Received: 3 July 2019
Revised: 28 October 2019
Accepted: 11 November 2019
DOI: 10.1002/2050-7038.12289
RESEARCH ARTICLE
Power quality assessment of microgrid using fuzzy
controller aided modified SRF based designed SAPF
Prasanta K. Barik1
| Gauri Shankar1 | Pradeepta K. Sahoo2
1
Department of Electrical Engineering,
Indian Institute of Technology (ISM),
Dhanbad, Jharkhand, India
2
Department of Farm Machinery and
Power, CAET, OUAT, Bhubaneswar,
Odisha, India
Correspondence
Prasanta K. Barik, Department of
Electrical Engineering, Indian Institute of
Technology (ISM), Dhanbad, Jharkhand,
India.
Email: prasantbarik05@gmail.com
Summary
Microgrid (MG), a localized modular power system comprising of distribution generations (DGs) and loads, acts as a single controllable unit in relation to grid. It may
either operate in standalone mode or grid connected mode. It offers benefits like efficient and sustainable energy supply, reduced carbon emission, deferring extension
of power distribution infrastructures, and so on. However, integration of DGs having
different characteristics results in various operational challenges in a MG network.
One of which is power quality (PQ) issue. Hence, in this article, impact of PQ issues
in an adopted standalone MG system (comprising of solar, wind and fuel cell based
DGs) is investigated in the presence of shunt active power filter (SAPF). The realization of SAPF is carried out using conventional synchronous reference frame (SRF)
and modified SRF (MSRF) techniques for reference current generation, proportional
integral (PI) controller, and fuzzy logic controller (FLC) for DC-link capacitor voltage
regulation and a basic hysteresis band current controller technique for generation of
switching pulse for the inverter. The simulation model of conventional SRF/MSRF
techniques and the proposed FLC approach based SAPF is developed under
MATLAB/SIMULINKR environment both at ideal and nonideal source condition
considering inductive and capacitive load. The results obtained using proposed
MSRF technique and FLC approach owing to different load scenarios is compared to
that of conventional SRF and MSRF technique with PI controller. The comparative
results obtained validate the superiority of proposed technique over other related to
harmonics elimination and DC-link capacitor voltage regulation.
KEYWORDS
distributed generation, harmonics, microgrid, power quality, shunt active power filter
List of Symbols and Abbreviations: AC, alternating current; APF, active power filter; DC, direct current; DG, distributed generation; FC, fuel cell;
FFT, fast Fourier transform; MSRF, modified synchronous reference frame; MPPT, maximum power point tracking; PCC, point of common coupling;
PEMFC, proton exchange membrane fuel cell; PMSG, permanent magnet synchronous generator; P&O, perturbs and observes; PQ, power quality; PI,
proportional integral; PLL, phase-locked loop; PV, photovoltaic; PWM, pulse width modulation; SRF, synchronous reference frame; THD, total
harmonic distortion; VSI, voltage source inverter; WECS, wind energy conversion system; C, capacitor; Ω, ohm; f, frequency; Vpv, diode voltage; Voc,
open circuit voltage; PwT, turbine mechanical power; β, pitch angle; λ, tip-speed ratio; ρ, air density; (ila, ilb, and ilc), three-phase instantaneous load
currents; (isa, isb, and isc), three-phase source currents; (isa*, isb*, and isc*), three-phase reference source currents; VDC, DC link capacitor voltage; (VDC,
ref), DC link reference voltage; Imax, peak value of the reference current; Vfc, fuel cell voltage; vf, each cell voltage; Rt, cell resistance; is, source current;
ic, compensating current; e(n), error signal; ce(n), integration of error signal.
Int Trans Electr Energ Syst. 2019;e12289.
https://doi.org/10.1002/2050-7038.12289
wileyonlinelibrary.com/journal/etep
Copyright © 2019 John Wiley & Sons, Ltd.
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BARIK ET AL.
1 | INTRODUCTION
Microgrid (MG) is a future trend of integrating renewable energy source (RES) based generating units in an electrical
distribution system. This may be seen as an alternative to depleting fossil fuel-based conventional units in reducing
energy supply scarcity. It may appear as a combination of RES (such as bio-energy, wind, solar photo voltaic [PV],
mini-hydro, fuel cell, and so on) based generating units and storage devices (such as batteries, flywheel, super capacitor,
etc.) along with controllable critical loads.1 The MG, basically, operates either in standalone mode or grid connected
mode. When any region is demographically inaccessible by the utility grid, in that case, standalone operation of MG is
the only viable option. While, in grid connected mode, the exchange of power takes place between MG and the utility
grid based on the energy requirement, quantum of power disturbance/severe fault within the system.2 The solar and
wind energy are intermittent/complementary in nature (as both depend upon climatic condition). Hence, in the present
work, to get an uninterrupted power supply and to maintain the continuity of load current, the proposed MG also have
a fuel cell together with solar and wind based distributed generators (DGs).3
It is well known that electric power system is mostly affected by power electronics-oriented nonlinear loads, such as
switch-mode power supplies, arc furnaces, converters, industrial/house hold electronic devices, and so on, fixed at the
distribution side.4,5 Thus, ensuring quality power to all consumers becomes a major challenge for the power utilities.
Moreover, the power quality (PQ) problems associated with currents are mostly due to unbalanced loads, harmonics,,
and insufficient reactive power. Additionally, these factors also affect the performance of other equipment connected at
the point of common coupling (PCC) as well.6,7 As a solution to the above problems, nowadays, shunt active power filters (SAPFs) are widely used for achieving superior PQ levels. These are employed to inject compensating currents for
generation/absorption of reactive power and harmonics suppression at the PCC.8 As surfaced in the literature, it is
observed that different configurations of SAPF together with control algorithms have been proposed in the past by different researchers.9,10 Akagi et al11 have developed a new reactive power compensator technique-based SAPF for threephase power system on the basis of the instantaneous value of voltage and current waveforms and, practically, it
requires no energy storage components. Authors in Reference 12 have developed a prototype model of SAPF and tested
it experimentally in the presence of nonlinear balanced and unbalanced loads to investigate its effectiveness in reactive
power compensation and harmonic elimination. Various control strategies of SAPF have been explored in Reference 13
for load compensation under different supply voltages and compared their performance in terms of the rms current,
total harmonic distortions (THD), power factor of source currents, and filter ratings. Many harmonic revealing control
concepts and approaches for SAPF such as fast Fourier transform, instantaneous active and reactive power, synchronous reference frame (SRF), direct testing and calculating method, notch filter, synchronous detection algorithm, flux
based controller, techniques have been proposed and suggested in the literature.14-16 Among these control schemes,
SRF technique is one of the most conventional and practically applicable method.17 Although, it performs an excellent
job, but it requires a phase locked loop (PLL) circuit for synchronization. Different types of PLL have been introduced
in the literature.14-17 However, the conventional types of PLL used in SRF technique exhibit poor performance in
extremely unbalanced and distorted networks. So, this article is aimed at establishing competence of the modified synchronous reference frame (MSRF) technique over the SRF method by replacing the PLL circuit with a unit vector generation circuit for synchronization. In most of the studied literature, it is found that the realization of SAPFs mostly
depends on three significant factors and these are control technique employed for (a) reference current generation,
(b) regulation of DC-link capacitor voltage, and (c) generation of switching pulses for inverter.18 In most of the literature, the reference current generation scheme is done employing conventional SRF and MSRF techniques. The inherent
disadvantages associated with conventional SRF method are minimized in the MSRF approach.19 On the other hand, in
most of the earlier reported work, the DC-link voltage control and reduction of its settling time are achieved by either
PI controller or FLC or fuzzy-PI controller schemes in SRF based designed SAPF for grid connected system.20 Moreover,
PI controller employed for this purpose requires accurate linear mathematical model of SAPF, which is very difficult to
achieve in practice. On the other hand, FLC has played a major task in keeping a stable voltage across the capacitors
associated with SAPF as it can handle nonlinearities present in the system very well. Also, it does not require an accurate mathematical model and is more robust in comparison to PI controller.21 Literature survey reveals that the PI controllers have been widely used for DC-link voltage control in both SRF and MSRF based designed SAPFs for enhancing
the PQ level of MG system operated under grid connected mode. While, use of FLC for DC-link voltage control is found
only in conjunction with SRF based designed SAPF in grid connected system. Whereas, hardly any work on the
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application of FLC for DC-link voltage control in MSRF technique-based designed SAPF is found in the standalone
mode operated MG system.22,23 Therefore, this motivates the present authors to investigate further the PQ issues of
adopted islanded MG system in the presence of SAPF designed using MSRF approach for reference current generation
and FLC strategy for DC-link voltage control. Henceforth, the proposed approach/model is referred as MSRF-FLC
based SAPF approach.
The main contributions of present work are as follows.
1. A MG system comprising of solar, wind, and fuel cell-based DGs is modeled for standalone mode of operation.
2. Design of MSRF-FLC based SAPF for the adopted MG system is carried out.
3. Considering ideal and nonideal source, the performance of the proposed SAPF model is tested in the presence of
nonlinear load under steady state and dynamic state.
4. Further, comparative performance analysis of proposed MSRF-FLC based SAPF with those of SRF-PI controller,
MSRF-PI controller based designed SAPF is presented at varying load condition.
The rest of the article is organized as follows. Modeling of studied MG system is presented in Section 2. In Section 3,
the design of SAPF with different control schemes are explained. Simulation results are presented and discussed in Sections 4 followed by conclusions of the present work in Section 5.
2 | PROPOSED MG SYSTEM
The topology of the MG system considered in the present work is depicted in Figure 1. The studied MG system is
designed based on solar, wind, and fuel cell DGs. The detail modeling of each of the considered DG is explained below.
2.1 | Modeling of solar PV system
A single diode model based solar PV cell is considered in the assembly of MG as shown in Figure 2A. The single diode
solar PV model is simple and easy to implement as compared to other existing models, especially, at lower illumination
levels.24 Hence, this model is considered as an appropriate model of PV cell, where its voltage and current are related
by following Equations (1)-(3)
I ph = ½I sc + K i ðT r − T Þ ×
I o = I rs
FIGURE 1
Basic diagram of MG with SAPF
G
1000
q × E go 1 1
T 3
exp
−
Ak
Tr
Tr T
ð1Þ
ð2Þ
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F I G U R E 2 Solar PV system (A) single diode model equivalent
circuit, (B) flowchart of P&O MPPT algorithm, (C) simulation
model with MPPT and boost converter, and (D) DC output voltage
(VO) waveform
q × V pv + I pv × Rse
−1
I pv = N p × I ph − N p × I 0 exp
N s × AkT
ð3Þ
where Isc is the short circuit current (in A), Ipv is the diode photo current (in A), Vpv is the diode voltage (in V), NP
indicates number of cells connected in parallel and Ns represents number of cells connected in series, Rse is the series
resistance (in Ω), I0 is the reverse saturation current of diode (in A), Vocrefers to open circuit voltage (in V), G is the
solar irradiation (in W/m2), Rsh is the shunt resistance (in Ω), q is the electron charge (in C), k is the Boltzmann
constant, T is the operating temperature (in οC), Tr is the reference temperature taken as 25οC, A is the diode ideality
factor. Based on (1)-(3), a single diode model based solar PV cell is developed using MATLAB/SIMULINKR.
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Mostly, the output voltage of a PV unit is significantly low, therefore, it is necessary to operate the PV unit at its peak
point so that the maximum power can be supplied to the load at any condition.25 Using perturbs and observed (P&O)
algorithm (a kind of maximum power point tracking [MPPT] method), a boost converter employed subsequent to the
PV unit, matches the impedance of the circuit to the PV unit impedance to obtain peak power. Impedance matching is
done by varying the duty cycle of the boost converter. The flowchart of P&O method is shown in Figure 2B. The simulation model of solar PV with P&O method and boost converter is shown in Figure 2C. The corresponding output voltage
is shown in Figure 2D, where the required voltage of 230 V is achieved. The parameters required for design of boost
converter are illustrated in Table 1.26
2.2 | Modeling of wind energy system
The wind generator considered for the studied MG system is realized based on permanent magnet synchronous generator (PMSG). The wind turbine output power27 is given by (4)
1
PwT = πρCP ðλ, βÞR2 V 3
2
ð4Þ
where, PwT represents the turbine mechanical power (in W), β is the pitch angle, λ is the tip-speed ratio given by
λ = ΩR/V, ρ is the air density (in kg/m2), R is the blade radius-speed of the wind (in m), and V is the wind velocity
(in m/s). Figure 3A shows the basic wind energy conversion system model, where the kinetic energy of wind is first
converted to rotational motion. Further, a gear box is used to match the speed of turbine with generator. The mechanical energy of turbine is converted to electrical energy with the help of generator.28 Power output from the wind generator is intermittent in nature, hence, a rectifier is used to convert the fluctuating AC voltage to DC voltage and,
thereafter, to keep the output voltage constant at a desired value of 230 V, a boost converter is employed.29 The simulation of PMSG based wind generator system together with rectifier and boost converter is shown in Figure 3B and its
corresponding output voltage (VwT) is presented in Figure 3C.
2.3 | Modeling of fuel cell
Fuel cells technology converts the hydrogen energy to electrical energy through chemical reactions. There are several
types of fuel cell available that are classified as per their electrolytes. Proton exchange membrane (PEM) based fuel cell
is one of them and is considered as another DG in the development of proposed MG system. Fuel cell offers advantages
such as high efficiency, low working temperature and has compact structure. It is comprised of a positive electrode
(as cathode), a negative electrode (as anode), and an electrolyte. The pressurized hydrogen gas enters the fuel cell from
anode side while oxygen enters at the cathode.30 The basic PEM fuel cell diagram is shown in Figure 4A. Expressions
pertaining chemical reactions at anode, cathode, and overall reaction are shown in (5)-(7), respectively.
TABLE 1
parameters
Boost converter
2H + + 2e − = H 2
ð5Þ
1
2H + + 2e − + O2 = H 2 O
2
ð6Þ
Parameters
Values
Input voltage (Vs)
80 V
Source inductance (Ls)
0.01 H
Source capacitance (Cs)
0.002 F
Load capacitance (Cl)
0.002 F
Load resistance (Rl)
24 Ω
Output voltage (Vpv)
230 V
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BARIK ET AL.
F I G U R E 3 Wind energy system
(A) block diagram representation,
(B) simulation model with PMSG and
rectifier, and (C) DC output voltage (VwT)
waveform
1
H 2 + O2 = H 2 O
2
ð7Þ
The electro-chemical equations are given by (8)-(13).31
1
E thermo = 1:229 −0:00085 × ðT −298:15Þ + 4:31 × 105 × T × lnðPH 2 Þ + lnðPO2 Þ
2
ð8Þ
V act = − ½ξ1 + ξ2 × T + ξ3 × T × lnðCO2 Þ
ð9Þ
V ohmic = ifc ðRm + Rc Þ
ð10Þ
Vf = Ethermo − Vact − Vohmic −Vcon
ð11Þ
V st = k × V f
ð12Þ
V con = ln 1 −
J
J max
× ð −BÞ
ð13Þ
BARIK ET AL.
FIGURE 4
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Fuel cell system (A) basic model, (B) model with boost converter, and (C) DC output voltage (Vfc) waveform
where, (Ethermo) is the thermodynamically predicted voltage, T is the temperature in οK,PH 2 and PO2 are the pressure of
H2 and O2, respectively, in atm. The voltage of the fuel cell (Vf) is given by (12), where the stack voltage (Vst) is simply
the product of the voltage of the cell and the number of cells (k) and Vohmic, Vact, and Vcon are the ohmic loss, activation
loss and concentration loss, respectively. Rc and Rm are the equivalent membrane resistance due to proton and electron
conduction (in Ω),respectively, ξ is the model coefficient and for each cell it is represented by ξ1, ξ2, ξ3, ξ4, and so on. J
is the current density (in A/cm2) and Jmax is its maximum value. The parameters required for design of fuel cell are
illustrated in Table 2.
A single fuel cell generates a small amount of DC voltage. In practice, many fuel cells are usually assembled into a
stack. In the present work, the fuel cell produces an output voltage (Vfc) of 230 V. The fuel cell is used in conjunction
with boost converter as shown in Figure 4B. The profile of output voltage of the adopted fuel cell is portrayed in
Figure 4C.
3 | M ODELING OF S APF
The SAPF is normally connected at PCC for the mitigation of harmonics of the source current (is). Figure 5
reveals the basic structure of SAPF. To eliminate the harmonics from the source current, an equal amount of
compensating current (ic) is injected at the PCC by SAPF in opposite phase to that of harmonic current appearing
in the load current (il) due to presence of nonlinear load.10,11 The voltage source inverter (VSI) and interfacing
inductor (Li) are the main elements of SAPF for generating ic. The voltage across Li determines the maximum di/
dt rating of the VSI which is essential to compensate the higher order harmonics.12,13 Hence, the choice of Li is
also vital in modeling of SAPF. The instantaneous source current ((is(t)) and the source voltage (vs(t)) of the SAPF
are expressed by (14)-(15), respectively.
is ðt Þ = il ðt Þ− ic ðt Þ
ð14Þ
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TABLE 2
Parameters
Values
Hydrogen percentage in fuel (H2)
99.56%
Oxygen percentage in air (O2)
59.3%
Number of cell (k)
65
Cell resistance (Rt)
0.70833 Ω
Each cell voltage(vf)
1.128 V
Load resistance (Rl)
5Ω
Fuel cell voltage (Vfc)
230 V
FIGURE 5
Fuel cell parameters
Basic structure of SAPF
vs ðt Þ = V m sinωt
ð15Þ
If the load is nonlinear, the load current can be expressed using Fourier series as in (16).
il ðt Þ = i1 sinðωt + Φ1 Þ +
∞
X
in sinðnωt + Φn Þ
ð16Þ
n=2
The instantaneous load power may be expressed as
pl ðt Þ = vs ðt Þ*il ðt Þ
= Vm il sin2 ωt*cosΦ1 + Vm il sinωt*cosωt*sinΦ1 + Vm sinωt*
ð17Þ
∞
X
in sinðnωt + Φn Þ
n=2
= p f ðt Þ + p r ðt Þ + p h ðt Þ
ð18Þ
This instantaneous load power pl(t) in (17) has three components, active fundamental power (pf(t)), reactive power (pr(t)),
and harmonic power (ph(t)) which are represented in (18). From (18), the pf(t) drawn by the load is calculated using (19).
P f ðt Þ = V m il sin2 ωt*cosΦ1 = vs ðt Þ*is ðt Þ
ð19Þ
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From (19), the current supplied by the source, after compensation is given by (20)
is ðt Þ = P f ðt Þ=vs ðt Þ = il cosΦ1 *sinωt = I sm sinωt
ð20Þ
Where Ism is ilcosΦ1. There are also some switching losses in the PWM converter, and hence, the utility must supply
a small overhead for the capacitor leakage and converter switching losses in addition to the real power of the load. The
total peak current supplied by the source is therefore, given by (21).
I sp = I sm + I max
ð21Þ
Where, Imax is the output current obtained from DC-link voltage controller. The compensating current offered by
the SAPF is expressed by (22).
ic ðt Þ = il ðt Þ− is ðt Þ
ð22Þ
Equation (22) reveals that for the exact compensation of reactive power and harmonics current, it is essential to
determine is(t).14
3.1 | Control strategies for SAPF
The control strategies for the generation of compensation currents can be achieved through frequency domain or time domain
techniques.15 In frequency domain, the control approach for the extraction of compensation current is obtained using Fourier
analysis of the current signals. But, this technique involves complex mathematical calculation, which requires more time to execute.16 Whereas, the time domain technique is, mathematically, simpler and easy to implement. Also, numerical filter plays a pertinent role in the separation of fundamental component from the harmonics to extract the information on compensation current
required to be injected.17 As observed from the literature survey that the realization of SAPFs mostly depends on three significant
factors and these are control technique employed for (a) reference current generation, (b) regulation of DC-link capacitor voltage,
and (c) generation of switching pulses for inverter.18 Each of these is briefly discussed in the subsequent subsections.
3.1.1 | Strategies for reference current generation
In the present work, realization of control strategy for reference current generation is carried out based on two widely
used simple techniques such as
1. SRF method and
2. MSRF method.
These are briefly discussed below.
SRF method
The normal arrangement of SRF technique contains PLL unit for vector orientation as shown in Figure 6A. The control
pattern includes the transfer of load current from a − b − c to d − q reference frame. The three-phase instantaneous
load currents (ila, ilb, and ilc) are converted to ild − ild using the park-transformation technique as expressed by (23).18
0
0 pffiffiffiffiffiffiffiffi
10 1
pffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffi
ila
1=2
1=2
1=2
B C pffiffiffiffiffiffiffiffiB
CB C
@ ild A = 2=3@ sinωt sinðωt −120Þ sinðωt + 120Þ A@ ilb A
ilq
ilc
cosωt cosðωt −120Þ cosðωt + 120Þ
il0
1
ð23Þ
The signals obtain from d − q transformation is dependent upon the unit vector angle (θ) which is generated
from PLL circuit. After,a − b − c to d − q transformation, the d-axis component of the load current (ild) is passed
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BARIK ET AL.
F I G U R E 6 Control strategies for
reference current generation scheme
(A) conventional SRF technique, (B) MSRF
technique, and (C) unit vector generation
scheme of MSRF method
through a low pass filter (LPF) for filtering the harmonic components of the load current, which allow only the
fundamental component, where as the q and 0 axis components, that is, ilq and il0 are set at zero value. Then the
DC-link capacitor voltage (VDC) of the VSI is compared with that of reference DC-link capacitor voltage (VDC, ref)
for calculating the voltage error. This voltage error is passed through a voltage controller to maintain the VDC constant at its reference level. The output of the voltage controller (Imax) is also considered as the loss component of
current of the VSI. Imax is then added with the filtered d-axis current (ildh) so that the losses occurring in the VSI
are also supplied by the source. Finally, ild − ilq current is transformed to three-phase stationary reference frame
current isa*, isb*, and isc* using inverse park-transformation technique as explained in (24). Thereafter, these currents are compared with the corresponding reference source currents isa, isb, and isc to generate the required pulses
for the inverter.
0 pffiffiffiffiffiffiffiffi
10 1
1=2
sinωt
cosωt
0
B * C pffiffiffiffiffiffiffiffiB pffiffiffiffiffiffiffiffi
CB C
@ isb A = 2=3@ 1=2 sinðωt − 120Þ cosðωt − 120Þ A@ ild A
pffiffiffiffiffiffiffiffi
0
i*sc
1=2 sinðωt + 120Þ cosðωt + 120Þ
0
i*sa
1
ð24Þ
MSRF method
In case of MSRF method, the θ is generated by a simplified unit vector generation scheme instead of PLL circuit as used
in case of SRF method.19 The block diagram representation of the MSRF scheme is shown in Figure 6B.20 In this
method, the three-phase load currents (ila, ilb, ilc) are converted to two-phase currents (iα − iβ) in stationary reference
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frame as given in (25). Currents iα − iβ are then transformed to id − iq current using the unit vector circuit presented in
Figure 6C. The expression for converting iα − iβ to id − iq is given by (26).
iα
iβ
0
10 1
1 1
ila
1
−
B
2ffiffiffi 2 pffiffiffi C
B C
B
C
p
=@
@ ila A
3
3A
−
0
ilc
2
2
id
iα
sinθ −cosθ
=
iq
iβ
cosθ sinθ
ð25Þ
ð26Þ
The id and iq currents are passed through a LPF circuit having a cutoff frequency of 50 Hz to separate the fundamental and distorted currents. The voltage controller output Imax is added with the d-axis filtered current to obtain the reference d-axis current (i*d ), whereas, the reference q-axis current i*q is directly fed. Once the harmonics components are
eliminated from the distorted load current, it is then that transformed to stationary frame reference currents i*α − i*β
using (27). In order to obtain the desired reference current i*sa ,i*sb , and i*sc , reference currents i*α − i*β are converted to a-b-c
coordinates using (28).
i*α
!
i*β
=
0
sinθ −cosθ
cosθ
sinθ
i*d
i*q
!
1
0
pffiffiffi
B
C i*sa
B 1 3
C i
B* C B−
C α
@ isb A = B 2 2
C
B
C iβ
p
ffiffi
ffi
*
@
isc
1
3A
−
2
2
0
1
ð27Þ
1
ð28Þ
The reference current generated is compared with that of actual current isa, isb, and isc and passed through the hysteresis band to produce the required pulse width modulated (PWM) signals for the operation of inverter. The unit vector
generation scheme is defined by (29)-(30).21
Vα
cosθ = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
ðV sα Þ + V sβ 2
ð29Þ
Vβ
sinθ = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðV sα 2 Þ + V sβ 2
ð30Þ
The main advantage of this design is that the angle θ is estimated directly from the source voltage which makes it to
be frequency independent.
3.1.2 | DC-link voltage control strategy
Using PI controller
The internal configuration of PI controller circuit along with LPF, VDC, ref, and VDC signals are shown in
Figure 7A.22 VDC is sensed by a voltage sensor and is compared with VDC, ref. The error signal e(n) generated from
the comparator is passed through a LPF filter whose cut-off frequency is set at 50 Hz to suppress the higher order
harmonics and to permits only fundamental components. The output of the PI controller is considered as Imax
which may be represented by Imax = en(Kp + Kidt), where Kp and Ki are the proportional and the integral gain of
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FIGURE 7
Schematic of (A) VDC
control using PI controller, (B) VDC control
using FLC, (C) membership function used
for FLC, and (D) switching pulse
generation using HCC for VSI
the controller. The value of Kp and Ki (which control the VDC of the VSI) are found by hit and trial method as
0.8 and 23, respectively.
Fuzzy logic controller
FLC is realized from fuzzy set theory propounded in 1965. FLCs are excellent choice where accurate mathematical formula based calculations are impossible. Figure 7B presents a complete block diagram of the FLC scheme (in discrete
mode) which consists of fuzzy controller with LPF, VDC, ref, and VDC as feedback signal.23,24 In this method also, error
signal (e(n)) between VDC and VDC, ref is passed through LPF with a cut-off frequency of 50 Hz to allow only the fundamental component to pass. A FLC translates a linguistic control approach into an automatic control approach, and for
this, fuzzy rules are constructed based on expert experience or knowledge database.25 The e(n) and its integral (ce(n))
are the two input variables considered for the FLC design and the output of the FLC is considered as Imax. Imax is added
with the MSRF output current for generating the desired reference currents (isabc*). The different membership function
for the two inputs (e(n) and ce(n)) and single output Imax are shown in Figure 7C.
Basically, FLC consist of four key processes such as fuzzification, rule elevator, defuzzification and data/rule base.
1. Fuzzification: It is the process of converting numerical variable to a linguistic variable. In the proposed system, triangular membership functions are used for fuzzification of the concerned variables e(n), ce(n), and Imax. Each of
BARIK ET AL.
TABLE 3
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Rule base table for FLC
ce(n)
approach
Imax
e(n)
NB
NM
NS
ZE
PS
PM
PB
NB
NB
NB
NB
NM
NM
NS
ZE
NM
NB
NB
NB
NM
NS
ZE
PS
NS
NB
NB
NM
NS
ZE
PS
PM
ZE
NB
NM
NS
ZE
PS
PM
PB
PS
NB
NS
ZE
PS
PM
PB
PB
PM
NS
ZE
PS
PM
PB
PB
PB
PB
ZE
PM
PB
PB
PB
PB
PB
these variable is assigned seven membership function such as negative big (NB), negative medium (NM), negative
small (NS), zero (ZE), positive small (PS), positive medium (PM), and positive big (PB) as given in Figure 7C.
2. Rule elevator: In case of conventional PI controller, the control variables are the combination of numerical values
but FLC uses linguistic variables instead of numerical variables. In this process, for fuzzy rule base table a collection
of simple linguistic “IF-THEN” control rules are implemented. The general form of the fuzzy IF-THEN rule is IF “x
is A” and “y is B” THEN “z is C” where, x and y are the input variables and z is the output variable.
3. Defuzzification: The process of converting linguistic variable to numerical values is known as defuzzification. Here
a “centroid’ type defuzzification is used as it is easy to execute. Data/rule base: The database stores the triangular
membership function which is required by rule evaluator. The 49 rules used in this proposed controller are presented in Table 3.
3.1.3 | Strategy for generation of PWM signal
There are several types of control techniques available in the literature for the generation of PWM signals such as sinusoidal PWM, space vector PWM, sinusoidal PWM with instantaneous current control, hysteresis current controller
(HCC) based PWM, selected harmonic elimination based PWM and so on.32 The HCC based PWM technique is used in
this article owing to its simplicity.
The configuration of hysteresis band current regulator which generates the required switching pulse for the inverter
is shown in Figure 7D. The current regulator generates the error signal by comparing the reference current (isabc*) and
actual current (isabc). The switching pulses required for the inverter is designed in such a way that when the error signal
goes beyond the upper band of hysteresis loop, the lower switches of the inverter are turned ON and the upper switches
are turned OFF.Similarly, the upper switches are turned ON and the lower switches are turned OFF when the error signal exceeds the lower band. In this way, the actual current is always tracked with respect to the reference current inside
the hysteresis band.33
4 | R E S U L T A N A LY S I S AN D DI SC USSI O N
The proposed SAPF is connected at the PCC of the MG through filter inductance as displayed in Figure 8. The modeling
of the proposed system is carried out using MATLAB/SIMULINKR. The best chosen values of the parameters used for
this design are: source voltage, vs = 230 V; supply frequency,f = 50 Hz and VDC, ref = 700 V. First, nonlinear load is
designed using a three-phase uncontrolled bridge rectifier feeding 20 W resistor and 50 mH inductor (as inductive load).
Second, nonlinear load is developed using similar rectifier feeding a series connected 50 W resistor and 2200 μF capacitor connected in parallel (as capacitive load). The parameters for SAPF in MG system are defined in Table 4.
The performance analyses of the studied MG system is investigated without and with proposed SAPF under the
action of different controllers for different loading condition and are denoted as different scenarios.
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F I G U R E 8 Studied MG system
feeding nonlinear load under the action of
different controllers
Parameters
Values
Source voltage (vs)
230 V (rms)
supply frequency (f )
50 Hz
source resistance (Rs)
10 Ω
source inductance (Ls)
0.1 mH
Interfacing inductor (Li)
5 mH
DC-link capacitor (CDC)
2200 μf
DC-link reference voltage (VDC, ref)
700 V
Switching frequency (fc)
25 kHz
TABLE 4
SAPF parameters
1. Scenario 1: Performance analysis under ideal source condition without SAPF and with SAPF employing SRF-PI controller approach.
2. Scenario 2: Performance analysis of SAPF employing MSRF-PI controller strategy.
3. Scenario 3: Performance analysis of MSRF-FLC based SAPF.
4. Scenario 4: Performance analysis under nonideal source condition without SAPF and with SRF-PI controller,
MSRF-PI controller and MSRF-FLC based SAPF approaches.
5. Scenario 5: Comparative performance analysis of MSRF-FLC based SAPF with those of SRF-PI controller and
MSRF-PI controller based designed SAPF under dynamic load condition.
4.1 | Performance analysis pertaining to scenario 1
In this scenario, firstly, the performance of the adopted MG system is analyzed without SAPF in the presence of
nonlinear load of inductive and capacitive types. The profile of source current (is) is shown in Figure 9A and its harmonics content (before compensation) using fast Fourier transform (FFT) analysis is presented in Figure 9B. It may be
observed from Figure 9A,B that the source current waveform is non-sinusoidal in nature having very high THD content
of 26.74% and 20.25% for inductive and capacitive load, respectively. In order to make is to be sinusoidal, SAPF
employing SRF-PI controller approach is turned on, which injects compensating current (ic) at the PCC as displayed in
Figure 9C. As a result, THD level comes down to 3.52% and 3.40% for inductive and capacitive load, respectively. The is
after compensation and its corresponding FFT analysis are portrayed in Figure 9D,E, respectively.
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F I G U R E 9 Profiles obtained pertaining to Scenario 1 under inductive and capacitive load of (A) is before compensation, (B) harmonics contents
before compensation, (C) ic generated by SRF-PI controller based designed SAPF, (D) is after compensation, and (E) harmonics content after compensation
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4.2 | Performance analysis pertaining to scenario 2
The performance of MSRF-PI controller based designed SAPF is investigated in this scenario. The profile of ic generated
by the SAPF for inductive and capacitive load are shown in Figure 10A. Figure 10B illustrates the is waveform after
compensation. It may be viewed from the output waveform that the profile of is is nearly sinusoidal in nature, due to
the injection of ic by the SAPF. The FFT analysis of is (after compensation) is presented in Figure 10C which ensures
further reduction of THD content to 2.63% and 2.54% for inductive and capacitive load, respectively, in comparison to
scenario 1.
4.3 | Performance analysis pertaining to scenario 3
This scenario considers the performance analysis of the proposed MSRF-FLC strategy based designed SAPF. The ic generated under this strategy is portrayed in Figure 11A. After compensation, the profile of is is shown in Figure 11B and
its harmonics content as a result of FFT analysis is presented in Figure 11C. The result demonstrates that is is almost
sinusoidal with very low THD content of 1.20% and 1.15% for inductive and capacitive load, respectively. As we know,
ic and VDC are interrelated, if VDC is not regulated properly then more harmonics will be present in the source current.
The FLC is used to estimate the magnitude of Imax by controlling the VDC effortlessly in comparison to conventional PI
FIGURE 10
Profiles obtained pertaining to Scenario 2 under inductive and capacitive load of (A) ic generated by MSRF-PI controller
based designed SAPF, (B) is after compensation, and (C) harmonics content after compensation
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F I G U R E 1 1 Profiles obtained pertaining to Scenario 3 under inductive and capacitive load of (A) ic generated by the proposed MSRFFLC based designed SAPF, (B) is after compensation, and (C) harmonics content after compensation
T A B L E 5 THD comparison of
source current under ideal source
conditions
With SAPF
Nonlinear load type
Without SAPF
SRF-PI
MSRF-PI
MSRF-FLC
Inductive
26.74%
3.52%
2.63%
1.20%
Capacitive
20.25%
3.40%
2.54%
1.15%
The bold values are the results obtain by the proposed method in order to highlight the result it is provided
in bold.
controller. The proposed controller reduces the ripple in the VDC to a certain level and makes the source current harmonics free and, simultaneously, reduces the settling time of VDC. Moreover, the FLC method also reduces the
switching power loss and improves the performance of the SAPF in comparison to conventional PI controller.
A comparative result of THD content under various conditions is presented in Table 5. The result ensures that the
THD of the source current is less than 5% in all the methods, which is in compliance with IEEE-519 and IEC61000-3
harmonics standards.
4.4 | Performance analysis pertaining to scenario 4
In this scenario, the comparative performance analysis of the studied SAPF models is carried out under nonideal source
condition. The nonideal source condition is achieved by introducing harmonics in the source voltage of phase A. First,
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F I G U R E 1 2 Profiles obtained pertaining to Scenario 4 under nonideal source condition considering inductive and capacitive load of
(A) is before compensation, (B) harmonics contents before compensation, (C) ic generated using SRF-PI controller based SAPF model, (D) is
after compensation, and (E) harmonics content after compensation
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F I G U R E 1 3 Profiles obtained pertaining to Scenario 4 under nonideal source condition considering inductive and capacitive load of
(a) ic generated utilizing MSRF-PI controller based SAPF model, (b) is after compensation and (c) harmonics content after compensation
the performance is analyzed without SAPF in the presence of the nonlinear load of inductive and capacitive types. The
profile of is and its harmonic content (before compensation) are shown in Figure 12A,B, respectively. It may be
observed from the Figure 12A,B that the source current waveform is non-sinusoidal in nature having very high THD
content of 28.23% and 33.68% for inductive and capacitive load, respectively. To make is sinusoidal, firstly SAPF
employing SRF-PI controller approach is turned on, which injects appropriate ic at the PCC as displayed in
Figure 12C. As a result, THD level comes down to 3.85% and 3.38% for inductive and capacitive loads, respectively. The
is after compensation and its corresponding FFT analysis are portrayed in Figure 12D,E, respectively. Second, the profile of ic generated by MSRF-PI controller based designed SAPF for inductive and capacitive load are shown in
Figure 13A and Figure 13B illustrates the is waveform after compensation. It may be viewed from the output waveform
that the profile of is is nearly sinusoidal in nature, due to the injection of ic by the MSRF-PI controller approach based
designed SAPF. The FFT analysis of is after compensation using this approach is presented in Figure 13C which ensures
further reduction of THD content to 2.68% and 2.15% for inductive and capacitive load respectively. Finally, for the proposed MSRF-FLC based designed SAPF, the profiles of ic generated, is(after compensation) and corresponding FFT
analysis are portrayed in Figures 14A-C, respectively. Using the proposed approach, is is found to be more sinusoidal in
nature than other two approaches. The THD content reduce to 1.82% for inductive and 1.75% for capacitive load (see
Table 6).
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FIGURE 14
Profile obtained pertaining to Scenario 4 under nonideal source condition considering inductive and capacitive load of (A) ic
employing proposed MSRF-FLC approach based SAPF model, (B) is after compensation, and (C) harmonics content after compensation
With SAPF
Nonlinear load type
Without SAPF
SRF-PI
MSRF-PI
MSRF-FLC
Inductive
28.23%
3.85%
2.68%
1.82%
Capacitive
33.68%
3.38%
2.15%
1.75%
T A B L E 6 THD comparison of
source current under nonideal source
conditions
The bold values are the results obtain by the proposed method in order to highlight the result it is provided
in bold.
4.5 | Performance analysis pertaining to scenario 5
In this scenario, under varying load condition, the performance of the proposed MSRF-FLC approach based SAPF is
investigated with respect to regulation DC-link capacitor voltage. The results yielded (in terms of undershoot, overshoot
and settling time) by it is compared to that of other studied conventional techniques at varying load condition. For this
scenario, profiles of is, ic, and VDC are obtained (see Figure 15) considering sudden load change from capacitive to
inductive at time t = 0.2 seconds. It is revealed from Figure 15A that very high undershoot in the profile of ic and large
overshoot and settling time in the profile of VDC are observed in case of SRF-PI controller based approach. Additionally,
it is clear that after load change from capacitive to inductive, the response time of the mitigated source current is very
high of 0.1 seconds. On the other hand, in case of MSRF-PI controller based strategy, still there is noticeable increment
to the magnitude of mitigated source current, but there is improvement in the profile of VDC (see Figure 15B. However,
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F I G U R E 1 5 Profiles obtained pertaining to Scenario 5 under dynamic load condition (from capacitive load to inductive load) of phase
A source current isa, phase A compensating current ica and VDC obtained employing (A) SRF-PI controller based SAPF model, (B) MSRF-PI
controller based SAPF model, and (C) the proposed MSRF-FLC approach based SAPF model
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F I G U R E 1 6 Pertaining to scenario
5, comparative profile of DC-link capacitor
voltage obtained under dynamic condition
using conventional techniques and the
proposed MSRF-FLC approach based
designed SAPF
Performance under different controller
Parameters
SRF-PI
MSRF-PI
MSRF-FLC
Voltage deviation (V)
30
18
5
Settling time (s)
0.10
0.06
0.04
T A B L E 7 Voltage regulations with
settling time reduction under dynamic
(load change from capacitive to
inductive) condition
The bold values are the results obtain by the proposed method in order to highlight the result it is provided
in bold.
it is able to complete its mitigation process in 0.06 seconds in comparison to earlier counterpart. Whereas, the proposed
MSRF-FLC approach based designed SAPF offers the lowest undershoot, fastest response time, and has significantly
improved the mitigation performance of SAPF in comparison to other two approaches. Based on Figure 15C, it is clear
that after sudden load change from capacitive to inductive at time t = 0.2 seconds, the mitigated source current is
observed to smoothly reach its required steady state in 0.04 seconds. For better understanding of the results obtained, a
comparative study of DC-link capacitor voltage regulation using studied SAPF models is portrayed in Figure 16. First,
the model is simulated with capacitive load and steady state position is achieved. The findings from Figure 16 show that
the VDC is stable before t = 0.2 seconds with capacitive load. When the load is altered from capacitive to inductive at
t = 0.2 seconds, VDC is deviated from its reference value of 700 V. Responses in terms of deviation in VDC with respect
to VDC, ref together with the settling time are summarized in Table 7. It is revealed from the Table 7 that the conventional SRF-PI controller approach performs poorly with a voltage deviation of 30 V and high settling time response of
0.1 seconds. In case of MSRF-PI controller strategy, the voltage deviation reduces to 18 V and settling time reduces to
0.06 seconds. However, in comparison to other approaches, the proposed MSRF-FLC approach offers superior performance with the lowest voltage deviation of 5 V and the fastest settling time of response of 0.04 seconds. Based on all the
results obtained from simulation works, it is shown that the proposed approach confirms that the source current is
almost sinusoidal after compensation and the settling time of the deviation in capacitor voltage is very less following
load change.
5 | C ON C L US I ON
The study carried reveals the SAPF designed based MSRF techniques for reference current generation in conjunction
with FLC approach for DC-link voltage control may render enough scope in improving the PQ problem of a standalone
MG system feeding to nonlinear load. The performance of the proposed approach using MSRF-FLC based realized
SAPF (to mitigate the THD content of the source current, regulate the DC-link capacitor voltage and to reduce its settling time under steady state and dynamic condition) is compared to that of SAPF designed based on reported strategies
such as SRF-PI controller and MSRF-PI controller approaches. Simulation results illustrates that the proposed MSRFFLC approach based designed SAPF provides superior and faster compensation due to its adaptive nature. The THD of
the source current is reduced to 1.20% and 1.15% under ideal source voltage for inductive and capacitive load, respectively. While, it is 1.82% and 1.75% under nonideal source voltage for inductive and capacitive load, respectively. The
proposed technique also performs outstandingly in curbing the deviation in DC-link capacitor voltage and reduction of
its settling time in comparison to other counterparts. The deviation and the settling time in the profile of DC-link capacitor voltage are found to be minimum under the proposed approach. Summarizing, it may be said that the use of the
proposed SAPF model in MG offers a benefit that it can reimburse all the PQ problems due to the presence of nonlinear
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load under ideal/nonideal source condition considering steady state and dynamic condition. Experimental validation of
the simulation based obtained results will be taken up as a future scope of work.
ORCID
Prasanta K. Barik
https://orcid.org/0000-0002-1640-4523
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How to cite this article: Barik PK, Shankar G, Sahoo PK. Power quality assessment of microgrid using fuzzy
controller aided modified SRF based designed SAPF. Int Trans Electr Energ Syst. 2019;e12289. https://doi.org/10.
1002/2050-7038.12289