Modified sub-gradient based combined objective technique and evolutionary programming approach for economic dispatch involving valve-point loading, enhanced prohibited zones and ramp rate constraints (original) (raw)
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IEE Proceedings - Generation, Transmission and Distribution, 2005
A simple and efficient algorithm based on evolutionary strategies is proposed for the solution of the economic dispatch (ED) problem with noncontinuous and nonsmooth/nonconvex cost functions and with generator constraints being considered. The proposed method solves both, the ED problem with nonconvex/nonsmooth cost functions due to valve-point loading and the ED problem that takes into account nonlinear generator characteristics such as ramp-rate limits and prohibited operating zones in the power system operation. The effectiveness of the algorithm is demonstrated using six different test systems and the performance is compared with other relevant methods reported in the literature. In all cases, the proposed algorithm either matches or outperforms the behaviour reported for the existing algorithms. This level of performance is obtained despite the simplicity of the approach.
Abstract—A security constrained non-convex power dispatch problem with prohibited operation zones and ramp rates is formulated and solved using an iterative solution method based on the modified subgradient algorithm operating on feasible values (F-MSG). Since the cost function, all equality and inequality constraints in the nonlinear optimization model are written in terms of the bus voltage magnitudes, the phase angles, the off-nominal tap settings, and the susceptance values of static-var (SVAR) systems, they can be taken as independent variables. The actual power system loss is included in the solution since the load flow equations are inserted into the model as the equality constraints. The proposed technique is tested on the IEEE 30-bus, 140 generator and 40 generator test systems and compared against the other methods based on heuristic and deterministic algorithms. The significant saving in the solution time is due to the elimination of the pow
This article presents how multiobjective bilevel programming (MOBLP) in a hierarchical structure can be efficiently used for modeling and solving environmental-economic power generation and dispatch (EEPGDD) problems through Fuzzy Goal Programming (FGP) based on genetic algorithm (GA) in a thermal power system operation and planning horizon. In MOBLP formulation, first the objectives associated with environmental and economic power generation are considered two optimization problems at two individual hierarchical levels (top level and bottom level) with the control of more than one objective, that are inherent to the problem each level. Then, the optimization problems of both the levels are described fuzzily to accommodate the impression arises for optimizing them simultaneously in the decision situation. In the model formulation, the concept of membership functions in fuzzy sets for measuring the achievement of highest membership value (unity) of the defined fuzzy goals in FGP formulation to the extent possible by minimising under-deviational variables associated with membership goals defined for them on the basis of their weights of importance is considered. Actually, the modeling aspects of FGP are used here to incorporate various uncertainties arises in generation of power and dispatch to various locations. In the solution process, a GA scheme is used in the framework of FGP model in an iterative manner to reach a satisfactory decision on the basis of needs in society in uncertain environment. The GA scheme is employed at two different stages. At the first stage, individual optimal decisions of objectives are determined for fuzzy goal description of them. At the second stage, evaluation of goal achievement function to arrive at the highest membership value of the fuzzy goals in the order of hierarchical of optimizing them in the decision situation. The effective use of the approach is tested on the standard IEEE 6-Generator 30-Bus System.
A security constrained economic dispatch problem with prohibited operation zones for a lossy electric power system is formulated. An iterative solution method that is based on modified subgradient algorithm operating on feasible values is employed to solve it. Bus voltage magnitudes and phase angles, off-nominal tap settings and susceptance values of svar systems are taken as independent (decision) variables in the solution algorithm. Since load flow equations are added into the model as equality constraints, actual power system loss is used in solution of the optimization model. The proposed technique is tested on IEEE 30-bus test systems. The minimum total cost rates and the solution times obtained from F-MSG algorithm and from the other techniques are compared, and the outperformance of the F-MSG algorithm with respect to the other methods in each test system is demonstrated.
Non-convex fuel cost rate curves Valve point effect Security constraints The modified subgradient algorithm based on feasible values F-MSG algorithm a b s t r a c t A security constrained power dispatch problem with non-convex total cost rate function for a lossy electric power system is formulated. Then, an iterative solution method proposed by us and based on modified subgradient algorithm operating on feasible values (F-MSG) is used to solve it. Since all equality and inequality constraints in our nonlinear optimization model are functions of bus voltage magnitudes and phase angles, off-nominal tap settings and susceptance values of svar systems, they are taken as independent variables. Load flow equations are added to the model as equality constraints. The unit generation constraints, transmission line capacity constraints, bus voltage magnitude constraints, off-nominal tap setting constraints and svar system susceptance value constraints are added into the optimization problem as inequality constraints. Since F-MSG algorithm requires that all inequality constraints should be expressed in equality constraint form, all inequality constraints are converted into equality constraints by the method, which does not add any extra independent variable into the model and reducing the solution time because of it, before application of it to the optimization model. The proposed technique is tested on IEEE 30-bus and IEEE 57 bus test systems. The minimum total cost rates and the solution times obtained from F-MSG algorithm and from the other techniques are compared , and the outperformance of the F-MSG algorithm with respect to the other methods in each test system is demonstrated.
Constrained Evolutionary Programming Approaches to Power System Economic Dispatch
2005
This paper proposes a novel methodology of Constraint evolutionary programming for solving dynamic economic dispatch. Dynamic Economic Dispatch is one of the main functions of power generation operation and control. It determines the optimal settings of generator units with predicted load demand over a certain period of time. The objective is to operate an electric power system most economically while the system is operating within its security limits. Ten units test system with smooth and non- smooth fuel cost functions are considered to illustrate the suitability and effectiveness of the proposed method.
Unit Commitment is the problem which finds the most economic production for power generation, when the power consumption and different constraints of the power plants are known. Also, economic dispatch as the operation of power plants to produce energy at the lowest cost to reliably serve consumers, and considering any operational limits related to generation and transmission is one of the most important calculations in power system. There are a lot of papers and researches to modeling the real constraints of these two problems. Economic dispatch considering prohibited operating zones and ramp-rate limits is one of the most important branches related to economic dispatch. This paper presents an effective algorithm for solving economic dispatch problem in power systems with units which have prohibited operating zones constraints and ramp-rate limits based on genetic algorithm. The proposed approach is a two stage algorithm which has two main advantages. First, it reduces the total costs of operation, and secondly, it increases the probability of convergences the solutions. The proposed algorithm has been tested successfully on 15 and 40 units and has been compared with other algorithm. The test results verify the advantages of the proposed method comparing to other works.
— Optimization is a mathematical technique that concerns the finding of maxima or minima of functions in some feasible region. There is no business or industry which is not involved in solving optimization problems. A variety of optimization techniques compete for the best solution. Economic Dispatch (ED) is also one of the optimization problem. ED is the process of determining optimal output of available number of electric power generating stations in order to meet total system load, at a minimum possible cost while serving power to the public in a robust and reliable manner satisfying physical and operational constraints. Scarcity of energy resources, ever growing production cost of generation and increased load demand, there is a need to optimize the economic dispatch problem. In this research work, a hybrid technique proposed to solve non-linear ED problem named as Hybrid Particle Swarm Optimization with Gravitational Search Algorithm (HPSO-GSA) considering/neglecting valve point effects, prohibited operating zones, ramp rate limits and transmission losses. In order to evaluate the performance of the proposed Hybrid PSO-GSA algorithm has been tested on different generating unit test systems with different constraints and defined load demands. The simulation results of proposed algorithm are in comparison with the techniques in literature proves the efficiency and effectiveness of the proposed algorithm.