Intelligent methods of economic distribution of active power between generators considering losses

Dissertation for Master's Degree in Electricity

Power Orientation

Abstract:

The production of electrical energy for power systems with the aim of minimizing the total cost of production for active units in the power network is one of the most important topics for today's modern systems. In other words, the purpose of economic load distribution is optimal and appropriate planning for production units, taking into account the non-linear factors and limitations in the power network and production units. In this thesis, the problem of economic distribution of load has been turned into an optimization problem by considering non-linear constraints such as transmission network losses, production and consumption balance equation in the system, production limits and increasing and decreasing rates, and finally it has been solved by particle swarm optimization algorithm. He used two methods of Lagrange coefficient and genetic algorithm for comparison. Instead of working on an optimal solution, the genetic algorithm works on several solutions called the population. In the genetic algorithm, each member of the population is not dependent on other members and evolves independently. Particle swarm optimization algorithm is a social search algorithm. It is modeled from the social behavior of flocks of birds. In this algorithm, the particles flow in the search space, the change of the location of the particles in the search space is influenced by their own and their neighbors' knowledge experience. Particles learn from each other and move towards their best neighbors based on the acquired knowledge. The proposed algorithms are applied on the 26-base system and the results obtained with the two mentioned algorithms have been compared. As a result, the real features and benefits of this method become more clear. Also, the simulation results show that the particle swarm optimization algorithm method is a fast method with acceptable accuracy. Keywords: economic load distribution, line losses, Lagrange coefficient, genetic algorithm, particle swarm optimization algorithm (PSO). The thought, idea or design proposed by a scientist or an engineer is improved during the optimization process. During optimization, the initial conditions are examined with different methods and the obtained information is used to improve an idea or method. Optimization is a mathematical tool that is used to find answers to many questions about how to solve various problems.

Optimization refers to finding the best solution for a problem. The word "best" implies that there is more than one answer to the problem in question, which, of course, do not have the same value. The definition of the best solution depends on the investigated problem, the solution method and also the amount of permissible error. Therefore, the way the problem is formulated has a direct effect on how to define the best answer. Some problems have specific answers: the best player in a sport, the longest day of the year, and the answer to a first order ordinary differential equation are among the examples that can be called as simple problems. On the other hand, some problems have multiple maximum [1] or minimum [2] solutions, which are known as optimal points or extremum [3], and the best solution is likely to be a relative concept. The lowest power plant production cost, the lowest transmission line losses, and the best power generation of a power plant are some of the examples that can be mentioned for such problems.

Optimization is changing the inputs and characteristics of a device, a mathematical or experimental process in such a way that the best output or result is obtained (Figure 1-1). Output is also defined as cost, profit or efficiency. In this article, in accordance with many articles related to the subject, all optimization problems are considered as minimizing the value of a cost function. It can be easily shown that any type of optimization problem can be defined in the form of a minimization problem [7]. In optimization, the inputs or variables are changed in such a way that the desired output is obtained. Figure (1-1) of the functional process that is optimized. so that losses decrease and the best production of real (active) power [8].. So that the losses are reduced and it has the best production of real (active) power [8]. The main task of a power plant is to convert energy from other forms such as chemical energy, nuclear energy, gravitational potential energy, etc. to electrical energy. The main task in almost all power plants is the generator. In a power plant, several generators are connected to the power grid in parallel to provide the required power. They are connected to a common point which is called Shin[9]. A generator is a rotating machine that converts mechanical energy into electrical energy. This machine converts mechanical energy into electrical energy through electromagnetic induction. The energy required to rotate a generator is provided in different ways and it often depends on the purpose of creating maximum efficiency and minimizing costs, as well as the availability of different energy sources in that area and the technical knowledge of the manufacturing group. The mechanical energy supply source may be a steam turbine, water turbine, wind turbine, or an internal combustion engine. 1-4 statement of the economic load distribution problem Economic load distribution (ED) is one of the important issues in the production and planning of power systems. The primary goal of the ED problem is to determine the optimal combination of power output of the production units in such a way as to respond to the required load demand with the lowest operational cost and by observing the equality and inequality constraints of the system. In the problem of economic distribution of common load, the cost functions of each generator are roughly equated with a simple quadratic equation. Then this problem is solved using different optimization methods. In these methods, different assumptions are used to implement the problem. 1-4-1 Objective of economic distribution of load The objective of economic distribution of load is to allocate the demand between the participating and predetermined units with the condition of minimizing the cost of fuel and providing rotating reserve. Economic exploitation is very important for a power system in terms of the return of the investment made, and the rates set by government bodies and the importance of saving fuel put pressure on power companies to achieve the maximum possible efficiency. The economic load distribution determines the output power of each power plant as well as each generating unit inside a power plant for each predicted load condition, so as to minimize the total fuel cost required to supply the system load. Other effective factors on power generation with the lowest cost are: the work efficiency of generators, fuel cost and transmission losses.

Producing power with the best efficiency in the system does not guarantee the minimum cost, because it is possible that this power producer is located in a place where the cost of fuel is high. Also, if the distance of the power plant from the load centers is large, the transmission losses can be significantly increased and therefore it is possible that the production of the power plant becomes uneconomical. Usually the input of the thermal power plant is expressed in terms of Btu/h and its output is expressed in terms of MW megawatts. A simplified input-output curve of a heat unit, which is called a heat rate curve, is shown in Figure 1-1(a). If the coordinates of the heat rate curve are converted from Btu/h to $/h, the fuel cost curve is obtained as shown in Figure 1-1(b).

Chart 1-1 Heat rate and fuel cost curves

In most cases, the fuel cost of the production unit is shown as follows with a quadratic function in terms of the actual power produced by that production unit:

You can also draw the derivative of the fuel cost curve in terms of real power to obtain the following characteristic, which is called the incremental fuel cost curve and is shown in Figure 1-2.

1-4-2 Economic distribution of load without taking into account losses and limitations of production units

The easiest and most convenient type of economic load distribution problem is the case where transmission line losses are not considered, i.e. the line losses are equal to zero.