Model for Power Shortage Estimation in Electric Power Systems: Interior Point Algorithms

Model for Power Shortage Estimation in Electric Power Systems: Interior Point Algorithms

Sergey Perzhabinsky (Department of Applied Mathematics, Melentiev Energy Systems Institute - Siberian Branch of the Russian Academy Sciences, Irkutsk, Russia) and Valery Zorkaltsev (Department of Applied Mathematics, Melentiev Energy Systems Institute - Siberian Branch of the Russian Academy Sciences, Irkutsk, Russia)
Copyright: © 2012 |Pages: 19
DOI: 10.4018/ijeoe.2012100105
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Abstract

This paper addresses the model for power shortage estimation in electric power systems. The model’s main component of methodology for analysis of electric power system (EPS) reliability that has been developed at the Energy Systems Institute, Siberian Branch of Russian Academy Sciences. The methodology is based on the Monte-Carlo method. Quality and implementation time of reliability analysis depend on realization of the model. The model is implemented in the computational software for electric power systems reliability analysis. The history of evolution of the model for power shortage estimation and mathematical properties of the model are discussed. The results of the state-of-the-art studies of the model for power shortage estimation in EPS are presented. The model for power shortage estimation in EPS with quadratic power losses in power lines is considered. Algorithms of the interior point method with quadratic approximations of constraints applied for realization of the model are discussed. Results of experimental studies of the algorithms are presented.
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Introduction

High reliability of electric power systems (EPS) is a basis for efficient control of their development and operation. The development of methods for analysis and control of reliability of electric power system is an important task. The reliability of EPS is characterized by some properties such that nondeficiency, repairability, survivability, controllability, stability, and safety. Further we will treat the reliability of electric power systems as degree of powersupply provision of consumers which is characterized by frequency, duration and depth of possible power shortage in system.

At the beginning of the 1970s the methodology for analysis of electric power system reliability was developed at Siberian Energy Institute, Siberian Branch of the USSR Academy of Sciences (Rudenko & Cheltsov, 1974). It is based on the method of statistical tests (the Monte-Carlo method) (Metropolis & Ulam, 1949). The methodology consists of three blocks.

  • 1.

    Probability block, in which random states of electric power system are formed with the help of the Monte-Carlo method. It allows to “play” various possible situations that arise in the operation of EPS (random fluctuations of loads, malfunction of equipment and power transmission lines, emergency and scheduled repair of equipment).

  • 2.

    Block of power shortage estimation for randomly formed EPS states (model for power shortage estimation in EPS).

  • 3.

    Block of EPS reliability indexes computation. Information accumulated using the numerous calculations by the model for estimation EPS power shortage is processed in this block. The main reliability indexes are computed in this block:

    • a.

      Probability of non shortage system: P(t)=1 – F(t), F(t) is the probability of the system failure;

    • b.

      Mathematical expectation of undersupply of energy (ME);

    • c.

      Coefficient of energy provision for consumers: П=1 – ME/En, En is the required power generation;

    • d.

      Mathematical expectation of generator power shortage in nodes and flow capacity limiting in transmission lines.

The above scheme is the most effective and universal to solve the problems of reliability analysis of the electric power system at present (Kovalev, Krupenev, & Lebedeva, 2010).

An electric power system is presented in the form of complicated multi-node scheme in the methodology of reliability analysis. A node of the EPS scheme is energy region which is characterized by total power of generating equipment and total load of electricity consumption in this region. A tie line among nodes is power line which had limited transfer capability. The transfer capability is determined either by electromechanical or thermal stability of power lines.

Forming of electric power system states is realized on the basis of state distribution functions of power generation, loads with random fluctuations in nodes, transfer capabilities of power lines. The state distribution series of system equipment, daily-load curves, transfer capabilities of power lines are the input data for determination of system states.

The central point of the methodology for reliability analysis is the model of power shortage estimation (PSE). Quality and implementation time of reliability analysis depend on realization of the model. Special requirements are imposed on the PSE model. The model should most adequately reflect physical and technical processes that occur in different situations in energy system. At the same time the model should be aggregated (the information can be easily added) and easily to implement. The lesser the computational time of the model for each of the generated situations, the larger the set of situations can be “played” and, thus, the accuracy of the calculated EPS reliability indices can be increased.

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