 Open Access
 Total Downloads : 219
 Authors : A.Surya Prakasha Rao, Associate Prof, M.Vijay
 Paper ID : IJERTV2IS100346
 Volume & Issue : Volume 02, Issue 10 (October 2013)
 Published (First Online): 15102013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Stochastic MultiObjective Short Range Fixed Head Hydrothermal Scheduling Using Classical, PSO & TLBO
A.Surya Prakasha Rao, Associate Prof.
Department of Electrical & Electronics Engineering Sir C R Reddy College of Engineering
Eluru, India
M.vijay
Department of Electrical & Electronics Engineering Sir C R Reddy College of Engineering
Eluru, India
Abstract
This paper presents the multiobjective optimal solution for short range fixed head hydrothermal scheduling using classical method, Newton rapshon method and pso. The problem is formulated as a nonlinear constrained multiobjective optimization problem. Considering the scheduling horizon period of 24 hours, hourly generation schedules are obtained for each of both hydro and thermal units for the three cases. The transmission losses are also accounted for through the use of loss coefficients. More no of simulations are carried out to obtain the best solution and the average value considered to improve the behaviour of pso. Numerical simulation of sample test system shows the effectiveness of the proposed algorithms. Index: pso, short range fixed head hydrothermal system, optimization technique, lagrangain relaxation.

Introduction
In the present setup of large systems with hydro and thermal power stations, the integrated operation of these power stations is inevitable and the economic aspect of such an operation cannot therefore be overlooked. The underlying idea of integrated operation is for optimum utilization of all energy sources in the most economical manner, so that an uninterrupted supply can be made available to the consumer. The operating cost of thermal plant is very high, though their capital cost is low. So it has become economical as well convenient to have both thermal and hydro plants in the same grid. The hydroelectric plant can be started quickly and it has higher reliability and greater speed of response. Hence hydroelectric
plant can take up fluctuating loads. But the starting of thermal plants is slow and their speed of response is slow. Normally the thermal plant is preferred as a base load plant whereas the hydroelectric plant is run as a peak load plant. The shortterm hydrothermal scheduling model has a time horizon of one week or one day with an hourly time interval..

HYDROTHERMAL SCHEDULING
Optimal scheduling of power plant generation is the determination of the generation for every generating unit such that the total system generation cost is minimum while satisfying the system constraints. The objective of the hydrothermal scheduling problem is to determine the water releases from each reservoir of the hydro system at each stage such that the operation cost is minimized along the planning period. The operation cost includes fuel costs for the thermal units, import costs from neigh boring systems and penalties for load shedding.
The HTC problem is usually solved by decomposition of the original problem into long, medium and short term problems each one considering the appropriate aspects for its time step and horizon of study.
It is also essential to take into consideration two basic aspects of the hydro system:

The available water quantity (water inflows) is stochastic in nature.

The decision for the energy allocated to hydro units is deterministic.


Need of Hydrothermal Scheduling
The operating cost of thermal plant is very high, though their capital cost is low. On the other hand the operating cost of hydroelectric plant is low, though their capital cost is high. So it has become economical as well convenient to have both thermal and hydro plants in the same grid. The hydroelectric plant can be started quickly and it has higher reliability and greater speed of response. Hence hydroelectric plant can take up fluctuating loads.

Short Range Problem
The load demand on the power system exhibits cyclic variation over a day or a week and the scheduling interval is either a day or a week. As the scheduling interval of short range problem is small, the solution of the shortrange problem can assume the head to be fairly constant. The amount of water to be utilized for the shortrange scheduling problem is known from the solution of the longrange scheduling problem.
A set of starting conditions (e.g. reservoir levels) is given, and the optimal hourly schedule that
minimizes a desired objective, while meeting hydraulic steam, and electric system constraints, is sought.
T
qj t dt Vj
0
(j = 1, 2, , M)
The short term hydrothermal scheduling problem is classified in to two groups

Fixed head hydro thermal scheduling

Variable head hydro thermal scheduling
where Vj is the predefined volume of water available in cubic meters and hydro performance qj is represented by the conventional quadratic model, i.e.
q t x P 2 t y P t z m3/h
j 1 jN j jN j
(j = 1, 2, , M)


HTS Problem formulation:
Where xj, yj, and zj and the discharge coefficients of the jth hydro plant.
5.4. Transmission Losses:
N M N M N M
N M N M N M
A common approach to model transmission losses in the system is to use Krons approximated loss formula:
PL t Pi t Bij Pj t Bi 0Pi t B00

Objective function:
The fixedhead hydrothermal problem can be defined considering the operating cost over the
MW
Where
i1
j1
i1
optimization interval to meet the load demand in each
B00, Bi0, and Bij are Bcoefficients.
interval. Each hydro plant is constrained by the
amount of water available for drawdown in the
q jk
is the rate of discharge from the jth hydro unit
interval. The problem is defined as
in interval k and is defined by
Minimize
q x P2 y P z m3/h
T
N
T
N
J tk Fi Pik
jk j jN ,k j j N ,k j
N is the number of thermal units M is the number of hydro units
Fi Pik
k 1 i1
is the cost function of thermal units in the
T is the overall period for scheduling.
The above objective as augmented by the
interval k and is defined by
2
constraints is given as
T N M
T N M
LP v t F P v t q
P
M N M

P P v V
Fi Pik ai Pik bi Pik ci Rs/h
ik , k , j
k i ik j k jk k Dk Lk ik j j
With ai, bi and ci as the cost coefficients.
Pik is the output of thermal and hydro units
k 1 i1 j1
k k 1
k k 1
t Fi PLk 0
i1 j1
(i = 1, 2,..,N; k = 1, 2,
during the kth interval.
Pik
Pik


Constraints:
,T)
q
v t jk
PLk
0 (j = 1, 2, ,

Load demand equality constraint:
j k P k P 1
N M
mk mk
M;
Where
Pi t PD t PL t
i1
m = N+ j; k = 1, 2, ,T)
where
is the incremental cost of power delivered in
PD(t) is the load demand during the subinterval.
PL(t) is the transmission loss during the sub interval.

Limits are imposed as
i i i
i i i
pmin P t pmax (i= 1, 2, , N + M)


Volume and discharge:
Eachhydro plant is constrained by the amount of water available for the optimization interval, i.e.
the system during the kth interval.
vj are the water conversion factor.


HTS methods:

Classical method:
The problem we wish to set up is the general, shortterm hydrothermal scheduling problem where the thermal system is represented by an equivalent unit, Psj. In this case, there is a single hydroelectric plant, PHj We assume that the hydro plant is not
sufficient to supply all the load demands during the period and that there is a maximum total volume of water that may be discharged throughout the period of Tmax hours.
6.1.1 Algorithm:
i i i
i i i

Read the number of thermal units N, the number of hydro units M, the number of subintervals T, cost coefficients, a , b , c i 1, 2,…, N ,Bcoefficients, Bij (i 1, 2,…, N M ; j 1, 2,…, N M ), discharge coefficients, xi , yi , zi i 1, 2,…, M ,demand PDk k 1, 2,…,T , the prespecified available water Vj j 1, 2,…, M .

Calculate the initial guess values of
P0 i 1, 2,…, N M , 0 and v0 j 1, 2,…, M


PARTICLE SWARM OPTIMISATION:
Particle swarm optimization (PSO) is a population based stochastic optimization technique developed by Dr.Ebehart and Dr.Kennedy in 1995, inspired by social behaviour of bird flocking or fish schooling. PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum
particles. PSO has been successfully applied in many
ik k j
j
j

Consider v0 j 1, 2,…, M as calculated in Step 2.

Start the iteration counter, r = 1.

Start hourly count, k = 1.
6. Consider P0 i 1, 2,…, N M and 0 .
areas: function optimization, artificial neural network training, fuzzy system control, and other areas where GA can be applied. It mainly consists
three operations mutation, de acceleration and migration

Calculate
ik
Pik i 1, 2,…, N M
k
and k ,
using the NewtonRaphson method. Gauss Elimination method is used to solve the following equations.
Flow chart:
k k P
k
pp p
ik p
k T
0 k
k
p

Calculate the new values of Pik i 1, 2,…, N M
and as Pnew P0 P and new 0
k ik ik ik k k k

Set limits correspondingly as
Pmax ;if Pnew Pmax
i ik i
ik i ik i
ik i ik i
Pnew Pmin
;if Pnew Pmin
Pnew ;
otherwise
ik
Disallow generator to participate, whose limits have been set either to lower or upper limit, in the scheduling by deleting that row and column.
ik ik
ik ik

Set P0 Pnew i 1, 2,.., N M and
k k
k k
0 new GOTO Step 7 and repeat.

If
k T , then GOTO Step 13, else k = k + tk,
GOTO Step 6 and repeat.
j
j

Calculate water withdrawals V j 1,…., M .
j j
j j

If  V V s or if (r R) then GOTO Step 14.
else V new v0 V V s /V s ,
j j j j j
j j
j j
V 0 V new i 1, 2,…, M
r r 1;
GOTO Step 5 and repeat.

Calculate the optimal cost and loss and stop.
TLBO:
The TLBO algorithm is a newly TableI. Analysis of cost & discharge values for these
developed metaheuristic optimization algorithm [17]. It is a populationbased optimization algorithm that is modelled based on the transfer of knowledge to the classroom environment, where learners first gain knowledge from a teacher (Teacher Phase) and then from fellow students (Learner Phase). TLBO is a population based algorithm, where a group of students (i.e. learner) is considered the population and the different subjects offered to the learners are analogous with the different design variables of the optimization problem. The results of the learner are analogous to the fitness value of the optimization problem. The best solution in the entire population is considered as the teacher. The operation of the TLBO algorithm is explained below with the teacher phase and learner phase.
The structure of the proposed algorithm can be explicated as follows:
Step 1: Initializing the problem and algorithm parameters
Step 2: Establishing the initial population learners.
Step 3: Compute the objective function. Step 4: Compute the mean of the population.
Step 5: Determine the best solution (Teacher). Step 6: Modify solutions based on the teacher knowledge according to teacher phase.
Step 7: Update solutions according to learner phase and Steps 3.
Step 8: Go to Step 4 until the iteration number arrives at the maximum iteration number.
methods.
Classical method 
PSO method 
TLBO method 

Load Mw 
COST Rs/h 
Q Mm3/h 
COST Rs/h 
Q Mm3/h 
COST Rs/h 
Q Mm3/h 
75 
501.70 
493.8 
504.3 
346.0 
506.33 
346 
190 
523.40 
536.1 
526.0 
346.0 
529.71 
346 
220 
572.40 
620.8 
578.6 
346.0 
582.02 
346 
280 
694.20 
790.9 
706.0 
559.1 
722.66 
346 
320 
794.60 
902.9 
801.0 
642.6 
809.96 
592.5 
360 
911.70 
1015.8 
910.4 
724.1 
913.74 
688.5 
390 
1011.2 
1100.5 
984.8 
883.3 
972.48 
1036.0 
410 
1083.5 
1156.9 
1054.7 
1010.3 
1024.6 
1136.2 
440 
1201.1 
1241.5 
1156.3 
1734.2 
1114.3 
1635.4 
475 
1353.4 
1340.3 
1267.3 
2108.0 
1252.3 
1690.6 
525 
1600.9 
1481.4 
1502.3 
2036.9 
1368.0 
2309.3 
550 
1739.0 
1551.9 
1595.4 
2294.3 
1478.7 
2436.9 
565 
1826.8 
1594.2 
1664.4 
2736.1 
1513.0 
2581.1 
540 
1682.6 
1523.7 
1526.7 
2064.1 
1489.9 
2151.4 
500 
1472.5 
1410.8 
1427.0 
1879.2 
1369.9 
1756.9 
50 
1242.9 
1269.8 
1181.7 
1241.4 
1204.2 
1306.1 
425 
1140.9 
1199.2 
1135.8 
1106.3 
1124.3 
1096.8 
400 
1046.7 
1128.7 
1049.6 
529.8 
1051.2 
878.2 
375 
960.20 
1058.1 
959.4 
429.5 
959.48 
589.6 
340 
851.00 
959.4 
884.8 
428.0 
904.67 
346.00 
300 
742.40 
846.5 
758.3 
415.6 
773.42 
346.00 
250 
629.20 
705.4 
634.0 
346.0 
658.83 
346.00 
200 
538.90 
564.3 
542.5 
346.0 
550.09 
346.00 
180 
508.70 
507.9 
510.0 
346.0 
513.60 
346.00 
.
TableI. Analysis of generations, losses and lamda values for these methods.
CLASICALMETHOD 
PSO METHOD 
TLBO METHOD 

Load Mw 
PG1 Mw 
PG2 Mw 
PG3 Mw 
PH4 Mw 
PL Mw 
PG1 Mw 
PG2 Mw 
PG3 Mw 
PH4 Mw 
PL Mw 
PG1 (Mw) 
PG2 (Mw) 
PG3 (Mw) 
PH4 (Mw) 
PL (Mw) 

175 
66.90 
36.10 
61.80 
16.8 
6.60 
1.6 
53.34 
40.00 
75.00 
10.0 
3.34 
56.51 
40.00 
69.84 
10.0 
1.35 
190 
72.40 
39.40 
67.30 
18.8 
7.80 
1.7 
55.98 
80.00 
50.00 
10.0 
5.98 
71.09 
40.00 
71.88 
10.0 
2.98 
220 
83.60 
46.10 
78.40 
22.5 
10.5 
2.0 
60.00 
75.71 
74.50 
10.0 
8.26 
90.68 
40.00 
82.58 
10.0 
3.26 
280 
176.3 
60.30 
100.8 
29.8 
17.3 
2.6 
60.00 
117.8 
92.18 
19.7 
10.6 
105.9 
76.16 
93.48 
10.0 
5.63 
320 
121.7 
70.50 
116.0 
34.6 
22.8 
3.1 
75.00 
131.9 
99.09 
27.0 
12.5 
112.9 
91.79 
101.4 
21.2 
7.54 
360 
137.4 
81.30 
131.4 
39.2 
29.3 
3.6 
70.00 
84.90 
159.4 
33.7 
15.0 
139.2 
99.16 
104.1 
25.4 
8.04 
390 
149.3 
89.80 
143.0 
42.6 
34.7 
3.9 
134.0 
105.2 
123.7 
38.9 
18.2 
145.9 
103.8 
112.4 
40.0 
12.2 
410 
157.3 
95.70 
150.7 
44.8 
38.6 
4.2 
186.4 
63.92 
80.19 
48.1 
21.8 
154.8 
105.1 
119.9 
44.0 
13.8 
440 
169.4 
105.0 
162.4 
48.1 
44.9 
4.6 
207.3 
103.9 
94.98 
66.4 
26.2 
156.2 
121.3 
123.7 
62.9 
24.2 
475 
183.7 
116.3 
176.1 
51.9 
53.0 
5.2 
138.9 
88.50 
170.4 
77.0 
29.0 
170.0 
133.9 
133.1 
64.8 
27.0 
525 
204.4 
133.7 
195.7 
57.2 
66.0 
6.0 
250.0 
60.56 
190.9 
79.4 
38.1 
175.0 
145.0 
145.0 
86.1 
36.1 
550 
214.8 
142.9 
205.5 
59.8 
73.1 
6.4 
199.7 
69.03 
214.7 
85.6 
47.1 
189.0 
151.0 
152.0 
91.3 
46.1 
565 
221.1 
148.7 
211.3 
61.4 
77.5 
6.7 
250.0 
72.13 
142.9 
99.8 
51.9 
192.0 
152.0 
157.0 
94.9 
48.9 
540 
210.6 
139.2 
201.6 
58.8 
70.2 
6.2 
234.1 
141.0 
122.0 
77.9 
46.6 
194.0 
148.0 
155.0 
90.6 
47.6 
500 
194.0 
124.8 
185.9 
54.6 
59.3 
5.6 
248.9 
145.6 
92.10 
71.5 
41.2 
186.0 
136.0 
149.0 
67.2 
38.2 
450 
173.5 
108.1 
166.3 
49.2 
47.2 
4.8 
50.00 
144.0 
178.0 
42.8 
36.5 
172.3 
122.7 
134.0 
50.6 
31.5 
425 
163.4 
100.3 
156.6 
46.5 
41.7 
4.4 
119.4 
82.14 
204.9 
23.4 
25.2 
162.7 
118.1 
125.3 
42.4 
21.2 
400 
153.3 
92.80 
146.8 
43.7 
36.6 
4.1 
201.3 
41.78 
143.0 
18.4 
21.2 
152.1 
113.1 
119.0 
33.5 
19.2 
375 
143.3 
85.50 
137.2 
40.9 
31.9 
3.8 
50.00 
122.7 
130.7 
13.8 
18.4 
139.7 
105.8 
111.1 
21.1 
15.4 
340 
129.5 
75.80 
123.7 
36.9 
25.9 
3.3 
61.49 
66.01 
164.3 
13.8 
14.5 
132.5 
98.50 
109.4 
10.0 
10.5 
300 
114.0 
65.30 
108.4 
32.2 
19.9 
2.9 
50.00 
116.9 
123.0 
13.2 
11.3 
121.7 
74.44 
102.1 
10.0 
8.33 
250 
94.90 
53.10 
89.50 
26.2 
13.7 
2.3 
50.00 
122.0 
64.16 
10.0 
9.78 
112.5 
61.49 
73.75 
10.0 
7.78 
200 
76.10 
41.60 
71.00 
20.0 
8.7 
1.8 
50.00 
82.75 
57.25 
10.0 
8.30 
84.19 
40.00 
71.11 
10.0 
5.30 
180 
68.70 
37.20 
63.60 
17.5 
7.0 
1.6 
50.00 
40.00 
80.00 
10.0 
6.50 
70.50 
40.00 
62.00 
10.0 
2.50 
COMPARISON OF COST OF DIFFERENT METHODS:
The operating costs of classical, PSO and TLBOmethod for 24 hours for given load demand. Cost obtained for TLBO less as compared with PSO and Classical methods. Comparison of cost for 24 hours
TableIII. Cost analysis for these methods.
Classical 
PSO 
TLBO 
Rs. 24630.00 
Rs. 23477.00 
Rs. 23387.00 
Fig: cost analysis for these methods.
CONCLUSION AND FUTURE WORK:
The scheduling of electrical power from hydro and thermal plants has been done using PSO and classical methods. The optimization of cost is obtained mainly by employing three basic approaches. The optimization of thermal costs has been done by three methods employing programming technique. Finally the results of optimization by both the methods are tabulated and analysed. Numerical results show that highly near optimal solutions can be obtained by T LB O. So it is clear that with the help of TLBO based algorithm it is possible to find a more nearly optimal solution to the existing hydrothermal scheduling problem.
Future works:
Hydro thermal scheduling problem with valve point loading can also be solved using EP. The valve point effect is modelled in two forms one is in the form of prohibited operating zones and the other is by including rectified sinusoidal component in the fuel cost function.
REFERENCES:
1). Power System Optimization by J.S.Dhillon & D.P.Kothari