Engineering Science and Technology, an International Journal xxx (2015) 1—24

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Engineering Science and Technology, an International Journal

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Full length article

AGC of a multi-area power system under deregulated environment using redox flow batteries and interline power flow controller

Tulasichandra Sekhar Gorripotu, Rabindra Kumar Sahu*, Sidhartha Panda

Department of Electrical Engineering, Veer Surendra Sai University of Technology (VSSUT), Burla 768018, Odisha, India

ARTICLE INFO

Article history: Received 20 January 2015 Received in revised form 25 March 2015 Accepted 7 April 2015 Available online xxx

Keywords:

Automatic generation control (AGC) Generation rate constraint (GRC) Interline power flow controller (IPFC) Redox flow batteries (RFB) Differential evolution (DE) Sensitivity analysis

ABSTRACT

In this paper, Proportional Integral Derivative with Filter (PIDF) is proposed for Automatic Generation Control (AGC) of a multi-area power system in deregulated environment. Initially, a two area four units thermal system without any physical constraints is considered and the gains of the PIDF controller are optimized employing Differential Evolution (DE) algorithm using ITAE criterion. The superiority of proposed DE optimized PIDF controller over Fuzzy Logic controller is demonstrated. Then, to further improve the system performance, an Interline Power Flow Controller (IPFC) is placed in the tie-line and Redox Flow Batteries (RFB) is considered in the first area and the controller parameters are tuned. Additionally, to get an accurate insight of the AGC problem, important physical constraints such as Time Delay (TD) and Generation Rate Constraints (GRC) are considered and the controller parameters are retuned. The performance of proposed controller is evaluated under different operating conditions that take place in a deregulated power market. Further, the proposed approach is extended to a two area six units hydro thermal system. Finally, sensitivity analysis is performed by varying the system parameters and operating load conditions from their nominal values.

Copyright © 2015, Karabuk University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Automatic Generation Control (AGC) is one of the important control problems in an interconnected power system design and operation. AGC is becoming more significant today due to the increasing size, changing structure, emerging renewable energy sources, new uncertainties, environmental constraints and complexity of power systems [1—3]. In a conventional power system configuration, the generation, transmission and distribution is owned by a sole entity called a Vertically Integrated Utility (VIU), which supplies power to the clients at regulated rates. In an open energy market, Generating Companies (GENCOs) may or may not participate in the AGC task as they are independent power utilities. On the other hand, Distribution Companies (DISCOs) may contract with GENCOs or Independent Power Producers (IPPs) for the transaction of power in different areas [4]. Thus, in deregulated environment, control is greatly decentralized and Independent

* Corresponding author. Tel.: +91 9439702316. E-mail address: rksahu123@gmail.com (R.K. Sahu). Peer review under responsibility of Karabuk University.

System Operators (ISOs) are responsible for maintaining the system frequency and tie-line power flows.

The researchers in the world over are trying to propose several strategies for AGC of power systems under deregulated environment in order to maintain the system frequency and tie-line flow at their scheduled values during normal operation and also during small perturbations. Donde et al. [5] have demonstrated the concept of restructured power system and DISCO Participation Matrix (DPM). Chidambaram et al. [6] have proposed AGC strategy for a two-area multi-units power system under deregulated environment in presence of Redox Flow Batteries (RFB) and Interline Power Flow Controller (IPFC). Recently, Parmar et al. [7] have studied the multi-source power generation in deregulated power environment using optimal output feedback controller. However, in the above literature the effect of physical constraints such as Time delay (TD) and Generation Rate Constraint (GRC) are not examined which needs further comprehensive study.

Flexible AC Transmission Systems (FACTS) controllers [8] play a crucial role to control the power flow in an interconnected power system. Several studies have explored the potential of using FACTS devices for better power system control since it provides more flexibility. Unified Power Flow Controller (UPFC) and Interline Power Flow Controller (IPFC) are among the most

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2215-0986/Copyright © 2015, Karabuk University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

versatile FACTS controllers which are connected in series with the transmission line or in tie-lines respectively to control the power flow [9,10]. Both UPFC and IPFC need at least two converters. It is observed from literature that, UPFC is employed to power flow control of a single transmission line whereas the IPFC is can provide power flow control for multi-line transmission system. Therefore, IPFC is attractive for compensating multi-line systems from economical point of view. IPFC can compensate each transmission line separately or concurrently so that the power optimization of the overall system can be obtained in the form of appropriate power transfer from over-loaded lines to underloaded lines [6]. In view of the above, an IPFC is considered in the present paper.

Balancing of power supply and demand is always a complex process particularly at peak loads. As a result, there may be serious concerns about reliable operation of power system. So, it is necessary to include Battery Energy Storage (BES) systems especially in the present deregulated scenario to improve the automatic generation control problem [11—18]. There are several types of battery energy storage systems used in power system applications such as lead acid batteries, flooded type batteries, Valve regulated (VRLA) type batteries, Sodium sulphur (NaS) batteries, Lithium ion (Li ion), Metal air and Redox Flow Batteries (RFB). Among all the batteries Redox Flow Batteries are

promising for the applications which require high power and long duration storage. Redox Flow Batteries (RFB) is an active power source which can be essential not only as a fast energy compensation device for power consumptions of large loads, but also as a stabilizer of frequency oscillations [19,20]. The RFB will, in addition to load compensating, can have other applications such as power quality maintenance for decentralized power supplies. But, due to the economical reasons it is not possible to place RFB in all the areas. When IPFC and RFB are present in the system, they should act in a coordinated manner so as to control the network conditions in a very fast and economical manner.

Several advanced controller structures and techniques have been proposed in literature for AGC [4—6], [26]. But, these advanced approaches are complicated and need familiarity of users to these techniques thus reducing their applicability. Alternatively, a classical Proportional Integral Derivative (PID) controller and its variant remain an engineer's preferred choice due to its structural simplicity, reliability and the favourable ratio between performances and cost. In a PID controller, the derivative mode improves stability of the system and increases speed of the controller response but it produces unreasonable size control inputs to the plant. Also, any noise in the control input signal will result in large plant input signals which often lead to

AREA 1

DISCOl

DISC02

to GENCOs

AREA 2

DISCQ3

DISC04

to GENCOs

ri r2

ACEX «1

from DISCOs

TPj->f^/hl

from DISCOs

AREA 1

Thermal Reheat System 1 with GRC

-> Governor 1 Turbine 1 GRC Reheat 1

Thermal Reheat System 2 with GRC

Governor 2

Turbine 2

Reheat 2 -I

_L A P actual

Power system 1

rTie 12

' &pf\fuled

ACE2 U2

TD}>|«P/2I|—► }

from DISCOs

Thermal Reheat System 3 with GRC

Governor 3 Turbine 3 -> GRC -> Reheat 3

TDTI—►[ apfzi I—> +

from DISCOs

Thermal Reheat System 4 with GRC

Governor 4

Turbine 4

Reheat 4

Power system 2

AREA 2

Fig. 1. Block diagram representation of two area power system with IPFC and RFB in deregulated environment.

complications in practical applications. The practical solution to these problems is to put a first filter on the derivative term and tune its pole so that the chattering due to the noise does not occur since it attenuates high frequency noise [21]. Surprisingly, in spite of these advantages, Proportional Integral Derivative with derivative Filter (PIDF) controllers structures are not attempted for the AGC under deregulated environment problems.

It is obvious from literature survey that the performance of the power system depends on the controller structure and the techniques employed to optimize the controller parameters. Hence, proposing and implementing new controller approaches using high performance heuristic optimization algorithms to real world problems are always welcome. Differential Evolution (DE) is a

population-based direct search algorithm for global optimization capable of handling non-differentiable, non-linear and multimodal objective functions, with few, easily chosen, control parameters [22]. DE uses weighted differences between solution vectors to change the population whereas in other stochastic techniques such as Genetic Algorithm (GA) and Expert Systems (ES), perturbation occurs in accordance with a random quantity. DE employs a greedy selection process with inherent elitist features. Also it has a minimum number of control parameters, which can be tuned effectively [23]. Having known all this, an attempt has been made in the present paper for the DE based PIDF controller for AGC in a deregulated environment with the consideration of GRC and TD for the coordinated application of IPFC and RFB.

DISCOl

cpf 11

cpf 21

cpf 41

cb ® (b

cpf 32

cpf 42

DISCOl

_AP„

AREA 1

Thermal Reheat System 1 with GRC

A P„,

Kr,T„s +1

*JiPg2 Thermal Reheat System 2 with GRC

m m m k^+i o+l

AlfiS?

pH qp/21

ACE2 u2

Cgrjp +

(4);-> (t)

► APg3 Thermal Reheat System 3 with GRC

2 xT„

T.ts +1

T.As+1

Thermal Reheat System 4 with GRC AREA 2

DISCOl

cpf 13

cpf 22

cpf 43

cpf 14

cpf 24

cpf 44

— DISC04

Fig. 2. Transfer function model of two area power system with IPFC and RFB in deregulated environment.

The main investigations of the present work:

i. To develop a strategy based on DE, for AGC of multi-area power system in deregulated environment.

ii. To optimize the parameters of PID controller with derivative filter and analyze the dynamic performance of power system with DE optimized PIDF controller for AGC.

iii. To study the effect of Interline Power Flow Controller (IPFC) and Redox Flow Batteries (RFB) in AGC studies.

iv. To analyze the effect of physical constraints such as Time Delay (TD) and Generation Rate Constraints (GRC) on system performance.

v. To carry out the sensitivity analysis for the proposed controllers and test its robustness to wide variations in loading pattern and system parameters as well as changes in size and locations of load perturbations.

vi. To test the effectiveness of proposed controllers in a two area six unit hydro thermal power system with IPFC and RFB.

2. Material and method

2.1. Power system model in a deregulated system

A two area multi unit interconnected power system has been proposed for AGC in deregulated environment. The system is widely used in literature for the design and analysis of AGC under deregulated scenario [6]. The block diagram representation of two area power system with IPFC and RFB in presence of GRC and TD under deregulated environment is shown in Fig. 1. Area 1 comprises of two GENCOs with thermal power system of reheat turbine and GRC combinations and two DISCOs, Area 2 comprises of two GENCOs with thermal power system of reheat turbine and GRC combinations and two DISCOs as shown in Fig. 1. A PIDF controller is considered for each area. The transfer function model of the above system is shown in Fig. 2. In Fig. 2, R1, R2 and R3, R4 are the regulation parameters of thermal units for area 1 and area 2 respectively in p.u. Hz.B1 andB2 represent the frequency bias parameters in p.u. MW/Hz. Tg1 and Tg2 are the speed governor time constants in sec for area 1; Tg3 and Tg4 are the speed governor time constants in sec for area 2; Tt1 and Tt2 are the turbine time constant in sec for area 1; Tt3 and Tt4 are the turbine time constant in sec for area 2; DPD1 and DPd2 are the load demand changes in p.u.; DPTie is the incremental change in tie-line power (p.u.); KPs1 and KPs2 stands for the power system gains; TPs1 and TPs2 represent the power system time constant in sec; T12 is the synchronizing coefficient in p.u. and DF1 and DF2 are the system frequency deviations in Hz,. For thermal plant a GRC of 3%/min [24] and a time delay of 50 ms [25] are considered in the present work. The relevant parameters are given in appendix A.

As there are several GENCOs and DISCOs in the deregulated environment, there can be various contracts between GENCOs and DISCOs. If DISCOs having contract with GENCOs of the same control area then it is known as "poolco based transaction". If DISCOs having contract with GENCOs of another area then it is known as "bilateral based transaction". If DISCOs violate the contract by demanding more than specified in the contract then it is known as "contract violation based transaction". To know the contracts between GENCOs and DISCOs the concept of DISCO Participation Matrix (DPM) is introduced [5].

DPM is a matrix in which the number of rows is equal to the number of GENCOs and the number of columns is equal to the number of DISCOs in the system. The elements of DPM are indicated with cpfj which corresponds to fraction of total load contracted by a DISCO towards a GENCO. The sum of all the entries in a

Derivative gain Derivative filter coefficient

Fig. 3. Structure of PID controller with derivative filter.

column in DPM is unity i.e. P^cpfi, = 1. In Fig. 1 GENCO1, GENCO2, DISCO1 and DISCO2 are in area 1. GENCO3, GENCO4, DISCO3 and DISCO4 are in area 2. Then the corresponding DPM is written as [5]

cpfu cpf 12 cpf 13 cpf 14

cpf21 cpf22 cpf23 cpf24

cpf31 cpf32 cpf33 cpf34

cpf41 cpf42 cpf43 cpf44

where cpf represents "contract participation factor" i.e. p.u. MW load of a corresponding DISCO.

The scheduled steady state power flow on the tie-line is given as [5].

APT^uled = (Demand of DISCOs in area 1 to GENCOs in area 2) - (Demand of DISCOs in area 2 to GENCOs in area 1)

The actual tie-line power is given as

DPITJ = ^ (AF1 - DF2)

At any time, the tie-line power error is given by [5].

A nerror _ a nactual A nscheduled Dl Tie12 = Dl Tie12 - Dl Tie12

DPji™2 vanishes in the steady as the actual tie-line power flow reaches the scheduled power flow. This error signal is used to generate the respective Area Control Error (ACE) signals as in the traditional scenario [5].

ACE1 = B1AF1 + APf™

ACE2 = B2DF2 + a12APfUÏ2

\ ^se,pq K

^'¡njj: jQinj,q

_ rsepr I _

nj,p JQinj.p jQinjj

Fig. 4. The equivalent power injection model of IPFC.

Fig. 5. General block diagram of redox flow batteries in AGC.

As there are two GENCOs in each area, ACE signal has to be distributed among them in proportion to their participation in the AGC. Coefficients that distribute ACE to GENCOs are termed as "ACE Participation Factors (apfs)". In a given control area, the sum of

participation factors is equal to 1. Hence, apfu, apf12 are considered as ACE participation factor in area 1 and apf21, apf22 are in area 2.

2.2. Controller structure and objective function

In the present paper, two dissimilar PIDF controllers have been considered for the two area system [21]. The structure of PID controller with derivative filter is shown in Fig. 3 whereKP, KI and KD are the proportional, integral and derivative gains respectively and N is the derivative filter coefficient. The control inputs of PIDF controller are the respective ACEs and the output of PIDF controllers are the input of power system u1 and u2 shown in Fig. 3.

( Start )

Specify the DE parameters

Initialize the population |Gen.=1

Evalute the population

Fig. 6. Flow chart of DE optimization approach.

Table 1

Tuned controller parameters for Poolco based transaction without GRC, TD, IPFC and RFB.

Parameters and performance index Fuzzy PIDF

Controller parameters Ki = 0.1253 K2 = 0.1302 K3 = 0.0924 K4 = 0.0078 KPI = -0.8983 K11 = -0.971 KDI = -1.504 N1 = 58.8709 Kp2 = 1.5299 K12 = -0.6979 KD2 = -1.9265 N2 = 70.8096

ITAE 11.7186 7.8174

Settling time TS (sec) AF1 15.42 20.05

AF2 17.88 19.60

APTie 27.31 13.91

Peak over shoot AF1 0.0324 0.0212

AF2 0.0299 0.0169

APTie 0 0.0089

Table 2

Tuned controller parameters for Poolco based transaction without GRC, TD (with IPFC and RFB).

Parameters and performance index

With IPFC Only

With IPFC and RFB

Controller parameters

Settling time TS (sec)

Peak over shoot

Kl2 Kd2 N2

-1.7134 -1.5927 -0.1827 57.0781 0.8433 -0.6979 -1.0405 162.3066 2.1414 12.59 12.93 9.09 0.0115 0.0089 0.0052

% Improvement

-1.7036 -1.9864 -1.9948 51.3204 -0.4245 -1.1173 -1.2433 87.742

1.8858 11.05 11.94 7.83 0.01 0.0077 0.004

% Improvement

44.88 39.08 43.71 52.83 54.43 55.05

The transfer function of the controller is given by:

Kp + l) + ^N

In the design of a modern heuristic optimization technique based controller, the objective function is first defined based on the desired specifications and constraints. Performance criteria usually considered in the control design are the Integral of Time multiplied Absolute Error (ITAE), Integral of Squared Error (ISE), Integral of

Time multiplied Squared Error (ITSE) and Integral of Absolute Error (IAE). ITAE criterion reduces the settling time which cannot be achieved with IAE or ISE based tuning. ITAE criterion also reduces the peak overshoot. ITSE based controller provides large controller output for a sudden change in set point which is not advantageous from controller design point of view. It has been reported that ITAE is a better objective function in LFC studies [21,26]. Therefore in this paper ITAE is used as objective function to optimize controller parameters of PIDF controller. Expression for the ITAE objective function is depicted in Eq. (8).

Table 3

Re-tuned controller parameters for Poolco based transaction in presence of GRC and TD.

Parameters and performance index

Without IPFC and RFB

With IPFC only

With both IPFC and RFB

Controller parameters

Settling time TS (sec)

Peak over shoot

AF2 APTie

AF1 AF2 APTie

-1.2385

-0.0424

-0.4606

246.9947

0.6672

-0.1205

-1.4102

41.9896

433.19

unstable

unstable

unstable

1.0468

0.0358

0.9201 -0.2082 -1.6679 72.3479 0.5333 -0.0748 -0.0109 172.8689 177.99

54.86 44.60 48.13 0.6920 0.7047 0.0252

-1.5235 -1.4186 0.0547 220.3304 -0.276 -1.602 -1.2598 21.1966 17.63

15.52 18.05 15.07 0.0855 0.1622 0.0416

Without re-tuning

39.2789

0.1058

0.0463

J = ITAE = f (\DF1\ + \DF2\ + \DPm\)-t-dt (8)

In the above equations, AF1 and AF2 are the system frequency deviations; APTie is the incremental change in tie-line power; tsim is the time range of simulation.

The problem constraints are the PIDF controller parameter bounds. Therefore, the design problem can be formulated as the following optimization problem.

Minimize J (9)

Subject to

KPmin < KP < KPmax; Kmln < K < KImax, KDmm < KD

< KDmax , Nmin < N < Nmax (10)

Where J is the objective function and KPIDFmin and KPIDFmax, are the minimum and maximum value of the PIDF control parameters. The minimum and maximum values of PID controller parameters

' 0 3 6 9 12 15 18 21 24 27 30

Tlme(Sec)

--- - - - - - -

............ ............

V^A : : !-T : : : * :

\\ (b) .......Fuzzy: Without IPFC & RFB ----PIDF: Without IPFC & RFB -----PIDF: With IPFC only -PIDF: Both IPFC & RFB

Time(Sec)

7 -0.04 cL ffi

^ -0.06 -0.08

0 5 10 15 20 25 30 35 40 45 50

Tlme(Sec)

Fig. 7. Dynamic responses of the system for poolco based transaction without TD & GRC (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation.

Et sUHU v ............ MT.TfT- — --------- --------- ---------

il : : : ii i : :

(c) .......Fuzzy: Without IPFC & RFB ----PIDF: Without IPFC & RFB -----PIDF: With IPFC only -PIDF: Both IPFC & RFB

1 I 1 I 1 1 1 1

_______r\i______i________

f \ j . *

\!i Ha l (a)

-----Without IPFC & RFB ----With IPFC only -Both IPFC & RFB

if i t

0 10 20 30 40 50 60 70 80 90 100

71me(Sec)

1 1 1 1 1 1 1 1 1 _________a________:________!________!________:________:________'________j________j_________

fi fi» ______>V;______I________

1 / TT r—/T^r**«— \I'J ! Y! i a »

I 1- \J\ (b)

-----Without IPFC & RFB ----With IPFC only -Both IPFC & RFB

0 10 20 30 40 50 60 70 80 90 100

71me(Sec)

-0.05 [

/N h ,

Ai/i fi/i Mliiii!.1

/j Vl i' lH if fo il! ! i* 'Hi 1II

pi f ' ' (C)

---- Without IPFC & RFB With IPFC only Both IPFC & RFB

V -

Tlme(sec)

Fig. 8. Dynamic responses of the system for poolco based transaction (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation.

are chosen as -2.0 and 2.0 respectively. The range for filter coefficient N is selected as 1 and 300.

2.3. Modelling of IPFC in AGC

The modelling of IPFC and RFB has been done in the same way as given in ref. [6]. However, in ref. [6] only an integral controller was used whose gain consists of products of a conventional control gain and fuzzy gain whereas in the present study a PIDF controller is proposed which increases the capabilities of IPFC and RFB in automatic generation control. Also, in the present manuscript the capabilities of IPFC and RFB are evacuated in the presence of

physical constraints such as Time Delay (TD) and Generation Rate Constraint (GRC).

The equivalent power injection model of IPFC is shown in Fig. 4 [6]. IPFC is a combination of two or more SSSCs which are coupled via a common DC link. With this scheme, IPFC has the capability to provide an independently controllable reactive series compensation for each individual line and also to transfer real power between the compensated lines. There has been growing interest recently in studying the IPFC modelling, its basic function to control power flow among transmission lines and oscillation damping. The IPFC installed in series with a tie-line and provides damping of oscillations the tie-line power. In Fig. 4, Vse is the series voltage magnitude and 4se is the phase angle of series voltage. The shunt converter

y^l |-------- r*mm

1 / \ f 1 (a)

-Case A: Without GRC & TD ———- Case B: With GRC & TD (without retuned parameters) -----Case B: With GRC & TD (with retuned parameters)

0 3 6 9 12 15 18 21 24 27 30

Tlme(Sec)

0 3 6 9 12 15 18 21 24 27 30

Tlme(Sec)

Tlme(Sec)

i » .«* \ \ \ .......GENC01 ----GENC02 -GENC03 -----GENC04

/ \ (d)

I \ --------^-»'¿w inn RAT. .J1L1U1L1 ■■ - ---- ---

1 i^T"

0 5 10 15 20 25 30 35 40 45 50

Hme(Sec)

Fig. 9. Dynamic responses of the system for poolco based transaction with both IPFC & RFB (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation (d) Change in generated powers of different GENCOs.

Table 4

Tuned PIDF controller parameters for Bilateral based transaction with TD & GRC.

Cases/Parameters Kp, Kp2 K,1 K¡2 Kd, Kd2 N, N2

Without IPFC & RFB With IPFC only Both IPFC & RFB -0.3619 -0.3619 -1.9760 1.6064 1.6064 -1.6497 -0.0620 -0.0620 -1.0010 —0.1213 -0.1213 -0.9535 -1.3287 -1.3287 -1.5502 —1.6686 -1.6686 -0.0209 193.6168 193.6168 146.4745 100.8839 100.8839 165.4745

injects controllable shunt voltage such that the real component of the current in the shunt branch balance the real power demanded by the series converter. It is clear from Fig. 4 that, the active and reactive power injections at the buses can be written as

Pinj,p ^ ] VpVse,pnbpn sin(qp _ qse,pn) n=q,r

Qinj,p = ~ y ] VpVse,pnbpn cos (qp _ qse,pn) n=q,r

Pinj,n = ~ y ] VnVse,pnbpn sin(qn ~ qse,pn) n=q,r

Qinj ;n — y ] VnVse,pnbpn cos (qn ~ qse,pn) n=q,r

where, Vse,pn — \Vse,in\:6se,in and n — q,r

(11) (12)

2.4. Modelling of RFB in AGC

In an interconnected power system during the presence ofsmall load perturbations and with optimized controller gains, the frequency deviations and tie-line power changes exist for long time durations. During such conditions the governor may not able to absorb the frequency deviations due to slow response and non-linearities present in the system. So, in order to reduce the frequency deviations and change in tie-line power, an active power source with quick response such as RFB can be expected to the most effective one [6,27]. The RFB are found to be superior over the other energy storage devices like superconducting magnetic energy storage (SMES) because of its easy operating at normal temperature, very small losses during operating conditions and have long service life [20]. As RFB are capable of ensuring a very quick response [6], AFi is being used directly as the input command signal for RFB to control frequency. A general block diagram of the RFB used for AGC in the interconnected power system is shown in the Fig. 5 [27]. During very low load duration battery charges and delivers the energy to the system during sudden load changes. The dual converter performs both rectifier and inverter action. For sudden step load perturbation the change of output of a RFB is given as [6].

1 + sTrfb

where Krß is gain of a RFB and Trfb is time constant of RFB in Sec

3. Overview of differential evolution algorithm

Differential Evolution (DE) algorithm is a population-based stochastic optimization algorithm recently introduced [22]. Advantages of DE are: simplicity, efficiency & real coding, easy use and speediness. DE works with two populations; old generation and new generation of the same population. The size of the population is adjusted by the parameter NP The population consists of real valued vectors with dimension D that equals the number of design parameters/control variables. The population is randomly initialized within the initial parameter bounds. The optimization process is conducted by means of three main operations: mutation, crossover and selection. In each generation, individuals of the current population become target vectors. For each target vector, the mutation operation produces a mutant vector, by adding the weighted difference between two randomly chosen vectors to a third vector. The crossover operation generates a new vector, called trial vector, by mixing the parameters of the mutant vector with those of the target vector. If the trial vector obtains a better fitness value than the target vector, then the trial vector replaces the target vector in the next generation. The flow chart of DE approach is shown in Fig. 6. The DE algorithm is explained in more detail in [24].

4. Simulation results and discussion

4.1. Implementation of DE

The simulations are carried out on an Intel, Core i-5 CPU of 2.5 GHz, 8 GB, 64-bit processor computer in the the MATLAB 7.10.0.499 (R2010a) environment. The model of the system under study shown in Fig. 2 is developed in MATLAB/SIMULINK environment and DE program is written (in.m file). Initially, dissimilar PIDF controllers are considered for each area without considering the physical constraints (time delay, generation rate constraints), IPFC and RFB under poolco based transaction. The developed model is simulated in a separate program (by.m file using initial population/controller parameters) considering a 20% step load increase in area 1. The objective function is calculated in the.m file and used in the optimization algorithm. In the present study, a population size of NP = 100, generation number G = 100, step size F = 0.8 and crossover probability of CR = 0.8 have been used. The strategy employed is: DE/best/1/exp. Optimization is terminated by the pre specified number of generations for DE. One more important factor that affects the optimal solution more or less is the range for unknowns. For the very first execution of the program, a wider

Table 5

Performance index values under Bilateral based transaction.

Parameters

Without IPFC & RFB

With IPFC only

Both IPFC & RFB

Ts (sec)

Peak over shoot

3028.6

unstable

unstable

unstable

3.0347

3.0427

0.2339

2930.5

unstable

unstable

unstable

2.8912

2.9121

0.2054

64.2 25.34 27.23 25.37 0.2314 0.4542 0.2050

1 1 1 1 1 1 1

/ i i 1 *

» i f—. \ ---^¿t'î

(a) ---- With IPFC only Both IPFC & RFB

Tlme(Sec)

I I I I I I I

\ 1 X !

-----Without IPFC & RFB ----With IPFC only -Both IPFC & RFB

\ i \ * b)

Tlme(Sec)

/7 \ ! \ \

a v. \ V-/ / \

d~/ i V / /

/ < / \ / // u i V / / / *

;"t:T \ 1 'i r \ t // \ * \ / j V • **

"v V7 (c) / -----Without IPFC & RFB ----With IPFC only -Both IPFC & RFB -

Tlme(Sec)

a. 0.6

.......GENC01 ----GENC02 -GENC03

i •*'I 1 ............

r \ \

! / V is Ç* '_________ Aa Vsv ..... ........... ___________

Hme(Sec)

Fig. 10. Dynamic responses of the system for bilateral based transaction (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation (d) Change in generated powers of different GENCOs.

Table 6

Tuned PIDF controller parameters for Contract violation based transaction with TD & GRC.

Cases/Parameters kpi kp2 k,1 K,2 Kdi Kd2 N, N2

Without IPFC & RFB -0.2122 1.8576 -0.1506 —0.0160 -1.9138 —1.2309 270.4589 122.8947

With IPFC only -0.0498 1.6603 -0.0407 -0.0628 -0.9035 —1.6356 203.1226 46.4113

Both IPFC & RFB -1.6370 0.1720 -0.8080 -0.4726 0.1355 -0.2939 77.2905 18.2415

solution space can be given and after getting the solution one can shorten the solution space nearer to the values obtained in the previous iteration. The optimization was repeated 50 times and the best final solution among the 50 runs is chosen as controller parameters.

In the present study, the controller parameters are tuned at three transactions that take place in a deregulated environment i. e. Poolco, Bilateral and Contract violation based transactions. Under each transaction scenario, three cases are considered i.e. without IPFC & RFB, with IPFC only and with both IPFC & RFB. Initially, a two area power system without any physical constraints is considered and the PIDF controller parameters are optimized under Poolco based transition. The superiority of PIDF over fuzzy controller is demonstrated in this case. Then physical constraints such as GRC and time delay are included in the system model and the PIDF controller parameters are retuned for different cases. To show the robustness of proposed approach, sensitivity analysis is performed under varied loading and system parameter conditions. The process is repeated i.e. the PIDF controller parameters are tuned under Bilateral and Contract violation based transactions in presence of physical constraints. Finally, the proposed approach is extended to a two area six unit hydro thermal power system with IPFC and RFB considering the physical constraints.

4.2. Case I: Poolco based transaction

In this scenario DISCOs have contract with GENCOs of the same area. It is assumed that the load disturbance occurs only in area 1. There is 0.1 (p.u. MW) load disturbance in DISCO1 and DISCO2, i.e. APL1 = 0.1 (p.u. MW), APL2 = 0.1 (p.u. MW), APL3 = APL4 = 0 (p.u. MW) as a result of the total load disturbance in area 1 i.e. ApD1= 0.2 (p.u. MW). Considering that there is an equal participation of GENCOs.

;.DPM --

GENCO participates in load frequency control as defined as following area participation factors i.e. apfu = 0.75; apf12 = 0.25; apf21 = 0.5; apf22 = 0.5. The scheduled tie-line power in this case is zero. In steady sate, generation of GENCOs must match the demand of the DISCOs in contract with it. The generated power or contracted power supplied by the GENCOs is given as

g>-J2CPÏÏ PLj j=1

0.5 0.5 0 0

0.5 0.5 0 0

0 0 0 0

0 0 0 0

By using Eq. (16) the values for APg1 can be calculated as

APg1 = cpf 11PL1 + cpf 12PL2 + cpf 13PL3 + cpf 14PM = (0.5)*(0.1) + (0.5)*(0.1) + (0)*(0) + (0)*(0) = 0.1 (p.u. MW).

Similarly, the values of APg2, APg3 and APg4 are obtained as 0.1 (p.u. MW), 0 (p.u. MW) and 0 (p.u. MW) respectively.

In order to investigate the significance of considering the physical constraints, two cases (Case A and Case B) are considered. In Case A, Time delay and Generation Rate Constraints are neglected. In Case B, Time delay and Generation Rate Constraints are considered. Initially, the physical constraints and IPFC & RFB are not considered in the system model. The final PIDF controller parameters for the above case are obtained as explained in Section 4.1 and given in Table . For comparison the results are compared with fuzzy logic controller (FLC). In case of FLC, ACE and its derivative are taken as input to the fuzzy logic controller and triangular membership functions are used [28]. The membership functions are used with five fuzzy linguistic variables such as NB (negative big), NS (negative small), Z (zero), PS (positive small) and PB (positive big) for both the inputs and the output. The input scaling factors (K1, K2, K3 and K4) of FLC are optimized using DE optimization technique employing the same ITAE objective function. The optimized parameters are given in Table 1. The performance index in terms of ITAE value, and settling times (2% band) in frequency and tie line power deviations are also shown in Table 1. It is clear from Table 1 that, with the same system (without GRC, TD, IPFC and RFB) a less ITAE value is obtained with PIDF controller (ITAE = 7.817) compared to fuzzy controller (ITAE = 11.7186). The overall system performance in terms of settling times and peak over shoots are also greatly improved with proposed DE optimized PIDF controller compared to fuzzy controller. Hence it can be conclude that PIDF controller outperform fuzzy controller.

Then an IPFC is incorporated in the tie-line to analyze its effect on the power system performance. Finally, Redox Flow Batteries (RFB) is installed in the area 1 and coordinated with IPFC to study their effect on system performance. The optimized controller parameters and the corresponding performance index are provided in Table 2. It is clear from Tables 1 and 2 that, ITAE value is further reduced to 2.1414 with only IPFC controller and smallest ITAE value (ITAE = 1.8858) is obtained with the coordinated application of IPFC and RFB. The corresponding performance indexes in terms of

Table 7

Performance index values under Contract violation based transaction.

Parameters

Without IPFC & RFB

With IPFC only

Both IPFC & RFB

Ts (sec)

Peak over shoot

DFi AF2

AFi AF2 APTie

30043.0

unstable

unstable

unstable

3.5134

3.5142

0.2021

7803.4

unstable

unstable

unstable

3.4846

3.5134

0.4126

109.4 32.59 34.16 28.80 0.2480 0.3874 0.2171

•n 0 I

-2 -3 -4 -5

n" 0 x

-2 -3 -4 -5

0.4 0.3 0.2 0.1 i o -0.1 -0.2 -0.3 -0.4 -0.5

_______._______ ---- _______

// ^ It _ V.

// — It ---- -----

\ // !

\ / (a) -----Without IPFC & RFB ----With IPFC only _ -Both IPFC & RFB

^^ 1 i i

25 30 35 Tlme(Sec)

/ : /j /■ ,______-

/ / ! 'J V- ------- r1"""

r ; : f

~ // ----- — - - —'—~

\ / (b) -----Without IPFC & RFB ----With IPFC only -Both IPFC & RFB

V -<'/ | i i

25 30 35 Tlme(Sec)

________

M V N, ......y.....\........

KA- v r-—--f V V, X. s

// ____/ --------- - -•s \ ✓ -----Without IPFC & RFB ----With IPFC only -Both IPFC & RFB

(c) X

20 25 30

Tlme(Sec)

....... GENC01

----GENC02

-GENC03

-----GENC04

Hme(Sec)

Fig. 11. Dynamic responses of the system for contract violation based transaction (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation (d) Change in generated powers of different GENCOs.

0.12 0.08 g- 0.04

% 0 -0.04 -0.08

1 1 /"\ ! ! \ !

\ \ \ \ v \ \v \ \\ *\

----------- V-... .......... —"" (a) *-*

-Poolco based transaction ----Bilateral based transaction

Time (sec)

0 5 10 15 20 25 30 35 40

Urne (sec)

Fig. 12. Dynamic performances of system with both IPFC and RFB (a) Power deviation of IPFC under different transactions (b) Power deviation of RFB under different transactions.

settling time and peak overshoots are accordingly reduced. The percentage improvements with IPFC only and with coordinated application of IPFC and RFB compared the system without IPFC and RFB are also provided in Table 2. It can be seen from Table 2 that system performance improves IPFC only and significant improvements are achieved with coordinated application of IPFC and RFB.

In the next step, physical constraints GRC and TD are included in the system model and the results are shown in Table 3. For comparison, the performance indexes without re-tuning the controller parameters are also provided in Table 3. It can be observed from Tables 1—3 that the system performance degrades when GRC and TD are included in the system model. This is due to the reason that, when GRCs are considered, the generation can only be changed at a certain rate. Similarly, due to the presence of TD, the controller action is delayed and hence the system performance deteriorates.

The dynamic performance of the system without GRC and TD for 20% step increase in load in area 1 is shown in Fig. 7(a—c). It can be seen from Fig. 7(a—c) that the system is oscillatory with fuzzy controller. It is also evident from Fig. 7(a—c) that oscillations are quickly suppressed with proposed DE optimized PIDF controllers. The system performance further improves with IPFC and the best dynamic performance is obtained with coordinated application of IPFC and RFB.

Fig. 8(a—c) show the dynamic performance of the system with GRC and TD with/without IPFC and RFB for the above disturbance. It can be seen from Fig. 8(a—c) that the system is highly oscillatory without IPFC and RFB in presence of GRC and TD. The dynamic performance is improved with IPFC and significant improvement in system performance is obtained with coordinated application of IPFC and RFB.

Table 8

Sensitivity analysis under poolco based transaction.

Parameter variation % Change Settling time in (Sec) Peak over shoot ITAE

AF1 AF2 DPTie AF1 AF2 APTie

Nominal 0 15.52 18.05 15.07 0.0855 0.1622 0.0416 17.63

Loading condition +25 15.55 18.06 15.70 0.0850 0.1377 0.0407 17.35

-25 15.51 18.04 15.70 0.0851 0.1468 0.0410 17.48

Tg +25 15.47 17.94 15.62 0.0854 0.1702 0.0419 17.89

-25 16.12 18.16 15.82 0.0855 0.1532 0.0412 17.61

Tt +25 15.48 18.01 15.63 0.0862 0.1620 0.0420 17.66

-25 15.58 18.09 15.80 0.0849 0.1623 0.0412 17.75

T12 +25 16.37 17.89 15.52 0.0844 0.1154 0.0424 17.32

-25 15.39 18.33 16.00 0.0846 0.2245 0.0424 18.95

Table 9

System eigen values under parameter variation with poolco based transaction.

Loading condition Tg Tt T12

+25% -25% +25% -25% +25% -25% +25% -25%

-220.32 -220.32 -220.33 -220.32 -220.33 -220.32 -220.32 -220.32

-98.04 -98.04 -98.05 -98.01 -98.05 -98.02 -98.04 -98.03

-25.85 -25.85 -24.73 -27.95 -25.13 -26.95 -25.81 -25.88

-15.45 -15.44 -13.40 -19.06 -14.92 -16.27 -15.43 -15.44

-4.37 ± 7.02i -4.37 ± 7.02i -3.65 ± 6.58i -5.4 ± 7.41i -4.18 ± 5.68i -4.48 ± 8.62i -4.17 ± 6.94i -4.52 ± 7.07i

-3.21 ± 4.55i -3.20 ± 4.55i -2.95 ± 4.41i -3.47 ± 4.65i -3.23 ± 3.96i -3.27 ± 5.31i -3.24 ± 4.56i -3.15 ± 4.54i

-0.68 ± 0.67i -0.68 ± 0.68i -0.69 ± 0.67i -0.69 ± 0.70i -0.69 ± 0.62i -0.67 ± 0.74i -1.12 -0.67 ± 0.74i

-0.77 -0.76 -0.77 -0.72 -0.91 -0.66 -0.66 ± 0.64i -0.46

-0.24 ± 0.08i -0.24 ± 0.08i -0.24 ± 0.08i -0.24 ± 0.08i -0.24 ± 0.08i -0.24 ± 0.08i -0.24 ± 0.08i -0.24 ± 0.07i

-0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.27

-12.50 -12.50 -10.00 -16.67 -12.50 -12.50 -12.50 -12.50

-12.50 -12.50 -10.00 -16.67 -12.50 -12.50 -12.50 -12.50

-3.33 -3.33 -3.33 -3.33 -2.67 -4.44 -3.33 -3.33

-3.33 -3.33 -3.33 -3.33 -2.67 -4.44 -3.33 -3.33

-0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10

-0. 10 -0. 10 -0. 10 -0.10 -0. 10 -0. 10 -0. 10 -0. 10

To evaluate the effect of GRC and TD and to show the need for retuning the controller parameters in presence of physical constraints, the system dynamic responses with IPFC and RFB for both the cases (without GRC and TD: Case A and with GRC and TD: Case B) without/with retuned controller parameters are shown in Fig. 9(a—c). It can be seen from Fig. 9(a—c) and Table 3 that better dynamic responses in terms of peak over shoots and settling times are obtained when the controller parameter are retuned in presence of physical constraints. For this case, the improvements in ITAE value are 58.92% with IPFC only and 95.93% with coordinated application of IPFC and RFB. The change in actual generated powers of various GENCOs in response to contract with DISCOs is shown in Fig. 9 (d). It is clear from Fig 9 (d) that the GENCO1 and GENCO2 contribute 0.1 p.u. each and the sum of power generations of GENCOs in control area-1 matches with load demand of 0.2 pu MW.

4.3. Case II: bilateral based transaction

In this type of transactions, DISCOs have the freedom to contract with any of the GENCOs within own area or with another area. Now the DISCO participation matrix can be express as

0.4 0.25 0.75 0.3

0.3 0.2 0 0.25

0.2 0.2 0.25 0.25

0.1 0.35 0 0.2

There is a load disturbance in DISCO1 is 0.15 (p.u. MW) and 0.05 (p.u. MW), 0.15 (p.u. MW), 0.05 (p.u. MW) in DISCO2, DISCO3, DISCO4 respectively. In this case, from Eq. (2) the scheduled tie-line power can be calculated as 0.0675 (p.u. MW).

Similarly from Eq. (16) the values of steady state power generated by the GENCOs are given as DPg1 = 0.2 (p.u. MW), DPg2 = 0.0675 (p.u. MW), DPg3 = 0.09 (p.u. MW), DPg4 = 0.0425 (p.u. MW).

The tuned PIDF controller parameters for Bilateral based transaction with GRC and TD are given in Table 4. The various performance indexes (ITAE, settling time and peak overshoot) under bilateral based transaction case are given in Table 5. It is clear from Table 5 that minimum ITAE value is obtained with coordinated application of IPFC and RFB (ITAE = 64.2) compared to only IPFC (ITAE = 2930.5) and without IPFC and RFB optimized PIDF controller (ITAE = 3028.6). The improvements in ITAE value for above case are 3.24% with IPFC only and 97.88% with coordinated application of IPFC and RFB. Consequently,

better system performance in terms minimum settling times in frequency and tie-line power deviations is achieved with proposed IPFC and RFB optimized PIDF controller compared to others as shown in Table 5. Hence it can be concluded that in this case also, the coordination of IPFC and RFB works satisfactorily.

It is worthwhile to mention that, in this example the values of GRC and TD as well as the magnitude of disturbance is so chosen that the system becomes unstable with IPFC for a better illustration of coordinated application of IPFC and RFB. However, in the realistic system, IPFC may be enough to stabilize the system. The dynamic performance of the system for the above case is shown in Fig. 10(a—c). Critical analysis of the dynamic responses clearly reveals that coordinated application of IPFC and RFB significantly improves the dynamic performance of the system. Improved results in settling times and peak overshoots of DF1, DF2 and DPTie are obtained with proposed DE optimized PIDF controller with coordinated application of IPFC and RFB compared to others. Fig. 10 (d) shows the change in actual generated powers of various GENCOs for the above case. It is clear from Fig 10 (d) that the steady state values of GENCOs are matching with the calculated values.

It is worthwhile to mention here that IPFC in general improves the AGC performance by controlling the tie-line power flow. In case of Bilateral based transactions, the scheduled tie-line power flow is 0.0675 (p.u. MW) as calculated according to the DPM matrix where as the load disturbance is 0.2 p.u. As the tie-line power flow is fixed to its scheduled value, the role of IPFC which controls the tie-line power flow is very limited for Bilateral based transactions. Due to the above reason a small improvement in ITAE value is obtained with IPFC only compared to the case when both IPFC and RFB are absent.

4.4. Case III: contract violation based transaction

In this case, there is a violation of contracts by demanding more power than that of specified in the contract. Considering Case II again with a modification that 0.1 (p.u. MW) of excess power demanded by DISCO1. Now DPD1 becomes DPD1 = DPL1 + DPL2 + DPuc1 = 0.3 (p.u. MW) and DPd2 is unchanged. In this case, as contract violation done by DISCO1 the values of DPg1 and DPg2 can be calculated as.

DPg1,violation — DPg1 DPg2,violation — DPg2

apf11*DPuc1 — 0.275 (p.u. MW) apf12*DPuc1 — 0.0925 (p.u MW)

-Nominal loading ———- -25% of nominal loading

0 5 10 15 20 25 30

Tlme(Sec)

(C) -Nominal loading -----25% of nominal loading

i ! ! i

0 5 10 15 20 25 30

Tlme(Sec)

Fig. 13. Dynamic responses of the system with variation of nominal loading (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation.

0.04 0.02 d o

% -0.02 -0.04 -0.06

0 5 10 15 20 25 30

Tlme(Sec)

Fig. 14. Dynamic responses of the system with variation of Tg (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation.

(C) -Nominal .......+25% of Tg -----25% of Tg

-Nominal .......+25% ofT, -----25% ofT,

Tlme(Sec)

-Nominal .......+25% ofT, -----25% ofT,

71me(Sec)

(c) -Nominal .......+25% of Tt -----25%ofTt

Tlme(Sec)

Fig. 15. Dynamic responses of the system with variation of Tt (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation.

q!~ -0.02

+25% 0fTr -----25% of T.,

0 5 i 10 15 Tlme(Seo) i 20 25 30

_____A_______ i I

k* l \ * \ \

(b) -Nominal .......+25%ofT12 -----25% ofT12

Tlme(Sec)

:/A /' ft 1 1

v a* i f | S h

t I A* I \\\ j it fi ft 4 (c) -Nominal .......+25% ofT12 -----25%ofT12

Tlme(Sec)

Fig. 16. Dynamic responses of the system with variation of T12 (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation.

The values of DPg3 and DPg4 are same as in Case II because contract violation is assumed in area 1.

Table 6 gives the tuned PIDF controller parameters for contract violation based transaction with GRC and TD. The various performance indexes in terms of ITAE, settling time and peak overshoot for the above case are given in Table 7. It can be seen from Table 7 that improved results are obtained with coordinated application of IPFC and RFB compared to others. The improvements in ITAE value for contract violation based transaction are 74.02% with IPFC only and 99.6% with coordinated application of IPFC and RFB. The frequency deviations and tie-line power are shown in Fig. 11(a—c). It is evident from Fig. 11(a—c) that the system is unstable without IPFC and RFB as

well as with IPFC only. This due to the reason that the situation in Case II is further worsened by demanding excess power in area 1. It is also evident from Fig. 11 (a—c) that the system is stable with coordinated application of IPFC and RFB and the oscillations are quickly damped out. The change in actual generated powers of various GENCOs for contract violation based transaction is shown in Fig. 11 (d) from which it can be seen that all the GENCOs contributes and their individual power generation matches with the calculated values. The output curves of IPFC and RFB for the above transactions are provided in Fig. 12(a—b). It is clear from Fig. 12(a—b) that both IPFC and RFB actively participate and contribute to the improvement of AGC.

AREA 1 AREA 2

DISCOl

DISC02

DISC03

DISC04

to GENCOs

to GENCOs

AREA 1

Thermal Reheat System 1 with GRC

Governor 1 Turbine 1 GRC Reheat 1

Fig. 17. Block diagram representation of the two area six unit hydro thermal power system with IPFC and RFB.

4.5. Sensitivity analysis

Sensitivity analysis is done to study the robustness the system to changes in the operating conditions and system parameters like speed governor time constant (Tg), Turbine time constant (Tt), Synchronizing time constant (T12) in the range of +25% to -25%. The performance index under normal and varied conditions is shown in Table 8. Table 9 gives performance of the system under varied operating load condition and system parameters with proposed DE optimized PIDF controller employing both IPFC and RFB. Poolco based transaction with IPFC and RFB is considered for the sensitivity analyses as minimum ITAE value is obtained in that case compared to other cases. Critical examination of Table 8 clearly shows that the performance indexes are

more or less same and the effect of the variation in operating loading conditions and system time constants on the system performance is negligible. It is also evident from Table 9 that the eigen values lie in the left half of s-plane for all the cases thus maintain the stability. Hence it can be concluded that, the proposed control approach provides a robust and stable control satisfactorily. To complete the analysis, the dynamic performance of the system with the varied conditions of loading, Tg, Tt and T12 are shown in Figs. 13—16. It can be observed from Fig. 13(a—c) that the effect of the variation of loading condition on the system performance is negligible. Also from Figs. 14(a—c), 15 (a—c) and 16 (a—c) clearly reveals that the effect of system parameters (Tg,Tt and T12) on the system performance is negligible.

Table 10

Tuned PIDF controller parameters for two area six units system under Poolco based transaction.

Cases/Parameters Without IPFC & RFB With IPFC only Both IPFC & RFB

Kpi -1.0714 -1.1570 -0.4925

Kp2 0.6782 1.1109 -0.3676

Kp3 -0.8396 1.0238 -1.7358

K,i -0.2927 -0.7070 -1.8303

K,2 0.2313 0.1535 -1.3551

K,3 0.2416 0.1499 -1.3448

Kdi -0.6553 -0.0486 -1.1918

Kd2 -1.8126 -1.5941 -0.9436

Kd3 0.7453 -0.8191 -0.0594

Ni 168.1922 53.5930 68.4587

N2 182.8122 157.4710 42.9118

N3 42.1501 187.6362 162.7192

4.6. Extension to two are six unit hydro thermal system

To demonstrate the ability of the proposed approach to cope with different sources of power generation, the study is further extended to a two area six unit hydro thermal power system with Generation Rate Constraint (GRC), time delay, IPFC and RFB as shown in Fig. 17. For thermal units a generation rate constraints (GRC) of 3%/min is considered. For hydro unit, GRC's of 270%/min for raising generation and 360%/min for lowering generation are considered [29]. Time delays can degrade a system's performance and even cause system instability. In the present paper, a time delay of 50 ms is considered [25]. The relevant parameters are given in Appendix B.

In this case only Poolco based transaction is considered. The area participation factors (apfs) of 0.4 for each thermal unit and 0.2 for hydro unit are assumed. A particular case of Poolco based transaction is simulated based on the following DPM:

0.35 0.35 0 0

0.35 0.35 0 0

0.30 0.30 0 0

0 0 0 0

0 0 0 0

0 0 0 0

By using Eq. (16), the changes in generated powers of different GENCOs are obtained as follows:

DPg1 = DPg2 = 0.07 p.u. MW, DPg3 = 0.06 p.u. MW, DPg4 = DPg5 = DPg6 = 0 p.u. MW

Initially, the system without IPFC and RFB is considered and dissimilar PIDF controllers are chosen for each unit. A step load disturbance of 20% is applied in area-1 and the final controller parameters of PIDF controller for the Poolco based transaction are obtained as explained in Section 4.1. In the next step, an IPFC installed in the tie-line to analyze its effect on the power system performance. Finally, RFB is placed in area-1 and coordinated with

IPFC to study their effect on system performance. All the above conditions are tuned separately to obtain final controller parameters for PIDF controller and provided in Table 10. The corresponding performance indexes are shown in Table 11. It can be seen from Table 11 that minimum ITAE value is obtained with coordinated application of IPFC and RFB (ITAE = 17.5927) compared to the cases when only IPFC is present (ITAE = 201.7875) and without IPFC and RFB (ITAE = 331.3957). The improvements in ITAE value for above case are 39.11% with IPFC only and 94.69% with coordinated application of IPFC and RFB. Similar improvements are also observed in the settling times and peak overshoots.

The dynamic response of the system is shown in Fig. 18(a—c). It is clear from Fig. 18(a—c) that in all the cases the system is stable as the magnitude of applied disturbance is small. However, responses are oscillatory without IPFC and RFB. The system performance improves with the application of IPFC. Further, significant improvements in system performance are obtained with coordinated application of IPFC and RFB. Fig. 18 (d) shows the change in actual generated powers of all the GENCOs for the above case from which it can be seen that the GENCO1, GENCO2 and GENCO3 of area 1 contribute 0.07, 0.07 and 0.06 p.u. MW respectively as calculated.

Finally sensitivity analysis for two area six unit hydro thermal system under poolco based transaction is performed as explained before and the results are summarized in Table 12. It can be observed from Table 12 that settling time, peak overshoots and ITAE values vary within acceptable ranges and are nearby equal to the respective values obtained with nominal system parameter. Hence, it can be concluded that the proposed controllers are robust and perform satisfactorily when system parameters changes in the range ±25%.

The novel contributions of the present work are:

(i) PID controller with derivative filter (PIDF) is proposed for AGC in a deregulated power environment. A filter is used in derivative block to overcome the adverse affects of noise on PID controller.

(ii) Important physical constraints such as generation rate constraints and time delay are included in the system model and PIDF controller parameters are optimized employing DE technique.

(iii) IPFC is then installed in the tie-line between the interconnected areas for high speed control of tie-line power through the interconnections and to stabilize the area frequency oscillations quickly. The effect of presence of IPFC on the system performance is investigated.

(iv) In order to further improve the system performance, Redox Flow Batteries (RFB) which is an active power source with fast response characteristics is used. The impacts of IPFC and RFB on the dynamic performance have been investigated.

(v) Sensitivity analysis is performed by varying the operating load condition and system parameters in the range of ±25% from their nominal values.

Table 11

Performance index values for two area six units system under Poolco based transaction.

Parameters

Without IPFC & RFB

With IPFC only

Both IPFC & RFB

Ts(sec)

Peak over shoot

AFi AF2

APTie AFi AF2 APTie

331.3957 unstable unstable unstable 1.0151 1.0609 0

201.7875 59.27 51.23 40.37 0.8122 0.8716 0.0763

17.5927 15.19 17.05 15.44 0.1034 0.1628 0.0403

Time (Sec)

1 1... 1 1 1 1 1 1

H i / \ :

/V ¿-J—\i /X ,„

vi \ \-f i: / : /

V: / / V •1 /-• i i i (b)

.......Without IPFC & RFB ----With IPFC only -Both IPFC & RFB

Yl \ \ *j> i i i i

Time (Sec)

II ! ! /—-

-------

ll A? /•'■•. i-i // ff J V/ i ■ / ! !" ~ V ~ ?1 Ê iïXuj/i \1\ \! \j " -------- if/ M (c) ........... ----- --------

.......Without IPFC & RFB ----With IPFC only - -Both IPFC & RFB

0 5 10 15 20 25 30 35 40 45 50

Time (Sec)

0.14 0.12 0.1 0.08 0.06 0.04 0.02 j ol

-0.02 L

1 ----GENC01 .......GENC02 -GENC03 -----GENC04 ----GENC05

I-» J ■» (d)

i 1......... 1 1

-------- —------ -------

k ^ ■-----^

T»- r 1 1 1 1 1 T

100 Time (Sec)

Fig. 18. Dynamic responses of the system under poolco based transaction (a) Frequency deviation of area 1 (b) Frequency deviation of area 2 (c) Tie-line power deviation (d) Change in generated powers of different GENCOs.

Table 12

Sensitivity analysis for two area six units system under poolco based transaction.

Parameter variation % Change Settling time in (Sec) Peak overshoot ITAE

AF1 AF2 DPTie DF1 DF2 DPTie

Nominal 0 15.19 17.05 15.44 0.1034 0.1628 0.0403 17.5927

Loading condition +25 15.24 17.08 15.45 0.1032 0.1567 0.0401 17.4978

-25 15.12 17.02 15.44 0.1036 0.1690 0.0406 17.7026

Tsg +25 15.04 16.96 15.38 0.1036 0.1705 0.0408 17.6946

-25 15.32 17.14 15.51 0.1031 0.1539 0.0399 17.4899

Tt +25 14.91 16.90 15.32 0.1044 0.1628 0.0405 17.5920

-25 15.47 17.23 15.59 0.1023 0.1627 0.0401 17.6237

Trh +25 15.26 17.11 15.45 0.1029 0.1619 0.0402 17.8214

-25 15.04 16.94 15.41 0.1040 0.1641 0.0405 17.4003

Tgh +25 15.22 17.06 15.44 0.1028 0.1619 0.0401 17.8788

-25 15.09 17.01 15.44 0.1043 0.1642 0.0406 17.0249

T12 +25 15.47 16.90 15.32 0.1035 0.1185 0.0401 17.1093

-25 14.57 17.22 15.57 0.1015 0.2214 0.0430 18.7608

R +25 14.04 16.14 15.40 0.1089 0.1585 0.0395 17.7816

-25 17.20 18.09 15.36 0.0978 0.1682 0.0418 17.8693

5. Conclusions

In this paper, a Differential Evolution Algorithm (DE) optimized PID controller with derivative filter (PIDF) has been proposed for Automatic Generation Control of multi area power system. Initially, a two area four unit thermal system is considered and the gains of PIDF controller parameters are optimized by employing DE technique. It is observed that better dynamic performance are obtained with proposed DE optimized PIDF controller compared to a fuzzy logic controller. Time Delay (TD) and Generation Rate Constraints (GRC) have been considered to have a more realistic power system. To get better insight of AGC problem, inclusion of GRC and TD is important for the dynamic performance study of the system. The system has been investigated all possible of power transactions that take place under deregulated environment. Interline power flow controller (IPFC) is then added in the tie-line for improving the system performance. As the tie-line power flow is fixed to its scheduled value, the role of IPFC which controls the tie-line power flow is very limited for bilateral based transactions. Due to the above reason a small improvement in ITAE value is obtained with IPFC only compared to the case when both IPFC and RFB are absent. Additionally, Redox Flow Batteries (RFB) is included in area 1 along with IPFC in order to improve the system performance. It is observed that in all the cases (poolco based, bilateral based and contract violation based) the deviation of frequency becomes zero in the steady state with coordinated application of IPFC and RFB which assures the AGC requirements. The proposed approach is also extended to a two-area six unit hydro thermal system. Sensitivity analysis is performed for both test systems under study by varying the system parameters and operating load conditions from their nominal values. From the simulation results it is observed that effect of system parameters and loading condition on the dynamic response of the power system is negligible.

Appendix

Nominal parameters of the system investigated are: A .Data for two area four unit thermal system [6].

Rated frequency = 60 Hz, Rating of each area = 2000 MW, Base power = 2000 MVA, R, = R2 = R3 = R4 = 2.4 Hz/p.u.MW, B, = B2 = 0.425 p.u.MW/Hz, Tg1 = Tg2 = Tg3 = Tg4 = 0.08s, Tri = Tr2 = Tr3 = Tr4 = 10 s, Tt, = Tt2 = Tt3 = Tt4 = 0.3 s, Kp1 = Kp2 = 120 Hz/p.u. MW, Tp1 = Tp2 = 20s, Kr1 = Kr2 = Kr3 = Kr4 = 0.5; a12 =-1, 2pT12 = 0.545 p.u.MW/Hz.

B .Data for two area six unit hydro thermal system

B1 = B2 = 0.425 p.u. MW/Hz; KPS1 = KPS2 = 120 Hz/p.u. MW;

TPS1 = TPS2 = 20 s; RjH1 = RTH2 = RTH3 = RTH4 = RHY1 = RHY2 = 2.4 Hz/

p.u.; Tti = Tt2 = Tt3 Tt4 = 0.3 s; Tsgi = Tsg2 = Tsg3 = Tsg4 = 0.08 s;

KR1 = KR2= KR3 = KR4 = 0.5; TR1 = TR2 = TR3 = TR4 = 10 s;

Tj2 = 0.0433; Tghi = TGH2 = 48.7 s; Twi = TW2 = 1 s;

TRSI = TRS2 = 0.513; TRH1 = TRH2 = 10; a12 = —1.

C .Data for RFB and IPFC [6].

Krfb = 0.6787, Trfb = 0 s, Tipfc = 0.01 s, Ki = —0.3, K2 = —0.2622.

D .MATLAB Programme to find system eigen values:

[A, B, C, D] = linmod ('Model'); % Model is the SIMULINK model

of system.

Eigen_Values = eig(A); %Computes the system eigen values.

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