To Optimize the Cost of Electricity Generated by Hydro Power Plant Using Artificial Neural Networks

To Optimize the Cost of Electricity Generated by Hydro Power Plant Using Artificial Neural Networks

Ms. Amninder Kaur, Dr. B.K. Sawhney, Dr.O.P. Gupta School of Electrical Engg.&IT *School of Electrical Engg. & IT *School of Electrical Engg. & IT College of Agricultural College of Agricultural College of Agricultural Engineering & Technology Engineering & Technology Engineering & Technology Punjab Agricultural University Punjab Agricultural University Punjab Agricultural University Ludhiana Ludhiana Ludhiana

Abstract

The paper presents a proposal for the optimization of the cost of generating units of hydro power plant by genetic algorithms. Genetic algorithm (GA) is used for optimization of integral gains and bias factors, which are applied to automatic generation control (AGC). Tie-line bias KI and frequency bias parameter B are optimized by using real coded GA. It is used to search for the optimal set of parameters (KI and B), which in turn optimize the frequency factor. . The objectives are to minimize the transient deviations in frequency so that constant power can be generated. Then the optimized cost of each area is calculated which turns out to be Rs.4.60.Average cost of the whole system is also calculated as Rs.7.90.

1. INTRODUCTION

   Economic operation and control of interconnected power systems involves the solution of difficult optimization problems that require good computational tools. Evolutionary Computation is an area of computer Science that uses idea from biological evolution to solve problems. Evolutionary computation is one such tool that has shown its ability in solving complex problems. It can be implemented in various forms such as genetic algorithms. In present work, the genetic algorithm is applied in the solution of Optimization of cost of electricity generated by hydro power plant.

   Genetic algorithms (GA) have been developed using the survival-of-the fittest concept in searching for better solution. GA , which are known as time intensive, can find global minimum. GAs have attractive features such as robustness, simplicity, etc. GAs have also been applied to power system problems such as optimal power flow, analysis of system topologies, the design of power distribution and to solve the economic dispatch.

   Hydro Power systems (HPS) are used to convert natural energy into electric power. It transports electricity to factories and houses to satisfy all kinds of power needs. To optimize the cost of generated electricity, it is important to ensure constant generation of electricity during a time period. It is well known that three-phase alternating current (AC) is generally used to transport the electricity. During the transportation, both the active power balance and the reactive power balance must be maintained between generating and utilizing the AC power. Those two balances correspond to two equilibrium points: frequency and voltage. When either of the two balances is broken and reset at a new level, the equilibrium points will float. A good quality of the electric power system requires both the frequency and voltage to remain at standard values during operation. It will be impossible to maintain the balances of both the active and reactive powers without control. As a result of the imbalance, the frequency and voltage levels will be varying with the change of the loads. Thus a control system is essential to cancel the effects of the random load changes and to keep the frequency and voltage at the standard values. As load increases, it will lead to deviation of frequency and hence generated power. The foremost task is to keep the frequency constant against the randomly varying active power loads, which are also referred to as unknown external disturbance. The objectives are to minimize the transient deviations in frequency and to ensure their steady state errors to be zeros, so that constant power can be generated. Once optimized power will be generated it will automatically optimize the cost of generated power because generated power and cost of generated power are directly proportional to each other.

   In current work the HPS is assumed to contain two hydro units in Area A1, Area A2, and Area A3.Each area includes two GENCOs (generation units) and two DISCOs (distribution units ).GENCO DISCO contract is imposed with DISCO participation matrix .Each entry of this matrix is the fraction of total load demanded by DISCO

   towards GENCO. This fraction is represented by contract participation factor (cp).The number of rows has to be equal to number of GENCOs and number of columns has to be equal to number of Discos. Area control error (ACE) signal must be shared by all GENCOs according to their participation. The sharing is represented by ACE participation factors (aps) .In case of three area power system scheduled steady state power flow is given as follows:

   Pi-j scheduled = [demands of DISCOs in area j from GENCOs in area i] – [demands of DISCOs in area j from GENCOs in area j] (1)

   P1 scheduled (k) =P1-2 scheduled (k) + a31P3-1scheduled (k) (2)

   P2 scheduled (k) =P2-3 scheduled (k) + a12P1-2 scheduled (k) (3)

   P3 scheduled (k) = P3-1scheduled (k) + a23P2-3 scheduled (k) (4)

   The errors for the above powers can be calculated as:

   P i error = P i actual – P i scheduled (5) ACE signals can be generated as:

   ACE i = P iactual – P jscheduled

   (6)

   Equations of the considered power system including three areas are given in steady state as follows:

   X = Anew X + Bnew U

   Where X is state vector and U is vector of demand of DISCOs, calculated as follows:

   X =

   [1PR1PR2PGIPG2Pref1xE1xE22PR3PR4PG3 PG4Pref2xE3PR1xE43xE5xE6PR5PR6PG5PG6Pr ef3P1-2P2-3P3-1 ]T

   U = [PL1PL2PL3PL4PL5PL6]

   In this study following case is considered:

   All of the ACE participation factors are the same as 0.5, so contribution of each area to AGC is assumed as equal. In the steady state, any GENCO generation must match the demand of DISCO in contract with it, as expressed as follows:

   P Mi = cp ij P Lj

   Where P Lj is the total demand of DISCOj .In this case GENCOs belonging to area 2 and area 3 are not contracted by any DISCO in another area for transaction of power, so changes in generated power by them are zero in steady state.

2. Optimization of ACE parameters

   A quadratic performance index that includes the parameters affecting to AGC is proposed as follows:

   I = [-KI1(P1)2 KI1B1(1)2 KI2(P2)2 – K12B2(2)2 – KI3(P3)2 – K13B3(3)2] dt [1]

   Where value of limit varies from 0 to . KIi and Bi (i=1,2,3..) and Pi (i=1,2)

   GAs effectively searches a design space to find global minimum of the performance index. Individuals in the GA population are formed and reproduced as in nature. Different population members are assigned different reproduction rates proportional to their fitness. The fitness corresponds to the objective function of the considered problem. A GA is based on a structure similar to a biological gene and an optimal solution is inspected applying selection, reproduction, crossover and mutation processes. The best individual survives during the optimization.

   Fig .1.Configuration of three area power system. [1]

   G3

   G3

   R3

   R3

   Steady state equations of the power system:

   P (s) 1 sKR3TR3 P

   (s)

   (12)

   (s) KP1 (P (s) P

   1 1 sT G1 G 2

   (s) PL1 (s)

   1 sTR3

   G4

   G4

   R4

   R4

   P1 P (s) 1 sKR4TR4 P

   (s)

   (13)

   -PL2(s) – P1 (s)) (1)

   1 sTR4

   P (s) 1 x

   (s)

   (2)

   P (s) KI2 B2 (s) P (s)

   (14)

   R1

   R1

   E1

   E1

   1 sTT1

   1

   ref2

   2 2 2 2

   1 1

   PR2 (s) 1 sT xE2 (s)

   (3)

   xE3 (s) 1 sT ap3Pref2 (s) 2R

   2 (s)

   T2

   G1

   G1

   R1

   R1

   P (s) 1 sKR1TR1 P

   (s)

   (4)

   G3

   3

   (15)

   1 sTR1

   1 1

   1 sK T

   xE4 (s) 1 sT ap4Pref2 (s) 2R 2 (s)

   PG2

   (s)

   R2

   1 sT

   R 2 PR2

   (s)

   (5)

   G4 4

   R2

   P (s) KI1 B1 (s) P (s)

   3

   3

   G5

   G5

   G6

   G6

   L5

   L5

   (6) K

   (16)

   ref1 1 1

   (s) P3 (P (s) P (s) P

   (s) –

   s 2

   1 sTP3

   1 1

   PL6(s) – P3(s)) (17)

   xE1 (s) 1 sT ap1Pref1 (s) 2R

   1 (s)

   1 1

   1 1

   G1

   xE5 ap5Pref 2 (s) 3 (s)

   1

   1

   (18)

   1 1

   (7)

   1 sT1

   1

   2R5

   1

   xE2 (s)

   ap2Pref2 (s)

   1 (s)

   xE 6 1 sT

   ap6Pref 2 (s) 2R

   3 (s)

   (19)

   1 sTG2

   2R2

   4 6

   (8)

   K

   PR5

   (s)1 sT2 x 1 sT3

   6

   6

   E5

   E5

   1 sT5

   (s)

   (20)

   2 (k) P2 (PG3 (s)- PG4 (s)PL3 (s)

   1 sTP2

   PR6 (s) 1 sT

   xE6 (s)

   (21)

   -PL4 (s) – P2(s)) (9)

   1 sT

   1 sT

   1

   PR3 (s) xE3 (S)

   T3

   (10)

   PG5

   PG6

   (s)

   (s)

   1 sTw

   1 0.5sTW

   1 sTw

   1 0.5sTW

   PR5

   PR6

   (s)

   (s)

   (22)

   (23)

   P (s) 1 x

   (S)

   (11)

   K B

   R4 1 sT E4

   Pref3 13 3 3 (s) P3 (s)

   (24)

   T4 s

   2

   P (s) T12 ( (s) (s)

   (25)

3. RESULTS

   12 2s 1 2

   T

   Following equations are implemented in MATLAB. Results with optimized values in table and deviation of

   P23(s) 23 (2 (s) 3 (s))

   2 s

   P (s) T31 ( (s) (s))

   (26)

   (27)

   values are represented in figures from fig [2] to fig [10].Fig [3]-fig [5] represents the deviation of frequency in three areas. Fig [6]-fig [8] represents change in Pi-j .fig

   [9]-fig [11] represents change in output of ACE. As the

   31 2s 3 1

   frequency curve reaches to constant position, its means constant power can be generated with standard cost.

   A Formal flow of work has been depicted below in Fig. 2

   Fig .3.The frequency deviation of area 1 for the first operation case

   Fig. 2. Flowchart of Simulation

   Fig .4.The frequency deviation of area 2 for the first operation case

   Fig .5.The frequency deviation of area 3 for the first operation case

   Fig . 6 .The deviation of P12

   Fig .7.The deviation of P23

   Fig . 8. The deviation of P31

   Fig. 9.The deviation of Pref 1

   Fig .10.The deviation of Pref 2

   Fig .11.The deviation of Pref 3

4. CONCLUSION

In this paper, cost of generated power is optimized by optimizing the frequency factor of generated power. ACE parameters are optimized for an appropriate performance index by using continuous parameter GA based on real values. This type of GA is chosen since the computational time is saved using this algorithm and it is more sensitive than simple GA. The cost of each area is calculated which turns out to be Rs.4.60.Average cost of the whole system is also calculated as Rs.7.90.Frequency Deviation in three areas is also depicted in graphs.

LIST OF SYMBOLS

Frequency

Angular speed

Kp Transfer function gain of generator

Tp Time constant of generator

TT Time constant of turbine

XE Governor Valve position

TG Time constant of governor

PG Fluctuation in turbine output power

Pref The output of ACE

PL Electrical load variations

T1 Time constant of hydro governor

T2 Time constant of hydro governor

T3 Time constant of hydro governor

TW Water starting time

R Regulation parameter

KI Integral controller gains

Bi Bias factor

X State vector

U Input vector

A,B State matrices

GENCO Generation units

DISCO Distribution units

DPM Disco participation matrix

Cpij Contract participation factor

api ACE participation factor

Pi-jactual Tie line real power

Pi-jscheduled Tie line scheduled power Pi-jerror Tie line power error

ACE Area control error

REFERENCES

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