Tie-line Constraints Research Articles

Fuzzified Particle Swarm Optimization Algorithm for Multi-area Security Constrained Economic Dispatch

This article presents a new computationally efficient fuzzified particle swarm optimization algorithm for solving the security-constrained multi-area economic dispatch of an interconnected power system. The core objective of the security-constrained multi-area economic dispatch is to determine the generation allocation of each committed unit in the system and the power exchange between areas so as to minimize the total generation cost without violating the tie-line constraint. The proposed fuzzified particle swarm optimization algorithm is based on the combined application of fuzzy logic strategy incorporated in the particle swarm optimization algorithm. The proposed method was tested on a system of three interconnected areas. The investigation reveals that the proposed method can provide an accurate solution with fast convergence and has the potential to be applied to other power system optimization problems.

Multi-area economic dispatch with tie-line constraints employing evolutionary approach

Economic dispatch (ED) has the objective of generation allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. For the sake of simplicity, ED is generally solved without accounting for transmission constraints. However, in deregulated power system environment it is essential to model the ED problem for practical multi-area cases with tie line constraints. Most of the conventional gradient based methods are time consuming, suffer from dimensionality problem and assume the fuel cost curves of generating units to be piecewise linear, monotonically increasing in nature. The resulting dispatch solutions are therefore inaccurate; sometimes producing infeasible solutions for modern generating units having non convex cost curves. On the other hand evolutionary methods do not suffer from convexity assumptions and achieve fast solutions even for complex non-linear, non-convex, multi-modal optimization problems. This paper reviews and compares some evolutionary techniques for multi-area economic dispatch (MAED). The paper presents an extensive comparison of the search capability and convergence behavior of i) Classical differential evolution (DE) and its various strategies ii) Classical particle swarm optimization (PSO) and iii) An improved PSO with a parameter automation strategy having time varying acceleration coefficients (PSO_TVAC) for solving MAED problems for two area and three area test power systems with 4, 10 and 40- generating units. The results are found to be superior compared to some recently published results. Keywords: Differential evolution, Multi-area economic dispatch, multiple fuel options, particle swarm optimization, transmission capacity constraints. Time varying acceleration coefficients (TVAC), Valve point loading effects.

Multi-Area Unit Commitment with Bilateral Contract Approach in Deregulated Electricity Market

The eventual goal of this paper is to help the generating companies and load-serving entities to choose appropriate relative levels of interconnected system versus bilateral trades while considering risk, and economic performance. In competitive power markets, electricity prices are determined by balance between demand and supply in electric power exchanges or bilateral contracts. The problem formulation is bilateral contract incorporated into Multi-area unit commitment with import/export and tie-line constraints. This proposed method considers maximizing own profit or minimize the operating cost among the generating companies in multi-area system. The feasibility of the proposed algorithm has been demonstrated using IEEE system with four areas and experimental results shows that proposed method is reliable, fast and computationally efficient

A Novel EP Approach for Multi-area Economic Dispatch with Multiple Fuel Options

This paper presents a novel approach to multi-area economic dispatch problems with multiple fuel options using a hybrid evolutionary programming method. The objective is to minimize the operation cost of the entire system while satisfying the tie line constraints. In this paper, EP-LMO (Evolutionary Programming with Levenberg-Marquardt Optimization) technique is proposed to solve multi-area economic dispatch problems with multiple fuel options. The EP-LMO is developed in such a way that a simple evolutionary programming (EP) is applied as a base level search to find the direction of the optimal global region. And Levenberg-Marquardt Optimization (LMO) method is used as a fine tuning to determine the optimal solution. The applicability and validity of the proposed approach on multi-area economic dispatch problems are presented in two parts. In Part I, two multi-area bench mark problems without fuel options are considered. In Part II, 10 unit system with both multi-area and multi-fuel options is considered. The proposed approach is compared with the results of Incremental Network Flow Programming, Spatial Dynamic Programming and Evolutionary Programming approaches. The results show that the EP-LMO gives the optimum generation cost than any other methods.

Evolutionary Programming-Based Multiarea Economic Dispatch with Tie Line Constraints

This paper presents a new approach to include tie line constraints in multiarea economic dispatch problems by using evolutionary programming (EP). The proposed method always finds the global or near global optimum for small and reasonable-sized multiarea economic dispatch (MAED) problems. The inclusion of tie line constraints to MAED does not introduce any complexity in the approach. The applicability and validity of the proposed method is shown by implementing it on three example systems - 2, 4, and 14 areas - and their results are compared with those obtained by classical economic dispatch, network flow programming, and dynamic programming methods, respectively. The results show that the proposed method can serve as a potential tool for solving MAED problems.

Multi-area economic dispatch with tie line constraints

This paper presents a new method for solving the multi-area power system economic dispatch (MAED) problem with tie line constraints. This formulation extends the traditional economic dispatch methods used in study applications such as unit commitment to include area demand constraints, area reserve constraints, and tie line capacity constraints between the modeled areas. The MAED is formulated as a capacitated nonlinear network flow problem which is solved using a high-speed network load flow code. The MAED determines the amount of power that can be economically generated in one area and transferred to another area to displace generation in the second area. The network flow model does not compute the actual power transfer between areas. The paper demonstrates that a significant number of the problem constraints may be formulated as network-type, and as a result, the method provides a robust, high-speed solution method for surprisingly large class of electric utility problems including the ability to analyze potential purchases and sales in a multi-area power system environment.

Composite system spinning reserve assessment in interconnected systems

Deterministic methods to evaluate unit commitment and spinning reserve requirements cannot explicitly recognise the stochastic nature of a power system. Probabilistic techniques can, however, be used to incorporate a wide range of stochastic system parameters. The usual techniques of probabilistic unit commitment in an interconnected power system consider the tie-line constraints but not the transmission facilities within the systems. In a real power system, the transmission facilities within the systems have limits and do fail. Units committed from only probabilistic generation studies, therefore, provide optimistic values. In the paper, the usual techniques of unit commitment are extended to calculate a risk value from a composite system point of view. The effect on the risk value of rapid start and hot reserve units are considered.

Optimal generation scheduling for constrained multi-area hydrothermal power systems with cascaded reservoirs

The optimization problem in this paper is targeted at large-scale hydrothermal power systems. The thermal part of the system is a multi-area power pool with tie-line constraints, and the hydro part is a set of cascaded hydrostations. The objective is to minimize the operation cost of the thermal subsystem. This is an integer nonlinear optimization process with a large number of variables and constraints. In order to obtain the optimal solution in a reasonable time, we decompose the problem into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. For the hydro subsystem, network flow concepts are adopted to coordinate water usage over the entire study time span, and the reduced gradient method is used to overcome the linear characteristic of the network flow method in order to obtain the optimal solution. In this study, load forecasting errors and forced outages of generating units are incorporated in system reliability requirements. Three case studies for the proposed method are presented.

Power generation scheduling for multi-area hydro-thermal systems with tie line constraints, cascaded reservoirs and uncertain data

The authors propose an approach to the short-term generation scheduling of hydro-thermal power systems (GSHT). The objective of GSHT is to minimize the total operation cost of thermal units over the scheduling time horizon. To solve the problem within a reasonable time, the problem is decomposed into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. A probabilistic method is employed in considering load forecasting errors and forced outages of generating units to satisfy system reliability requirements. For the hydro subsystem, network flow concepts are adopted to coordinate water use over the entire study time span and the reduced gradient method is used to overcome the linear characteristic of the network flow method to obtain the optimal solution. Three case studies for the proposed method are presented. >

Decomposition Approach to Nonlinear Multiarea Generation Scheduling with Tie-line Constraints Using Expert Systems

Decomposition Approach to Nonlinear Multiarea Generation Scheduling with Tie-line Constraints Using Expert Systems

Application of the equivalent area model to multi-area generation scheduling with tie-line constraints

In this paper, a new method is proposed for solving the multi-area generation scheduling problem. The problem includes unit commitment and economic dispatch modules. The objective is to obtain an economic operation without violating various system constraints. This is a mixed integer-nonlinear optimization process. In the proposed method, an artificial neural network (ANN) is used to obtain the initial unit commitment schedule for every area, with the assumption that there are no transmission flows among areas. In order to get the minimum operation cost for the entire system while preserving constrained units, areas and tie-lines, an iterative procedure is used to coordinate unit combinations and energy dispatch schedules. An expert system is employed to modify the initial unit commitment pattern of each area by reducing the number of committed units to a minimum while satisfying the area constraints. To consider tie-line limitations and incorporate transmission losses in the economic dispatch, an equivalent model for each area combined with the equal incremental cost method (λ method) is adopted for computing the generation assigned to every area and the power allocated to all committed units. A four-area system with 26 thermal units in each area is used to test the algorithm. The algorithm is implemented on a PC/386 and the experimental results show that the method is reliable, fast and computationally efficient.

A decomposition approach to nonlinear multi-area generation scheduling with tie-line constraints using expert systems

The authors propose a rigorous method to treat multiarea generation scheduling with tie line limits. An expert system was used for obtaining the initial solution. As the generation scheduling problem involves unit commitment and economic dispatch, the method adopts an iterative procedure to deal with these two phases. The hourly load demand and the area power generation will cause the tie flows to change. To maintain the operation security in every area, the spinning reserve should comply with the area power generation rather than its load demand. After economic dispatch, it is necessary to adjust the unit commitment in each area for preserving the spinning reserve requirements. Heuristics were used to modify the generation unit combinations. The objective is to find an economic generation schedule for a multiarea system. The interchange transactions among areas represent the transportation problem, embedded within the nonlinear optimization process. The equivalent system concept is adopted, and the transmission losses are included in this study. A four-area system with each area consisting of 26 units was used to test the efficiency of the proposed algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Heuristic multi-area unit commitment with economic dispatch

An improved multi-area unit commitment and economic dispatch algorithm is proposed. The approach supplements the traditional dynamic programming unit commitment with heuristic adjustments to refine the commitment schedule in each area. A global economic dispatch scheme coordinates the transactions between areas. A new tie-line constraint checking is included which is simple and effective. The overall algorithm can be implemented on an IBM-PC, which can process a fairly large system in a reasonable period of time. Experimental results show the application potential of this method to general multi-area power generation scheduling problems.

Interconnected System Spinning Reserve Requirements

There has been a considerable amount of work done in the area of static capacity reliability evaluation in interconnected systems. The first important paper in this subject1 utilized a two dimensional probability array upon which the tie line constraints were imposed. The basic generating unit statistics in static and spinning reserve studies are fundamentally different and in the latter case the problem is a question of will the capacity immediately available to the system be capable of satisfying the load in the event of possible capacity and load changes. The possible assistance under these conditions from an interconnected system cannot therefore be neglected in determining the risk of just carrying or failing to carry the system load. In a static capacity interconnected system study, the tie line is normally rated at its nominal value. In a spinning study, the tie line rating or inter-system transfer capability will depend upon the immediate and known conditions between each system, i. e., the existing transmission configuration, the scheduled generation pattern, etc. etc. These could be quite variable even over the course of a day.