Optimization of Pool Contracts Using Intelligent Techniques and Calculation of Transmission Prices for Bilateral Contracts S K Gupta* and H D Sharma**
The paper analyzes the approaches for transmission cost allocation and centralized pool-based electricity price calculation. It is required to identify the contribution of individual generators and loads to the line flows. A study on IEEE 26 bus system has been presented in this research work for calculating transmission prices for bilateral contracts between GENCOs and DISCOs at different buses. Intelligent techniques have been applied to minimize pool prices and optimize pool generation by minimizing transmission losses. The intelligent techniques used are Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) and compared with conventional ELD method. MW-mile method is used to calculate the transmission pricing. The results of these techniques are compared, which show better performance of ELD+GA technique over ELD+PSO and ELD techniques. Keywords: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Pool contracts, Transmission pricing, DISCO Participation Matrix (DPM), Independent System Operator (ISO)
Introduction The electrical transmission systems are interconnected to each other and are supposed to provide maximum reliability and least production cost. In Economic Load Dispatch (ELD), the total operating cost of the system is to be minimized which means that the fuel prices of generating units should be minimized. Transmission losses cost millions of rupees as these are treated as additional load to the system. Therefore, transmission losses should also be minimized for optimal load dispatch. The entire electricity market is characterized into Generation Companies (GENCOs), Transmission Companies (TRANSCOs) and Distribution Companies (DISCOs). The GENCOs try to minimize the production cost, TRANSCOs reduce the transmission losses and DISCOs negotiate with the GENCOs for lower prices. ISO tries to minimize the prices of pool generation. The power industry in the world is undergoing a profound restructuring process (Lai, 2001). The main goal is xxxxxxxxxxxxxxxxxx, Electrical Engineering Department, Deenbandhu Chhotu Ram University of Science Author pls * and Technology, Murthal (Sonepat) Haryana, India. E-mail:
[email protected] c h k d e s i g n s . * * xxxxxxxxxxxxxxxxxx, Electrical Engineering Department, Deenbandhu Chhotu Ram University of Science and Technology, Murthal (Sonepat) Haryana, India. E-mail: xxxxxxxxxxxx and mail id are missing © 2016 IUP. All Rights Reserved.using Intelligent Techniques Optimization of Pool Contracts and Calculation of Transmission Prices for Bilateral Contracts
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to introduce competition in the electric market so as to serve higher quality of power to the consumers at the minimum prices. Therefore, the pool market model is introduced to perform price-based dispatch of power plants and provide a platform for setting the system prices and handling electricity trades (Saeh and Khairuddin, xxxx). The model of bilateral contracts is that the buyers and sellers trade quantity of power by entering into the transaction, and the prices for the use of transmission network are calculated according to the flow of power in the transmission line (Rau, 1989). A number of bilateral contracts can enter in the transaction but not all the generation units have bilateral contracts with the load buses, and similarly not all the load buses have bilateral contracts with the generators. The pricing of the transmission system is calculated for each year of the transaction period using the replacement cost, average service life and depreciation reserve of line capital investment (Happ, 1994). Bilateral contracts are individual negotiation between a buyer and a seller, as defined by Galiana and Phelan (2000). ELD problems may not have fixed cost functions rather it changes with the coal quality. Therefore, curve fitting technique is used to obtain the coefficients of the cost curve and the results are compared with Artificial Neural Network (ANN) technique (Gupta and Chawla, 2015). In this paper, the proposed techniques are implemented on IEEE 26 bus test system but the techniques proposed are general and can be applied to any system. The method of transmission pricing used in this paper is MW-mile method. The basic concept of MWmile method is that the power flow on each transmission line in MW due to a transaction is calculated by multiplying the power flow and distance of the line. How much each transaction uses the grid is the total of all the additional power flow in the transmission system. The price of the transmission system used by a transaction is the multiplication of total power flow of the transmission to the cost/MW-mile (Rau, 1989). GENCOs input the power as per the contract. There is no differentiation of power being input by different GENCOs. Therefore, no need of tracking of power being input. It is important to ensure that parties do not exercise monopoly power and price transmission service according to consistent rules or principle (Galiana and Phelan, 2000). The pricing of transmission with the bilateral pool contracts is calculated by convention method. Intelligent techniques are used to optimize the prices for pool contracts. The results are compared with the pricing calculated by intelligent optimization techniques, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Author pls chk and confirm all equations and symbols
Objective function
C PD PL in Pl
...(1)
where is Lagrange multiplier, C is the net prices for pool generation, PD is the total power demand, PL is the total power losses and n are the number of generating units. GENCOs price function is represented by the following equation:
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The IUP Journal of Electrical & Electronics Engineering, Vol. IX, No. 3, 2016
Author pls chk: year is missing
Ci ai bi Pi ci Pi 2
...(2)
where ai , bi and ci are the cost coefficients of generating unit i and Pi is the power of ith generator. The constraints of GENCOs are shown in Equation (3). Pi min Pi Pi max ; i 1, 2, 3...n
...(3)
where Pimin and Pimax are the upper and lower limits of generating unit i respectively.. The power balance equation is represented by Equation (4). n
i
Pi PL PD
...(4)
where PL are the transmission losses, which are calculated with the help of the Bcoefficients. The equation of transmission loss is given by Equation (5). PL PT BP PT B0 B00
...(5)
where B, B0 and B00 are the loss coefficients.
Intelligent Techniques PSO for Calculating ELD A heuristic global optimization technique, namely, PSO was first developed by Kennedy and Eberhart (1995). The PSO is applied in two-dimensional spaces with the simulation of birds flocking or fish schooling. Each bird or fish position is called agent or particle and represented by a point (Yuen and Lo, 2003). The PSO technique is applied to many power system problems like PSS design, power flow control, and voltage control and speed and rotor flux estimation of an induction motor drive (Laamari et al., 2015). The present position of the particle is called pbest value. The gbest value is the value of the agent or position of the agent in the whole group among pbest. Each particle tries to modify its velocity and position. v ik 1 v ik E1 rand1 ( pbesti Cik ) E2 rand2 (gbesti Cik )
...(6)
where vik = Velocity of agent i at iteration k/generation of ith generator
= Weighting function E1 and E2 = Weighting factor (by default value given is 2.0) rand1 and rand2 = Random number function between 0.0 to 1.0 rand1 (pbesti – Cik) = Self-confidence range Optimization of Pool Contracts using Intelligent Techniques and Calculation of Transmission Prices for Bilateral Contracts
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rand1 (gbesti – Cik) = Swarm range Cik = Current position of agent i at iteration k/Current price ith GENCO at any value of Pgi
pbesti = Personal best position of agent i/Price of ith GENCO at any value of Pgi gbesti = Best position of agent i within whole group/Final price of ith GENCO The weighting function () can be expressed as:
max
(max min ) iter itermax
...(7)
where
min = Final weight (by default the value given is 0.4) max = Initial weight (by default the value given is 0.9) Itermax= Maximum number of iterations Iter = Current iteration number The following equation is used to modify the current position of particle: Cik 1 Cik vik 1
...(8)
Genetic Algorithm A genetic algorithm is a global search heuristic used to compute the exact or approximate solution of the search problem and optimize the search solutions. GAs have successfully been applied to various real-world applications. GA uses techniques inspired inheritance, mutation, selection and crossover of the biology evaluation (Kaur et al., 2014). The basic idea of GA is to mimic the evolution process of nature. A population representation of candidate solutions to an optimization problem evolves towards better solution. Solutions are represented in the form of strings (in the form of 0’s and 1’s) but can also be represented in other forms too. The evolution basically starts with the population generation and occurs in generation. The population is generated randomly with some individuals. In each generation cycle, the fitness of every individual is calculated. Then multiple individuals are selected from the present population depending upon their fitness and are then modified to form a new population. Then new population is used in the next cycle of the algorithm. The algorithm terminates when a satisfactory fitness level has been reached. Once we have the genetic representation and the fitness function defined, GA proceeds to initialize a population of solutions randomly, and then improve it through repetitive application 4
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(Gargeya and Pabba, 2013; and Sahu and Swarnkar, 2014). Decimal integers from binary string population are obtained using Equation (9). yj
l j 1
2 i1bij
(j = 1, 2,...L)
...(9)
where y j is the equivalent decimal integer, bi j is the ith binary digit of jth string, l is the length of string and L is the number of strings or population size. The power generated is computed from the decoded population using Equation (10). pij Pi min
( Pi max Pi min ) j yi 2e 1
(i = 1, 2 ..., n; j = 1, 2 ..., L)
...(10)
where yi j is the binary value of the ith substring. Figure 1: Flowchart for Problem Formulation Start Form bus admittance matrix using base data
Power flow solution by Newton-Ralphson method Obtain the loss formula coefficients
GA/PSO
Generate optimum dispatch of generation Compute the line flow and line losses Bilateral pool contracts Compute cost with conventional methods, PSO and GA. Compute the wheeling charges and dispatch of generation for every pool contract
No
Given no. of transactions completed Yes Compute cost with conventional methodd, PSO and GA. Compute the total wheeling charges received and dispatch of generation with all bilateral contracts End
Optimization of Pool Contracts using Intelligent Techniques and Calculation of Transmission Prices for Bilateral Contracts
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The stochastic nature of GA and PSO may lead to different results in different runs. In order to analyze the performance of these algorithms, optimum number of runs is made so as to converse the optimum result. The flowchart for problem formulation is given in Figure 1.
Results and Discussion The standard data of IEEE 26 bus system has been considered. The bilateral MW contracts between GENCOs and DISCOs over and above the base demand considered are given in Table 1. Table 1: DPM Showing Bilateral Contracts Between GENCOs and DISCOs (MW) DISCO
D6
D12
D22
D25
GENCO G8
40
0
50
40
G12
60
30
0
70
G16
70
40
60
30
G20
50
0
20
0
DISCO6 has bilateral contract of 40 MW with GENCOs8 and 60 MW with GENCOsl2 and so on. The pool contract is for 1263 MW demand as per base load connected on IEEE 26 bus system. The lengths of transmission lines assumed to evaluate the transmission prices are shown in Table 2 and the wheeling charges considered are 0.50/MW-Km. Additional power flow for each bilateral contract on each transmission line is calculated through load flow study using Newton-Ralphson method. MW length utilization is calculated by multiplying this additional power with length corresponding to transmission line. The MW length is multiplied with transmission rate to obtain net wheeling charges for that particular transaction. Wheeling charges to be paid to ISO for transaction between D6 and G8 comes out to 45851426.60, as shown in Table 3. Total wheeling charges received considering all bilateral contracts simultaneously and utilized transmission line obtained are represented in Table 4. The difference of two columns shows additional income of ISO which may be used for extending infrastructure. The dispatches of generators using conventional method for each bilateral transaction obtained are given in Table 5. The total power required to be generated after each transaction is given in the 8th column of table, losses after each transaction are given in 9th column and pool charges considering each bilateral contract separately calculated using conventional ELD are given in last column of the table. The dispatches of generators using ELD+PSO method for each bilateral transaction obtained are given in Table 6. The total power required to be generated after each transaction is given in the 8th column of table, losses after each transaction are given in 9th column and pool charges considering 6
The IUP Journal of Electrical & Electronics Engineering, Vol. IX, No. 3, 2016
Table 2: Length of Transmission Lines (Km) BUS from
BUS to
Length (Km)
BUS from
BUS to
Length (Km)
1
2
40
10
22
80
1
18
70
11
25
25
2
3
30
11
26
90
2
7
50
12
14
30
2
8
30
12
15
70
2
13
40
13
14
50
2
26
60
13
15
120
3
13
30
13
16
70
4
8
30
14
15
60
4
12
50
15
16
70
5
6
25
16
17
140
6
7
25
16
20
100
6
11
50
17
18
170
6
18
25
17
21
30
6
19
80
19
23
60
6
21
130
19
24
50
7
8
50
19
25
40
7
9
40
20
21
50
8
12
60
20
22
40
9
10
40
21
24
50
10
12
30
22
23
80
10
19
25
22
24
50
10
20
70
23
25
50
Table 3: Transmission Prices for Each Transaction Separately ( ) DISCO
D6
D12
D22
D25
GENCO G8
4585.14
0
6370.32
17413.42
G12
13325.07
0.028
0
25732.32
G16
10855.50
4807.47
7337.19
18009.61
G20
7195.72
0
951.81
0
Optimization of Pool Contracts using Intelligent Techniques and Calculation of Transmission Prices for Bilateral Contracts
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Table 4: Total Wheeling Charges Received Considering All Bilateral Contracts and Utilized Transmission Line Total
Wheeling Charges
MW Length Utilized ( )
116583.61
53179.80
Table 5: Economic Dispatch of Generations for the Given Bilateral Transactions (MW) Generators P1
P2
P3
P4
P5
P6
Transactions
Total Losses Pool Generation Charges (in )
G8-D6
447.76 173.31 263.26 137.94 166.33 87.57
1276.17
13.0780 15451.15
G8-D22
447.86 173.41 263.69 138.87 165.69 87.37
1276.89
13.9159 15462.54
G8-D25
447.79 173.44 263.46 138.35 165.81 89.17
1278.02
15.0601 15477.69
G12-D 6
447.84 173.20 263.17 137.28 166.77 87.89
1276.15
13.1783 15452.32
G12- D12
447.69 173.19 263.48 138.81 165.58 87.02
1275.77
12.8003 15447.72
G12-D25
448.07 173.89 263.70 138.05 165.98 91.11
1280.80
17.8236 15514.45
G16-D6
447.87 173.13 261.48 138.46 167.31 87.29
1275.54
13.5729 15457.85
G16-D12
447.68 173.13 262.53 139.60 165.79 87.15
1275.88
12.9068 15449.33
G16-D22
447.91 173.37 262.33 139.83 166.11 87.68
1277.23
14.2598 15449.33
G16-D25
447.74 173.28 262.71 138.88 165.98 88.69
1277.28
14.3138 15467.88
G20-D6
447.70 173.07 262.95 137.83 166.46 87.55
1275.56
12.5900 15444.65
G20-D22
447.71 173.21 263.44 138.85 165.62 87.07
1275.90
12.9245 15449.37
Table 6: ELD+PSO Dispatch of Generations for the Given Bilateral Transactions (MW) Generators P1
P2
P3
P4
P5
P6
Transactions
8
Total Losses Pool Generation Charges ( )
G8-D6
446.99 173.22 263.82 138.36 166.14 86.97
1275.53
12.52252 15443.91
G8-D22
447.43 173.19 263.96 138.91 166.07 86.76
1276.32
13.3237 15462.54
G8-D25
447.57 173.14 263.62 138.45 166.18 88.43
1277.40
14.4061 15462.54
G12-D6
447.34 173.04 263.60 137.22 167.00 87.42
1275.62
12.6378 15452.32
G12-D12
447.71 172.98 264.04 138.81 165.31 86.39
1275.26
12.2578 15452.32
G12-D25
447.91 173.91 264.34 137.45 165.90 90.60
1280.01
17.0204 15514.45
The IUP Journal of Electrical & Electronics Engineering, Vol. IX, No. 3, 2016
Table 6 (Cont.) Generators P1
P2
P3
P4
P5
P6
Transactions
Total Losses Pool Generation Charges ( )
G16 -D6
447.88 173.11 261.53 138.47 167.22 87.90
1276.04
13.1227 15450.54
G16-D12
447.52 172.54 263.26 139.28 165.77 86.98
1275.38
12.3745 15450.54
G16-D22
447.70 173.31 263.15 139.56 165.72 87.19
1276.66
13.6630 15450.54
G16-D25
447.53 172.71 263.18 138.98 166.09 88.18
1276.71
13.7045 15450.54
G20-D6
447.89 172.37 263.29 137.96 166.63 86.93
1275.07
12.0727 15444.65
G20-D22
447.40 172.90 263.86 138.69 165.98 86.53
1275.38
12.3853 15449.38
each bilateral contract separately calculated using conventional ELD + PSO are given in last column of the table. The dispatches of generators using ELD+GA method for each bilateral transaction obtained are given in Table 7. The total power required to be generated after each transaction is given in the 8th column of table, losses after each transaction are given in 9th column and pool charges considering each bilateral contract separately calculated using conventional ELD + GA are given in last column of the table. Table 7: ELD+GA Dispatch of Generations for the Given Bilateral Transactions (MW) Generators P1
P2
P3
P4
P5
P6
Transactions
Total Losses Pool Generation Charges ( )
G8-D22
449.94 171.45 263.77 141.91 162.25 86.58
1275.47
12.4442 15374.43
G8-D25
444.53 165.91 265.21 143.84 172.57 84.26
1276.35
13.3238 5384.91
G12-D6
445.69 171.47 261.81 138.87 175.22 84.44
1277.35
14.5097 15384.91
G12-D12
446.30 174.99 265.12 135.17 165.14 88.90
1275.59
12.6507 5375.80
G12-D25
445.16 173.87 265.31 136.43 169.44 85.11
1275.29
12.3398 5375.80
G16-D6
446.88 170.83 268.82 144.06 163.91 85.42
1280.04
16.9493 15434.97
G16-D12
440.58 171.03 268.78 135.15 175.28 85.34
1276.07
13.1837 5381.05
G16-D22
452.02 171.52 261.45 139.06 161.97 89.33
1275.45
12.3431 5381.05
G16-D25
445.45 174.45 263.57 137.45 167.24 88.55
1276.68
13.7104 5381.05
G20-D6
443.89 180.62 261.48 135.60 169.30 85.88
1276.79
13.7839 5381.05
G20-D22
455.95 170.20 263.08 135.57 168.20 82.12
1275.10
12.1482 15368.90
Optimization of Pool Contracts using Intelligent Techniques and Calculation of Transmission Prices for Bilateral Contracts
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Net prices to be paid to GENCOs and losses calculated by each technique considering all bilateral contracts simultaneously are given in Table 8. Generations considering all bilateral contracts simultaneously are obtained, as shown in Table 9. Comparison of pool prices and losses are also shown in Figures 2 and 3. It can be observed that ELD+GA method is better than ELD+PSO. ELD+PSO is better than ELD. Table 8: Comparison of Pool Prices and Losses Considering All Bilateral Contracts Simultaneously S. No.
Intelligent Techniques
Price ( )
Losses (MW)
1.
Without Economic dispatch
17153.51
40.1391
2.
Conventional ELD method
15809.33
39.9093
3.
ELD+PSO
15781.34
37.8460
4.
ELD+GA
15712.45
37.8953
Table 9: Generation Considering All Bilateral Contracts Generation with Conventional Method (MW)
Generation with ELD + PSO (MW)
Generation with ELD + GA (MW)
Pl(MW)
448.76
448.74
452.06
P2(MW)
177.10
176.41
174.38
P3(MW)
261.52
261.73
265.37
P4(MW)
138.18
138.48
134.68
P5(MW)
175.80
175.50
172.75
P6(MW)
101.53
99.94
101.64
Power Output
GA
41 40 39 38 37 36
PSO
GA
PSO
Conventional
Without...
18,000 17,000 16,000 15,000 14,000
Conventional
Losses Comparison
Without...
Price Comparison Price ( )
Figure 3: Comparison of Losses Considering All Bilateral Contracts
Price ( )
Figure 2: Comparison of Price Considering All Bilateral Contracts
Conclusion In this paper, the pricing for transmission line usage for IEEE 26 bus system is calculated using MW-mile method. The prices for pool contract are reduced by applying GA and 10
The IUP Journal of Electrical & Electronics Engineering, Vol. IX, No. 3, 2016
PSO. The pool prices considering each bilateral contract separately and considering all bilateral contracts simultaneously are calculated, using conventional ELD method, ELD + PSO method and ELD + GA method. The transmission losses caused by pool demand and bilateral contract are minimized. The net benefits are calculated and compared. It is seen that ELD + GA is giving better results than conventional ELD method and ELD + PSO method too for optimization of pool prices. The methods and computer program developed in MATLAB 14 are general and can be applied to any system.
References 1. Galiana F D and Phelan M (2000), “Allocation of Transmission Losses to Bilateral Contracts in a Competitive Environment”, IEEE Transaction on Power Systems, Vol. 15, No. l, pp. 143-150. 2. Gargeya Anuj M and Pabba Sai Praneeth (2013), “Economic Load Dispatch Using Genetic Algorithm and Pattern Search Methods”, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, No. 4. 3. Gupta S K and Chawla P (2014), “Economic Load Dispatch in Thermal Power Plant Considering Additional Constraints Using Curve Fitting and ANN”, Review of Energy Technologies and Policy Research, Vol. 2, No. 1, pp. 16-28. 4. Happ H H (1994), “Cost of Wheeling Methodologies”, IEEE Transaction on Power Systems, February, pp. 147-156. 5. Kaur Arunpreet, Singh Harinder Pal and Bhardwaj Abhishek (2014), “Analysis of Economic Load Dispatch Using Genetic Algorithm”, International Journal of Application or Innovation in Engineering & Management (IJAIEM), Vol. 3, No. 3, ISSN 2319 - 4847. 6. Kennedy J and Eberhart R C (1995), “Particle Swarm Optimization”, Proc. IEEE International Conference Neural Networks, Vol. 4, pp. 1942-1948, Perth, Australia. 7. Laamari Yahia, Chafaa Kheireddine and Athamena Belkacem (2015), “Particle Swarm Optimization of an Extended Kalman Filter for Speed and Rotor Flux Estimation of an Induction Motor Drive”, Electr Eng, Vol. 97, pp. 129-138, DOI10.1007/S00202014-0322-1. 8. Lai Loi Lei (2001), Deregulation of Electric Utilities, Power System Restructuring & Deregulation, John Wiley & Sons Ltd, p. 50. 9. Rau N S (1989), “Certain Consideration in the Pricing of Transmission Service”, Author, IEEE Transaction on Power Systems, August, pp. 1133-1139. pls chk 10. Saeh I S and Khairuddin A (xxxx), “Implementation of Artificial Intelligence Technique year is for Steady State Security Assessment in Pool Market”, International Journal of missing Optimization of Pool Contracts using Intelligent Techniques and Calculation of Transmission Prices for Bilateral Contracts
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Engineering (IJE), Vol. 3, No. 1. 11. Sahu Gajendra and Swarnkar Kuldeep (2014), “Economic Load Dispatch by Genetic Algorithm in Power System”, International Journal of Science, Engineering and Technology Research (IJSETR), Vol. 3, No. 8. 12. Yuen Y S C and Lo K L (2003), “Simulations of Bilateral Energy Market Using MATLAB”, International Journal of Computation and Mathematics in Electrical & Electronics Engineering, Vol. 22, No. 2, pp. 424-443.
Appendix Generator Data ai
bi
ci
Pi min(MW)
Pi max(MW)
240
7.0
0.0070
100
500
200
10.0
0.0095
50
200
220
8.5
0.0090
80
300
200
11.0
0.0090
50
150
220
10.5
0.0080
50
200
190
12.0
0.0075
50
120
PSO Parameters Function
Value
Local best acceleration count
2
Global best acceleration count
2
Initial inertia weight (min)
0.9
Final inertia weight (max)
0.4
Min. global error gradient
10-10
Epochs before error gradient criterion terminates run
5000
PSO type flag
0
GA Parameters Function Population size
12
Value 50
Generations
500
Time limit
200
Stall time limit
100
Reference # 59J-2016-07-xx-01
The IUP Journal of Electrical & Electronics Engineering, Vol. IX, No. 3, 2016
