Hydrothermal power system AGC with GA optimized Controllers and Capacitive Energy Storage

Chavali Krishna Bharadwaj

B.Tech 4th year, Department of Electrical Engineering, Malaviya

National Institute of Technology, Jaipur, Rajasthan- 302017,

India E-mail: ch.krishnabharadwaj@gmail.com

Rajesh Joseph Abraham Assistant Professor,

Department of Avionics, Indian Institute of Space Science & Technology, Thiruvananthapuram,

Kerala -695 022, India.

E-address: rajeshja@gmail.com

Abstract— In this work, the Automatic Generation Control of an interconnected hydrothermal power system with a small capacity Capacitive Energy Storage augmented to both thermal and hydro area has been investigated. The effect of an integral controller as well as a PID controller whose gains are tuned by Genetic Algorithm technique has been examined and compared. The optimum values of the integral and PID controller gains without and with capacitive energy storage (CES) for both the areas are obtained by minimizing Integral Time Squared Error (ITSE) criterion. Simulation studies and a comparison of the dynamic responses reveal the improvement of AGC in terms of peak amplitudes and deviations in frequencies of both the areas, as well as tie line power with the PID controller and augmentation of Capacitive Energy Storage unit.

Keywords— Automatic Generation Control, Capacitive Energy Storage, Genetic Algorithm, PID

I. INTRODUCTION Automatic Generation Control (AGC) of interconnected

power systems is gaining importance in modern power systems. Increasing demand for electrical power and the complexity of load patterns has necessitated the design of interconnected power systems. Interconnected power systems consist of different control areas which are linked through tie-line grid. The primary objectives of a control area are to satisfy its local consumer demands and to respond to the variation in demand of other control areas so that the entire power system can supply consumer demands at nominal frequency and voltage levels. For this, the load demand should equal generation capacity. But in practice, the load is continuously changing. Further, due to physical/technical limitations, the ability of generation to track the varying load is limited. Thus the power system equilibrium cannot be satisfied in practice. Hence the primary objective of an AGC system is to instantaneously match the generation of the system with varying load demand so that the reliability of the power system can be enhanced [1-4].

An energy storage device with a quick response time can be added to power system to reduce the oscillations of system frequency and tie line power due to random load pattern. Several energy storage devices have been designed and proposed in the last few decades such as flywheels, battery

storage, compressed air, pumped hydro, fuel cells and Superconducting Magnetic Energy storage (SMES), etc. However, they have their own practical limitations as pointed out in [5-7]. Capacitive Energy Storage (CES) is one of the latest in energy storage devices [8, 9]. Relative cheapness, maintenance free, environment friendly as opposed to other systems etc are a few of the advantages of the CES unit to mention. This paper investigates the dynamic performance of both integral and PID controllers and the use of CES unit in an interconnected hydrothermal power system to improve the system performance.

The optimal gain settings of the Integral and PID controllers are obtained by using Genetic Algorithm technique [10-12] and minimizing the Integral Time Squared Error (ITSE) criterion for a unit step load disturbance in either of the areas. The modeling of hydrothermal system is described in sections 2& 3, section 4 describes CES modeling, sections 5& 6 explains optimization of both PID and integral controller gain parameters using genetic algorithm and the dynamic response of the hydrothermal system to load perturbations is studied in sections 7& 8.

II. HYDROTHERMAL POWERSYSTEM MODEL The AGC system under analysis is composed of an

interconnection of two areas. Area 1 consists of thermal system and area 2 comprises a hydro system. Typical generation rate constraints of 10%/min. for thermal area and 270%/min. (4.5%/sec.) for raising generation and 360%/min. (6%/sec.) for lowering generation in the hydro area is considered as in IEEE Committee Report on power plant response to load changes [13]. The transfer function models used for analysis are developed as in IEEE Committee Report on dynamic models for steam and hydro turbines in power system studies [14]. Fig.1 shows the linear time invariant transfer function block diagram of the two area hydrothermal power system. Fig.2 shows the CES unit transfer function block diagram. The CES unit is fitted in both thermal and hydro area and the performance of the system is studied for unit step load disturbance in either of the areas. The values of the constants in block diagram for both the areas and the CES unit are given in the appendices.

PROCEEDINGS OF ICETECT 2011

978-1-4244-7926-9/11/$26.00 ©2011 IEEE 105

III. MATHEMATICAL MODELLING The linear time invariant model of the power system under consideration can be modeled using standard state space representation technique. The state space equation of the present system for analysis can be represented as in (1).

ΓP BU AX X ++= (1) Where X, U and P are the state, input and disturbance vectors while A, B, and Г are real constant coefficient matrices associated with the corresponding vectors respectively and are given in (2), (3) and (4).

[ ]Tdidit2t1r1g2g1tie1221 ΔEΔIΔPΔPΔPΔPΔPΔPΔfΔfX= (2)

[ ]T21 UUU = (3)

[ ]Td2d1 ΔPΔPP = (4)

IV. CAPACITIVE ENERGY STORAGE UNIT A capacitor stores the energy in its electrostatic field

created between its plates in response to applied potential across it. So for realizing a CES unit we need a 3-phase ac to dc rectifier and a dc to ac inverter system and a capacitor bank. The capacitor bank consists of many small capacity capacitors connected in parallel. The capacity of the CES unit can be increased at any time by adding capacitors in parallel to the capacitor bank. Fig. 2 shows the electrical circuitry of a typical CES unit.

The area control error (ACE) of the control area is fed as control signal to the CES unit. The area control error (ACE) of the ith control area is defined as (7)

jtiei,iii ΔPΔfBACE += ; i, j=1, 2 (7) ACE being a linear function of frequency deviation and tie line power deviation is a better option to damp the oscillations and reduce response time. After a sudden load disturbance, in either of the areas, the restoration time of capacitor bank to normal voltage is slow. For quick restoration, a negative feedback is applied by sensing the voltage deviation in the control loop of the CES unit as in Fig. 3. The voltage deviation (∆Edi) of the CES unit is limited to ±15% of the nominal value. With ACE as the control signal to the CES unit,

[ ]divdiiCESiDCi

di ΔEKΔACEKsT11ΔI −⎥

⎦

⎤⎢⎣

⎡+

= ; i, j = 1, 2 (8)

The output power from the CES unit is given by (9), (10) ( )

diΔE

d0E

d0ΔI

CESΔP +×= ; i =1, 2 (9)

Where

ii

didi

R1sC

ΔIΔE

+= ; i =1, 2. (10)

P1

P1sT1

K+TsT1

1+GsT1

1+s

K I1−

B11R

1

− −+

+

+

sT2 12Π

−

+

−

+

P2sT1P2K

+2

RsT1sT1

++

1sT11

+sK I2−

B22R

1

a12a12

W

W0.5sT1

sT1+

−

+

++

−

+

−

−

d2ΔP

1Δf

2Δf

tie12ΔP

−

g1ΔP

g2ΔP

t1ΔP

t2ΔP r1ΔP

Area Hydro

CES

d1ΔP

1ACE

Area Thermal

++

1U

2U

1ACE

2ACE

CES

2ACE

+

+

Figure 1. LTI model of interconnected hydrothermal system with CES

106

Figure 2. CES Unit: Block diagram representation

V. GENETIC ALGORITHM

Figure 3. Flow chart of Genetic Algorithm

Genetic algorithms are inspired by the fundamental principles of natural evolution in biological systems [10-12]. They work with a set of population of candidate solutions represented by strings called chromosomes. The initial population consists of randomly generated individuals. At each iteration of the algorithm, fitness of each individual in current population is computed. The population is then transformed in stages to yield a new current population for next iteration. The transformation is done in three stages by applying the following genetic operators: (1) Selection (2) Crossover and (3) Mutation. In the first stage, selection operator is applied as many times as there are individuals in the population. In this

stage, every individual is replicated with a probability proportional to its relative fitness in the population. In the next stage, the crossover operator is applied. Two individuals/parents are chosen and combined to generate two new individuals. The combination is done by choosing at random, a cutting point at which each of the parents is divided into two parts; these are exchanged to form the two offspring’s which replace their parents in the population. In the final stage, the mutation operator changes the values in a randomly chosen location on an individual. This process continues till one of the stopping criteria are met or global minimum is attained and the best individual generated during the run is considered to be the solution. Flowchart shown in Fig. 3 gives the schematic of the GA process for tuning the integral and PID controller parameters for the AGC system.

VI. OBJECTIVE FUNCTION The performance index/fitness function is formulated by the integral Time squared error (ITSE) technique. The fitness function (J) used for optimizing the gain settings is

( ) dtt ΔPΔfΔfJt

0

2tie12

22

21 ×++= ∫ (11)

Thus, the optimization problem can be stated as Minimize J subjected to

maxjp,Kjp,Kmin

jp,K << (12)

maxjI,KjI,Kmin

jI,K << (13)

maxjd,Kjd,Kmin

jd,K << (13)

Where Kp,j KI,j Kd,j correspond to the PID controller gains of the jth control area. The GA tool provided in MATLAB 7 is used for optimizing the fitness function J with the options as in Table 1.

TABLE I. GA OPTIONS

No. of generations 100 Population size 50 Selection function Roulette Crossover Heuristic Mutation Uniform

The performance index is minimized for a unit step load disturbance in either of the areas to obtain optimal gain settings. Since a two area system with different units is investigated, the optimum gain settings are obtained separately by considering the other area uncontrolled. Table 2 &3 shows the values of optimal gain settings for both the thermal area as

DCi sT11

+iR

1sC

1

i +

vdiK

Π

0 K

d0E

+-

++

di ΔI

di ΔE

di ΔI

CES ΔP

i ACE

107

well as hydro area without and with CES units in both the areas. The optimal values of the gain settings for both the PID and integral controller with and without CES units in both the areas as tabulated below are applied for simulation studies.

TABLE II. OPTIMAL INTEGRAL CONTROLLER GAIN

SETTINGS

TABLE III. OPTIMAL PID CONTROLLER GAIN SETTINGS

Area Kpi kii kdi

Without CES unit

Thermal 0.51315 -0.04151 -0.1131 Hydro -0.47717 -0.06084 0.57091

With CES unit in both areas

Thermal -0.59679 -0.07372 -0.9088 Hydro -0.94722 -0.20606 0.25471

VII. SIMULATION AND DISCUSSION The dynamic responses of the hydrothermal power system without and with CES unit with both integral and PID controllers are studied for a 1% step load disturbance in either of the areas (ΔPd1=0.01 p.u MW or ΔPd2=0.01 p.u MW). The responses for frequency deviations (Δf1 and Δf2), tie-line power fluctuations and power generation deviations (ΔPg1 and ΔPg2) are plotted and are compared with those obtained by adding CES unit in both areas with different controllers. Fig. 4 shows the dynamic responses for the frequency deviations (Δf1 and Δf2) and tie-line power fluctuations (ΔPtie12) for a 1% step load perturbation in the thermal area without and with CES unit. It is evident that, the transient behavior of the area frequencies and tie-power has improved significantly in terms of peak deviations in the presence of the CES unit.

Figure 4. Dynamic responses for frequency perturbations (∆f1and ∆f2) and

tie-line perturbations (∆Ptie,12) following a 1% step load disturbance in thermal area

Fig. 5 depicts the generation responses for both the thermal and hydro areas (ΔPg1 and ΔPg2) without and with CES unit with both integral and PID controllers. As the step load perturbation has occurred in the thermal area, it may be noted that, the thermal unit should adjust its output at the earliest so as to take up the local load perturbations in its area as per its obligation and this is reflected in Fig. 5. Further, according to the approved practices of interconnected operations, the hydro area need not contribute to the local load fluctuations in the thermal area and hence should settle down to zero steady state value as early as possible as is evident from Fig. 5. It may further be noted that, the initial negative deflection of the transient response of the output of the hydro unit is attributed to water hammer effect. PID controller due to its predictive capability dampens out the oscillations effectively compared to integral controller with and without CES units.

Area

Without CES unit

With CES unit in both areas

Thermal area (Ki1) 0.24804 0.08059

Hydro area (Ki2) 0.05026 0.38755

Time (s)

Time (s)

ΔPtie

12 (p

u M

W)

Time (s)

Δf2

(Hz)

Δf1

(Hz)

108

Figure 5. Generation responses for the thermal and hydro units (ΔPg1 and

ΔPg2) with 1% step load disturbance in thermal area Similar findings were also observed with a step load perturbation of 1% in the hydro area as plotted in Fig. 6 and Fig. 7.

Figure 6. Dynamic responses for ∆f1, ∆f2 and ∆Ptie,12 with 1% step load

disturbance in hydro area

ΔPg1

(pu

MW

)

Time (s)

Δf1

(Hz)

Δf2

(Hz)

ΔP

tie12

(pu

MW

)

Time (s)

Time (s)

ΔPg1

(pu

MW

)

Time (s) Time (s)

Time (s)

ΔPg2

(pu

MW

)

109

Figure 7. Generation responses for the thermal and hydro units (ΔPg1 and

ΔPg2) with 1% step load disturbance in hydro area

VIII. CONCLUSIONS In the present work a comprehensive mathematical modeling of the AGC of a hydrothermal power system for both integral and PID controllers with and without CES unit has been studied. Appropriate Generation Rate Constraints for the thermal and hydro systems have also been considered in the analysis. Genetic Algorithm has been applied to obtain the optimum values of the integral and PID controller gain settings and the performance index has been formulated using the Integral Time Squared Error technique. It has been shown that, the system frequency and tie-line power oscillations following small load perturbations can be effectively damped out with the use of a PID controller and CES units in both the areas. Thus, the AGC performance of a hydrothermal power system can be improved by incorporating a PID controller and CES unit.

APPENDIX (A) System Data

KP1 = KP2 = 120 Hz/p.u. MW TP1 = TP2 = 20 s R1 = R2 = 2.4 Hz/p.u. MW B1 = B2 = 0.4249 TG = 0.08 s, TT = 0.3 s, T12 = 0.0866, T1 = 41.6 s, T2 = 0.513 s, TR = 5 s, TW = 1 s D1 = D2 = 8.333 × 10-3 p.u. MW/Hz PR1 = PR2 = 1200 MW

(B) Capacitive energy storage data Kvd=0.1KV/KA, K0=70KV/Hz, TDC=0.05s, C=1F, R=100Ω, Ed0=2KV

NOMENCLATURE TP1, TP2 Power system time constants KP1, KP2 Power system gains TT Turbine time constant

TG Governor time constant of thermal area TW Water time constant TR, T1, T2 Time constants of the hydro governor R1, R2 Governor speed regulation parameter

of thermal and hydro areas, respectively

PR1, PR2 Rated area capacities (a12 = PR1/PR2) T12 Ssynchronising coefficient B1, B2 Frequency bias constant of thermal and

hydro areas, respectively KI1, KI2 Integral gains of thermal and hydro

areas, respectively Kii, kdi, kpi Integral, derivative and proportional

gain constants of the PID controllers where i=1,2 for thermal and hydro areas.

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ΔPg2

(pu

MW

)

Time (s)

110