ELECTRICAL ENGINEERING
POWER SYSTEM OPERATIONS
EXPERIMENT No. 1
STUDY AND PLOT OF DIFFERENT TYPES OF LOAD CURVES FROM
GIVEN DATA USING MATLAB
PURPOSE:
To learn
1. How to build a load curve, load duration curve and integrated load duration for a
given data.
2. Valuable information extracted from these load curves.
SOFTWARE USAGE: MATLAB
INTRODUCTION:
The demand for power has increased exponentially over the last century. This has increased the
emphasis on the performance and efficiency of power supplies used in everyday electronics as
well as sophisticated electronic and communication systems. A power supply is a component,
subsystem, or system that converts electrical power from one form to another. In power system, it
is important to know the daily-load curve that consists of demand pattern by various classes of
users.
Load Curve: A graphical plot showing the variation in demand for energy of the consumers on a
source of supply with respect to time is known as the load curve.
If this curve is plotted over a time period of 24 hours, it is known as daily load curve. If it’s plotted
for a week, month, or a year, then it’s named as the weekly, monthly or yearly load curve
respectively.
From out of the load connected, a consumer uses different fractions of the total load at various
times of the day as per his/her requirements. Since a power system has to supply load to all such
consumers, the load to be supplied varies continuously with time and does not remain constant. If
the load is measured (in units of power) at regular intervals of time, say, once in an hour (or halfan-hour) and recorded, we can draw a curve known as the load curve.
Load Duration Curve: The load–duration curve is a plot of the load demands (in units of power)
arranged in a descending order of magnitude (on the y-axis) and the time in hours (on the x-axis).
A load duration curve enables us to determine the number of hours per year, when the load is
greater or lesser than any given amount. Similarly it also shows the loads that are carried for more
or lesser than particular direction.
Information obtained from load curves:
Area under the load curve = Units generated,
Highest point of the curve = Maximum Demand
(Area under curve) / (by total hours) = Average load
It helps in selection of the rating and number of generating units required. To further assess the
usefulness of the generating plants from these curves, various factors are also computed. Some
of them are:
𝑳𝒐𝒂𝒅 𝑭𝒂𝒄𝒕𝒐𝒓 =
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑳𝒐𝒂𝒅
𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝑫𝒆𝒎𝒂𝒏𝒅
𝑫𝒆𝒎𝒂𝒏𝒅 𝒇𝒂𝒄𝒕𝒐𝒓 =
𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝑫𝒆𝒎𝒂𝒏𝒅
𝑪𝒐𝒏𝒏𝒆𝒄𝒕𝒆𝒅 𝑳𝒐𝒂𝒅
𝑷𝒍𝒂𝒏𝒕 𝑪𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝑭𝒂𝒄𝒕𝒐𝒓 =
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑳𝒐𝒂𝒅
𝑷𝒍𝒂𝒏𝒕 𝑪𝒂𝒑𝒂𝒄𝒊𝒕𝒚
(𝟏. 𝟏)
(𝟏. 𝟐)
(𝟏. 𝟑)
PROCEDURE:
Generally load curves are built by recording the values of load demands for every instant during a
certain time interval and plot a graph of load demands against a time for which it occurs. The
procedure for plotting Load Curves in MATLAB is as:
1. Open a new M-file in MATLAB.
2. A function is initialized that takes input variable data and in output we obtain plot of load
cycle for a given interval.
Function[]=loadcurve(data)
3. First of demand interval and load is defined by the variable data in a three column matrix.
For Example:
4. The first two columns are the demand interval and third column is load value. The demand
interval may be minutes, hours, and months in ascending order and load values are
generally in KW or MW. In above example first row of data variable shows that for first
two hours (00-02) load demand is 6 MW.
5. Now type the following commands at M-file window.
C1Ti=data(:,1)
C2Tf=data(:,2)
Td=C2Tf-C1Ti
Power=data(:,3)
MWH=Power*(Td')
Pavg=MWH/24
Dmax=max(Power)
Loadfactor=Pavg/Dmax
L=length(data)
Total_Time=[C1Ti C2Tf]
t=sort(reshape(Total_Time,1,2*L))
for n=1:L
P(2*n-1)=Power(n);
P(2*n)=Power(n);
end
plot(t,P)
xlabel('Time')
ylabel('load')
title('Load Curve')
6. Save the commands above in your thumb drive directory, save as load curve.m
7. Now execute the above function and following load curve plot will be obtained.
However the procedure for plotting a load duration curve is different from load curves that is given
below:
8. Determine the peak load and duration for which it occurs.
9. Then take the next lower load and find the total time during the year when this and the
previous greater load occurs.
10. Plot the load against the number of hours during the year, month or day for which it occurs,
or against the percentage of time during the year.
11. Further some useful information can also be extracted from these curves. i.e. Total Energy
from area under the curve, load factor etc.
E=Power’*(t2-t1)
Pavg=W/sum(t2-t1)
Peak=max(Power)
LF=(Pavg/Dmax)*100;
OBSERVATIONS AND CALCULATIONS:
Task 1:The load on power plant for a particular day is given below:
Time
0-4
4-8
8-18
18-20
20-22.
22-24.
Load (KW)
15
35
70
80
90
15
Plot the load curve, load duration curve.
(i)
Load Curve:
As the load demands are given for 24 hours, so daily load curve plotted for a given load by
adopting above mentioned procedure is shown below:
(ii)
Load Duration Curve:
1. First of all peak load demand and duration for which it is occurs are determined. In this
example peak demand is 90 MW and it occurs for 2 hours.
2. Starting from peak load demand following table is constructed to determine various points
on load duration curve.
Load (KW)
Hours in a day
% Time
90
2
8.33
80
2+2=4
16.66
70
4+10=14
58.33
35
14+4=18
75
15
18+6=24
100
3. Now plot the load demands against calculated time in table 2.
clear all
data = [0 2 90
2 4 80
4 14 70
14 18 35
18 24 15];
C1Ti=data(:,1)
C2Tf=data(:,2)
Td=C2Tf-C1Ti
Power=data(:,3)
MWH=Power*(Td')
Pavg=MWH/24
Dmax=max(Power)
Loadfactor=Pavg/Dmax
L=length(data)
Total_Time=[C1Ti C2Tf]
t=sort(reshape(Total_Time,1,2*L))
for n=1:L
P(2*n-1)=Power(n);
P(2*n)=Power(n);
end
plot(t,P)
xlabel('Time')
ylabel('load')
title('Load Curve')
EXERCISE-1
A generating station has the following daily load cycle:
Time
0-6
6-10
10-12
12-16
16-20.
20-24
Load (KW)
20
25
30
25
35
20
Draw the load curve and find (i) maximum demand (ii) Units generated per day (iii)
Average Load (iv) Load Factor
MATLAB CODE
data = [0 6 20; 6 10 25; 10 12 30; 12 16 25; 16 20 35; 20 24 20];
C1Ti = data(:,1);
C2Tf = data(:,2);
Td = C2Tf - C1Ti;
Power = data(:,3);
MWH = Power*(Td');
Pavg = MWH/24;
Dmax = max(Power);
LoadFactor = Pavg/Dmax;
L = length(data);
Total_time = [C1Ti C2Tf];
t = sort(reshape(Total_time, 1, 2*L));
for n = 1:L
P(2*n-1) = Power(n);
P(2*n) = Power(n);
end
figure('Name','Exercise 1','NumberTitle','off');
plot(t, P); grid on;
ylim([15 40]);
xlabel('time');
ylabel('Load');
title('Load Curve');
%% Load Duration
LoadDuration = sort(P, 'descend');
figure('Name','Exercise 1','NumberTitle','off');
plot(t, LoadDuration); grid on;
ylim([15 40]);
xlabel('time (in hours)');
ylabel('Load');
title('Load Duration Curve');
From Graph
1. Maximum demand
Maximum Demand = Highest point of the curve
Maximum demand = 35kV
2. Units generated per day
Units generated = Area under the load curve
Units generated per day = 600 units
3. Average Load
Average load = (Area under curve) / (by total hours)
Average load = 25kW
4. Load Factor
Average Load
Load Factor = Maximum Demand
Load Factor = 0.7143
EXERCISE-2
A consumer has a connected load of 12 lamps each of 100 W at his/ her premises. His/ her
load demand is as follows:
From midnight to 5 A.M.: 200 W.
5 A.M. to 6 P.M.: no load.
6 P.M. to 7 P.M.: 700 W.
7 P.M. to 9 P.M.: 1,000 W.
9 P.M. to midnight: 500 W.
Draw the load curve and calculate the (i) energy consumption during 24 hours, (ii) demand
factor, (iii) average load, (iv) maximum demand, and (v) load factor
MATLAB CODE
data = [0 5 200; 5 18 0; 18 19 700; 19 21 1000; 21 24 500];
C1Ti = data(:,1);
C2Tf = data(:,2);
Td = C2Tf - C1Ti;
Power = data(:,3);
MWH = Power*(Td');
Pavg = MWH/24;
Dmax = max(Power);
LoadFactor = Pavg/Dmax;
L = length(data);
Total_time = [C1Ti C2Tf];
t = sort(reshape(Total_time, 1, 2*L));
for n = 1:L
P(2*n-1) = Power(n);
P(2*n) = Power(n);
end
figure('Name','Exercise 2','NumberTitle','off');
plot(t, P); grid on;
ylim([0 1100]);
xlabel('time');
ylabel('Load');
title('Load Curve');
%% Load Duration
LoadDuration = sort(P, 'descend');
figure('Name','Exercise 2','NumberTitle','off');
plot(t, LoadDuration); grid on;
ylim([0 1100]);
xlabel('time (in hours)');
ylabel('Load');
title('Load Duration Curve');
1. Energy consumption during 24 hours
Energy consumption during 24 hours = 5.200 kWh
2. Demand factor
Demand factor =
Maximum Demand
Connected Load
Demand factor = 0.19233,
3. Average load
Average load = (Area under curve) / (by total hours)
Average load = 216.67W
4. Maximum demand
Maximum Demand = Highest point of the curve
Maximum demand = 1kW
5. Load factor
Load Factor =
Average Load
Maximum Demand
Load factor = 0.217
CONCLUSION:
Plotting of different types of load factors and their significance has been studied. There are various
performance factors related to the load curves. Energy consumption during different periods can
be calculated using load curves.
Teacher / Supervisor’s Signature: ______________________________________________