Optimizing the Controller of PV System To Enhance The Dynamic Stability of Smart Grid Network

Muhammad Haris Khan Department Of Electrical Engineering

King Fahd University Of Petroleum And Minerals P.O Box 8638, Dhahran 31261, Saudi Arabia

mhariskhan@kfupm.edu.sa

M. A. Abido Department Of Electrical Engineering

King Fahd University Of Petroleum And Minerals P.O Box 183, Dhahran 31261, Saudi Arabia

mabido@kfupm.edu.sa

Abstract—This paper presents a study for demonstrating the capability of photovoltaic system (PV System) in enhancing the damping of the inter-area oscillations in a smart grid network. In this context, investigations are conducted on a single-machine infinite bus (SMIB) system. PV-based stabilizer is designed for enhancing power system dynamic stability. The stability action is achieved through the independent control of real power flow from the controller and voltage at a point of common coupling between controller and the grid system. A novel approach of tuning controller is proposed by particle swarm optimization (PSO). The advantages of adopting the PSO in this research include easy implementation, a high computational efficiency and stable convergence characteristics and the proposed work is demonstrated through time-domain simulation.

Keywords; PV system, Inter-area oscillation, PV-based stabilizer, Smart grid, Particle swarm optimization (PSO).

I. INTRODUCTION In the recent years, because of rapid increase of energy

consumption, limited traditional energy resources, global warming and the effects of carbon emissions had an important impact over the entire world, a demand for clean and sustainable energy sources like wind, sea, sun and biomass have become a considerable alternatives to the conventional resources [1]. In this regard, harnessing the energy from the sun using photo-voltaic (PV) system has received much attention[2], [3]. The cost of the PV system is relatively high compared to other renewable energy. If the functionality of the PV system is enhanced then it also capture the attractiveness of the renewable energy market. Power system oscillations instability is either local or global in nature. Local modes of oscillations are those associated with a single generator or plant, while global ones are related to groups of generators or plants. The term inter-area is used when referring to global modes of oscillations. Such electromechanical oscillations are inherent when large power systems are interconnected [4]. Low frequency inter-area oscillations have been long recognized as a major source of instability problems in interconnected power systems. Instability problems caused by inter-area oscillations are caused by insufficient system damping and relatively weak

tie-line interconnectors. If no appropriate action takes place then this oscillation may endanger the network [5-10]. In this paper PV system is considered to provide dynamic stability to the smart grid network at the time of disturbance. A new evolutionary called particle swarm optimization (PSO) has been proposed. PSO has been motivated by the behavior of organisms such as fish schooling and bird flocking [11]. Unlike the other heuristic techniques, PSO has a flexible and well-balanced mechanism to enhance the global and local exploration abilities.

The organization of this paper is as follows. Section II describes the PV damping system. Section III describes the analysis of the PV damping action. Section IV gives description of linearized model of the system. Section V provides the designing of the control system. In section VI, the basic concepts of PSO are explained. Section VII provides responses of the optimized controllers under small disturbances and simulations. Finally, the concluding remarks appear in section VIII.

II. ANALYSIS OF PV DAMPING SYSTEM

PV system includes PV panel, inverter system, filtering reactor, and step-up transformer for grid connection[12]. The schematic diagram of the PV-based grid-connected stabilizer system is shown in Fig 1.

Fig. 1. Schematic diagram of the PV-based grid-connected stabilizer

system.

2012 Third International Conference on Intelligent Systems Modelling and Simulation

978-0-7695-4668-1/12 $26.00 © 2012 IEEE

DOI 10.1109/ISMS.2012.31

96

Solar cells and modules using this PV effect are ideal energy generators in that they require no fuel, generate no emissions, have no moving parts, can be made in any size or shape, and rely on a virtually limitless energy source, namely the sun. The photoelectric effect occurs when a beam of ultraviolet light, composed of photons (quantized packets of energy), strikes one part of a pair of negatively charged metal plates. This causes electrons to be "liberated" from the negatively charged plate. These free electrons are then attracted to the other plate by electrostatic forces [13]. This flow of electrons is an electrical current. This electron flow can be gathered in the form of direct current (DC). This DC can then be converted into alternating current (AC), which is the primary form of electrical current in electrical power systems that are most commonly used in buildings. PV devices take advantage of the fact that the energy in sunlight will free electrical charge carriers in certain materials when sunlight strikes those materials. This freeing of electrical charge makes it possible to capture light energy as electrical current[14]. The inverter system consists of fast switching IGBT, usually operating under PWM scheme. The switching pattern of the PWM is governed by a controller acting on the input three-phase AC voltages , ,a b ce e e and currents

, ,a b ci i i . In this research single machine infinite bus (SMIB)

system is considered, shown in Fig. 2. The schematic diagram shows that generator is connected at one end of the transmission line and PV system bisects the transmission line to provide P and Q to the load.

Fig 2. Schematic diagram of SMIB With PV System

In the below diagram E′q represents generator emf where δ denotes the rotor angle of the generator. X1 and X2 is the transmission line reactance with generator d-axis reactance and Xf is the reactance of the line between PV system and the intermediate bus M. VM is the intermediate bus voltage and Vv is the PV system output voltage and � is its angle. The power which is coming from generator is Pe + jQe and the power coming from PV system is Ppv + jQpv so the power going towards load or infinite bus is equal to Ps + jQs (Pe + jQe + Ppv + jQpv).

Fig 3. Equivalent Circuit Diagram

III. PROPOSED APPROACH The linearized model of power system can be written as

ddt οδ ω ωΔ = Δ (1)

1 ( )2 D e

d K Pdt H

ω ωΔ = − Δ − Δ (2)

Where δΔ is rotor angle variation while ωΔ is rotor speed variation, H is the inertia constant, DK is the machine

damping coefficient and ePΔ is generator electrical output variation. As shown in fig. 3 the electrical power coming from the generator becomes

'

1

me

E qVP sinX

φ= (3)

So power at intermediate bus M becomes

'

1 2

( )m m spv

E qV V Vsin P sinX X

φ δ φ+ = − (4)

Linearizing (3) and (4) yields

' '

1 1

cos sinme m

E qV E qP VX X

οο οφ φ φΔ = Δ + Δ (5)

' '

1 1

2

2

cos sin

cos( )( )

sin( )

mm pv

m s

sm

E qV E q V PX X

V VXV VX

οο ο

οο

ο

φ φ φ

δ φ δ φ

δ φ

Ο

Ο

Δ + Δ + Δ =

− Δ − Δ

+ − Δ

(6)

Extract φΔ from (5)

97

1'

sincos cose m

m m

X P VE qV V

ο

ο ο ο ο

φφφ φ

Δ = Δ − Δ (7)

Substitute from (7) into (6)

e a pv b m cP B P B V B δΔ = − Δ + Δ + Δ (8)

Where aB , bB and cB are the coefficients of the system at nominal conditions.

'2

'2 1

coscos cos( )a

s

E qXBE qX V X

ο

ο ο

φφ δ φΟ

=+ −

(9) '

'2 1

sincos cos( )

sb

s

E qVBE qX V X

ο

ο ο

δφ δ φΟ

=+ −

(10) '

'2 1

cos cos( )cos cos( )s m

cs

E qV VBE qX V X

ο ο ο

ο ο

φ δ φφ δ φ

Ο

Ο

−=+ −

(11)

PI controller will be designed to enhance the system stability.

A. Intermediate Bus Voltage Feedback Controller Design For stability of the system apply various techniques to

control the power system. In this section intermediate bus voltage feedback controller will be designed by applying well known frequency technique. Fig 4. shows the block diagram of power system with intermediate bus voltage feedback controller and pvP feedback controller. In this

case pvP =0 to determine the controller gains K2 and K4.

From Fig 5 . the open loop transfer function mV

δΔΔ

becomes

ωΔo

sω1

2 DHs K+

δΔ

cB

2 4

o

K K ss ω+

bB

1 3

o

K K ss ω+

aB

mVΔ

Fig 4. Block diagram of power system with intermediate bus voltage

feedback controller and pvP feedback controller

ωΔo

sω1

2 DHs K+

δΔ

cB

2 4

o

K K ss ω+

bBmVΔ

Fig 5. open loop transfer function mV

δΔΔ

22b

m D c

BV Hs K s B

ωδω

Ο

Ο

Δ =Δ + +

(12)

Plot the frequency response of (9) and find the cutoff frequency, gain GM and phase angle Gθ at crossover point

cs jω= . The desire loop gain should be equal to 1 and

phase angle should be equal to ( 180 )PMΟ− + . Here PM is the phase margin.

42( ) (cos sin )

cos( 180 ) sin( 180 )

cG G G

c

jKK Mj

PM j PM

ω θ θω ωΟ

Ο Ο

+ + =

− + + − + (13)

For the controller gain K2 and K4 separate real and imaginary parts of (10).

2

4

sin( ) ,

cos( )

G

c G

G

G

PMKM

PMKM

ω θω

ω θ

Ο

Ο

−=

− −= (14)

The recommended PM is 75Ο .

B. PV Feedback Controller Design In this section PV system is going under consideration. .

Fig 6. shows the block diagram of power system with PV feedback controller. For the PV controller gains K1 and K3

derive the open loop transfer function pvPδ−Δ

Δ from Fig 6.

98

ωΔo

sω1

2 DHs K+δΔ

cB

2 4

o

K K ss ω+

bB

1 3

o

K K ss ω+

aB

mVΔ

Fig 6. open loop transfer function pvPδ−Δ

Δ

22 42 ( )

a

pv D b c b

BP Hs K B K s B B K

ωδω

Ο

Ο

−Δ =Δ + + + +

(15)

Fig 7. Bode plot of open loop transfer function pvPδ−Δ

Δ

From the frequency response of (12) and find the cutoff frequency cpvω , gain GPVM and phase angle GPVθ at

crossover point cpvs jω= . Although the desire loop gain

should be equal to 1 and phase angle should be equal to ( 180 )PMΟ− + . Where PM is the phase margin.

31( ) (cos sin )

cos( 180 ) sin( 180 )

cpvGPV GPV GPV

cpv

PV PV

jKK Mj

PM j PM

ωθ θ

ω ωΟ

Ο Ο

+ + =

− + + − +

(16)

For the controller gain K1 and K3 separate real and imaginary parts of (13).

1

3

sin( ) ,

cos( )

GPV PV

cpv GPV

GPV PV

GPV

PMKM

PMKM

ω θω

ω θ

Ο

Ο

−=

− −= (17)

IV. PSO ALGORITHM A PSO algorithm is an evolutionary computation method inspired by social behaviors of bird �ocking during searching food. Each bird may be called a “particle” in a population, that is a “swarm” moving over a “search space” to achieve an objective. In a PSO algorithm, the position of a particle illustrates the solution of an optimization problem. Each particle moves in the search space with a velocity according to the previous optimum individual solution and the previous optimum global solution [15]. It uses a population of N particles, which is the dimension

of the search space. The state of the ith particle is represented as,

[ ]1 2( ) ( ), ( ),........, ( )i i i iNx t x t x t x t= (18) The previous best state is written as,

[ ]1 2( ) ( ), ( ),........, ( )i i i iNp t p t p t p t= . (19) The index of the best state in the global set, gbest , is represented as ,

1 2( ) ( ), ( ),........, ( )g g g gNp t p t p t p t� �= � � (20)

The moving velocity, ( )iv t is represented as,

[ ]1 2( ) ( ), ( ),........, ( )i i i iNv t v t v t v t= (21)

A PSO algorithm can be implemented using (22) and (23)

1 1 2 2( 1) ( ) ( ( ) ( )) ( ( ) ( ))i i i i g iv k v k c rand p k x k c rand p k x kω+ = + − + − (22)

( 1) ( ) ( 1)i i ix k x k v k+ = + + (23)

where k is an iteration number, ω is an inertia weight factor, 1c and 2c are constants, which represent the control

parameters of the PSO algorithm. If 1c and 2c are selected as small values, the individual may move far from the

99

objective regions before being tugged back. However, if 1c

and 2c are selected as large values, the individual may move

in sudden towards objective regions. Generally, 1c and 2c

are selected around 2. The parameters 1rand and 2rand are random values, which are uniformly distributed random numbers in [0, 1]. It is important to know that these values are randomly generated, and they may change during each iteration [16].

As mentioned previously, the purpose of using the proposed PSO algorithm is to search the optimal parameters of the controller gains.

V. RESPONSES OF THE CONTROLLERS UNDER SMALL DISTURBANCES

In this section simulations have been observed. For

intermediate bus voltage feedback controller pvP =0, for PV

feedback controller pvP =0.24 and for both cases eP =0.32.

For viewing the PV damping system stability enhancement, introduce the disturbance of 0.05p.u in the input mechanical power of generator and observe the response of rotor speed and rotor angle variation.

A. Simulation and Remarks The proposed control strategy is tested on hybrid power

system installed with conventional generator and PV system. All the simulation are set in MatLab. The analysis of simulation will show the comparison between results of [17] and this robust control strategy.

Remark 1: When the power system is facing disturbance by the result of faults or any other disturbance. Without controller, power system cannot come back to its stable state. Fig 8. depicted that rotor speed and rotor angle is not going to stable state after disturbance although they are deviations. Remark 2: After artificial disturbance, the optimized intermediate bus voltage feedback controller stabilize the system as fast as shown in the reference paper as shown in Fig 9. Remark 3: When intermediate bus voltage feedback and intermediate bus voltage and PV feedback controller will active then time of stabilization will reduce to 0.75 sec from 1.5 sec. Remark 4: After implement of proposed technique, when intermediate bus voltage and PV feedback controller is active then stabilizing time will reduce to 2.0 sec to 0.75 sec as compared to reference.

Fig 8. Rotor angle and rotor speed deviation without any controller.

Fig 9. Rotor angle and rotor speed deviation with intermediate bus voltage feedback controller

Fig 10. Rotor angle and rotor speed deviation with intermediate bus voltage feedback controller and PV feedback controller

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Fig 11. Comparison between reference intermediate bus voltage and PV feedback controller and optimized intermediate bus voltage and PV

feedback controller

VI. CONCLUSION The paper presented a model-based control scheme for a

small PV connected to smart grid network. The simulation shows how PV system take part in improvement of dynamic stability to the system. PV system not to supply only power, it also promising to provide dynamic stability to system even when no sun light will there. On the other hand, PSO provides optimization of the controller gains to maximum the efficiency of this robust technique. This system will work as a conventional STATCOM. In this regards consumer also play a role in optimizing the operation of the system.

ACKNOWLEDGMENT The author indebted to the support of King Fahd

University Of Petroleum and Minerals (KFUPM) through electrical power and energy system research group.

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