Yeosun Kyung, Joo-woong Kim,Sung-Boo Jung, Ki-Hwan Eom - Optimal Control Method for a Hydroelectric Power Development in Multi Level Dams

1. INTRODUCTION

Korea has four distinct seasons, but rainy season is restricted to July and August. Therefore, water resource for hydroelectric generation is too limited to particular season. Actually, about 67% of hydropower generation is depending on the rainy season. Since the operation ratio of power system for drainage system in Han River of Seoul is 30%, the cost for thermal power generation is saved when the hydroelectric power generation becomes higher. There is a problem that reserves the water below the current average water level to prevent from flood in July and August, flood season. February and March are dry season. Water for generation is insufficient in this season. In flood season, enough water should be reserved by means of the precise system that predicts, and prevents the flood. In this paper, we propose the optimal control method of electric power generation in multilevel water dams for plummeting of water resources problem. In order to verify the development rate of the proposed optimal control method, and to compare it with the rainy season, we perform simulation on the total control system for hydroelectric power in Han River of Seoul.

2 Power system optimal control method by the regulation of dam water level -Simple Model

2.1 Optimal control of water level

Consider the following feedback problem.

Variables: x(t): dam water level at time t. u(t): generation speed(amount of release) at time t. x0: water level at t = 0, starting point. x: target water level of x(t). u : target value for generation speed(amount of release), u(t). h: penalty for the deviation of water level at time t, x(t), from target water level(x). c: penalty for the deviation of generation speed, u(t), from the target value, u. ?: a constant for easy calculation by the computer. Let T = k, (0 f,x < 1); unnecessary to solve the differential equation, a: natural extinction rate of water level(drying rate data is given) s(t): water level change rate by external source (+inflow – drinking water – water for agriculture: data is given). u(t): water level change rate by random source; 0, average of f(t), x variance. E: expected value of integral. The model above is to minimize the cost for dam water level and for dam water release during the period [0,T] when there is relationship of differential equation (2) between water release, inflow, and water level. The determinant variable, u(t), should be defined for dam water releasing rate at each time to minimize the total cost. If u(t) is determined, then the optimized x(t) is also solved by equation (2), and the cost function (1) becomes minimized. The optimization of a general model for the problem stated above is like shown below [1],[2],[3].

Next, we apply the optimized general model to the problem of water level control

The algorithm to find an optimized solution is derived as follows by letting the function like below.

From last equation shown above, it should be 0 in order to satisfy x(t), (water level), at any time. That is

S,q,r are sub-variables. The optimization is shown below by using partial derivatives. From last equation shown above, it should be 0 in order to satisfy x(t), (water level), at any time. That is,

2.2 Simulation of a model – Hwacheon Dam-

We can review Hwacheon dam, independently. In other words, the impact of change in the amount of release from Hwacheon dam can be relieved at dams in downstream such as Chuncheon dam, Uiam dam, and Chungpyung dam.

3 Total Optimal Control Method for Hydroelectric Power Plant in Han River

3.1 Discrete optimization model

The previous researches have been on similar problems to next model with cost reduction model to generate the power.

3.2 Total Optimized control model

The problem above can be converted to an optimized control problem.

Lagrangian function L is defined above, l(t) and sub variables like z(t), and z(t) are inserted. In order to solve in numeral method, effectively, multiply l/2 to inequality sign, and relative term, and square them. The converted problem can be solved by numerical method, Gradient method. Euler method is used to solve the differential equations, and I can simplify if there is no restriction. The algorithm for optimal numerical method is used for this system. Superscript i means an ith approximate value improved, calculate xg{bt value improved in left side by using the value in the right side. The calculation period and boundary condition are shown next

Let’s review to optimize all three dams in Han River: Paldang dam which is important for hydroelectric power, supplying water to Seoul, and flood control, and Chungpyung dam, and Chungjoo dam which are connected to Paldang dam. The general model of vector matrix above can be rewritten like the following:

Subscript 1 in all variables indicates the Chungpyung dam, subscript 2 is Chungjoo dam, and subscript 3 is Paldang dam. a1, a2, and a3 indicate natural evaporation from the amount of water reserved in dams. g1(1), g2(t), and g3(t) are the amount of inflow from raining, and other region. u1(1), u2(t), and u3(t) are the amount of released, and v1(t), v2(t), and v3(t) are drinking water and the amount of water released for flood control.

To find out the best optimum solution for 3 dam models with the algorithm to calculate the general optimization solution above, see below.

Generally, about (67%) of hydropower generation is depend on the rainy season. In other word the process of development of water resources is too limited to a particular season. In order to develop this problem, we proposed an optimal control method of hydroelectric power development in multi level water dams. To verify the development rate of the proposed optimal control method, we simulated on the total control system for hydroelectric power in Han River of Seoul. Simulation results show that the proposed optimal control method indicates development rate in Chungpyung Dam is about a 40%, 25% in Chungju Dam and 37.5% in Paldang. The main advantage of the proposed optimal control method is stabilization of the amount of power generate in dams. Through the system for simple model, Hwacheon Dam, the development rate of hydropower is stabilized without big impact from inflow even in the rainy season or dry season. It would be helpful to maintain the water level in each dam not exceeding the limits, and the generate rate would be kept the constant power generation. However, this system has some negative side because of labile factor. It has not been performed that accurate measurement of each element in Han-River. The data of each element in this paper is approximate number derived by a formula. When the data of each factors correctly attained, this system can be valuable method.

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