Analysis & Plot of Convex and Non –Convex heat rate characteristics of thermal generating units Using MATLAB.

Objectives

Discontinuity Of heat rate characteristics occurs when we consider wall operation in Thermal Generating Units. This is called Non-Convex Heat rate Characteristic. This multiwall or step wise curve is different from Single wall heat rate curve.

So our objective is to

ü  Analyze & Plot  Non-Convex Heat rate curves

ü  Compare Convex & Non-Convex Curves

Theory

Introduction

Most Power system Contain Multi-Machine, Multiwall operations systems for generation of power ,therefore their heat rate curves are not simply linear but are Stepwise curves At switching of different walls.

Non-Convex Characteristics equation and Convex Characteristic Equation is given by

Explanation

Where c, b and a are the fuel cost coefficients of the respective unit, e and f are the valve-point coefficients of the respective unit. The units of the above coefficients are ($/MW2 h), ($/MWh), ($/h), ($/h) and (1/MW), respectively. Pmin (in MW) is the minimum capacity limit of unit. The added sinusoidal term in the production cost function reflects the effect of valve-points. Hence this problem is non-convex and non-differentiable considering valve-point effects

MATLAB Program

Code

clc

clear all

disp('Analysis and Plot of Convex & Non-Convex Characteristics Of thermal Operating unit');

syms a b c e f

g=input('Generator Total Power Capacity (MW) = ');

Pmin=input('Lower Limit Of Operation Zone(Pmin) = ');

Pmax=input('Upper Limit Of Operation Zone(Pmax) = ');

ss=input('Enter Const Suitable step size = ')

x=Pmin:ss:Pmax;

c=input('Value of p1(2nd Degree Coefficient) =');

b=input('Value of p2(1st Degree Coefficient) =');

a=input('Value of p3(3rd Degree Coefficient) =');

disp('Enter Values of  valve-point coefficients of the unit')

e=input(' e =  ');

f=input(' f = ');

m=abs(e*sin(f*(Pmin-x)));

p=[c b a];

fx1=polyval(p,x);

fx=fx1+m;

plot(x,fx,'o')

hold on

plot(x,fx1,'---')

xlabel('P');

ylabel('f(x)=a*P^2 + b*P + c + |e*sin(f*Pmin-P)| ');

title('300W Generating Unit(Comparison of Convex & Non-Convex Characteristics)');

Matlab Interface

Resulting Curve