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CHAPTER 3

MODELLING OF PV SOLAR FARM AS STATCOM

3.1 INTRODUCTION

Today, we are mostly dependent on non renewable energy that have

been and will continue to be a major cause of pollution and other

environmental degradation. Finding the sustainable alternative is becoming

increasingly urgent because of these problems and the dwindling supply of

petroleum. Perhaps, the greatest challenge is in devising a sustainable future,

which relies on integration and control of renewable energy sources in grid

distributed generation.

This chapter presents the modelling of current and voltage module of

PV arrays and their characteristics. The formation of PV array using VPV

module is also explained. Also the basics of STATCOM along with the

controller are also presented. The modelling of PV array as STATCOM along

with the MPPT algorithm for constant and variable insolation values are

carried out using MATLAB SIMULINK.

3.2 PV CELL

PV cell is very similar to that of the classical diode with a PN junction.

In figure 3.1, when the junction absorbs light, the energy of absorbed photons

is transferred to the electron–proton system of the material, creating charge

carriers that are separated at the junction. The charge carriers may be

electron–ion pairs in a liquid electrolyte or electron–hole pairs in a solid

semiconducting material. The charge carriers in the junction region create a

potential gradient, get accelerated under the electric field and circulate as

current through an external circuit. The square of the current multiplied by the

resistance of the circuit is the power converted into electricity. The remaining

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power of the photon elevates the temperature of the cell and dissipates into

the surroundings.

Figure 3.1 PV effect converts the photon energy into voltage across the

PN junction

3.2.1 PV CELL TECHNOLOGIES

In comparing alternative power generation technologies, the most

important measure is the energy cost per kilowatt hour delivered. In PV

power, this cost primarily depends on two parameters: the PV energy

conversion efficiency and the capital cost per watt capacity. Together, these

two parameters indicate the economic competitiveness of the PV electricity

[33].

The conversion efficiency of the PV cell is defined as follows

electrical power outputη=solar power impinging cell

The primary goals of PV cell research and development are to improve

the conversion efficiency and other performance parameters to reduce the cost

of commercial solar cells and modules. The secondary goal is to significantly

49

improve manufacturing yields while reducing the energy consumption and

manufacturing costs and reducing the impurities and defects. This is achieved

by improving our fundamental understanding of the basic physics of PV cells.

The continuing development efforts to produce more efficient low-cost cells

have resulted in various types of PV technologies available in the market

today in terms of the conversion efficiency and the module cost.

Types of PV Cells

• Single crystalline silicon

• Polycrystalline and semi crystalline silicon

• Thin film cell

• Amorphous silicon

• Spherical cell

• Concentrator cell

• Multi junction cell

3.2.2 MODULE AND ARRAY

The solar cell described in the preceding subsection is the basic

building block of the PV power system. Typically, it is a few square inches in

size and produces about 1 W of power. To obtain high power, numerous such

cells are connected in series and parallel circuits on a panel (module) area of

several square feet. The solar array or panel is defined as a group of several

modules electrically connected in a series–parallel combination to generate

the required current and voltage as shown in figure 3.2 [34].

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Figure 3.2 PV cells, Module and Array

3.3 ELECTRICAL EQUIVALENT CIRCUIT

PV cell can be represented by the equivalent electrical circuit shown in

figure 3.3. [41]. The circuit parameters are as follows.

RS- Internal series resistance

RP - Shunt resistance of the diode

RL – Load Resistance

ISC – Source current

ID – Current through Diode

VD – Voltage across Diode

IPV– output current of PV cell

VPV – Output voltage of PV cell

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Figure 3.3 Equivalent circuit of a solar cell

Applying KCL,

(3.1)

The voltage of the cell VPV is given by the following by applying KVL,

(3.2)

The diode current is given by the expression

(3.3)

3.4 MODELLING OF PV ARRAY

The two models of PV module are current input (IPV module) and

voltage input module (VPV module). The IPV module is well suited for the

case when modules are connected in series and share the same current and

VPV module is well suited for the case when modules are connected in parallel

and share the same voltage.

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3.4.1 IPV Module

Figure 3.4 IPV Module

The MATLAB SIMULINK circuit of the IPV module is given by

Figure 3.5 Circuits inside the Current IPV Model

3.4.2 VPV Module

Figure 3.6 VPV Module

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Figure 3.7 Circuit inside the Voltage VPV Module

3.4.3 I-V AND P-V CURVES

The electrical characteristic of the PV cell is generally represented by

the current vs. voltage curve. The MATLAB SIMULINK Simulation diagram

for obtaining the electrical characteristics of PV cell is shown in figure 3.8.

Figure 3.9 shows the I-V characteristic of a PV module under different values

of Insolation. (200, 400, 600, 800, 1000 W/m2)

Figure 3.8 SIMULINK Circuit for PV Module characteristics

2Ppv

1Ipv

Ipv

Insolation

Vpv

Ppv

PV module (I)

f (z) zSolve

f(z) = 0

Algebraic Constraint2Insolation

1Vpv

Vpv

Vpv

Insolation

Ipv

Ppv

PV module (V)

PV1

PV power

Insolation

I-V characteristic

VpvVpv

Ipv

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Figure 3.9 Current vs. Voltage characteristic of the PV module for

different insolation levels

The power output of the panel is the product of the voltage and current

outputs. Figure 3.10, shows the P-V characteristic of a PV module under

different values of Insolation. (200, 400, 600, 800, 1000 W/m2)

Figure 3.10 Power vs. Voltage characteristic of the PV module

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3.5 MAXIMUM POWER POINT TRACKING

A controller that tracks the maximum power point locus of the PV

array is known as the Maximum Power Point Tracking (MPPT). The points of

maximum array power form a curve is termed as the maximum power locus.

Due to high cost of solar cells, it is necessary to operate the PV array at its

maximum power point.

Several MPPT algorithms have been proposed from time-to-time.

Some of the popular schemes are the hill climbing method, incremental

conductance method, constant voltage method, modified hill climbing

method, β method, system oscillation method and the ripple correlation

method, perturb and observe method, open and short circuit method, fuzzy

logic and artificial neural network [40].

3.5.1 Perturb and Observe Method

The perturb and observe method, also known as perturbation method,

which is the most commonly used MPPT algorithm in commercial PV

products. This is essentially a “trial and error” method. The PV controller

increases the reference for the inverter output power by a small amount and

then detects the actual output power. If the output power is indeed increased,

it will increase again until the output power starts to decrease, at which the

controller decreases the reference to avoid collapse of the PV output due to

the highly non-linear PV characteristic [39].

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Figure 3.11. Perturb and Observe Method flow chart

Figure 3.11 shows the flow chart of the P&O method. The present

power P(k) is calculated with the present values of PV voltage V(k) and

current I(k), and is compared with the previous power P(k-1). If the

incremented power increases, keep the next voltage change in the same

direction as the previous change. Otherwise, change the voltage in the

opposite direction as the previous one. [40]

3.5.2 Incremental Conductance Algorithm

In the incremental conductance method, the MPP is tracked by

matching the PV array impedance with the effective impedance of the

converter reflected across the array terminals. The latter is tuned by suitably

increasing or decreasing the value of ‘M’. [39].

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Figure 3.12. Incremental Conductance Algorithm flow chart

The main task of the incremental conductance algorithm is to find the

derivative of PV output power with respect to its output voltage, which is

dP/dV. The maximum PV output power can be achieved when its dP/dV

approaches zero. The controller calculates dP/dV based on measured PV

incremental output power and voltage. If dP/dV is not close zero, the

controller will adjust the PV voltage step by step until dP/dV approaches zero,

at which the PV array reaches its maximum output.

The main advantage of this algorithm over the P&O method is its fast

power tracking process. However, it has the disadvantage of possible output

instability due to the use of derivative algorithm. Also the differentiation

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process under low levels of insolation becomes difficult and results are

unsatisfactory. [42].

3.5.3 β method

The other method is based on β tracking which has the advantage of

both fast and accurate tracking. It is observed that the value of β remains

within a narrow band as the array operating point approaches the MPP.

Therefore by tracking β, the operating point can be quickly driven to close

proximity of the MPP using large iterative steps. Subsequently, small steps

(i.e. conventional MPPT techniques) can be employed to achieve the exact

MPP. Thus, β method approximates the MPP while conventional MPPT

technique is used to track the exact MPP. Flow chart for the β method

algorithm is given in figure 3.13. [42]

Figure 3.13. β method flow chart

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3.5.4 Open and Short circuit Method

The open and short circuit current method for MPPT control is based

on measured terminal voltage and current of PV arrays. By measuring the

open-circuit voltage or short-circuit current in real-time, the maximum power

point of the PV array can be estimated with the predefined PV current-voltage

curves. This method features a relatively fast response and do not cause

oscillations in steady state. However, this method cannot always produce the

maximum power available from PV arrays due to the use of the predefined

PV curves that often cannot effectively reflect the real-time situation due to

PV nonlinear characteristics and weather conditions. Also, the online

measurement of open-circuit voltage or short-circuit current causes a

reduction in output. [40]

3.5.5 Fuzzy Logic and Other Algorithms

Since the PV array exhibits a non-linear current-voltage or power-

voltage characteristic, its maximum power point varies with the insolation and

temperature. Some algorithms such as fuzzy logic or artificial neural network

control with nonlinear and adaptive in nature fit the PV control. By

knowledge based fuzzy rules, fuzzy control can track maximum power point.

A neural network control operates like a black box model, requiring no

detailed information about the PV system. After learning relation between

maximum power point voltage and open circuit voltage or insolation and

temperature, the neural network control can track the maximum powerpoint

online. [40].

In the proposed MPPT algorithm, the following conditions are considered

• It is assumed that the Boost output voltage Vout= VDC is constant

• Iref is used as the control variable for the Boost DC-DC converter

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• PV array current ideally tracks the Boost input current reference: IPV=Iref

The Perturb and observe algorithm is applied in this method where the

value of Ipvi s adjusted to Iref to operate at MPP. The flowchart for the perturb

and observe method applied is given in figure 3.14.

Figure 3.14 Flowchart for Perturb and Observe Algorithm

3.5.6 MPP Tracking Operation

For a six module PV of 85 Watts each connected in series at full sun

the maximum power of 510.8 W is achieved as shown in the figure 3.15 and

the MPP tracking results are shown in the figure.3.16.

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Figure 3.15 MPP for Six 85W module connected in series

Figure 3.16 MPP tracking operation

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3.6 FORMATION OF PV ARRAY

The PV array is formed by connecting six IPV modules, in series as

shown in the figure 3.17.

Figure 3.17 Formation of PV Array

3.7 PRINCIPLE AND OPERATION OF STATCOM

STATCOM is a shunt-connected reactive-power compensation device

that is capable of generating and absorbing reactive power and in which the

output can be varied to control the specific parameters of an electric power

system. It is in general a solid-state switching converter capable of generating

or absorbing independently controllable real and reactive power at its output

terminals when it is fed from an energy source or energy-storage device at its

input terminals. Specifically, the STATCOM considered in this chapter is a

voltage-source converter that, from a given input of dc voltage, produces a set

of 3-phase ac-output voltages, each in phase with and coupled to the

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corresponding ac system voltage through a relatively small reactance (which

is provided by either an interface reactor or the leakage inductance of a

coupling transformer) [7].

To summarize, a STATCOM controller provides voltage support by

generating or absorbing reactive power at the point of common coupling

without the need of large external reactors or capacitor banks.

3.7.1 The Principle of Operation

A STATCOM is a controlled reactive-power source. It provides the

desired reactive-power generation and absorption entirely by means of

electronic processing of the voltage and current waveforms in a voltage-

source converter (VSC). A single-line STATCOM power circuit is shown in

figure. 3.18 (a), where a VSC is connected to a utility bus through magnetic

coupling. In figure3.18 (b), a STATCOM is seen as an adjustable voltage

source behind a reactance—meaning that capacitor banks and shunt reactors

are not needed for reactive-power generation and absorption, thereby giving a

STATCOM a compact design, or small footprint, as well as low noise and

low magnetic impact. The exchange of reactive power between the converter

and the ac system can be controlled by varying the amplitude of the 3-phase

output voltage, Es, of the converter, as illustrated in figure3.18 (c). That is, if

the amplitude of the output voltage is increased above that of the utility bus

voltage, Et, then a current flows through the reactance from the converter to

the ac system and the converter generates capacitive-reactive power for the ac

system. If the amplitude of the output voltage is decreased below the utility

bus voltage, then the current flows from the ac system to the converter and the

converter absorbs inductive-reactive power from the ac system. If the output

voltage equals the ac system voltage, the reactive-power exchange becomes

zero, in which case the STATCOM is said to be in a floating state. Adjusting

the phase shift between the converter-output voltage and the ac system

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voltage can similarly control real-power exchange between the converter and

the ac system.

Figure 3.18 The STATCOM principle diagram: (a) a power circuit;

(b) an equivalent circuit; and (c) a power exchange

The reactive- and real-power exchange between the STATCOM and

the ac system can be controlled independently of each other. Any combination

of real power generation or absorption with var generation or absorption is

achievable if the STATCOM is equipped with an energy-storage device of

suitable capacity, as depicted in figure 3.19. With this capability, extremely

effective control strategies for the modulation of reactive and real output

power can be devised to improve the transient and dynamic system stability

limits.

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A STATCOM can improve power-system performance in the following areas:

1. dynamic voltage control in transmission and distribution systems

2. power-oscillation damping in power-transmission systems

3. transient stability

4. voltage flicker control

5. control of not only reactive power but also (if needed) active power in

the connected line, requiring a dc energy source.

Figure 3.19 The power exchange between the STATCOM and the ac

system

Figure 3.20 An elementary 6-pulse VSC STATCOM

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An elementary 6-pulse VSC STATCOM is shown in figure 3.20,

consisting of six self-commutated semiconductor switches (IGBT, IGCT, or

GTO) with antiparallel diodes. In this converter configuration, IGBTs

constitute the switching devices. With a dc-voltage source (which may be a

charged capacitor), the converter can produce a balanced set of three quasi-

square voltage waveforms of a given frequency by connecting the dc source

sequentially to the three output terminals via the appropriate converter

switches.

3.8 CONVENTIONAL STATCOM AND SOLAR FARM PV ARRAY

BASED STATCOM

There has been many compensating devices performing reactive power

compensation, voltage regulation, etc. but device that has the structural

advantage is necessary for the system assumed. STATCOM proves to have

the structural advantage to act as the compensating device for the assumed

system. PV array and the inverter setup are analogous to the design of

conventional STATCOM. From figure 3.22 it is clear to understand how PV

array setup can be utilized as STATCOM.

Figure 3.21 conventional STATCOM VS PV based STATCOM

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A structural advantage that helps in utilization of PV array as

STATCOM is PV array output is dc voltage which is used as capacitor as in

conventional STATCOM. Also, inverter design is made to operate as

converter in the PV array arrangement. So PV array along with inverter is

been conveniently used as STATCOM for the assumed system.

3.9 MODES OF OPERATION OF PV BASED STATCOM

The operation of the proposed STATCOM has been divided into three

modes. The modes are (i) day time excess power mode, (ii) day time mode,

(iii) night time mode.

i. Day time excess power mode: In this mode, the output voltage of the

PV array drives the boost converter based STATCOM for

compensating the source as well as charges the battery.

ii. Day time mode: When continuous compensation is required, if the PV

output voltage is equal to the requirement of the boost converter input,

the PV array can directly connect to the boost converter so as to step-

up the voltage and match the dc link voltage of the three-leg VSC. In

this mode, the battery is not charged.

iii. Night time mode: In this mode, PV output is absent and only the

battery supplies the boost converter for providing compensation at the

night time.

3.10 CONTROL OF DC LINK VOLTAGE WITH BOOST

CONVERTER

The boost converter is used to step up the input voltage to obtain a

desired output voltage. The circuit operation is divided into two modes. In

mode 1, when the switch is in on condition, the input current supplies energy

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to the inductor for a period Ton. Similarly in mode 2, when the switch is off,

the inductor voltage adds to the source voltage and current is forced to flow

through diode and the load for a period Toff. The PV or battery voltage is fed

to the boost converter and the output voltage of the boost converter is

obtained to maintain the dc link voltage of the three-leg voltage source

converter. The output voltage, Vout is greater than the input Voltage Vin and

the output equation is shown in the following equation.

(3.4)

Where Vout=Vdc, Vin=V

(3.5)

where V is the PV or battery voltage, D is the duty cycle, Ton is the ON time

and Toff is the OFF time.

3.11 CONTROL OF PV BASED STATCOM

There are many control algorithms available for the generation of

reference source currents for the control of proposed STATCOM in the

literature such as, synchronous reference frame theory, instantaneous reactive

power theory (p–q theory), power balance theory etc.[44],[47],[71]. The

synchronous reference frame theory is found suitable for the control of VSC.

A block diagram of the controlling algorithm is shown in figure 3.22. The

feedback signals are sensed from the load currents, PCC voltages and dc bus

voltages of STATCOM. The load currents from the a–b–c frame are first

converted to a–b–0 frame and then to d–q–0 frame using the following

equation,

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(3.6)

A three phase PLL (phase locked loop) is used to synchronize these

signals with the PCC voltage. The dc component of id and iq are obtained by

passing a d–q–0 current component through the low pass filter. The input of

first PI (Proportional Integral) controller is the error between the reference dc

bus voltage (Vdc*) and the sensed dc bus voltage (Vdc) of STATCOM. The

output of PI controller is the loss component of the current (iloss).

(3.7)

where Vde(n) is the error between reference and sensed dc voltage at the nth

sampling instant. Kpd and Kid are the proportional and integral gains of the

DC bus voltage PI controller. Therefore the reference source current is,

(3.8)

Similarly, the amplitude of actual PCC voltage and its reference value

are fed to another PI controller for regulating the PCC voltage. The output of

the PI controller is added to the dc component of iq because this is a

quadrature component of current required for regulating the ac voltage.

(3.9)

where Vde(n) is the error between reference (Vs*) and sensed supply voltage

(Vs(n)) amplitude at the nth sampling instant. The proportional and integral

gains of the PCC voltage PI controller are Kpq and Kiq.

The reference supply quadrature axis current is,

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(3.10)

By using reverse Park’s transformation, the resultant d–q–0 currents

are again converted back to reference source currents. The reference currents

in all the three phases (isa*, isb*,isc*) are used for generating the gate pulses

for three-leg VSC based STACOM. A PWM current controller is used for

generating the gating signals for the IGBT’s in VSC by using the reference

and sensed source currents.

Figure 3.22 Control Algorithm of STATCOM

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3.12 SIMULATION OF PV ARRAY SYSTEM

In this case, the model parameters are the standard PV module data-

sheet parameters:

• short-circuit current Isc

• open-circuit voltage Voc

• rated current IR at maximum power point (MPP)

• rated voltage VR at MPP

• Under standard test conditions (1kW/m2, 1.5 AM, 25oC). A bypass

diode (a single diode across the entire module) can be included.

Temperature effects are not modelled. PV array consisting of 6 PV

modules connected in series.

• PV array is operated at the maximum power point (MPP) under all

conditions. Vpv, Ipv is set as operating point for MPP. 6-module (85 W

each) PV array with full sun (1,000 W/m2 insolation).

• PV array operates at MPP: Ppv = 6 * 85 W = 510 W.

• The DC output is then fed to boost converter and then to DC-AC

converter for obtaining the required AC output voltage Vinv

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3.12.1 PV Array Simulation for Constant Insolation

Figure 3.23 PV array system combined with DC-DC boost convertor and

DC-AC Inverter for constant Insolation

Figure 3.24 Simulink Block of Constant insolation

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The PV array combined with DC-DC boost convertor and DC-AC

inverter for a constant insolation value of 1000 kW/m2 is simulated and the

output voltage, output current, input and output power of inverter is obtained.

The output voltage from the inverter gives a constant value of 158 W

for a constant insolation as shown in the figure 3.25.

Figure 3.25 Output Voltage of Inverter for constant insolation

Figure 3.26 Output current from inverter for constant insolation

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The output current is also a constant value of 5.8 A for a constant

insolation value as shown in the figure 3.26. Similarly the various outputs

such as Inverter duty and input and output power of a PV array is also a

constant value for the constant insolation as shown in figure 3.27 and 3.28

respectively.

Figure 3.27 Inverter Duty cycle for constant insolation

Figure 3.28 Input and Output power for constant insolation

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3.13.2 PV Array Simulation for Variable Insolation

Figure 3.29 PV array system combined with DC-DC boost convertor and

DC-AC Inverter for variable Insolation

The PV array combined with DC-DC boost convertor and DC-AC

inverter for a variable insolation value as shown in figure 3.29 is simulated

and the output voltage, output current, input and output power of inverter is

obtained.

The insolation values chosen here are 0, 400, 850, 950, 1000, 950, 850,

400, 0 kW/m2 for a time duration 0, 60, 120, 180, 240, 300, 360, 420, 480

seconds respectively as shown in figure 3.30.

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The simulation outputs of voltage, current, input and output power is

shown in the figure 3.31, 3.32, 3.33, 3.34 and 3.35 respectively. The values of

all the parameters are varying with respect to the insolation values.

Figure 3.30 Simulink block for variable insolation

Figure 3.31Output Voltage of Inverter for Variable insolation

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Figure 3.32Output current of Inverter for Variable insolation

Figure 3.33 Efficiency of Inverter for Variable insolation

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Figure 3.34 Duty cycle of Inverter for Variable insolation

Figure 3.35 Ideal, input and output power of Inverter for

Variable insolation

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Thus the simulation results shows that the PV array responds to the

different insoltaion values by giving the corresponding variations in the

outputs. Hence this model can be used for different insolation values.

3.13 SUMMARY

A new concept of using a PV solar power plant as STATCOM is

introduced here. A MATLAB/SIMULINK based model of PV array is

discussed in this chapter. The Utilization of the PV array and the converter as

a STATCOM device is explained with simulations. Various MPPT algorithms

are introduced and perturb and observe method is utilized. The simulation

results show the various outputs of PV array for different insolation levels.

This newly developed system thus can act as a FACTS device providing a

flexible control over both active and reactive power on a transmission line.

The PV based STATCOM can be implemented during night hours when PV

solar plant produces no real power. The configuration can possibly be realized

during daytime hours too. The PV based STATCOM can be used to regulate

the transmission/distribution line voltages, to support inductive load VAR

requirements, to improve the system performance during dynamic

disturbances and to suppress harmonics.