Optimal Dynamic Dispatch Owing to Spinning-Reserve and Power-Rate Limits

Rosen J.B.

more constraints or equations, with either a linear or nonlinear objective function. This distinction is made primarily on the basis of the difficulty of solving these two types of nonlinear problems. The first type is the less difficult of the two, and in this, Part I of the paper, it is shown how it is solved by the gradient projection method. It should be noted that since a linear objective function is a special case of a nonlinear objective function, the gradient projection method will also solve a linear programming problem. In Part II of the paper [16], the extension of the gradient projection method to the more difficult problem of nonlinear constraints and equations will be described. The basic paper on linear programming is the paper by Dantzig [5] in which the simplex method for solving the linear programming problem is presented. The nonlinear programming problem is formulated and a necessary and sufficient condition for a constrained maximum is given in terms of an equivalent saddle value problem in the paper by Kuhn and Tucker [10]. Further developments motivated by this paper, including a computational procedure, have been published recently [1]. The gradient projection method was originally presented to the American Mathematical Society

van den Bosch P.P., Honderd G.

Ross D., Kim S.

A set of procedures and algorithms are developed for dynamic economic dispatch of generation units. When coupled with a short-term load predictor, look- ahead capability is provided by the dynamic economic dispatch that coordinates predicted load changes with the rate-of- response capability of generation units. Dynamic economic dispatch also enables valve-point loading of generation units. Two examples are provided which demonstrate that our approach overcomes the severe limits on the number of units that could be dynamically dispatched in past approAches.

Dillon T.S., Edwin K.W., Kochs H.-., Taud R.J.

A method for determining the unit commitment schedule for hydro-thermal systems using extensions and modifications of the Branch and Bound method for Inteler Programming has been developed. Significant features of the method include its computational practicability for realistic systems and proper representation of reserves associated with different risk levels. Contracts relating to power interchange have also been adequately modelled for such an approach.

Bechert T.E., Nanming Chen

Current research in Automatic Generation Control emphasizes coordination of the regulation and the economic dispatch functions into a single systems problem. A dynamic optimal control problem formulation has previously been suggested. In this paper optimal trajectories are found for up to five maneuverable generators, using a new multi-pass dynamic programming method to make such solutions feasible. Dynamic valve point loading and singular solutions are considered. Computer studies have applied the method to several examples, including sudden changes in area load, and supplying the morning rise in area load.

Fletcher R.

Niu Q., Wang L., You M.

The increasing complexity of modern power systems has led to the emergence of large-scale dynamic economic dispatch (DED) problems. To solve a large-scale DED problem with high-dimensional decision variables and various constraints is still a challenge using most existing evolutionary algorithms. In this paper, we propose a covariance matrix adaptation evolution strategy based on cooperative co-evolutionary framework (CC-CMA-ES) using delta grouping for solving large-scale DED problem. The experiment results suggest that the CC-CMA-ES is a fast and accurate approach for large-scale DED problems in terms of computation time, solution quality and convergence speed. Integrating CMA-ES into CC the framework can reduce the computation time by 97.5%, compared with basic CMA-ES, revealing the great potential of CC-CMA-ES for solving more difficult large-scale DED problems.

Pattanaik J.K., Basu M., Dash D.P.

This paper presents a comparative study for five artificial intelligent (AI) techniques to the dynamic economic dispatch problem: differential evolution, particle swarm optimization, evolutionary programming, genetic algorithm, and simulated annealing. Here, the optimal hourly generation schedule is determined. Dynamic economic dispatch determines the optimal scheduling of online generator outputs with predicted load demands over a certain period of time taking into consideration the ramp rate limits of the generators. The AI techniques for dynamic economic dispatch are evaluated against a ten-unit system with nonsmooth fuel cost function as a common testbed and the results are compared against each other.

Pattanaik J.K., Basu M., Dash D.P.

Hashemi P., Eghtedarpour N.

One of the important optimization problems in power systems operation is Dynamic Economic Load Dispatch (DELD). Economic load dispatch for a time interval of few hours is done considering the constraints related to maximum rate of change of active power generated by units and other system constraints such as prohibited operating zones and the valve effect. These constraints cause the optimization problem to be non-smooth and non-convex. An improved Harmony Search Algorithm (HSA) is presented in this paper to solve the DELD problem in the presence of Flexible AC Transmission System (FACTS) devices considering the above mentioned constraints. The FACTS devices considered in this paper are Static VAR Compensator (SVC) and Thyristor Controlled Series Compensator (TCSC). The proposed algorithm is evaluated on IEEE 30-Bus Test System. Results show high strength of the proposed method for solving the DELD problem.

Chunghun Kim, Yonghao Gui, Chung Choo Chung, Yong-Cheol Kang

This paper develops dynamic economic dispatch (DED) using model predictive control (MPC) based on Weibull probabilistic distribution function (PDF). Firstly we performed economic dispatch (ED) based onWeibull PDF.We considered the probabilistic cost about over-estimated and under-estimated cost of wind power by using Weibull PDF. Secondly we implemented DED formulated in a MPC framework using the maximum wind power capability from the ED results since ED does not consider the ramp rate constraint. By using dispatch error cost, we could consider the current status of reliable generation by using the proposed MPC method. It turns out that the DED using MPC method is very effective in coping with intermittent resource such as wind variability.

Sun W., Cai J.

As valuable energy in iron- and steel-making process, by-product gas is widely used in heating and technical processes in steel plant. After being used according to the technical requirements, the surplus by-product gas is usually used for buffer boilers to produce steam. With the rapid development of energy conservation technology and energy consumption level, surplus gas in steel plant continues to get larger. Therefore, it is significant to organize surplus gas among buffer boilers. A dynamic programming model of that issue was established in this work, considering the ramp rate constraint of boilers and the influences of setting gasholders. Then a case study was done. It is shown that dynamic programming dispatch gets more steam generation and less specific gas consumption compared with current proportionate dispatch depending on nominal capacities of boilers. The ignored boiler ramp rate constraint was considered and its contribution to the result validity was pointed out. Finally, the significance of setting gasholders was studied.

Thenmalar K., Allirani A.

Economic load dispatch (ELD) is an important optimization task in power system. It is the process of allocating generation among the committed units such that the constraints imposed are satisfied and the energy requirements are minimized. There are three criteria in solving the economic load dispatch problem. They are minimizing the total generator operating cost, total emission cost and scheduling the generator units. In this paper Firefly Algorithm(FA) solution to economic dispatch problem is very useful when addressing heavily constrained optimization problem in terms of solution accuracy. Results obtained from this technique clearly demonstrate that the algorithm is more efficient in terms of number of evolution to reach the global optimum point. The result also shows that the solution method is practical and valid for real time applications In this paper the Firefly Algorithm(FA) solves economic load dispatch (ELD) power system problem of three generator system, six generator system with emission constraints and twelve generator system with introduced population-based technique - is utilized to solve the DED problem. A general formulation of this algorithm is presented together with an analytical mathematical modeling to solve this problem by a single equivalent objective function. The results are compared with those obtained by alternative techniques proposed by the literature in order to show that it is capable of yielding good optimal solutions with proper selection of control parameters. The validity and quality of the solution obtained Firefly Algorithm(FA) based economic load dispatch method are checked and compared with Artificial colony algorithm(ABC), Particle Swarm Optimization Algorithm (PSO), simulated Annealing Algorithm(SA).

Basu M.

Dynamic economic dispatch deals with the scheduling of online generator outputs with predicted load demands over a certain period of time so as to operate an electric power system most economically. This paper proposes a hybrid methodology integrating bee colony optimization with sequential quadratic programming for solving dynamic economic dispatch problem of generating units considering valve-point effects. This hybrid method incorporates bee colony optimization as a base level search which can give a good direction to the optimal region and sequential quadratic programming as a local search procedure which is used to fine tune that region for achieving the final solution. Numerical results of a ten-unit system have been presented to demonstrate the performance and applicability of the proposed method. The results obtained from the proposed method are compared with those obtained from hybrid of particle swarm optimization and sequential quadratic programming and hybrid of evolutionary programming and sequential quadratic programming.

Elaiw A.M., Xia X., Shehata A.M.

Dynamic economic emission dispatch (DEED) problem is used to determine the optimal generation schedule of online generating units by minimizing both fuel cost and emission simultaneously under load demand constraint, ramp rate constraint and other constraints. DEED with the consideration of valve-point effects is a complicated non-linear constrained multi-objective optimization problem with non-smooth and non-convex characteristics. The first purpose of this paper is to solve the DEED problem using a hybrid method which combines differential evolution (DE) and sequential quadratic programming (SQP). DE is used as a global optimizer and SQP is used as a fine tuning to determine the optimal solution at the final. A five-unit system with non-smooth fuel cost function has been taken to illustrate the effectiveness of the proposed method compared with other methods. The second purpose of this paper is to modify the DEED problem such that its optimal solution can be periodically implemented.

Abu-Mouti F.S., El-Hawary M.E.

Power utilities strive for optimal economic operation of their electric networks while considering the challenges of escalating fuel costs and increasing demand for electricity. The dynamic economic dispatch (DED) occupies a prominent place in a power system's operation and control. It aims to determine the optimal power outputs of on-line generating units in order to meet the load demand subject to satisfying various operational constraints over finite dispatch periods. Similar to most real-world complex engineering optimization problems, the nonlinear and nonconvex characteristics are more prevalent in the DED problem. Therefore, obtaining a truly optimal solution presents a challenge. In this paper, the artificial bee colony (ABC) algorithm - a recently introduced population-based technique - is utilized to solve the DED problem. Integrating a renewable-energy source and analyzing its impact is considered as well. A sample test system with a dispatch period of 24-hour is designated to validate the outcomes. The promising results prove that the ABC algorithm has a great potential to be applied in different electric power system optimization areas.

Abu-Mouti F.S., El-Hawary M.E.

Meta-heuristic optimization algorithms have gained popularity in solving complex, constrained optimization problems. The dynamic economic dispatch (DED) problem represents an example of such complex, constrained optimization problems. The aim of DED is to operate online units economically to meet the load demand, subjected to satisfying highly nonlinear and non-convex practical constraints. Therefore, it is possible that computational methods may not yield a global extremum as many local extrema may be encountered. This paper presents a novel constrained search-tactic to solve the DED problem. Two recently introduced meta-heuristic techniques, namely sensory-deprived optimization algorithm (SDOA) and artificial bee colony (ABC) algorithm, are adopted to evaluate the performance of the proposed constraint search-tactic. Two test systems are used to reveal the effectiveness of the offered tactic which successfully accelerates the employed algorithms' performance toward the optimal feasible region. After comparing the results, the outcomes when integrating the constrained search-tactic either outperformed or matched those obtained using other well-known methods.

Chen D., York M.

In contrast with conventional Economic Dispatch (ED) problems which optimally allocates the generation of all dispatchable generating units, the economic dispatch with time is concerned with optimal allocation of unit generation projected for multi-intervals over a period of future. This paper aims at applying a new approach to the so-called dynamic economic dispatch based on the Dantzig-Wolfe decomposition method. The formulation of the dynamic dispatch problem in this paper is very similar to that of the conventional economic dispatch problem with the exception that temporal constraints are introduced for the dynamic economic dispatch problem. Even though the solution scheme for the dynamic economic dispatch is more complicated, the solution still shares the popular ”equal lambda” property per each time interval of the dispatch horizon.

Noman N., Iba H.

This paper proposes cellular differential evolution (cDE) algorithm for solving dynamic economic dispatch (DED) problems with valve-point effects. DEDs are high dimensional optimization problems with many equality and inequality constraints. The problem of premature convergence in solving high dimensional optimization problems using evolutionary algorithms (EAs) could be fought using population structuring. This work investigates the suitability a structured DE algorithm, called cDE, in solving these large dimensional optimization tasks. The suitability and effectiveness of the proposed algorithm is validated using two test systems consisting of 10 and 13 thermal units respectively. Numerical results clearly show that the proposed method outperforms existing methods in terms of solution quality and robustness.

Xia X., Zhang J., Elaiw A.

Two formulations exist for the problem of the optimal power dispatch of generators with ramp rate constraints: the optimal control dynamic dispatch (OCDD) formulation based on control system models, and the dynamic economic dispatch (DED) formulation based on optimization. Both are useful for the dispatch problem over a fixed time horizon, and they were treated as equivalent formulations in literature. This paper first shows that the two formulations are in fact different and both formulations suffer from the same technical deficiency of ramp rate violation during the periodic implementation of the optimal solutions. Then a model predictive control (MPC) approach is proposed to overcome such a technical deficiency. Furthermore, it is shown that the MPC solutions, which are based on the OCDD framework, converge to the optimal solution of an extended version of the DED problem and they are robust under certain disturbances and uncertainties. Two standard examples are studied: the first one of a ten-unit system shows the difference between the OCDD and DED, and possible ramp rate violations, and the second one of a six-unit system shows the convergence and robustness of the MPC solutions, and the comparison with OCDD as well.

Basu M.

Dynamic economic dispatch determines the optimal scheduling of online generator outputs with predicted load demands over a certain period of time taking into consideration the ramp rate limits of the generators. This paper proposes artificial immune system based on the clonal selection principle for solving dynamic economic dispatch problem. This approach implements adaptive cloning, hyper-mutation, aging operator and tournament selection. Numerical results of a ten-unit system with nonsmooth fuel cost function have been presented to validate the performance of the proposed algorithm. The results obtained from the proposed algorithm are compared with those obtained from particle swarm optimization and evolutionary programming. From numerical results, it is found that the proposed artificial immune system based approach is able to provide better solution than particle swarm optimization and evolutionary programming in terms of minimum cost and computation time.