg Pgmin
'Pgmin d 'Pg d 'Pgmax g
1, 2,......N g
Pgmax Pg
(9)
Power Limit of Generator:
Pgmin d Pg 'Pg d Pgmax
g
1, 2,......N g (10)
Power Balance:
(2)
Ng
where Vi and įi are the voltage magnitude and angle at bus-i. Yij and Ϊij are the magnitude and angle of ijth element of YBus matrix. Generator Sensitivity factor (GSF) defines a change in real power flow over a transmission line k connected between bus i and bus j to the change in generator (g) real power supply [7]. Mathematically, (3) GSF ( 'P / 'P ) ij
(7)
g 1
The real power flow Pij in a line-k connected between bus-i and bus-j can be written as:
g
PROBLEM FORMULATION
Total rescheduling amount required by the selected generator is obtained by:
GENERATOR SENSITIVITY FACTOR
Pij | Vi || V j || Yij | cos(Tij G i G j ) Vi 2Yij cos Tij
wG i
IV.
Where ȕ0 is the attractiveness at r = 0, the second term is due to the attraction and third term is randomization with the vector of random variables İi being drawn from a Gaussian distribution. The distance between any two fireflies i and j at xi and xj can be the Cartesian distance rij= || xi - xj ||. For most cases, in our implementation, we can take ȕ0 Į[0,1], DQGȖ III.
(6)
wPij
Generators which are having strongest and non-uniform flow of sensitivity indexes are selected here for rescheduling purposes.
The firefly’s movement i is attracted to another more attractive (brighter) firefly j is determined by t i
ViV jYij sin(T ij G j G i )
wG j
Fig. 1. Pseudo code of firefly algorithm
t 1 i
wPij
E ij
¦ 'P
g
0
(11)
g 1
Where, Cg: Cost of the active power rescheduling corresponding to the incremental/decremented price bids submitted by generator-g participating in congestion management. These are the prices at which the generators are willing to adjust their real power outputs.
Gg
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management problem. Out of remaining generators, G2-G3 and G8-G10 are indicating non-uniform flow of GSF values and also strong impacts towards congested line power flow. So these five generators will participate in congestion management problem. Generator number 1 i.e. G1 is a slack bus generator. This G1 is rescheduled at the end of optimization process to minimize system active power loss.
¨Pg: Active power adjustment of the generator-g. min
Pg
max
& Pg
min
: Real power generation limits of generator- g.
max
: Minimum and maximum limits of the ǻPg , ǻPg change in generator active power output respectively. Fk0: Power flow in the transmission line k, caused by all contracts requesting the transmission service.
V.
Rescheduling Amount (p.u)
Fkmax : MVA flow limit of kth transmission line connected between bus-i and bus-j. RESULTS AND DISCUSSIONS
The present work focused on application of Firefly algorithm (FA) to the congestion management problem. Rescheduling of generator is done by firefly algorithm and tested on IEEE 39 bus New England test system. The data’s for 39 bus system is taken from [18]. The result of this firefly based solution is compared with results of [7] and [8]. Base case solution shows that transmission line connects between the buses 14 and 34 (L14–34), is loaded to 262.3MVA (flow limit 600MVA). Now force outage of line L14–34 creates overload to the line L15–16, the flow being 628.6MVA from bus 16 to bus 15 (flow limit is 500MVA). Using load flow analysis, this overload problem is being found.
1 0.9 0.7 0.5 0.3 0.1 -0.1 -0.3 -0.5 -0.7 -0.9 -1.1 -1.3 -1.5 -1.7 -1.9 -2.1 -2.3 -2.5
Gen1
Gen 2
Gen 3
Gen 8
Gen 9
Gen 10
Participating Generators Fig. 3. Comparison results of various methods
Figure 3 shows the comparison results of various techniques. In [7], all the generators are rescheduled whereas in [8] only six number of generators are rescheduled. So only for comparison purpose rescheduling amount of six generators are being shown. FA based solution shows generator 1 rescheduled its output large in quantity, so active power loss will be less by proposed technique.
Generator rescheduling cost depends on incremental/ decremental price bids submitted by GENCOS. Moreover, the proposed FA based solution compared with following reported results. M 1): Result reported in [7].
TABLE I
M 2): Result reported in [8].
GENERATOR RESCHEDULING USING FA
M 3): Proposed FA based solution. Generator Sensitivity Factor (GSF)
Result Reported in [7] Result Reported in [8] Proposed FA based result
0.7 0.6 0.5 0.4
Amount of Rescheduling (MW)
Gen Number
Result Reported in [8]
Result Reported in [7]
Proposed FA based solution
1
-99.59
-149.1
-228.53
2
98.75
65.6
79.36
0.3 0.2
3
-159.64
-129
-8.06
0.1
4
12.34
Not Participated
Not Participated
0 -0.1
5
24.69
Not Participated
Not Participated
-0.2 -0.3
6
24.69
Not Participated
Not Participated
-0.4 -0.5
7
12.34
Not Participated
Not Participated
8
24.69
75.4
52.2
9
12.34
52.1
13.0
10
49.38
83.0
92.1
Net Amount (MW)
518.45
554.2
473.25
-0.6 -0.7
G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G 9 G 10
Generator Buses
Fig. 2. Generator sensitivity factor for 39 Bus New England Test System
Figure 2 indicates the generator sensitivity factor (GSF). Selection of generators is fully based on GSF values. Few generators like G4-G7 shows uniform flow of sensitivities values. So these generators will not participate in congestion
Table 1 shows tabulated data’s of various techniques. It is noticed that FA based solution gives less amount of net
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rescheduling (MW) as compared with other techniques. Reduction of rescheduling amount reduces rescheduling cost also.
lines like L12-13, L13-14 and L25-8. Though these lines power flow are within limits but their critical conditions cannot be ignored. Figure 4 shows the comparison of critical lines loading factor before and after rescheduling. Line number 26 i.e.; L15-16 is congested line. Prior to rescheduling line number 26 shows huge loading factor and it reduces below marginal after rescheduling. Few lines show their increment in loading factor but without harming the system.
Table 2 indicates most important parameters in the system i.e.; System active power loss and system minimum voltage. The effect of rescheduling changes these parameters. TABLE II
EFFECT ON SOME IMPORTANT PARAMETERS
Ploss (MW) Vmin (p.u.)
Amount of Rescheduling (MW)
Before Resched uling
Result Reported in [8]
Result Reported in [7]
58.0
57.31
59.9 0.934
0.932
Proposed FA based solution
1.4 1.3
55.3
0.945
0.948
The comparative results of active power loss and system minimum voltage are tabulated in table 2. It is been clearly seen that FA based solution shows minimum real power loss and better voltage profile than other reported methods
Line Number
1.25
L15-16
[7]
solution
1.02
0.98
0.99
0.43 0.57 0.52 0.49 0.75 0.72 0.41 1.25 0.51
0.43 0.57 0.52 0.54 0.76 0.89 0.54 0.99 0.51
519.10 683.63 575.51 539.46 825.85 431.99 250.68 628.60 614.72
519.90 683.80 575.50 591.50 838.50 534.30 322.20 499.40 614.80
0.8 0.7 0.6 0.5 0.4 0.3
0
0
46
43
42
41
40
32
30
26
17
0
Line Number Fig. 4. Line loading comparison before and after Rescheduling
Table 5 shows the rescheduling cost in $/Day. Generators are rescheduled by minimizing objective function for congestion management. TABLE V
RESCHEDULING COST USING FA
TABLE IV EFFECT ON SOME CRITICAL LINES DUE TO RESCHEDULING Line Overload factor Actual Flow (MVA) Line Lines / No. flow Transfo Before After Before After limit r--mers (MVA) connect ed between buses
36 43 42 41 40 32 30 26 17
1 0.9
0.1
Table 3 shows the overload factor reported in various methods. Thermal limit of congested line i.e.; L15-16 is 500 MVA. Prior to rescheduling line (L15-16) is too overloaded, which reduces further below its thermal limit by applying various rescheduling methods.
L39-5 L22-6 L23-7 L25-8 L29-9 L12-13 L13-14 L15-16 L21-22
1.1
0.2
TABLE III OVERLOAD FACTOR OF CONGESTED LINE Amount of Rescheduling (MW) Before Result Result Proposed Rescheduling Reported in Reported in FA based [8]
Before Rescheduling After Rescheduling
1.2
Line Loading (p.u)
System Paramet ers
1200 1200 1100 1100 1100 600 600 500 1200
Control Variables
FA based solution
PG1 (MW)
3.2673
PG2 (MW)
10.7936
PG3 (MW)
6.4194
PG8 (MW)
5.922
PG9 (MW)
8.43
PG10 (MW)
3.421
Rescheduling Cost ($/Day)
84.02
Figure 5 shows the convergence characteristic of Firefly Algorithm (FA). With the increase of number of iteration, system cost is becoming minimum and it converges fully after 100 iteration.
From table 4, it is seen that congested line is no more overloaded but it’s effect can be observed clearly in some other
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[12] Ashwani Kumar, Charan Sekhar, “Congestion management with FACTS devices in deregulated electricity market ensuring loadability limit”, International jurnal of eletrical power & energy systems, 46, 258-273, 2013. [13] Ch Venkaiah, D.M. Vinod Kumar, “Fuzzy adaptive bacterial foraging congestion management using sensitivity based optimal active power rescheduling of generators”, Applied Soft Computing, 11, 4921–4930, 2011. [14] Subhasish Deb, Sadhan Gope, Arup Kumar Goswami, “Congestion management considering wind energy sources using evolutionary algorithm”, Electric Power Components and Systems, 43(7), 723-732, 2015. [15] A.K. Singh, S.K. Parida,”Congestion management with distributed generation and its impact on electricity market”, International jurnal of eletrical power & energy systems, 48, 39-47, 2013. [16] Xin-She-Yang, Seyyed Soheil Sadat Hosseini, Amir Hossein Gandomi,”Firefly Algorithm for solving non-convex economic dispatch problem with valve loading effect”, Applied soft computing 12, 11801186, 2012. [17] Xin-She-Yang, “Multiobjective firefly algorithm for continuous optimization”, engineering with computers, 29, 175-184, 2013. [18] K. R. Padiyar, Power System Dynamics: Stability and Control. NewYork: Wiley, 1996, p. 601.
Fig. 5. Convergence characteristic of FA
VI. CONCLUSION Congestion management has become an important issue in modern day of power system. Generator rescheduling technique is one of the old methods applied by SO in various condition. Here generator sensitivity factor is used to identify the participating generators. Moreover, FA based solutions explores its involvement in rescheduling methods. FA is one of the new metaheuristic algorithm applied here for congestion management problem. Studies revealed that FA based solution shows better results as compared with results of previous methods. REFERENCES [1]
Mohammad Shahidehpour, M. Alomoush, “Restructured Electric Power System”, Marcel Dekkar, 2001. [2] M Shahidehpour, H Yamin, Z Li, “Market Operations in electric Power System”, A John Wiley and Sons Inc, 2002. [3] K. Bhattacharya, M.H.J. Bollen, & J.E. Daalder, “Operation of Restructured Power Systems” Kluwer Academic Publishers, 2001. [4] Fang RS, David AK. “Transmission congestion management in an electricity market”., IEEE Trans Power Systems, 14(3):877–83, 1999. [5] A. J. Conejo, F. Milano, and R. G. Bertrand, “Congestion management ensuring voltage stability,” IEEE Trans. Power Syst., vol. 21, no. 1, pp. 357–364, 2006. [6] A. Kumar, S. C. Srivastava, and S. N. Singh, “A zonal congestion management approach using real and reactive power rescheduling,,” IEEE Trans. Power Syst., vol. 19, no. 1, pp. 554–562, Feb. 2004 [7] S. Dutta, S.P. Singh, “Optimal rescheduling of generators for congestion management based on particle swarm optimization”, IEEE Transactions on Power Systems 23 (4), 1560–1569, 2008. [8] G. Yesuratnam and D. Thukaram, “Congestion management in open access based on relative electrical distances using voltage stability criteria,” Elect. Power Syst. Res., vol. 77, pp. 1608–1618, 2007. [9] Kanwardeep Singh, N P Padhy, J Sharma, “Congestion Management considering hydro-thermal combined operation in a pool based electricity market”, International jurnal of eletrical power & energy systems, 33, 1513-1519, 2011. [10] A Kumar, Charan Sekhar, “Comparison of Sen Transformer and UPFC for congestion management in hybrid electricity market”, International jurnal of eletrical power & energy systems, 47, 295-304, 2013. [11] Masoud Esmaili,Heidar Ali Shayanfar,”Locating series FACTS devices for multi objective congestion management improving voltage and transient stability”, European journal of operational research, 236, 763773, 2014.
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