Optimum Dispatch of Hybrid Solar Thermal (HSTP) Electric Power Plant Using Non-Smooth Cost Function and Emission Function for IEEE-30 Bus System

The basic objective of economic load dispatch (ELD) is to optimize the total fuel cost of hybrid solar thermal electric power plant (HSTP). In ELD problems the cost function for each generator has been approximated by a single quadratic cost equation. As cost of coal increases, it becomes even more important have a good model for the production cost of each generator for the solar thermal hybrid system. A more accurate formulation is obtained for the ELD problem by expressing the generation cost function as a piece wise quadratic cost function. However, the solution methods for ELD problem with piece wise quadratic cost function requires much complicated algorithms such as the hierarchical structure approach along with evolutionary computations (ECs). A test system comprising of 10 units with 29 different fuel [7] cost equations is considered in this paper. The applied genetic algorithm method will provide optimal solution for the given load demand.


INTRODUCTION
The basic theme of economic dispatch is to determine the optimal combination of power outputs of the generating units in electric power system so as to optimize the total fuel cost for a certain load demand satisfying operational constraints. The economic load dispatch (ELD) problem is analyzed basically through the input output characteristic or through the heat rate input output characteristic by taking real power output of ith generating unit (PGi) in the X axis and Fuel input in rupees per hour in the Y axis. Input-Output characteristic is approximated as a single quadratic variation curve which gives sub-optimal solutions. Usually the nature of Input-Output characteristics of modern generating units is non-linear because of multi-fuel effects (M F E) using combined cycle power plants (CCPP) and valve loading effects, which may lead to multiple local minimum points of cost functions. Hence it is more realistic to represent the Input-Output characteristic as a piece wise quadratic cost function to avoid huge revenue loss over time problems. This project develops algorithm approach for solving the economic dispatch problem for a test system of 10 plants having 29 fuel cost options. A salient feature of proposed approach is that solution time grows approximately linear with problem size. More over the inclusion of solar power plant in tandem with the thermal power plant reduces the emission level so as to maximize the power generation for solar plant leading to minimum utility of the solar generation. The quadratic cost function so chosen is minimized following the reduction in emission level of Sulphur dioxide (SO2), carbon monoxide (CO), nitrous oxide N2O and other greenhouse gasses. The quadratic programming approach so chosen for the hybrid solar thermal power system optimizes the cost of generation of solar thermal power plant and simulation time as well.

II. ECONOMIC LOAD DISPATCH
The ELD [3] problem is to determine the optimal combination of power outputs of all the generating units to minimize the total fuel cost while satisfying the load demand from the operational constraints. Minimum fuel costs are achieved by the economic load scheduling of different generating units. Here we mean to ascertain the generation of distinct generators so as to obtain the total fuel cost as minimum so that the load demand is met out by net generation.

A. Economic Load Dispatch Problem
However, economic load scheduling was not of relevance when there were small power generating plants for each locality, such as urban power system, but now with the growth in the power demand and at the same time guarantee regarding the continuity of power supply to the consumer under normal conditions have forced the power system engineers to develop grid system. For such system the economic dispatch problem has become increasingly important. The objective in the economic dispatch of power system is to minimize the cost of meeting the energy requirements of the system over some appropriate period of time and in a manner consistent with reliable service. The appropriate period may be as short as few minutes or as long as a year or more depending on the nature of the energy sources available to the system.

B. Problem Statement for ELD with Non-Smooth Cost Function
Let N be the number of units.
i PG be the power supplied by the th i unit.
PD be the load demand in MW PAPER OPTIMUM DISPATCH OF HYBRID SOLAR THERMAL (HSTP) ELECTRIC POWER PLANT USING NON-SMOOTH COST… The generation cost objective function for the thermal power plant in proposed method can be represented by cost function [2] : Neglecting valve point loading [3] and incorporating transmission loss using conventional method the cost of thermal generation is expressed as

C. Cost Criteria for Economic Load Dispatch Problem
Using Lagrangian multiplier method fuel cost and emission cost functions incorporating transmission loss were expressed in equation (1) and equation (2) respectively.
By differentiating the above equations we get: " are generation cost coefficients for the th i generating unit subjected to condition Genetic algorithm (GA), was first propounded by John Holland in early seventies, is a flagship among various techniques of function optimization. Genetic algorithm criss-crosses all the above limitations of conventional algorithms by using the basic building blocks that are distinct from those of conventional algorithms. The following differential aspects are as follows: 1. GA works with a coding of the parameters set and not the parameters themselves. 2. GA searches from a population of points and not from a single point like conventional algorithm. 3. GA uses objective function information, not derivative or other auxiliary data. 4. GA uses probabilistic transition rules by stochastic operands, not by deterministic rules. The initial step of GA [8] is the random selection of initial search points from the total search space. Each and every point in the search space corresponds to one set of values for the parameters of the problem. Each parameter is coded with a string of bits. The individual bit is called "gene". The content of each gene is called "allele". The total string of such genes of all parameters written in a sequence is called a "chromosome". So there exists a chromosome for each point in the search space. The sea of search points selected and used for processing is called a population. That means population is a set of chromosomes. The no of chromosomes in population is called "population size" and the total number of genes in a string is called "string length". The population is processed and evaluated through various operators of GA to generate a new population and this process is carried out till global PAPER OPTIMUM DISPATCH OF HYBRID SOLAR THERMAL (HSTP) ELECTRIC POWER PLANT USING NON-SMOOTH COST… optimum point is reached. The two parts of the process are called "generation and evaluation".
For the evaluation of GA we define a fitness function and evaluate the fitness for each chromosome of a population. This fitness is an indication of the suitability of the values of the parameters, as represented by that chromosome and acts as a solution of the optimization problem [9] under consideration. This fitness is used as bias for selecting the parents and generating a new population from the existing one.

V. RESULT AND PERFORMANCE CHARACTERISTIC
The various program specific arguments for the optimization of cost and emission function of hybrid Solar thermal power plant were tabulated in the tables-1,2 and 3.
The increment in solar generation is accompanied by decrement in emission level in the thermal power plant thereby optimizing the cost of generation of the thermal power plant as shown in Fig-1.
Average  Following the increased generation level of solar power plant the generation [1] cost of thermal power plant decreases. As a result of this deviation between cost of generation incorporating valve point loading for cost and emission function in the proposed method and the conventional method without valve point loading with respect to various power demands undergoes a change as reflected in Fig-3. The IEEE 30 bus test case system used for the Present dissertation is shown in Fig-4.  Various soft computing methods like neural network, fuzzy logic etc. were used for optimal dispatch for optimizing the cost of generation of thermal power plant with multi-objectives [5] wherein the computation time for simulation and convergence of the result became cumbersome and sluggish. So at its favor the concept of hybrid solar thermal power plant (HSTP) owning quadratic programming [6] method, an emerging evolutionary programming technique that was involved in the current dissertation, found useful in regulating greenhouse gasses optimizing the emission level so as to maximize the real power generation by reducing the global warming level. The use of multi-objective generation dispatch incorporating the cost of generation and emission as well with nonsmooth cost and emission function with valve point loading and quadratic programming approach can be incorporated for reduction in emission level of SO2, CO, N2O and other greenhouse gasses so as to maximize real power generation level for yielding the optimum cost of generation.