INTERNATIONAL JOURNAL OF PROFESSIONAL ENGINEERING STUDIES

Volume V /Issue 4 /SEP 2015

APPLICATION OF FUZZY BASED THREE-PHASE INVERTER IN DISTRIBUTED GENERATION BY IMPLEMENTING UNIFIED CONTROL STRATEGY MUKKU MURALI1, DR. K VENKATESWARLU2 1 2

PG Scholar, Malineni, Lakshmaiah Engineering College, Andhra Pradesh, India

Assistant professor, Malineni, Lakshmaiah Engineering College, Andhra Pradesh, India

Abstract-By eliminating need of separate

generation system using the renewable energies is on

controllers or critical islanding detection, this paper

a falling trend and is expected to fall further as

proposes a fuzzy based three-phase inverter in

demand and production.

distributed generation which can be implemented for

DG delivers power to the utility and local critical

both islanded and grid-tied operations. In the

loads in grid-connected mode. Upon outage of any

proposed strategy the three-phase inverter is

generator connected to the utility the islanding is

regulated as just current source by inner inductor

formed. Under these situations, DG must be tripped

current loop in grid-tied and for islanding mode a

and must stop to energize according to IEEE standard

voltage loop in the synchronous reference frame will

929-2000. In order to continue to feed the local

automatically regulates the load voltage. This paper

critical load by disconnecting DG’s and some local

proposes a unified load current feedforward to

load in order to improve the power reliability. Load

maintain the grid current waveforms in grid-tied

voltage is fixed by the DG in the islanded mode and

mode and load voltage waveforms in islanding mode

by the utility in the grid mode operation. So,

to be undistorted even under nonlinear local load.

maintaining the load voltage is important. In order to

The effectiveness of the proposed strategy is

reduce transients in the load DG must take over the

validated by simulation.

load as soon as possible which is challenging

Index Terms— Fuzzy Logic Controller,

operation for the DG.

unified control, islanding, load current, seamless transfer, Distributed generation (DG), three-phase inverter, unified control.

In this paper voltage control mode is nothing but Droop-based control is used widely for the sharing of power among parallel inverters and can be applied to DG to realize power sharing between DG and utility

INTRODUCTION

in grid-tied mode [11-12]. Under this operation, load voltage is guaranteed during transitions of operation

The distributed generation (DG) concept

modes and inverter is regulated as voltage source by

emerged as a way to integrate different power plants,

voltage loop is good only steady-state performance

increasing the DG owner’s reliability, reducing

whereas dynamic performance is poor because

emissions, and providing additional power quality

bandwidth of voltage loop is higher than of the

benefits [4]. The cost of the distribution power

external power loop, realizing droop control. In

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addition to the (phase locked loop) PLL and the

With the occurrence of utility outage the interval

virtual inductance, the inrush grid currents during

during to change it to voltage mode, the load voltage

transition from islanded mode to grid-tied mode

is neither regulated by DG nor fixed by the utility but

always exists it means grid current is not controlled

the length of the time interval is determined by the

directly [13].

islanding detection process. The main issue in this

Better dynamic performance can be achieved by

approach is that quality of load voltage can heavily

hybrid voltage and current mode type control for DG.

reliant on the speed islanding detection method

In which inverter is controlled as current source by

accuracy [7]-[10].second issue is under non-linear

one sets of controller in grid-tied mode, and as a

local load with aforementioned approaches is the

voltage source by other sets of controller in the

quality waveform of the grid current and load

islanded mode. Inrush grid currents are almost

voltage.

eliminated in the output by directly controlling the

The output current of DG is generally desired to be

output current in grid-tied mode. There is no need to

pure in

grid-tied mode

[13].

The harmonic

change the switch of the controller when the

component will fully flow into the utility when

operation mode of DG is changed, with the use of

nonlinear load is fed. The harmonic components of

hybrid voltage and current control mode.

the grid current can be mitigated by harmonics

Fig. 1. Schematic diagram of the DG based on the proposed control strategy.

injected by single-phase DG in [4]. DG will emulate

grid current in the grid-tied mode and on load voltage

a resistance at harmonic frequency is being controlled

in island mode and improving both of them for

by voltage mode control and then the harmonic

unified strategy is rarely used.

current flowing into the utility can be mitigated. In

This paper discusses about unified control strategy

the islanding mode, the nonlinear load may distort.

that avoids the aforementioned shortcomings. With a

With the use of multi-loop control method, resonant

given reference in the synchronous frame (SRF) the

controllers, sliding mode control and many control

three-phase inverter is controlled in DG act as a

schemes have been proposed to improve the quality

current source using traditional current loop. A novel

of the load voltage. Existing control strategies, DG

voltage controller is presented to supply reference for

with nonlinear local load will mainly concentrate on

the inner inductor current loop in D-axis and Q-axis

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proportional-plus-integral (PI) compensator and a proportional (P) compensator are employed. The load

DISTRIBUTED GENERATION (DG)

voltage is dominated by the utility and the voltage

AND IT’S APPLICATIONS

compensator in D-axis is saturated, while the output of the voltage compensator in Q-axis is forced to be zero by the PLL. The reference of the inner current loop cannot be regulated by the voltage loop. With the occurrence of grid outage, the load voltage is no more determined by the utility. The voltage controller is automatically activated to regulate the load voltage. Hence proposed control strategy does not need a forced switching between two different sets of controllers. So, there is no need of detecting islanding quickly and accurately is no more critical in approach. For better dynamic performance, the proposed control strategy utilizes the feedback control for both current and voltage compares to voltage control mode. And paper is enhanced by introducing a unified load current feedforward, is implemented by adding the load current into the reference of the inner current loop in order to deal with the issue caused by the nonlinear local load. The benefits of the proposed load current feedforward can be extended into the islanded operation mode, due to the improved quality of the load voltage. This paper is arranged as follows. Section II discusses about Distributed generation (DG) and its applications. Section III describes the proposed unified control strategy for three phase inverter in DG which includes the power stage, the basic idea and control diagram. Section IV discuss about fuzzy logic controller. The parameter design and small signal analysis of the proposed control system are given in Section V. The simulation results for the proposed system are shown in Section VI. Finally, the conclusion and remarks are given in section VII.

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Distributed generation (or DG) generally refers to small-scale (typically 1 kW – 50 MW) electric power generators that produce electricity at a site close to customers or that are tied to an electric distribution system [12]. Distributed generators include, but are not limited to synchronous generators, induction generators, reciprocating engines,

microturbines

(combustion turbines that run on high-energy fossil fuels such as oil, propane, natural gas, gasoline or diesel), combustion gas turbines, fuel cells, solar photovoltaic, and wind turbines. There are many reasons a customer may choose to install a distributed generator. DG can be used to generate a customer’s entire electricity supply; for peak shaving (generating a portion of a customer’s electricity onsite to reduce the amount of electricity purchased during peak price periods); for standby or emergency generation (as a backup to Wires Owner's power supply); as a green power source (using renewable technology); or for increased reliability. In some remote locations, DG can be less costly as it eliminates the need for expensive construction of distribution and/or transmission lines. Islanding: Islanding occurs when a DG system is still generating power to the distribution system when the main breaker from the Wires Owner is open. In this case, the DG system would be the sole supplier of electricity to the distribution system. This is a concern for several reasons. i. Safety concern for system maintenance if the Wires Owner's line workers are not aware that the DG system is still running, they may be electrocuted working on the line or other equipment connected to the line.

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ii. Equipment damage to other Wires Owners

after the islanding has been detected by the DG and

customers. If the DG is still generating while the

DG will be transferred to islanded mode from grid-

main breaker from the wire owner is open, the

tied mode. The DG will be resynchronized with the

voltage and the waveform from the DG may fluctuate

utility only after when the utility is restored and the

and may not meet the acceptable standard. Existing

switch

customers who are connected to the distribution line

the grid.

will be turned ON to connect the DG with

are then fed by very poor quality of power from the DG. As a result, their light fixtures, motors and other electric equipment may be damaged or its life may be shortened. If the situation persists unnoticed for an unacceptably long time, a fire hazard may exist. iii. Damage to the DG owner's generator if the DG is still generating while the main breaker from the wires owner is open, the DG equipment may be damaged when the wires owner’s main breaker is closed due to closing out of synchronism.

Fig. 2. Overall block diagram of the proposed unified control strategy.

SYSTEM PROPOSED CONTROL

B. Basic Idea with the proposed control modes (hybrid voltage and

STRATEGY

current mode) the inverter is controlled as a current

A. Power Stage: To operate in both grid-tied and islanded modes this

source to generate reference power +

+

in

paper proposes unified control strategy for three-

grid-tied mode, output power

phase inverter in DG. The DG is equipped with a

the power injected into the grid

three-phase interface inverter with a LC filter. The

demand can be expressed as follows by assuming the

energy from prime mover is converted in electrical

load is represented as a parallel RLC circuit:

energy and then into DC by front end power

=

converter, the DC voltage is regulated represented by

=

connected in the ac side of the inverter. The two and

and the utility

will control the utility protection switch

. Under

and load

3 ∙ 2

3 ∙ 2

∙

1

functions are different. DG will

control the inverter transfer switch

+

------- (1)

as shown in figure. Local grids are directly

switches

should be

− --------- (2)

Where frequency

the amplitude of load voltage and f is is the of

load

voltage.

Considering

the

normal operation, the DG in the grid-tied mode

fundamental component still equivalent to the

injects power to the utility and both

parallel RLC circuit when the nonlinear local load is

and

switches are ON. When the utility is in fault, the

fed. The load voltage will neither be fixed by the

utility instantly trips the switch

and then the

utility nor regulated by the inverter during the time

Switch will be disconnected

interval the moment of switching the control to the

islanding is formed.

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instant of islanding mode. The load voltage may drift

reference generation module. In order to mitigate the

from the normal range.

couplings due to the inductor, is implemented by the

The inverter will still controlled as current source

PI compensator in both D- and Q-axes and /

and kept it output power almost unchanged during

decoupling

this time interval. The power injected to utility

Decoupling capacitor 1/

decreases to zero rapidly, and then the power

current loop

consumed by the load will be imposed to the output

space vector modulation (SVM) that control the

power of DG. If considered both active power and

switches of the three-phase inverter. Where

reactive power injected into the grid is positive in the

denotes the voltage gain of the inverter which equals

grid-tied mode, then

to half of the dc voltage in this paper.

and

will increase the

of

the

cross

coupling

.

and output of inner

sets the reference for the standard

after the islanding mode. The amplitude and

The widely used SRF PLL in three-phase power

frequency of the load voltage will rise and drop

converter to estimate the utility frequency and phase

according to equations (1) and (2).

is also proposed in the control strategy [15], in order

Comparing to the traditional analysis, the output +

power of inverter

can be regulated to

to hold the frequency of the load within the normal range in the islanded operation a limiter is inserted

match the load demand by changing the current

between the PI compensator

reference before islanding is confirmed. The load

From figure it can be concluded that the inductor

voltages excursions will be mitigated which is

current is regulated to follow the current reference

implemented in this paper. By regulating the three-

and the current phase is synchronized to the

phase inductor current

only the output power of

grid voltage

and integrator.

.

the inverter is controlled in the proposed control strategy, while the magnitude and frequency of the load voltage

are monitored. While islanding is

about to operate, the magnitude and frequency of the load voltage may drift from normal range and then they are controlled automatically and recovered to normal range by regulating the output power of the inverter.

Figure 2 shows the proposed unified overall control

Fig 3 Block diagram of the current reference generation module. If current reference is constant, the inverter is just

block diagram. The sensed values from the block

controlled to be a current source, which is same with

diagram are the utility voltage

, the inductor

the traditional grid-tied inverter. The new thing in

. The three-

this paper is the current reference to guarantee the

phase variables of the three-phase inverter will be

power match between the DG and local load and

represented in dc quantity is controlled in the SRF.

enables to operate in islanded mode. In this module

The main modes of the control diagram are the

even unified load current feedforward to cope with

inductor current loop, the PLL, and the current

nonlinear local load is implemented. Figure 3

C. proposed Control strategy:

current

and the load current

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provides the current reference for the inner current

In [18] the inductor current control shown in Fig 2

loop in both grid-tied and islanding modes. An

was proposed for grid-tied operation of DG. Inspired

unsymmetrical structure is used in D- and Q-axis

from [18] this paper proposes a unified control

where PI compensator in D-axis with an extra limiter

strategy for DG in both grid-tied and islanded modes

and P is employed in Q-axis. Load current

can

is

be represented by the current reference

being added to the final inductor current reference

generation module in figure 3.This module can be

by the load current feedforward. The benefits

summarized in two aspects for this contribution.

from figure 3 are represented by two parts: 1) without

First, PI compensator in D and P compensator Q-axis

critical

transfer

respectively, upon occurrence of islanding voltage

capability; and 2) in both grid-tied and islanded

controller is activated automatically and maintained

operations improving the power quality. In D and Q-

inactive during grid-tied mode. There is no need for

axes the current reference

switching different controllers and load voltage

islanding

detection

seamless

composes of four

parts namely: 1) controller output voltages the reference grid current

; 2)

; 3) the load current

and 4) the current through filter capacitor

.In

quality during transition from grid-tied mode to the islanded

mode

can

be

improved.

Another

contribution of this module is to provide load current feedforward to deal with the issue caused by the

grid-tied mode, the load voltage

is decided by

the utility. The load voltage and current reference are irrelevant due to saturation of PI compensator in Daxis and the output of P compensator being zero in Q-axis. Thus,

the inverter operates as a current

source. Voltage controller takes automatically to control the load voltage by regulating current reference when islanding occurs and makes the inverter to operate as a voltage source to provide

nonlinear local load, by which load voltage quality in islanded mode is enhanced and the grid current waveform in grid-tied can also improved. It should be noted that the unbalance three-phase local load currents cannot be fed by the DG with the proposed control strategy, because there is no flow path for the zero sequence current of unbalanced load, and the regulation of zero sequence current is beyond the scope of the proposed control strategy.

stable voltage to the local loads. The advantage of this control scheme is that it relieves from different control architecture. The other distinguished function of the current generation module is the load current feedforward. In order to compensate the harmonic component the sensed load current is added as a part of the inductor reference current

in the grid current under the nonlinear

local load. But in the islanded mode still the load current feedforward operates and the disturbance caused by the nonlinear load can be suppressed by

FUZZY LOGIC CONTROLLER The error value of the dc-bus voltage Δvdc= v∗dc−vdc is passed through a Fuzzy-type compensator to regulate the voltage of dc bus (vdc) at a fixed value. The operation of FLC is as follows. FLC contains three basic parts: Fuzzification, Base rule, and Defuzzification. FLC has two inputs which are: error and the change in error, and one output. The Fuzzy Controller structure is represented in fig.6. The role of each block is the following:

the fast inner inductor current loop and finally the quality of the load voltage is improved.

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Fig 4. Membership function of voltage error

Fig 2: The general structure of Fuzzy Logic Controller

Fuzzifier converts a numerical variable into a linguistic label.. In a closed loop control system, the

Fig 5. Membership function of output field voltage

error (e) between the reference voltage and the output voltage and the rate of change of error (del e) can be labeled as zero (ZE), positive small (PS), negative small (NS), etc. In the real world, measured quantities are real numbers (crisp). The FLC takes two inputs, i.e., the error and the rate of change of

Rule base stores the data that defines the input and the output fuzzy sets, as well as the fuzzy rules that describe the control strategy. Mamdani method is used in this paper. Seven membership functions were used leading to 49 rules in the rule base.

error. Based on these inputs, The FLC takes an intelligent decision on the amount of field voltage to

Table 1

be applied which is taken as the output and applied

Rule base for fuzzy controller

directly to the field winding of generator. Triangular membership functions were used for the controller.

Fig 3. Membership function of voltage

Inference engine applies the fuzzy rules to the input fuzzy variables to obtain the output values. Defuzzifier achieves output signals based on the output fuzzy sets obtained as the result of fuzzy reasoning. Centroid defuzzifier is used here.

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----------- (5)

PARAMETER DESIGN AND SMALL Where

SIGNAL ANALYSIS OF THE

= magnitude of the grid voltage, ∗

= the actual phase angle.

PROPOSED CONTROL SYSTEM

is regulated to zero by the PLL, so magnitude of the utility voltage The fuzzy based proposed unified control strategy with operating principle of DG is illustrated in detail in this section. The four states of DG are as follows:1) grid-tied mode, 2) transition from the gridtied mode to islanded mode, 3) the islanded mode, 4)

equals the

. As the filter

capacitor voltage equals the utility voltage in the gird-tied mode, utility voltage

equals the magnitude of the , and

equals zero. In the D-axis,

the inductor current reference

can be expressed

by (6) according to Fig. 3

from islanded mode to the grid-tied mode.

=

i. Grid-Tied mode: under normal case of utility, by

+

−

∙ ------- (6)

inductor current loop the DG is controlled as current source and will supply active and reactive power

In steady state, the given voltage reference

through current D- and Q- axis independently. For

larger than the magnitude of the utility voltage

that utility voltage phase angle is obtained through

and the first part is the output of the limiter. So the PI

PLL by park transformation, PI controller, a limiter

compensator, denoted by GVD in the following part

and an integrator.

will saturate and the limiter outputs its upper

2 = 3

cos

cos

− sin

− sin

2 3 2 − 3

+

− cos − sin

value

2 3 2 + 3 +

×

An inductor current reference

seems little

complex and compared with the instantaneous filter inductor current which is transformed into SRF by the park transformation. The inductor current is regulated to track the reference compensator

= cos

∗

cos

cos( ∗

∗

−

−

2 3

∗

− ) ∗ − )

the

·

,

is the

capacitance of the filter capacitor. It is fixed as depends on the utility voltage. The given reference and the load current the current reference

=

is being imposed by and independent of the

consists of four parts as ∙

+

+

+

∙ ------ (7)

Where

The SRF transformation of the utility voltage is cos( sin(

that

is the rated angle frequency, and

reference

------- (4)

= =

is

load current.

where

2 ) 3

expressed as

part

load voltage. In the Q-axis, the inductor current

three-phase utility voltages are expressed as =

second

The third is the proportional part −

by the PI

. The utility is assumed stiff, the

The

characteristics of local load will determine Daxis

-------- (3)

.

is

denoted by the output of

= parameter of the P compensator, in the following part. The first part is , which is zero as the

has been

regulated to zero by the PLL. The second part is the given current reference

, and the third part

represents the load current in Q-axis. The final part

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is the proportional part− since

·

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, which is fixed

inverter switch

. As switch

is in ON state, in first

interval the utility voltage

depends on the utility voltage.

voltage

will be same as load

because dynamic of the inductor

current loop and the voltage loop is much faster than the PLL [15] but load voltage and current are varying dramatically

considering

load

voltage

angle

frequency to be not varied. In the grid-tied mode, it is assumed that the DG injects active and reactive power into the utility, which can be expressed by (8) and (9), and that the local critical load, shown in (10), represented by a series connected RLC circuit with the lagging power factor Fig. 4. Simplified block diagram of the unified control strategy when DG operates in the grid-tied mode Therefore, external voltage drop will not influence the current reference

.but, the current reference

will determine the given reference the load current

and

Fig. 5. Operation sequence during the transition from the grid-tied mode to the islanded mode.

.the control diagram of the

inverter is simplified n grid-tied mode, with the analysis of previous cases and the inverter is controlled as a current source with inductor current reference

and

the

load

Fig. 6. Transient process of the voltage and current

current

determined by the inductor current loop will track the current

reference

and

the

load

when the islanding happens.

current.

represents the grid currents if steady state

=

3 ∙ 2

+

=

3 2

error is zero will be explained in next section.

------- (8)

ii. Transition mode from grid –tied mode to the islanded mode: By opening utility switch

, the

=

3 ∙ 2

+

=

3 2 --------- (9)

islanding mode begins; frequency and load voltage will drift because of active and reactive power

=

+

−

mismatch between DG and the load demand. The transition is divided into two time intervals where first is from the instant of turning off of turning off

to the instant

when islanding mode is confirmed.

=

+ =

−

1

1

+ ------- (10)

The second one starts from instant of turning off

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In islanding mode,

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will decrease from positive to

If

is fixed, load voltage in Q-axis

will be

will increase from negative to zero.

negative. With the help of power relationship the

During this time load current will vary in the opposite

variation of frequency and amplitude can be

direction. From equations (11) and (12) it can be

understandable. When the islanding happens, the

concluded that D- and Q-axes load voltage each

local load must absorb the extra power injected to the

consists of two terms. The load voltage in D-axis

grid, as the output power of inverter is not changed

will increase as both terms increase. But in Q-axis

instantaneously. From (1) the magnitude of load

zero, and

is uncertain because the first term decreases and

voltage

will rise with the increase of

. In

the second term increases, and it is not concerned for

meanwhile the angle frequency ω should drop, in

a while

order to consume more power with (2). Results from =

∙

−

power relationship coincide with the previous

∙ ------ (11)

=

∙

−

from the instant when the switch

∙ ------ (12)

The input of PI compensator

analysis. The second time interval transition begins

will become

opens after the

islanding detection method. If switch load voltage

opens the

is independent with the grid

negative with the increase of the load voltage in D-

voltage

. In the mean time

will reduce to

axis

zero theoretically as the switch

has opened. The

, when it reaches and exceeds

so its

output will decrease. Then the output of limiter will

angle frequency is invariable and then, input of the

not imposed to

compensator

reference

any longer and the current will drop. In the regulation of the

inductor current loop, D-axis

load current will

decrease. The load voltage in D-axis and recover to

. If

will drop

has almost fallen to the

normal value, the load voltage in Q-axis

will

drop according to (12). The PI compensator

will

going to be negative if

is decreased from zero to

negative and its output will drop. The angle frequency ω will be reduced. If it falls to the lower value of the limiter at

, the angle will be fixed

. At the end of the first time interval the load

voltage in D-axis

will increase and fix at

drop.PLL can still operate normally if the value is

the load voltage in Q-axis

will be zero.

of the first time interval. The inverter is controlled to be a voltage source when

is regulated by the voltage loop. Under

islanding operation, the load voltage is restricted to particular range to drift the amplitude and frequency and the inverter is transferred from the current source operation mode to the voltage source operation mode autonomously. With the increase in the time of delay, the drift becomes worse in the hybrid voltage and current mode control. So, the time delay of islanding detection is critical to drift of the frequency and magnitude in the load voltage. In proposed control strategy this phenomenon is avoided.

and angle frequency of the load voltage ω will also

higher than the lower value of the limiter

becomes zero and fixed to the end

, and

iii. Islanded Mode: in this state switching

and

both in OFF state. The PLL cannot track the utility voltage normally, and angle frequency is fixed. Since voltage compensator load voltage

and

can regulate the

, the DG is controlled as a voltage

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source. In D-axis the voltage reference is

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and in

b. The magnitude of the load voltage

is larger

Q-axis voltage reference is zero respectively and the

than the utility voltage magnitude

, the reference

magnitude of the load voltage equals to

voltage

by toggling the

approximately, elaborated in next section. The

selector S from terminals 1 to 2. The load voltage

control diagram of three-phase inverter for islanded

will equal t the utility voltage in both phase and

mode can be simplified and is shown in figure 7. If

magnitude.

there is any disturbance in the load current, it will be

c. The switch

suppressed quickly by the inductor current loop and a

reset to terminal 1 where load voltage is held by

stiff load voltage can be achieved. Finally, the load

utility. As

current

magnitude

is partial reference of the inductor

current loop.

Tied Mode:

is turned on, and the selector S is =

of

compensator

iv. Transition from the Islanded Mode to the Grid-

which is larger than the

the

utility

voltage

,

so

PI

will saturate, and the output of

limiter is its upper value

meanwhile

is

regulated to zero by the PLL from equation 5. The

a. If the utility switch

made ON after the restoring

output of

the utility, the DG should be connected with utility by turning ON switch

. There are several steps

before preparation before turning on switch

.as

soon as utility voltage is restored, the PLL will track the phase of the utility voltage which results that the phase angle of utility voltage grid voltage

will be changed to

will follow the

. If the load voltage

is in

phase with the utility voltage, according to equation 5 will equal the magnitude of the utility voltage.

and

will be zero. By inactivating , DG is controlled as a current source by

inductor current loop. Analysis and Design: This section briefs about the proposed fuzzy based control strategy is analyzed and designed in both steady state and transient state along with three-phase inverter. In the steady state, the operating points of both gridtied and islanded modes of DG are analyzed where limiters and references are selected. Whereas in transient state, compensators in both inductor current loop and the external loop are designed based on the small-signal model and the effect of load current feedforward is also analyzed as well. A. Steady State 1) Analysis of Operation Points: 2) Selection of References and Limiters

1) Analysis of Operation Points: in the grid-tied mode, the inverter is controlled as a current source, and the current reference for the inductor current Fig 7 Simplified block diagram of the unified control strategy when DG operates in the islanded mode.

loop

is expressed according equation (6) and

(7). The steady-state error will be zero with the Fuzzy Logic Compensator in the inductor current loop, so

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the inductor current in steady state can be expressed

compensator

as follows:

zero and = ∙

=

− +

∙

can be expressed as follows:

+

∙

=

+

+

------- (18)

------- (13)

Where

In the SRF, the relationship between the voltage and the current of the filter capacitor in steady state can be expressed by =− =

, so the steady state error will be

is

is in D-axis. In the Q-axis, the regulator compensator, so the steady state error may

not be zero. As the load current is added to the inductor reference, the condition shown as below can

∙

be achieved

∙

∙

-------- (14)

=0

represents the angle frequency of the DG

------ (19)

denotes capacitance of the filter capacitor. As a

And then, the load voltage in Q-axis can be expressed

Where and

+

result, the output current of the inverter

can be

by (20). It should be noted that the absolute value of

gained = − = = − = +( − ) ∙

−( ∙

which is related to the reactive power injected

− ) +

∙

+

rises with the increase of the current reference

into the utility . =−

------- (15)

------ (20)

As angle frequency ω is very close to the rated angle frequency

, it can be found that the output current

follows

and the load current

, as

equals

The magnitude of the load voltage represented

as

follows.

zero in the grid-tied mode. The active and reactive

approximately, because

power injected into utility can be obtained as follows.

than

It

can be

equals

to

should be much lower

with proper current reference

Consequently, the active power and reactive power =

flowing from the inverter to utility can be given by

and

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

3 = ∙ 2

≈

, respectively

------- (21) During islanding operation, the angle frequency is

(

− =

3 = ∙ 2

+

(

)+

−

restricted in the given range by the limiter. During

3 ∙ 2 −

transition from grid-tied mode to the islanded mode, In first-time interval only the angle frequency is )−

−

determined. If current reference

3 = ∙ 2

then

is set to zero,

is zero. It means that the angle frequency

----- (17)

does not vary in the first time interval of the

In the islanded mode, the inverter is controlled as a

transition, and it should equal the angle frequency of

voltage source by the external voltage loop. In the D-

the utility before islanding happens

axis,

is

regulated

by

the

Fuzzy

. the angle

Logic

IJPRES 229

INTERNATIONAL JOURNAL OF PROFESSIONAL ENGINEERING STUDIES

frequency of the load voltage

Volume V /Issue 4 /SEP 2015

in the islanded mode

is determined by the current reference

, where

represent the upper values of the limiter and

Besides,

the

between

angle and

frequency

is

restricted

in the islanded mode, and it

should not drift from the normal value too far. So, and

represent the lower values of the limiter shown

are selected as the maximum and

minimum angle frequencies allowed by the utility

in fig 2 ,

>0 =0