Multi-objective Hydrothermal Generation Scheduling based on Heuristic Algorithms

Abstract

Electric power today plays an exceedingly important role in the life of the community and in the development of various sectors of economy. In view of increase in the demand of electricity, considerable attention is given to interconnection between different systems. The hydro plants have high capital cost and low operating cost as compared to thermal plants. Hydro resources are considered to provide a clean and environment friendly energy option. Hydro plants are usually scheduled for peak load periods and thermal plants are normally scheduled for base-load period as hydro units are started-up and shut-down efficiently as compared to thermal units. Hence, the exploitation of hydro resources becomes important. The major concern of hydro resources is stochastic nature of availability. So, the integration between hydro and thermal systems is essential for the welfare, development and economic progress of our society. The fundamental requirement of hydro-thermal generation scheduling (HTGS) is to utilize the limited amount of water available to its fullest extent, such that the total system production cost and pollutants emission of thermal units are minimized while satisfying hydraulic and power system network constraints. The integrated operation of the hydro-thermal system is split into long-term and short-term generation scheduling problems. The planning period is one or more years for long-term HTGS problems. For short-term HTGS, planning period is an hour or a day or a week as the load demand on the power system exhibits cyclic variations. The amount of water to be utilized for short-range HTGS problem is known from the solution of the long-range HTGS problem. Conventional hydroelectric plants are classified into run-of-river plants and storage plants. Run-of-river plants have little storage capacity, and utilize water as it becomes available. Storage plants are associated with reservoirs, during periods of low power requirements water is stored in the reservoirs and then released when the demand is high. Hydroelectric power plants are situated on different streams and on the same stream. The operation is different in case when the hydro plants are located on the same stream or on different streams. The operation of down steam plant depends on the immediate upstream plant. However, downstream plant influences the immediate upstream plant by its effect on tail water elevation and effective head. Hydro-thermal generation scheduling is a large scale and complex problem owing to the large number of constraints, so it has been characterized as a nonlinear and non-convex optimization problem. The HTGS problem becomes difficult to solve due to stochastic nature of water availability. Various types of probabilistic variations are sources of uncertainties in HTGS problem, which leads to deviation from optimal operation and results rise in the production cost due to uncertain factors. Besides electric energy, thermal units also produce pollutant emissions, which deteriorate air quality. In general, a large-scale system typified by an electric power system also possesses multiple objectives to be achieved viz. economics operations, reliability, security, and environment. In essence, the HTGS is visualized as a multi-objective optimization problem. Optimization techniques applied to solve HTGS problem are broadly divided into two main categories that are local search and global search techniques. Further, local search techniques are classified into gradient and direct search methods. Most of the gradient methods are applied to solve the HTGS problem with number of simplifying assumptions in order to make the optimization problem more tractable and simple. Sometimes implications may lead to false global optimum solution by virtue of simplifications. Direct search techniques do not require any information about the gradient and higher order gradients of the objective function whereby these techniques perform the search by explorative and pattern moves. One of the main disadvantages of direct search method is that when the search space is large or non-convex and function is multimodal, solution may converge to local solution. Global search techniques are a class of stochastic optimization also known adaption techniques, which are inspired, by natural evolution or nature. Global search techniques have multi-point search strategies as compared to local search techniques, which have single-point search strategies. Despite of number of advantages offered by global search techniques these are comparatively inefficient in fine tuning the solution. Real-world multi-objective optimization problems give rise to set of optimal solutions called non-inferior solutions in place of single optimal solution. Mainly, multi-objective optimization techniques are grouped under two major categories: non-interactive and interactive. In the non-interactive method, a global performance function of the objectives is identified and optimized with respect to the constraints. On the other hand, in the interactive method, a local preference function or trade-off among objectives is identified by interacting with decision makers (DMs) and the solution process proceeds gradually towards the globally satisfactory solution. Solution methodologies for solving interactive multi-objective problem differ in two ways: the procedure used to generate non-inferior solution, the ways used to interact with the DMs, and the type of information made available to DM such as trade-offs. The main objective of DM is to fulfill the conflicting goals while satisfying the system constraints. A hydro-thermal electric power system possesses multiple conflicting objectives to be achieved like economic operation and minimal impact on environment with due consideration of inaccuracies and uncertainties in the system data. The optimization techniques search the best possible solution with minimal effort that means there is a trade-off between the computational effort and the quality of the solution. When the dimension or search space of the problem is wide or problem is multimodal, the optimization techniques need different exploration and exploitation strategies. The local search techniques are more exploitation oriented whereas global search techniques are more explorative oriented. So, there is need of heuristic optimization technique that can provide a balance between exploration and exploitation to speed up the process of finding a satisfactory solution. For multi-objective problems, various techniques are proposed to generate non-inferior solutions. Out of which weighting method is one of the most promising approaches, however in this method there is no rational basis to decide objective weights. So, there is a need to evaluate objective weights so that unified objective function should not lose any information. In previous studies of stochastic HTGS problem, expected volume deviations are not considered since hydro power output and coefficients of water discharge rate are random variables. So, there is a scope to study the effect of reservoir volume deviations. In the thesis work, heuristic optimization techniques are proposed in which global and local search techniques are integrated to take advantages of both search techniques while offsetting their disadvantages. Global search techniques exploit the search area to identify parts with high quality solutions and local search techniques intensify the search in promising areas. The predator-prey optimization (PPO) and evolutionary programming (EP) are undertaken as global search techniques. The PPO technique is based on PSO with additional predator effect. In PPO, predators attract towards the global best prey particle that helps to explore the search area more effectively. In EP, chromosomes share information with each other and population moves like a one group towards an optimal area. Predator-prey optimization and EP update their information in different approaches. Predator-prey optimization does not have mutation operator as used in EP. The PPO and EP algorithms have excellent global search capabilities but these techniques have some limitations in local search. In proposed heuristic optimization techniques, Powell’s pattern search (PPS) is taken as a local search technique. Powell’s pattern search is based on conjugate direction method and is expected to speed up the convergence of nonlinear objective functions. Further, the optimum operational strategies for integrated hydro-thermal electric power system has been explored by applying proposed heuristic optimization techniques using selective favourable features of PPO, EP and PPS. The proposed optimization techniques are applied to search optimum solution of fixed/variable-head and multi-chain short-term HTGS problems. The proposed optimization techniques are also validated on long-term HTGS problems. In the research work, two approaches are applied to solve multi-objective optimization problem. In one approach, objective functions are modeled using fuzzy set theory. The DM decides the solution interactively by considering unified affect of participating objectives by exploiting their membership functions. Highest cardinal priority ranking provides maximum satisfaction level of the participating objectives. In second approach, weighting method is explored to convert multi-objective optimization problem into scalar optimization problem. The best weight pattern is proposed to compute relevant weights. By applying best weight pattern evaluation, DM does not allow to skip the weight combination that actually corresponds to the ‘best’ compromising solution during simulation process. In practice, there are several inaccuracies and uncertainties in the input system information. So, the multi-objective HTGS problem has been posed as a stochastic multi-objective HTGS problem with explicit recognition of uncertainties and inaccuracies in system production cost, pollutant emission, rate of water discharge and system load. The significant contributions of various authors related to HTGS problems and its relevant topics have been briefly reviewed in chapter 1. The requisite theoretical, mathematical, and computational backgrounds of different local and global optimization techniques are reviewed which are utilized in the present study to determine the solution of optimization problem. In chapter 2, three heuristic optimization techniques are proposed whereby local and global optimization techniques are integrated. In first attempt, PPO and PPS techniques are integrated. The local best solutions obtained by PPO technique are considered as base points for PPS method to further improve the quality of solution locally. In second attempt, EP and PPS techniques are integrated whereby, members of EP technique acts as base points for PPS method. In third attempt, two global search techniques PPO and EP are implemented initially. Afterwards, local best solutions obtained from PPO and members of population obtained from EP are combined to form a pool. The pool of particles/members is arranged in ascending order according to their objective function value to select the base point for PPS. The proposed heuristic optimization techniques have advantage of exploration and exploitation property of global and local search techniques. Optimal operation of multi-objective hydro-thermal system is obtained using the proposed optimization techniques with due consideration of transmission losses of power system network. Hydro units having fixed and variable-head are engaged in HTGS problem. Valve-point loading effect is considered in operating characteristics of thermal generators. Multi-objective HTGS problem undertakes two conflicting objectives that are the operating cost and emission of gaseous pollutants Compromised solution is selected by finding the consolidated affect of participating objectives using their membership functions. Penalty method requires multiple runs to fine tune the penalty factor leading to a high computational cost. In this work, the constraints are satisfied by perturbing the decision variables in a systematic procedure. The proposed approach is tested on four electric power systems out of which three electric power systems have fixed-head hydro models and one system has variable-head hydro model. In ensuing chapter, the proposed heuristic optimization techniques are applied on non-convex HTGS problem, considering multi-chain hydro model. The travel time between reservoirs is taken into account. Water discharge rate of the hydro units and power output of the thermal units are searched to find out the optimum solution. The variable elimination method is applied to satisfy the equality constraints. Inequality constraints are treated as objectives to maximize along with other objectives of the optimization problem. Inequality constraint is converted into objective by exploiting fuzzy set theory. The decision regarding the best solution of multi-objective HTGS problem is taken by applying max-min operator on membership functions of participating objectives. In successive chapter, multi-objective HTGS problem is converted into single objective optimization problem by applying weighting method. Weight patterns are computed by conventional statistical measures, which characterize the correlation coefficients matrix evolution. The weights are updated, during the movement, according to best weight pattern using membership function of local best solutions of swarm or members of population obtained from proposed heuristic optimization techniques presented. The major advantage of weight pattern evaluation is that it provides rational basis of determining adequate weights. So, DM has all relevant weight combinations. The heuristics are applied to satisfy power balance, reservoir volume equality constraint, volume storage, and hydro power inequality constraint. The proposed optimization techniques with best weight pattern evaluation are applied to search optimum solution for four electric power systems. In the succeeding chapter, proposed optimization techniques are extended for long-term multi-objective HTGS problems and are tested on two electric power systems which have scheduling period of one year. To handle equality constraints, variable elimination method is implemented. An objective function is included to handle inequality constraints by assigning their membership functions using fuzzy set theory. Highest cardinal priority ranking is computed to decide the best compromised solution. The proposed optimization techniques search the solution without taking any approximation and are proved to be computationally efficient. In chapter 6, multi-objective HTGS problem is formulated with explicit recognition of uncertainties and inaccuracies in system production cost, pollutant emission, rate of water discharge and system load demand. The stochastic model is converted into its deterministic equivalent. The short-term fixed-head HTGS problem is solved in multi-objective framework in which main objectives such as operating cost, gaseous pollutant emission, expected power deviation, and expected volume deviation are minimized simultaneously. In this work, power generations have been considered as random and are correlated with each other. Further, operating cost, gaseous emission of pollutants and water discharge coefficients have been considered as random. The correlation between time-interval of hydro power generations is also considered. The results reveal that there is an additional cost and pollutant’s emission because of uncertainties and inaccuracies in system data. In the thesis, the validity and effectiveness of the proposed heuristic techniques to solve multi-objective HTGS has been extensively verified and numerically tested by analyzing on small, medium, and large electric power systems. The eleven numerical examples in diverse situations having several thermal and hydro coordinated units are considered. The performance of each employed technique is compared with the reported results in literature. Finally, the main conclusions of thesis are presented and suggestions for future research in this area are indicated.