Unit commitment with probabilistic reserve: An IPSO approach

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Abstract

This paper presents a new algorithm for solution of the nonlinear optimal scheduling problem. This algorithm is named the iteration particle swarm optimization (IPSO). A new index, called iteration best, is incorporated into particle swarm optimization (PSO) to improve the solution quality and computation efficiency. IPSO is applied to solve the unit commitment with probabilistic reserve problem of a power system. The outage cost as well as fuel cost of thermal units was considered in the unit commitment program to evaluate the level of spinning reserve. The optimal scheduling of on line generation units was reached while minimizing the sum of fuel cost and outage cost.

A 48 unit power system was used as a numerical example to test the new algorithm. The optimal scheduling of on line generation units could be reached in the testing results while satisfying the requirement of the objective function.

Introduction

Because of the fast growing load of power systems and the large load gap between heavy load and light load periods, the unit commitment problem has become a crucial task in the economic operation of a power system. The main objective of the unit commitment problem is to determine the optimal on line generation units such that the total fuel cost of the thermal units can be minimized [1]. A standard unit commitment problem is often formulated subject to several constraints, including the real power operating limits of the generation units, electric power balance and spinning reserve of the power system.

Most utilities use deterministic criteria to determine the spinning reserve level and on line generation units. Their operating rules are to keep the spinning reserve level greater than the generation of the largest on line generator or a fraction of the system load. However, these policies do not match the stochastic nature of power systems. A more consistent and realistic method would be one based on probabilistic methods. A risk index based on such methods would enable a consistent comparison to be made between various operating strategies and the economics of such strategies [2].

Unit commitment with probabilistic reserve (UCPR) considers the effects of outage cost on the solution of the unit commitment problem and uses a risk index to evaluate the spinning reserve level. A good generation scheduling solved by UCPR would reduce the operating costs, increase the system reliability and maximize the energy efficiency of the generation units.

Considerable efforts have been devoted to study the spinning reserve scheduling problem. Most of the results show that a considerable fuel cost saving or a reasonable spinning reserve schedule can be reached. These approaches include dynamic programming, Monte-Carlo simulation method [3], Lagrangian relaxation [4] and Bender’s decomposition [5]. Although the features of these approaches are quite different, they were proposed in order either to decrease the computation time or to reduce the fuel costs of the power systems.

Recently, with the appearance of artificial and computational intelligence technologies, such methodologies as neural networks, genetic algorithms and simulated annealing have also been applied to deal with the spinning reserve scheduling problem. In the neural network application, once the networks are well trained, the on line operation will be merely a simple arithmetic operation. A new generation schedule can, thus, be obtained immediately. This method was proved feasible. However, the network needs to be retrained whenever the scenario varies [6]. Simulated annealing mimics the physical operation of an annealing process. It was also presented to solve the near optimal solution of the spinning reserve scheduling problem. It is easy to implement, yet the complicated annealing schedule is closely related to the optimization performance. A poor tuning of the annealing schedule may inadvertently affect the performance of simulated annealing [7]. The genetic algorithm is inspired by the principles of natural evolution. It is very popular in solving the optimization problem in power systems. The drawbacks of this approach are attributed to the long computing time and the complicated process in coding and decoding the problem [8].

Particle swarm optimization (PSO) was originally presented by Kennedy and Eberhart in 1995 [9]. It was originally inspired by observation of the behaviors of bird blocks and fish schools. The main advantages of PSO are its simple concept, computational efficiency and easy implementation. PSO has been successfully applied to various fields of power system optimization, such as economic dispatch, reactive and voltage control and power system stabilizer design.

In this paper, an efficient algorithm, which is modified from particle swarm optimization [9] is developed to solve the UCPR problem of power systems. A new index, called iteration best, is incorporated into PSO to improve the solution quality and computation efficiency. The effects of outage cost as well as fuel cost are considered in the unit commitment program to evaluate the level of spinning reserve. Besides, the lowest spinning reserve level is restricted at least to be the generation of the largest on line generation unit. This new algorithm can minimize the sum of fuel cost and outage cost when the optimal on line generation scheduling is reached.

Finally, a 48 unit power system was used as a numerical example to test the new algorithm. Results show that the solution of the UCPR problem can be achieved when the minimum of the summation of fuel cost and outage cost during the study periods is reached. Finally, these results are also compared with the results of dynamic programming and another artificial algorithm to show the effectiveness of the presented approached.

Section snippets

Problem formulation and the objective function

The outage cost as well as fuel cost of generation units should be considered in power system operation [2]. The new approach presented in this paper solves the optimal hourly on line unit number while minimizing the sum of fuel cost and outage cost of a power system during the study period. The objective function of this problem is expressed asMinimizeTSC=d=1D(TCd+w1×OCd)OCd=EENSd×VOLLTCd=n=1N[FCn(PGn,d)+SCn,d]FCn(PGn,d)=An+Bn×PGn,d+Cn×PGn,d2where TSC is the total social cost of the power

Particle swarm optimization

Particle swarm optimization is a parallel search technique with characteristics of high performance and ease of implementation. Originally, it mimics the sociality of bird blocks and fish schools. Through a tracking of two best values, i.e. Pbest and Gbest, the global optimum may be achieved by this optimization technique [9]. Pbest is the best value of the fitness function of every particle of the population considered. Gbest is the best value of the fitness function that has been achieved so

Iteration particle swarm optimization

A new index named “Iteration Best” is incorporated in Eq. (12) in this paper to improve the solution quality and computation time. Eq. (14) shows the new form of Eq. (12). This type of PSO is named IPSO in this paper.Vjk+1=Vjk+c1×rand×(Pbestjk-Xjk)+c2×rand×(Gbestk-Xjk)+c3×rand×(Ibestk-Xjk)where IbestK is the best value of the fitness function that has been achieved by any particle in iteration k and c3 represents the weighting of the stochastic acceleration terms that pull each particle toward

Solution method and implementation of IPSO

The main computational processes of the algorithm presented in this paper to solve the UCPR problem of power systems are discussed in the following subsections. This algorithm is an implementation of IPSO.

  • Step 1:

    Initialize the IPSO parameters

    • Set up the set of parameters of IPSO, such as,

    • number of particles Q = 120,

    • weighting factors c1 = 0.01, c2 = 0.01, c3 = c1 · (1  eck),

    • maximum number of iterations ITmax = 4000.

  • Step 2:

    Create an initial population of particles randomly

    Each particle contains the real power generation

Numerical examples

A 48 unit power system with 168 h load is used as an example to test the proposed algorithm. The largest unit in this system is a 900 MW unit, the VOLL was set as 135 NT$/kW h [10] and the weighting factor w1 in Eq. (1) was set as 1.0.

The parameters of IPSO are selected as: the number of particle Q = 120, weighting factors c1 = 0.01 and c2 = 0.01, c3 = c1 · (1  eck), ITmax = 4000, penalty factors γ1 to γ5 are selected as 5000.

The results show that the solution of UCPR problem was reached within 24 min on an

Conclusions

This paper shows how a probabilistic reserve can be applied in the unit commitment problem to evaluate the spinning reserve requirement that can help power systems to overcome unscheduled generators outages and major load forecasting errors without load shedding.

A highly complex problem of unit commitment with probabilistic reserve can be solved by the proposed IPSO method. The results are compared with the results of applying the DP, GA and PSO methods. The test results demonstrate the

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