IEEE 2 Column Format

4 downloads 3859 Views 2MB Size Report
optimize the real and reactive power scheduling of each ... Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, ...
International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.76 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm

A COMPARATIVE METHOD OF OPTIMAL POWER FLOW FOR IEEE-30 BUS SYSTEM Veerapandiyan V1, Mary D 2, Kanimozhi S3 1 P.G Scholar, Department of Electrical Engineering, Government College of Technology, Anna University Coimbatore- 641013, Tamilnadu, India, Mobile: +918754092650. 2 Professor, Department of Electrical Engineering, Government College of Technology, Anna University Coimbatore- 641013, Tamilnadu, India. 3 P.G Scholar, Department of Electrical Engineering, Government College of Technology, Anna University, Coimbatore-641013, Tamilnadu, India. 1 E-mail: [email protected] 2 E-mail: [email protected] 3 E-mail: [email protected]

economic information to optimize the power flow solution and to meet the power system demand with minimum fuel cost. The OPF utilizes all control variables to minimize the cost of generation. This is done by minimizing the objective function while maintaining an acceptable system performance in terms of generating capability limits and the output of the compensating devices. In this paper an optimal power flow method using Newton, Genetic Algorithm, Particle Swarm Optimization and Interior Point Method are compared and the results are validated using MATLAB Software.

Abstract-

Optimal Power Flow (OPF) in a power system is an optimal method of reducing the cost of generation by properly scheduling and updating the generation. The optimum condition can be attained by adjusting the available controls (Generator Dispatch) to minimize the objective function subject to operational constraints. In this paper a comparison is made by Newton, GA, PSO and IPM based Optimal Power Flow method using MATLAB software. The IEEE-30 bus system is used as a test system. Keywords: Interior Point Method (IPM), Optimal Power Flow (OPF), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Newton Method.

2. OPTIMAL POWER FLOW OPF aims to minimize the single or a multi objective function, thereby reducing the cost of generation and to utilize the power system assets in an efficient manner. There are various OPF solution methodologies they are:

1. INTRODUCTION

A. Conventional Methods

In a practical power system, the generating stations are located far away from the load center and their fuel costs are also different. During normal operating condition of the system the generation capacity is more than total demand and losses. Thus, there are many different options for scheduling generation. The main objective of this paper is to optimize the real and reactive power scheduling of each power plant in such a way to reduce the operating cost. This allows the generator’s active and reactive power to vary freely within the limits so as to optimize the cost of the power system operation. It also gives the

1. Gradient Methods a) Generalized Reduced b) Reduced Gradient c) Conjugate Gradient 2. 3. 4. 5.

B. Intelligent Method

359

Hessian - based Newton – based Linear Programming Interior Point

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.76 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm

International Journal of Applied Engineering Research (IJAER) Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, February 2015)

1. Artificial Neural Networks 2. Fuzzy Logic 3. Evolutionary Programming 4. Ant Colony 5. Particle Swarm Optimization

𝑃𝑖 = 𝑃𝐿𝑜𝑎𝑑 + 𝑃𝐿𝑜𝑠𝑠 Qi = QLoad + QLoss 4.2 Inequality Constraints

These methods are used to calculate power flow problems such as Gauss Seidal Method, Newton Raphson Method, Fast De-Coupled Method, Linear Programming Method, Non-Linear Programming Method, Quadratic Programming Method, Interior Point Method etc. All these methods have its own disadvantage. In this paper optimal power flow using Newton Method, GA and PSO based Newton Method and Interior Point Method are discussed. Among these methods the later one converges quickly than the other three methods and this method has advantages of 

Ease of handling inequality constraints by logarithmic barrier functions



Speed of convergence and



The Initialization is not required [6].

Pgi min ≤ Pgi ≤ Pgi max 𝑄𝑔𝑖 𝑚𝑖𝑛 ≤ 𝑄𝑔𝑖 ≤ 𝑄𝑔𝑖 𝑚𝑎𝑥 The objective function can be minimized only when the power system is running under normal condition while the network components are operating within limits. 5. NEWTON OPF METHOD:

3. OBJECTIVE FUNCTION The Objective function commonly used are (a) Fuel or active power cost optimization (b) Active power loss minimization In this paper the fuel cost and losses are considered as the objective function they are 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐹𝑖 = (𝑐𝑖 + 𝑏𝑖 𝑃𝑔𝑖 +𝑎𝑖 𝑃𝑔𝑖 2 ) Where Pgi is the amount of generations in MW at generator i. ai, bi, ci are the cost coefficients. 4. POWER FLOW EQUATION

Figure 1: Newton Method of OPF

The net injected power at each bus and exchanged through In Power system the power flow equation is solved by a well known method called Newton method. It is a flexible method that can be adopted to develop different OPF algorithms suited to the requirements of different applications. The Newton approach would not be possible to develop practical OPF programs because the admittance matrix is highly sparse. So a special technique is needed to

the lines connected to this bus is given by 𝑃𝑖 = 𝑉𝑖 𝑄𝑖 = 𝑉𝑖

𝑁 𝑗 =1 |𝑉𝑗 | |𝑌𝑖𝑗 | 𝑁 𝑗 =1 |𝑉𝑗 | |𝑌𝑖𝑗 |

cos(𝛿𝑖 − 𝛿𝑗 − 𝜃𝑖 ) sin(𝛿𝑖 − 𝛿𝑗 − 𝜃𝑖 )

4.1 Equality Constraints 360

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.76 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm

International Journal of Applied Engineering Research (IJAER) Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, February 2015)

solve the practical problem. Apart from this drawback, Newton’s method has an advantage of rapid convergence and the system voltages are maintained near the rated value. Figure 1 shows the Newton method of solving OPF. 6. GA OPF METHOD: In GA based Optimal Power Flow, Genetic Algorithm is used as a search technique for optimization of power flow in different lines of the power system. In this the chromosome is initialized randomly (i.e) nothing but the generation and the fitness function is evaluated to find the best generation to reduce the cost of the system. Then the chromosomes, which are generated should satisfy the constraint and then the load flow analysis is carried out using Newton Raphson method. The iteration retains until the generation cost of generator reduces. Genetic Algorithm is accomplished using three primary operations: Parent reproduction, crossover and mutation [3]. The details of important operations during the solution of GA based Optimal Power Flow are as follows:

the cost and losses of the system. The scheduling can be improved by increasing the velocity of the bird. This method changes the velocity of each particle at each time step towards its pBest and gBest. Initially the particle is initialized randomly and later due to updating of particle, the generation dispatch is varied and an optimum value is reached. It is the fastest method compared to GA; the problem formulation is shown in figure 3.

Figure 3. PSO OPF Method

Figure 2. GA OPF Method

7. PSO OPF METHOD: Particle Swarm Optimization (PSO) is an evolutionary algorithm that may be used to find optimal (or near optimal) solutions to numerical problems. Particle Swarm Optimization was originally developed using the flocking behavior of birds [1]. In simulations, birds would begin by flying around with no particular destination and spontaneously formed flocks until one of the birds flew over the roosting area. Due to the simple rules the birds used to set their directions and velocities, a bird pulling away from the flock in order to land at the roost would result in nearby birds moving towards the roost. This helps in scheduling the generator similar to that of birds, the velocity determines the optimal scheduling of each generator and thereby reducing 361

8. IPM OPF METHOD: Interior Point Method is an optimization method, to optimize the quadratic type of objective function in an easier manner and it does not require any initial point. The inequality constraints are handled easily. The primal-dual method of IPM is used to solve OPF problem. However, we consider the voltage in rectangular coordinates to solve the problem and the problem formulation is discussed as shown in figure 4.

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.76 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm

International Journal of Applied Engineering Research (IJAER) Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, February 2015)

10. RESULTS AND DISCUSSION 10.1 Comparative Results Table 1: Cost and Loss Variation

Figure 4. IPM OPF method

9. TEST SYSTEM: The IEEE 30 Bus Test Case shown in figure 5, represents a portion of the American Electric Power System (in the Midwestern US) as of December, 1961. Basically, it has 30 bus out of which 6 buses are generator bus and 3 synchronous condensers. The maximum and minimum voltage at each bus should be within the limit of 0.95≤ V≤1.06.

System Parameter

NR

GA

PSO

IPM

TC($/h)

944

918.236

801.84

891.67

Loss(MW)

9.9093

9.0

7.79

6.89

The Table 1 shows that the total cost of generation and real power loss of an IEEE 30 bus system by various method of Optimal Power Flow. The GA method reduces the cost and losses of the system by properly scheduling the generator than Newton method. The PSO, which schedule the generation based on number of particles, also reduces the generation and cost to very reasonable value than GA. The interior point method is a conventional method which is the most efficient method in terms of loss reduction and cost of generation is also optimized.

10.2 Losses and Voltage Variation

Real Power Losses (MW)

12 10 8 6 4

Losses(MW)

2 0 NR

GA

PSO

Methods

Figure 6: Real Power loss Figure 5. One line diagram of IEEE 30 bus system

362

IPM

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.76 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm

International Journal of Applied Engineering Research (IJAER) Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, February 2015)

Voltage (p.u)

Voltage 1.15 1.1 1.05 1 0.95 0.9 0.85

Nominal Voltage NR Method GA PSO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

IPM

No. of buses Figure 7: Voltage variation at each bus for IEEE-30 bus system

Figure 6 shows the variation losses by various optimal algorithms, the plot shows that the total real power loss are very much reduced by ACOPF using Interior Point

Method (IPM). The voltage variation at each bus is shown in figure 7 in various optimal power flow method.

10. 3 Generations dispatch variation

Real Power Generation P (MW)

200

150 Newton

100

PSO

50

GA

0 PG1

PG2

PG13

PG22

PG23

PG27

IPM

Various Generator

Figure 8: Generation Dispatch Results

Figure 8 shows the variation of real power generation dispatch for each case of OPF. Here the dispatch is varied in order to optimize the objective function of optimal power flow. 11. CONCLUSION This thesis work significantly compared the various optimal power flow algorithm such as Newton Method, Genetic Algorithm, Particle Swarm Optimization and Interior Point Method. Among these methods the 363

generation cost and transmission losses of an IEEE-30 bus system are reasonably reduced by Interior Point Method OPF than the intelligence method. Since, the intelligence method uses the Newton method for load flow analysis the cost, losses are not much reduced and the convergence also slower. Therefore the intelligence method with an interior

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.76 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm

International Journal of Applied Engineering Research (IJAER) Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 2, February 2015)

point method of load will further enhance the convergences speed and other characteristics as shown in Table 2. Table 2: Comparison Results for OPF [

Method

Convergence

Description

Domain The fastest and most efficient deterministic algorithms. IPM

Local

Many researches to select parameters and assure convergence. It has quadratic convergence, but require penalty terms.

Newton

Local

Intelligence

Local

Used asa local solver in any other method. It minimizes the objective function, but the

(GA, PSO)

losses are not much reduced. Since Newton Method is used for load flow convergence is slow.

REFERENCES [1] Pathak Smita “Optimal Power Flow by Particle Swarm Optimization for Reactive Loss Minimization”, International Journal of Science & Technology Research, vol. 1, Issue 1, Feb 2012. [2] Florin Capitanescu et.al “An interior-point method based optimal power flow”. [3] Sharanya Jaganathan et.al, “Formulation of Loss minimization Problem Using Genetic algorithm and Line-Flow-based Equations”, IEEE, March 30 2010 [4] S.-Y. Lin, Y.-C. Ho, and C.-H. Lin, “An ordinal optimization theory based algorithm for solving the optimal power flow problem with discrete control variables,” IEEE Trans. Power Syst., vol. 19, no. 1, pp.1187-1195, Aug. 2003. [5] Mirko Todorovski and Dragoslav Rajičić, “A power flow method suitable for solving OPF problems using genetic algorithm,” in Proc. IEEE Region 8 EUROCON, vol. 2, 2003, pp. 215-219. [6] Rabih A. Jabr, Alun H. Coonick, and Brian J. Cory, “A Primal-Dual Interior Point Method for Optimal Power Flow Dispatching”, IEEE Trans. Power Syst., vol. 17, no. 3, August 2002. [7] F. Capitanescu, M. Glavic, D. Ernst, L. Wehenkel, May 2006, “Interior-point based algorithms for the solution of optimal power flow problems” Electric Power Systems Research 77, pp 508-517. [8] Allen J. Wood and Bruce F. Wollenberg, 2003, “Power generation, operation and control”. [9] Andrea A. Sousa, Geraldo L. Torres “Robust optimal power flow solution using trust region and interior-point methods” IEEE Trans. Power Syst. [10] http://www.ee.wasshington.edu/research/pstca. [11] Allen J. Wood and Bruce F. Wollenberg, 2003, “Power generation, operation and control”.

364