The optimisation of power system operation over periods of time of the order of one or more years requires simulation models which combine reasonable accuracy with high computation speed The development of a model suitable for such studies and based on probability techniques is described

Power System Simulation Model Based on Probability Analysis

(1979). Reliability Modeling in Electric Power Systems. Journal of the Operational Research Society: Vol. 30, No. 8, pp. 769-769.

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Reliability modeling in electric power systems

Impact of wind generation on the operation and development of the UK electricity systems

This paper discusses application of generalized Benders' decomposition in a model for planning least-cost investments in electricity generating capacity subject to probabilistic reliability constraints. The planning problem is decomposed into a set of subproblems, each representing the operation of a set of generating plants of fixed capacity in 1 year, and a master problem, representing optimal capacity investments over the entire planning horizon. The subproblems are solved using a procedure called probabilistic simulation, which calculates the expected cost of operating the generating system, the reliability level, and dual multipliers reflecting the value of small changes in the plant capacities. The master problem is a linear program which uses these dual multipliers to approximate the nonlinear cost and reliability functions. The solution to the capacity expansion problem is found by iteratively solving the master problem and the subproblems.

Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders' Decomposition

Important power system planning and operation problems have been formulated as mathematical optimization problems. Such problems as the economic dispatch, in many of its facets; var scheduling and allocation; pollution dispatch; maximum interchange; hydrothermal unit commitment and dispatch; generation, transmission, and distribution expansion planning; maintenance scheduling and substation switching, have been formulated and solved. Modern mathematical optimization techniques, such as nonlinear, quadratic, linear, integer and dynamic programming and their many combinations and extensions, have been exploited. Some of the formulations and solutions to these problems as presented in the recent literature within the power systems field are reviewed. The large number of papers available is a measure of the current immense activity in this area. Attempts are made to point out some specific areas where more work needs to be done.

Some applications of optimization techniques to power systems problems

As a goal, the evaluation and computation of electric power system reliability requires that a consistent technique be used for all portions?generation, transmission, and distribution. At present, a number of different methods are used for the generation system, while the frequency and duration of outages seems to be developing as a standard measure for the analysis of the distribution system. This paper and a subsequent one will present a reliability calculation method for the generation system that incorporates the frequency and duration of unit outages and includes consideration of the loads. This method leads to calculated generation reliability measures which are the availability, frequency of occurence, and mean duration of reserve states. These are cumulative states in that they specify system reserve conditions of a given magnitude or less. This paper is concerned with the procedure for calculating the availability, frequency, and outage duration for a number of generating units connected in parallel to form a single system. Numerical data are used to illustrate the technique and make comparisons with other methods.

Frequency and Duration Methods for Power System Reliability Calculations: I - Generation System Model

This paper is a continuation of the work started in [1] and is aimed at incorporating a model of the power system load with the generation system model developed previously. Combination of this load and the generation model permits computation of the availability, frequency of occurrence, and mean duration of generation reserve, or margin states. The results of this work are illustrated by continuation of a simple numerical example begun in Part I. The most widely applied of the previously developed techniques for assessing generation system reliability, the loss-of-load and loss-of-capacity methods, assume fixed outage or load duration intervals. The present model, on the other hand, uses an exponential distribution of durations. The reserve margin states developed using the exponential distributions contain data giving both the availability of each margin state and the expected frequency of recurrence. Previous methods yield only the availability of the reserve margin states, or else availability and frequency data for generating capacity states, not considering the load. The method presented and illustrated may be extended t o consider the calculation of operating reliability or the inclusion of the effects of a simple transmission system.

Frequency and Duration Methods for Power System Reliability Calculations: II - Demand Model and Capacity Reserve Model

This chapter contains sections titled: Introduction, Background and Historical Development, Resume of the Contents of the Monograph, References

Power-System Reliability Calculations

In the planning and design of a high-voltage transmission network it is sometimes desirable to install controllable kilovar ar capacity at several locations to support bus voltages during emergencies. This problem arises when transmission line or generation outages cause bus voltage magnitudes to decrease below desirable limits. The problem of selecting where and how much kilovar capacity is required has many feasible solutions which satisfy the conditions imposed. A method for locating that solution with the minimum total installed capacity is presented. This nonlinear programming problem will be solved by using a linear approximation, solving the linear programming problem, and then correcting the linear approximation through the use of differences between the linear and nonlinear results. The method is illustrated by an application to a portion of a large high-voltage network.

Linear Programming as an Aid in Planning Kilovar Requirements

The interconnection of two power systems offers the opportunity to achieve an appreciable gain in the reliability of the two generation systems and planned economies as a result of capacity sharing. Use of the probabilistic methods described permits evaluation of these reliability and reserve benefits. The methods described extend the single system probability techniques to two interconnected systems. A digital computer program has been developed to implement these methods.

Allen J. Wood

Papers

Frequency and Duration Methods for Power System Reliability Calculations: I - Generation System Model

Frequency and Duration Methods for Power System Reliability Calculations: II - Demand Model and Capacity Reserve Model

Power-System Reliability Calculations

Linear Programming as an Aid in Planning Kilovar Requirements

Determination or Reserve Requirements or Two Interconnected Systems