 Open Access
 Total Downloads : 987
 Authors : Julia Tholath Jose
 Paper ID : IJERTV2IS4990
 Volume & Issue : Volume 02, Issue 04 (April 2013)
 Published (First Online): 26042013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Comparison Of Economic Load Dispatch Of Wind Hydrothermal Systems
Julia Tholath Jose
Assistant professor, Birla Institute of Technology Offshore Campus Ras Al Khaima
Abstract
Economic Load Dispatch (ELD) is one of the important issues in Power system operation. The goal of ELD is to obtain the optimal allocation of various generating units available to meet the system load. Due to the popularity of renewable resources, it is necessary to include them in ELD problem. A general algorithm is developed for a thermal, hydrothermal and hybrid system having any no. of generating units. The validation is done for thermal system, hydrothermal system and hybrid system by particle swarm optimization. The performance of the proposed method is compared with the genetic algorithm. The simulation results show that the proposed PSO method is capable of obtaining higher quality solutions efficiently. Moreover, the hybrid system is found to be more economical than thermal and hydrothermal systems.

Introduction
Electrical power systems should be capable of producing sufficient power to meet the load and losses. Since electricity cannot be stored, it is necessary to start up and shutdown a no. of generating units at various power stations each day. Hence Economic Load Dispatch (ELD) problems play major role in electrical power system. Prior to the widespread use of alternate sources of energy, the ELD problem involved only conventional thermal energy power generators, which use non resources such as fossil fuels. Popularity of renewable energy resources due to their reduced cost, improved reliability and lower green house gas emissions, more and more researches have been investigated into power systems incorporating wind power. One of the major benefits of wind energy is that, after the initial land and capital costs there is essentially no cost involved in the production of power from wind energy.
The ELD problem has been tackled by many researchers in the past. ELD has been widely used in
paper uncertain nature of wind is predicted using weibull propability density function [2].
With the stochastic wind speed characterization based on the weibull probability density function, the optimization problem is numerically solved for a hybrid system involving thermal, hydel and wind units. In this work, the goal is to incorporate hydal and wind powered generators into the classical economic dispatch problem and to investigate the problem via numerical solutions.
Particle Swarm Optimization algorithm is employed for solving Economic Load Dispatch problem. The proposed algorithm is first applied to conventional thermal system. Then hydel units are integrated with the thermal units. Finally the economic load dispatch of a hybrid power system having thermal units, hydro units and wind farms was done. The fuel cost of thermal, hydrothermal and hybrid (thermal, hydal and wind) systems were compared. The performance of the PSO algorithm will be compared with conventional method and real coded genetic algorithm.

Cost Model

Thermal Unit
In the thermal unit, cost equations are obtained from the heat rate characteristics of the generating machine. Smooth costs are linear, differentiable and convex functions. The generated real power accounts for the major influence on fuel cost. The individual real generation is raised by increasing the prime mover torques, and this requires an increased expenditure of fuel. The reactive generations do not have any measurable influence on cost, as they are controlled by controlling by field current.
=
=
The fuel cost function of each thermal generating unit is expressed as a quadratic function. The total fuel cost in terms of real power output can be expressed as
power system operation and planning discussed by
= 1 ( )
1
Wood and Woollenberg in [1]. There is uncertainty in availability of wind power. Many efforts have done to predict the nature of wind and its parameters. In this
= + + 2 (2)
where
No. Of thermal units
Output of thermal unit
, , Cost coefficients of thermal unit

Hydel Unit
The coordination of the operation of hydroelectric plants, involves, of course, the scheduling of water releases. The hydroscheduling problem involves the forecasting of water availability and the scheduling of reservoir water discharges for an interval of time that depends on the reservoir capacities.
Imbalance cost of wind farm due to over generation
Imbalance cost of wind farm due to under generation
, Actual wind power from wind farm
Rated output of wind farm
Scheduled output of wind farm The three cost terms can be represented by
= (8)
= ,
= (9)
The hydro power generation is considered to be a
=
( )
function of discharge rate only
,
= (3)
The cost of generation is directly proportional to the
power generated
= 4
The hydraulic operational constraints comprise the
water balance equations for each hydro unit as well as the bounds on reservoir storage and release targets. These bounds are determined by the physical reservoir and plant limitations as well as the multipurpose requirements of the hydro system. These constraints include:
Water discharge rate limits
> > imin (5)
The values of water release must be chosen to stay
within hydraulic constraints. These may be determined by use of the hydraulic continuity equation.
+1 = + (6)
Where
Discharge rate of generator
= (10)
0
where
Cost coefficient of wind farm
Penalty cost coefficient for over generation of
wind farm
Reserve cost coefficient for under generation of
wind farm
() Probability density function(pdf) of wind power output
In this wind speed distribution is modelled as Weibull probability density function. The pdf of wind power output is represented by
= ((1+ ) )1 exp 1+ (11)
for 0< <
0 = 1 exp + 0 (12)
Maximum Discharge rate of generator
= exp + 0 (13)
Minimum discharge rate of generator
Power generated by hydro generator
where
Cost coefficient of hydro generator
= and =
Inflow rate in interval
0
Water discharge rate in interval
Spillage rate in interval

Wind Farm
The objective cost consists of (i) the cost of purchase power (ii) the penalty cost because of the expected surplus wind power which is not utilized and
(iii) the reserve power cost because of the expected deficit of wind power
= + , +
K and c weibull pdf parameters
and l intermediate variables
, rated,cut in and cut out wind speeds


Particle Swarm Optimization
The sequential steps to find the optimum solution are
Step 1:
Initialize the particles (power generation) ith random values for all the populations by satisfying constraints. Step 2:
Initialize the velocity in the range [Vmax and Vmin]
=1 =1
=1
=1
, (7)
Where
Operating cost of wind farm
Step 3:
The cost function of each individual P, is calculated in the population using the evaluation function which is the operating cost of generation.
The present value is set as the pbest value.
Step 4:
Each pbest values are compared with the other pbest values in the population. The best evaluation value among the pbest is denoted as gbest.
Step 5:
The member velocity v of each individual Pg is updated according to the velocity update equation
+ 1 = + 1 1
+ 22
(14)
where k is the number of iteration.
Step 6:
The velocity components constraint occurring in the limits from the following conditions are checked
= 0.5
= +0.5 (15)
Step 7:
The position of each individual Pi is modified according to the position update equation
+ 1 = + + 1 (16)
(4.15)
Step 8:
= 0.001942 + 7.851 + 310 /
1
1
1
1
= 0.004822 + 7.971 + 78 /
The unit operating ranges are
100 < 1 < 600
100 < 1 < 400
50 < 1 < 200
The water discharge rate of the hydro plant is given as
= 330 + 4.97 /
The initial and final volumes of water in the reservoir are 100000 acreft and 60000 acreft respectively. The minimum and maximum volumes of water are 60000 acreft and 120000 acreft in all intervals. The water inflow rate is assumed to be constant at 2000 acreft/h and the spillage is not counted.
The hydel unit operating range is
0 < < 500
The cost coefficients of the two wind farms are d1 =1 and d2 = 1.1.The wind speed parameters are cut in speed vi =5, rated speed vr = 15, and vo = 45.The weibull function parameters are k=2 and c=10.The penalty and reserve factors are set to kpi =2 and kri=4

Thermal system
Check all the constraints within limits
Step 9:
The cost function of each new individual is calculated. If the evaluation value of each individual is better than previous pbest, the current value is set to be pbest. If the best pbest is better than gbest, the value is set to be gbest.
Step 10:
If the number of iterations reaches the maximum, then go to step 11.Otherwise, go to step 5.
Step 11:
The individual that generates the latest gbest is the
1.0851
1.085
1.085
Fuel Cost Rs/hr
Fuel Cost Rs/hr
1.0849
1.0849
1.0848
1.0848
1.0847
1.0846
4
x 10
Convergence Characteristics PSO
optimal generation power of each unit with minimum total generation cost.
0 5 10 15 20 25 30 35 40 45 50
No. of iterations
Figure 1.Cost curve for thermal system by GA
4 Test Systems
The developed algorithm is validated through case studies. The validation is done for thermal, hydrothermal and hybrid systems using PSO and GA. The best one suggested is PSO. All these simulations are done on MATLAB environment.
The power demand is taken as1100 Mw. The generation loss is assumed as 3% of total power demand. The total power to be generated is PG = PD + PL i.e. 1133 Mw
The cost function characteristics of three unit thermal
1.0847
1.0847
1.0847
Fuel Cost Rs/hr
Fuel Cost Rs/hr
1.0847
1.0847
1.0847
1.0847
1.0847
4
x 10
Convergence CharacteristicsGA
system are given by following equations.
1
1
= 0.001562 + 7.921 + 561 /
1.0847
0 5 10 15 20 25 30 35 40 45 50
No. of iterations
Figure 2.Cost curve for thermal system by PSO
Table.1 Cost of thermal system
4.3 Six unit Hybrid system
PSO
GA
PG
1133
1133
P1
557.6875
558.007
P2
400
399.6365
P3
175.3125
175.3628
No.of iterations
19
27
Cost Rs/Hr
10847
10847
PSO
GA
PG
1133
1133
P1
557.6875
558.007
P2
400
399.6365
P3
175.3125
175.3628
No.of iterations
19
27
Cost Rs/Hr
10847
10847
Convergence Characteristics PSO

Four unit hydrothermal system
6700
6650
6600
6550
Fuel Cost Rs/hr
Fuel Cost Rs/hr
6500
6450
6400
6350
6300
7050
7040
Convergence Characteristics PSO
6250
6200
0 5 10 15 20 25 30 35 40 45 50
No. of iterations
7030
Figure 1.Cost curve for wind hydrothermal system by PSO
Fuel Cost Rs/hr
Fuel Cost Rs/hr
7020
7010
7000
6990
0 5 10 15 20 25 30 35 40 45 50
No. of iterations
Figure 3.Cost curve for hydrothermal system by PSO
6700
6650
6600
6550
Fuel Cost
Fuel Cost
6500
6450
6400
6350
Convergence Characteristics GA
7120
7100
Convergence CharacteristicsGA
6300
6250
0 20 40 60 80 100 120 140 160 180 200
no. of iterations
7080
Fuel Cost
Fuel Cost
7060
7040
7020
7000
6980
0 10 20 30 40 50 60 70 80 90 100
no. of iterations
Figure 1.Cost curve for wind hydrothermal system by GA
PSO 
GA 

PG 
1133 
1133 
PT1 
173.1083 
223.0408 
PT2 
243.7734 
231.3912 
PT3 
116.0350 
86.0347 
PH1 
500 
498.6780 
PW1 
50 
50 
PW2 
45.3091 
48.5462 
No. of iterations 
16 
168 
Cost Rs/Hr 
6235.9 
6279.1 
PSO 
GA 

PG 
1133 
1133 
PT1 
173.1083 
223.0408 
PT2 
243.7734 
231.3912 
PT3 
116.0350 
86.0347 
PH1 
500 
498.6780 
PW1 
50 
50 
PW2 
45.3091 
48.5462 
No. of iterations 
16 
168 
Cost Rs/Hr 
6235.9 
6279.1 
Table.3 Cost of wind hydrothermal system
PSO 
GA 

PG 
1133 
1133 
PT1 
292.8574 
309.7676 
PT2 
249.0737 
231.4583 
PT3 
90.9704 
91.7883 
PH 
500 
499.9858 
No.of iterations 
12 
52 
Cost Rs/Hr 
6992.6 
6994 
PSO 
GA 

PG 
1133 
1133 
PT1 
292.8574 
309.7676 
PT2 
249.0737 
231.4583 
PT3 
90.9704 
91.7883 
PH 
500 
499.9858 
No.of iterations 
12 
52 
Cost Rs/Hr 
6992.6 
6994 
Figure 4.Cost curve for hydrothermal system by GA Table.2 Cost of hydrothermal system

Conclusion
ELD is used in realtime energy management power system control by most programs to allocate the total generation among the available units. In this work
a methodology to solve the ELD of a hybrid system which includes Independent power producers under large integration of renewable energy sources was presented. An economic dispatch model incorporating wind power is developed. Based on the traditional economic dispatch model, the influence of randomicity of wind power is taken into consider, and penalties cost are proposed. The uncertain nature of the wind speed is represented by weibull pdf. In addition to the classic economic dispatch factors, factors to account for both overestimation and underestimation of available wind power are included.
In this work particle swarm optimization has been successfully introduced to obtain the optimal solution of load dispatch. The validation is done for three unit thermal system, four unit hydrothermal system and six unit wind hydrothermal system. It is found that hybrid system is more economical than thermal and hydrothermal system. The results have been compared with genetic algorithm. The simulation results have shown that PSO is capable of maintaining better results.

References

A.J. Wood and B. F. Wollenberg, Power Generation Operation and Control.New York: Wiley, 1984

J Hetzer, DC Yu, K Bhattarai, An economic dispatch model incorporating wind power, IEEE Trans. Energy Conversion, vol. 23,pp. 603611, June 2008.

Orero.S.O. and Erving M.R.Economic dispatch of generators with prohibited operating zones: a genetic algorithm approach.IEEE Proc.Gen. Transm.
Distrib.143 ,529534,1996

Gaing Z.L.Particle swarm optimization to solving the economic dispatch considering the generator constraints,IEEE Trans.Power Syst.18(3) 11871195
,2003.

Jayabarathi.T, Jayaprakash.T and Raghunathan.T,Evolutionary programming techniques for different kinds of economic dispatch problems
Elet.Power Syst.Res.73, 169176,2005

Lin.W.M., Gow.H.J. and Tsay.M.T.,A partition approach algorithm for non convex economic dispatch. Elect.Power Energy Syst.29,432438,2007.

Noman.N and Iba.H.,Differential evolution for economic dispatch problems, Elect.Power Syst.Res.78,13221331,2008

Chiou.J.P,Variable scaling differential evolution for large scale economic dispatch problemsElect.Power.Syst.Res.77,212218,2007

Abdelaziz.A.Y,Mekhamer.S.F, Badr MAL and Kamh.M.Z,Economic dispatch using an enhanced Hopfield neural network,Elect.Power Compon.Syst.36,719732, 2008

J.Kennedy and R.Eberhart,Particle swarm optimization,in Proc IEEE Conf, Neural Networks,vol 4,pp.19421948,1995

P.H.Chen and H.C.Chang. ,Largescale economic dispatch approach by genetic algorithm,IEEE Trans.on Power Systems,vol 8,no.3 pp.13251331,1993

A.Bakrirtzis,V.Petrides and S.Kazarlis,Genetic algorithm solution to the economic dispatch,IEEEProc.Gener.Transm.Distrib.,vol.141,no. 4 pp 377382,July 1994

Miranda V.,Hang P.S,Economic dispatch model with fuzzy wind constraints and attitudes of dispatchers,IEEE Trans.Power Syst.,2005,pp.2143 2145

Wang L.,Singh C,Balancing risk and cost in fuzzy economic dispatch including wind power peneteration based on particle swarm optimimzation,Electr.Power Syst.Res.,2008,78,pp 603611

Tsikalakias A.G.,Katsigiannis Y.A, Georgilakis P.S,Hatziargyriou N.D, Determining and exploiting the distribution function of wind power forecasting error for the economic operation of autonomous power systems,IEEE Power Engineering General Society Meeting,2006

Chen H.,Chen J.,Duan X,Multistage dynamic optimal power flow in wind power integrated system.IEEE/PES Transmission and Distribution Conf.Exhibition:Asia and Pacific,2005 [17]A.T.AlAwami,E.Sortomme,M.A.ElSharkawi,Opti mizing Economic / Environmental dispatch with wind and thermal unit