A survey is presented of papers and reports that address various aspects of economic dispatch. 4, november 1990 a review of recent advances in economic dispatch this paper presents a survey of papers and reports which methodologies, automatic generation control, security constrained dispatch, dynamic dispatch, non conventional generation sources. Dispatch, literature review, improved introduction economic dispatch is defined as the process of allocating generation levels to the generating units in the mix, so that the system load may be supplied entirely and most economically. A general survey of the present status of economic dispatch is done in this paper. The papers and reports reviewed here have been published subsequent to the comprehensive surveys done by happ i and an ie working group 2,3. Both happ and the ie working group present the work of authors from the inception of economy loading to the status existing in 1979. Happ reviews the progress of optimal dispatch going as far back as the early 1920’s, when engineers were concerned with the problem of economic allocation of generation or the proper division of the load among the generating units available.

Prior to 1930, various methods were in use such as: a the base load method where the next most efficient unit is loaded to its maximum capability, then the second most efficient unit is loaded, etc. B best point loading, where units are successively loaded to their lowest heat rate point, beginning with the most efficient unit and working down to the least efficient unit, etc. It was recognized as early as 1930, that the incremental method, later known as the equal incremental method, yielded the most economic results.

The theoretical work on optimal dispatch later led to the development of analog computers for properly executing the coordination equations in a dispatching environment. A transmission loss penalty factor computer was developed in 1954 and was used by aep in conjunction with an incremental loading slide rule for producing daily generation schedules in a load dispatching office. Analyzer was developed for use in economic scheduling for off line or on line use by 1955. The use of digital computers for obtaining loading schedules was investigated in 1954 and is used to tnis day. An electronic differential generation dispatch has been widely studied and reported by several authors in books 4,5,6,7,8.9,10,11,12,13,14,15,16. Some authors present various aspects of optimal power flow while others present the development of interfaces between such control actions such as economic dispatch ed and load frequency control lfc.

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Economic dispatch and load blacksburg, va 24061 such that it matches the area load while, simultaneously, both area frequency and the net tie line exchange are at their set points. Now both of these control actions fall under a single activity called automatic generation control agc . Traditionally, there was minimal interface between area control economic dispatch plus load frequency control and local unit control. Two recent papers 17,18 published in the ie proceedings also stress on economic dispatch in the perspective of other control functions within a control center. Optimal power flow the optimal power flow procedure consists of methods of utilizing load flow techniques for the purpose of economic dispatch. While some authors have used the ac load flow model others have used the dc load flow model.

The ac optimal load flow problem on the other hand consists of finding the active and reactive power output and the voltage magnitudes at any generator unit, in order to minimize the operating cost while meeting various security constraints. Security constrained dispatch involves those dispatch activities which are constrained to respect selected system security limits. In general, optimal power flow requires use of network modeling as well as resource modeling and naturally results in higher system costs. The latter is based on the p q the techniques used in solving optimal power flow as reported in the literature range from improved mathematical techniques to more efficient problem formulation.

Classical economic dispatch classical economic dispatch is limited to real power optimization, taking losses into account, but without security. The non compact methods include the injections method, the hessian approach, the dommel timney reduced gradient method and the generalized reduced gradient method. Reviewed are linear and non linear optimization methods which use several different algorithms.

The compact methods a review of the optimal power flow opf methods is also provided by talukdar, et al. The authors in both of these references discuss the relative performance criteria for different methodologies being employed in these procedures. General static optimization compact methods several authors have presented more efficient algorithms in the application of linear and non linear programming methods. 221 propose the conversion of the nonlinearly constrained dispatch problem to a series of constrained linear programming problems.

System voltages, active and reactive generation, and the phase angles are considered as part of the opf problem. According to the authors, the method is fast and has good convergence characteristics. 1231 introduce a two level optimization method for optimal power flow, the first level problem consists of the minimization of certain performance indices subject to a number of local constraints and power balance equation. The second level is the search for a global optimum obtained by choosing on the suprema1 level, the values of proper coordinating variables. A highly sparse factorization of the basis matrix is maintained during execution of the algorithm. In case of feasible solutions, the constraints are relaxed so as to reach a feasible luo, et al. 25 reduce the economic dispatch problem to a concise set of quasi linear equations resulting in a solution form similar to that of an electric network.

The equations are in terms of the bus incremental cost, otherwise known as the lagrange multipliers. Zs using ideas from their previous paper 25 develop a network model for the economic dispatch problem using the bus incremental costs as potential quantities. According to the authors’ theory, an area system may be reduced to a thevenin equivalent for economic dispatching by means of the network model.

271 use a linearized formulation of the general optimal load flow problem and apply minimization technique to an augmented cost function which contains a piecewise differentiable penalty cost function term. Lugtu 281 introduces the combined use of the differential algorithm and the simplex procedure of optimization in the security constrained dispatch. The constraints considered by the author are generation operating limits and response constraints, transmission constraints and system reserve constraints. According to the authors, significant storage reductions are achieved owing to the tableau sparsity, compared to the dantzig wolfe algorithm or quadratic programming. Another method using a sparsity technique and linear decompose the problem into n subproblems and a master chose the initial basis of the master problem by introducing artificial variables and setting up the appropriate phase i feasibility and phase ii optimality objective functions. Compute an objective function for each subproblem and solve each subproblem using the revised simplex method.

1321 reformulate the economic dispatch problem by introducing an added constraint on maximum frequency deviation following a postulated disturbance. The main difference between the frequency deviation constrained dispatch and the conventional economic dispatch is the allocation of the total system margin. In the latter case, the margin allocation is made without consideration of the minimum frequency following a specified disturbance. The method of solution adopted by the authors is a dantzig wolfe decomposition technique followed by several linear programming solutions. This reduces the dimension of the problem into several subproblems which correspond to physical areas that can be identified in the power network. The optimization routine is based on the revised simplex method in association with a fast decoupled load flow method. 34 present an alternative approach for computation of loss coefficients, or more popularly known as b constants.

The authors have used the method of least squares to this end and have demonstrated the simplicity and computational advantages over methods based on the earlier kror’s method. The method used a linear relationship between real and reactive power outputs of a generator as well as an optimally ordered factorization method for direct solution, thus avoiding the formation of 2 bus explicitly. The authors incorporate this method of computing loss coefficients in a classical economic dispatch and demonstrate its computational advantage over a dispatch method using load flow techniques. 35 study the relative performance of four algorithms used for parameter estimation in models used for optimal power flow. The models are 1 weighted least squares, 2 gauss newton method or bard algorithm, 3 marquardt algorithm, and 4 powell regression algorithm. The authors found an overall better performance by the weighted least squares method.

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36 compare the performance of a hybrid method of powell and the newton raphson method. Faster solution of the coordination equations are achieved dy the former method thus making its convergence characteristics superior. A method which combines linear programming with the newton approach for solving optimal power flows is described by maria et al. 381 use linear programming techniques in their solution of the opf but with the additional capability of rescheduling the active power control to make corrections for voltage magnitude problems. The authors contend that no additional computing time would be required when the corrections are achieved by reactive means. 39 introduce a method based on three separate modules but coupled to one another.