2013 Annual IEEE India Conference (INDICON)
Generator Rescheduling for Congestion Management with Incorporation of Wind Farm using Artificial Bee Colony Algorithm Subhasish Deb
Sadhan Gope
Arup Kumar Goswami
Department of Electrical Engineering National Institute of Technology, Silchar Silchar, India-788010 Email:
[email protected]
Department of Electrical Engineering Mizoram University Aizawl, India-796004 Email:
[email protected]
Department of Electrical Engineering National Institute of Technology, Silchar Silchar, India-788010 Email:
[email protected]
Abstract— Power system congestion is a major problem for independent system operator (ISO) in a deregulated environment as it violates system security and cost. So it is an important task for ISO to maintain congestion free power system. In this paper generator rescheduling technique has been adopted with incorporation of wind farm in the system. Present work is three folded. Firstly location of wind farm is selected based upon power transfer distribution factor (PTDF). Secondly generator sensitivity factor (GSF) has been determined to reduce number of participating generator in congestion management. Thirdly selected generators have been rescheduled using Artificial Bee Colony (ABC) optimization techniques to mitigate transmission congestion. The proposed method is applied on IEEE 39 bus New England test system. Keywords— Power transfer distribution factor, Generator sensitivity factor, fixed speed wind farm, generator rescheduling, artificial bee colony, transmission congestion management.
I.
INTRODUCTION
In a deregulated power system, proper planning of electric power system is an important task as the growth of electric power demand is increasing day by day with diminutive increment of power generation. As a result some transmission lines may reach beyond to their thermal limit and congestion occurs. As soon as congestion occur, in some area prices will increase and in other areas decrease. So, it is an important task for ISO to maintain security of power system fairly for the continuity of power supply to the consumers. In recent years, wind energy has become an increasingly important source of electric power system [1]. For this reason, it is necessary to incorporate wind farm in power system analysis and optimization [2]. To relieve transmission congestion ISO employs generator rescheduling techniques along with incorporation of wind farm in the system. After re-dispatch, the network is operated with no violation or congestion. Several works regarding transmission congestion management have been reported in the literature [3]. Prederegulated and post deregulated structures of electricity market have been given in [4]-[5]. A cluster based congestion management method has been proposed in [6] which identify the group of system users according to their impact on
transmission constraint of interest. These clusters are type 1; type 2 etc. based on transmission distribution factor. A zone based congestion management has been reported in [7]-[8]. Zones are identified based on active power transmission congestion distribution factor (PTCDF) and Reactive power transmission congestion distribution factor (QTCDF). In [9] rescheduling of generator real power based on relative electrical distance (RED) for overload alleviation has been introduced. All the generators having different price bids must reschedule their outputs to get minimum rescheduling cost. However this technique shows system stability by minimizing system losses and maintains better voltage profile. Generator rescheduling based on fuzzy adaptive bacterial forging has been reported in [10]. In [11] a technique for reducing the number of participating generators and optimum rescheduling of their outputs for congestion management using Particle Swarm Optimization (PSO) has been reported. Generator real power rescheduling based on PSO [12] and artificial bee colony (ABC) optimization [13] for mitigation of transmission congestion using generator sensitivity factor has been reported. Also system active power loss and minimum voltage reported in [12]-[13]. In this paper, location for wind farm has been chosen based on power transfer distribution factor (PTDF). Incorporation of wind farm in most congested bus not only reduces system violation, it also reduces system active power loss and improves minimum voltage profile. Next generator sensitivity factor has been identified to select particular generators for rescheduling and results are compared with result reported in [13]. Generators which are having less impact and uniform flow of sensitivity indexes are not considered here for rescheduling. Incorporation of wind farm drastically reduces number of participating generator in congestion management. II.
WIND POWER FLOW MODEL
A wind farm model has been considered with a fixed speed wind turbine generating unit (FSWTGU) where FSWTGU system always draws reactive power from the grid. To compensate the reactive power consumption capacitors are connected. PQ model of wind farm which is the steady state model of induction generator is shown in Fig. 1.
The work was supported by SERB project no: SR/FTP/ETA-12/2011.
978-1-4799-2275-8/13/$31.00 ©2013 IEEE
Fig.1. Induction machine steady- state model The conservation of complex power theorem or Boucherot’s theorem is applied in this model and expression for reactive power consumed by the machine can be written as [2].
Q =V2
(V2 +2RP) −4P2(R2 + X2) Xc − Xm V +2RP +X 2 2 2 −X XC Xm 2(R + X ) 2(R2 + X2)
Q V2
Xc − Xm X 2 + P XC X m V 2
(1)
(2)
Where P is the active power (positive when injected into the grid), V is the rated voltage, X is the sum of the stator and rotor leakage reactance, Xc is the reactance of the capacitors bank, and R is the sum of the stator and rotor resistances. In [2], active power calculation for the FSWTGU can be expressed as P=
1 ρ AU 3CP 2
(3)
Where A is the rotor area, ρ is the density of air, U is the wind speed and Cp is the power coefficient. III.
ARTIFICIAL BEE COLONY ALGORITHM Artificial Bee Colony (ABC) optimization algorithm is a population-based swarm intelligence algorithm that was originally proposed by Karaboga, Erciyes University of Turkey in 2005 [14]-[18]. It simulates the foraging behaviour that a swarm of bees perform. In this algorithm there are three groups of bees, the employed bees (bees that determines the food source (possible solutions) from a prespecified set of food sources and share this information (waggle dance) with the other bees in the hive), the onlookers bees (gets the information of food sources from the employed bees in the hive and select one of the food source to gathers the nectar) and the scout bees (responsible for finding new food sources). The position of a food source represents a possible solution to the optimization problem and the nectar amount of a food source corresponds to the quality (fitness) of the associated solution. In the algorithm, the first half of the colony consists of employed artificial bees and the second half constitutes the onlookers. The number of the employed bees or the onlooker bees is equal to the number of solutions in the population. At the first step, the ABC generates a randomly distributed initial population of NP solutions (food source positions), where NP denotes the size of population. Each
solution xi where i =1, 2... NP is a D-dimensional vector, where D is the number of optimization parameters. After initialization, the population of the positions (solutions) is subjected to repeated cycles, C =1, 2... MCN of the search processes of the employed bees, the onlooker bees and scout bees. An employed bee produces a modification on the position (solution) in her memory depending on the local information (visual information) and tests the nectar amount (fitness value) of the new source (new solution). Provided that the nectar amount of the new one is higher than that of the previous one, the bee memorizes the new position and forgets the old one. Otherwise she keeps the position of the previous one in her memory. After all employed bees complete the search process; they share the nectar information of the food sources and their position information with the onlooker bees on the dance area. An onlooker bee evaluates the nectar information taken from all employed bees and chooses a food source with a probability related to its nectar amount. As in the case of the employed bee, she produces a modification on the position in her memory and checks the nectar amount of the candidate source. Providing that its nectar is higher than that of the previous one, the bee memorizes the new position and forgets the old one. An artificial onlooker bee chooses a food source depending on the probability value associated with that food source pi, calculated as (1):
pi =
fiti NP
∑ fit
(4)
i
i =1
Where fiti is the fitness value of the solution i which is proportional to the nectar amount of the food source in the position i and NP is the number of food sources which is equal to the number of employed bees. In order to produce a candidate food position from the old one in memory, the ABC uses the following (4):
vij = xij + φij ( xij − xkj )
(5)
Where k ∈{1, 2… NP} and j∈{1, 2, …, D} are randomly chosen indexes. Moreover, k ≠ i. Øij is a random number between [-1, 1]. It controls the production of neighbour food sources around xij and represents the comparison of two food positions visible to a bee. This can be seen from (2), as the difference between the parameters of the xij and xkj decreases, the perturbation on the position xij decreases, too. Thus, as the search approaches to the optimum solution in the search space, the step length is adaptively reduced. After each candidate source position is produced and evaluated by the artificial bee, its performance is compared with that of its old one. If the new food source has equal or better quality than the old source, the old one is replaced by the new one. Otherwise, the old one is retained. If a position cannot be improved further through a predetermined named “limit”, then that food source is assumed to be abandoned. The corresponding employed bee becomes a scout. The abandoned position will be replaced with a new food source found by the scout. Assume that the abandoned source xi, then the scout discovers a new food source to be replaced with xi. This operation can be defined as in (3):
N
j
j min
xi = x
j max
+ rand ( x
j min
−x
)
(6)
where xmaxj and xminj are upper and lower bounds of parameter j, respectively. IV.
MATHEMATICAL FORMULATION
The real power flow Pij in a line-k connected between bus-i and bus-j can be written as: A. Pij =| Vi || V j || Yij | cos(θ ij − δ i + δ j ) − Vi 2Yij cos θ ij
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: Ng
∑((GSF )ΔP ) + F g
g
k
0
≤ Fkmax
(8 )
Δ Pn
Ramp Limit: Pg − Pgmin = Δ Pgmin ≤ Δ Pg ≤ Δ Pgmax = Pgmax − Pg
(9) (1 0 )
(1 1)
= (Δ P / Δ P ) ij Gg
(1 2 )
The detail derivations for GSF are discussed in [12], [13].
G S Fg =
∂ Pij ∂ δ j ∂δ i + . ∂ PG g ∂ δ j ∂ PG g
(1 3)
= V iV j Yij sin(θ ij + δ j − δ i )
(14)
∂ Pij ∂δ i
.
g = 1, 2,...... N g
(19)
Power Balance: Ng
∑ ΔP
= 0
(20)
Where, Cg: Cost of the active power rescheduling corresponding to the incremental/decremental 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. ∆Pg: Active power adjustment of the generator-g.
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 [12],[13]. Mathematically, g
Pgmin ≤ Pg + ΔPg ≤ Pgmax
g =1
B. Generator sensitivity Factor (GSF)
G SF
(18)
Power Limit of Generator:
g
The detail derivations for PTDF are discussed in [8]. PTDFnk = a ij m in + bij + m jn Where a ij = V iV j Y ij s in (θ ij + δ j − δ i ) b ij = − V iV j Y ij sin (θ ij + δ j − δ i )
(17)
g = 1, 2,...... N g
Active power transfer distribution factor for a congested line k can be defined as change in active power in line k connected between bus i and bus j to the change in nth bus power [8]. Mathematically, Δ Pij
k = 1,2,...........n1
g =1
A. Power Transfer Distribution Factor (PTDF)
P T D F nk =
(1 6 )
g =1
(7)
where Vi and δi are the voltage magnitude and angle at bus-i. Yij and Өij are the magnitude and angle of ijth element of YBus matrix.
g
M in im iz e ∑ C g ( Δ Pg ) Δ Pg
Pgmin and Pgmax: Real power generation limits of generator-g.
ΔPgmin, ΔPgmax : Minimum and maximum limits of the change in generator active power output respectively. Fk0: Power flow in the transmission line k, caused by all contracts requesting the transmission service. Fkmax : MVA flow limit of kth transmission line connected between bus-i and bus-j.
Where,
α ij =
β ij =
∂ Pij ∂δ i ∂Pij
∂δ j
= −ViV jYij sin(θ ij + δ j − δ i ) = −
∂Pij ∂δ i
(15)
Generators which are having strongest and non-uniform flow of sensitivity indexes are selected here for rescheduling purposes. C. Problem formulation Total rescheduling amount required by the selected generator is obtained by:
V.
SYSTEM STUDIES
The proposed concept Generator rescheduling for congestion management using Particle Swarm optimization Technique has been illustrated on IEEE 39 bus New England Test System [19]. 39 bus systems is a simplified representation of 345 KV transmission system of New England region having 10 generators and 29 load buses.
TABLE II
GSFS VALUES AT DIFFERENT WIND POWER GSFs for 15-16 congested line Gen. No. With Wind With Wind With Wind farm farm Farm (30 MW) (50 MW) (100 MW) 1 2 3 4 5 6 7 8 9 10
0.0000 -0.5552 -0.0812 -0.4188 -0.4107 -0.4145 -0.4120 -0.5527 -0.5041 -0.5908
Fig. 2. IEEE-39 bus New England Test System
0.0000 -0.5541 -0.0807 -0.4179 -0.4199 -0.4136 -0.4112 -0.5517 -0.5032 -0.5897
0.0000 -0.5515 -0.0796 -0.4159 -0.4179 -0.4116 -0.4192 -0.5493 -0.5010 -0.5871
TABLE III POWER FLOW THROUGH CONGESTED LINE 15-16 BEFORE RESCHEDULING
The ABC parameter selected for the above problem is as follows: Colony Size: 40 Maximum Cycle Number (MCN): 200. Employed Bees: 20. Onlooker Bees: 20. Number of food Sources: 20. Value of Limit: 100. All the parameters regarding induction generator for wind farm are taken from [2]. TABLE I PTDFS VALUES AT DIFFERENT WIND POWER FOR SELECTED BUSES PTDFs Bus No.
Without Wind farm
With Wind farm (30 MW)
With Wind farm (50 MW)
With Wind farm (100 MW)
1 8 9 10 12 14 16 19 25 27 34 38
0.0000 -0.0207 0.0281 -0.0411 -0.0414 -0.2567 -0.0057 -0.0338 -0.0225 0.0476 0.4175 0.0194
0.0000 -0.0200 0.0287 -0.0386 -0.0386 -0.2495 -0.0021 -0.0294 -0.0211 0.0510 0.4225 0.0236
0.0000 -0.0198 0.0289 -0.0384 -0.0384 -0.2493 -0.0020 -0.0293 -0.0210 0.0511 0.4227 0.0238
0.0000 -0.0196 0.0291 -0.0381 -0.0381 -0.2490 -0.0018 -0.0290 -0.0207 0.0514 0.4230 0.0241
PTDFs are calculated for a line 14-34, which is considered as congested line. It is seen that bus 14 and bus 34 have strong values of PTDFs. Location of wind farm has been decided optimally in bus 14 as it has strong value of PTDF. Incorporation of wind farm at different output power results in variation of PTDFs values which are given in Table I. It is seen that incorporation of wind farm at different power levels results in variation of bus distribution factor. Now as a consequence of outage of congested line 14-34 results in violation of line 15-16 or line 15-16 said to be congested. Values of generator sensitivity factor (GSF) have been given in Table II for different wind power. The power flow through line 15-26 at different wind power is shown in Table III.
Line Power
With Wind farm (30 MW)
With Wind farm (50 MW)
With Wind Farm (100 MW)
L15-16 (MVA)
604
588
548
Considering wind power of 30MW, Gen No. 2, 8, Gen No. 4, 5 and Gen No. 6, 7 have uniform flow of sensitivity indexes. Only Gen No. 3, 9 and 10 have non-uniform flow of sensitivity values. So these three generators are rescheduled to minimize transmission cost. TABLE IV GENERATOR RESCHEDULING USING ABC Gen No.
Amount of Generator Rescheduling (MW) Result Result reported in [13] By proposed method reported in with 30MW wind farm [9]
1 2
-99.59 98.75
-131.0 63.2
-138.72 Not Rescheduled
3 4 5 6 7
-159.64 12.34 24.69 24.69 12.34
-132.0 Not Rescheduled Not Rescheduled Not Rescheduled Not Rescheduled
-48.54 Not Rescheduled Not Rescheduled Not Rescheduled Not Rescheduled
8 9
24.69 12.34
72.2 49.1
Not Rescheduled 6.96
10 Net (MW)
49.38
78.8
181.31
518.45
526.3
375.53
It is seen that incorporation of wind farm drastically reduces number of participating generator for congestion management as compared to [11]-[13]. Generator 1 is a slack bus which is rescheduled at the end of optimization. In Table IV it is observed that participation of 30 MW wind farm and sensitivity based optimal selection of generators not only reduces the number of participating generator in congestion management, it also reduces the net amount of generator rescheduling.
TABLE VII CONDITION OF CRITICAL LINES BEFORE AND AFTER RESCHEDULING USING ABC WITH PRESENCE OF WIND FARM
Result of [9] Result of [13] Result of proposed work
Gen 1
Gen 3 Generator Buses
Gen 10
Fig. 3. Comparison results of 39 bus New England System.
Result of proposed work with presence of 30MW wind farm has been compared with result reported in [9] and [13] which is shown in fig. 3. Generator 1 is a slack generator which is rescheduled to reduce system active power loss. Both The generators 1 and 10 rescheduled with huge amount as compared with result reported in [9] and [13] and it shows their strong participation in congestion management. In this paper, generators are re-dispatching by minimizing objective function i.e. cost of rescheduling ($/MW-Day) which is shown in Table VI. As compared with results reported in [12] & [13], this method shows significant reductions of generator re-dispatch cost with less number of participating generators. TABLE V SYSTEM ACTIVE POWER LOSS AND MINIMUM VOLTAGE BEFORE & AFTER RESCHEDULING Parame ters
P loss (MW) V min (p. u.)
With out Wind farm
Before Rescheduling With wind With wind farm farm (30MW) (100MW
After Rescheduling Result Proposed reporte method with d in [9] 30MW wind farm
59.9
58.8
58.7
58.0
57.9
0.935
0.9464
0.9461
0.932
0.9518
Lines / Transfo rmers connect ed between buses
Lin e No.
Before Rescheduling with 30 MW wind farm
L39-5
36
517.33
518.63
517.38
1200
L22-6
43
680.83
682.89
680.91
1200
L23-7
42
574.35
575.21
574.38
1100
L25-8
41
540.23
611.84
539.73
1100
L29-9
40
826.18
874.12
832.89
1100
L12-13
32
416.26
536.52
524.33
600
Actual Flow (MVA) Result After reported in Reschedulin[13] after g with 30 MW reschedulewind farm ng with using ABC ABC
Line flow limit (MVA)
L13-14
30
217.39
321.5
292.63
600
L15-16
26
604.06
499.5
499.9
500
L21-22
17
612.78
614.21
612.83
1200
Table VII shows power flow of some critical lines before and after rescheduling using ABC considering with and without presence of wind farm. L15-16 is the most violated line but in presence of wind farm power flow reduces below normal power flow limit. But some other lines shows increment in their line flows after rescheduling. Line no. 26 is the congested line, shows decrement in line power flow below marginal whereas , line no. 41, 40, 32 and 30 shows increment in their line flow after rescheduling. But line flow of all the critical lines reduces to the normal power flow limit. Result of proposed method is compared with result reported in [13]. It is observed that presence of wind farm not only reduces congested line power flow, it also reduces power flow of other critical lines and result is better than reported result of [13]. From the convergence characteristic it has been seen that with the increase of number of iteration system cost becomes minimum. Appropriate selection of ABC parameter shows the perfect convergence characteristic. 90 88
In Table V it is observed that proposed method with 30 MW wind farm shows minimum active power loss as compared with result reported in [9] considering with and without wind farm before and after rescheduling. Moreover improvement in system minimum voltage indicates system stability. TABLE VI RESCHEDULING COST OF VARIOUS METHODS
Rescheduling Cost ($/MW-Day)
Result reported in [12]
Result reported in [13]
Proposed method with 30MW wind farm
92.817
92.039
64.2261
RESCHEDULING COST ($/MW-DAY)
Amount of Rescheduling (p.u.)
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 -1.6 -1.8 -2
86 84 82 80 78 76 74 72 70 68 66 64 62 60
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 ITERATION
Fig. 4. Convergence Characteristic of ABC.
VI.
CONCLUSION
In this paper, effect of presence of wind farm in congestion management has been shown. Incorporation of wind farm along with GSF based generator selection drastically reduces number of participating generator for congestion management. All the selected generators have been rescheduled using ABC. ABC based solution gives better result and solution shows system stability with less re-dispatch cost and less system active power loss. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]
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