Single Phase VSI Behavior Improvement using Combined Feedback
and Feedforward Controllers
MOHAMMAD A. OBEIDAT
Department of Electrical Power and Mechatronics Engineering, College of Engineering,
Tafila Technical University,
Tafila 66110, JORDAN
MUSTAFA ALZGHOUL
Jordan Customs, Engineering Department,
Amman, JORDAN
KHALED A. MAHAFZAH
Electrical Engineering Department, College of Engineering,
Al-Ahliyya Amman University,
Amman 19328, JORDAN
HESHAM AL SALEM
Department of Mechanical Engineering, College of Engineering,
Tafila Technical University,
Tafila, 66110, JORDAN
Abstract: - Nowadays, the demand for power electronics technology has increased due to the importance of its
applications such as power inverters. The power inverter is required to modify the DC power from PV cells to
AC power. One of the most common issues of on-grid PV systems is the high variations of the generated DC
voltage. This will affect the stability of the generated AC voltage at the Point of Common Coupling (PCC) with
the grid. This paper combines the Feed-Forward and Feedback (FFFB) controller in a novel way to reduce the
variation of the PV cells DC voltage. This paper presents both mathematical and Simulink models of single-
phase voltage source inverters VSI. Then, a case study of 15% disturbance of DC-generated voltage is
considered. The static and dynamic behaviour of the single-phase H-bridge inverter is analysed under different
loads. The new combination is used to reduce the effect of the disturbance on the performance of the system.
Also, the proposed closed-loop controller (FFFB) can reduce the overshoot by 50% less than the feedback
controller only. The settling time has been improved by 41%, 61% for RL and induction motor.
Key-Words: - Voltage Source Inverter, Feedback control, Feed-forward control, Combined Controller,
Disturbance rejection.
Received: March 16, 2022. Revised: November 7, 2022. Accepted: December 8, 2022. Published: December 31, 2022.
1 Introduction
Power electronics transform electric power from
one form to another with different features.
Around 70% of electricity in the US is now
running by power electronics, which will gradually
increase to 100 percent, [1]. Smart Grids (SG)
provides more adaptable, stable, and sustainable
power systems. It integrates many types of power
sources effectively, [2]. Solar energy is typically
extracted from a Photovoltaic (PV) cell that
converts solar irradiance into Direct Current (DC),
where an inverter is required to modify the
generated DC power from the PV cell to
Alternating Current (AC) electricity, [3].
The inverter forms aback-bone of diving
systems, integration of PVs with electrical grids.
The inverter comprises a DC voltage source, DC
link capacitor, two switching devices (half bridge
invert-er), four switching devices (H-bridge
inverter), or six switching devices (three-phase
inverter). Additionally, it has freewheeling diodes
to guarantee a bidirectional current flow, [4]. Load
variations during the operation of the inverter is
one crucial issue since it causes a voltage
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fluctuation. This affects the power quality of the
supplied power and increases the output current
ripple, [5]. Hence, it reduces the inverter’s
efficiency, [6], [7].
Regarding voltage fluctuations, more
attention has been paid in literature. In [8], the
authors introduced the voltage fluctuation issue at
the output of a single-phase inverter due to the
voltage disturbances of the coupling capacitor. The
researchers showed that the fluctuation of the DC
link voltage directly affected the input current,
thus, the maximum power tracking. The control
strategy was compensating the voltage and the
current of the capacitor bus using two Proportional
Integral (PI) controllers. To verify their results, a
3-kW prototype was investigated to realize the
ability of the control technique. In [9] the
researchers proposed the double closed loop
control based on ADRC to reduce the excessive
voltage disturbances, and low harmonics of
voltage source inverter. The adopted approach was
compared to the conventional use of PID control
method, and the results showed that the proposed
method provided better performance compared to
PID, and accordingly the authors recommended its
use in grid connected application. In [10], the
authors reviewed two strategies to regulate the
output voltage of the grid connected inverters.
Power curtailment and reactive power
compensation were introduced to control the
inverter voltage under high PV penetration.
Many of the voltage quality were reviewed
such as voltage rise, voltage harmonics, DC
injection, voltage dips and voltage unbalance. In
[11], the authors replaced the use of filters by
current control strategies to minimize the
harmonics and to regulate the voltage of single-
phase grid connected inverters. Current Hysteresis
Control (CHC), Voltage Oriented Control (VOC)
and Proportional Resonant based (PR-based)
control were conducted and compared. The
obtained results showed that VOC and PR-based
provided the better performance in terms of volt-
age regulation, dynamic response, and harmonics
distortion minimization. In [12], the
optimized feed-forward controller of DC-DC
converter is used to achieve almost zero DC audio
susceptibility. The proposed method was presented
based on the non-optimal operation between the
input-output voltages of the DC converters. In
[13], the authors proposed a state feedback current
controller depending on the Equivalent Input
Disturbance (EID) to adjust the current of the grid
tied inverter and to achieve the maxi-mum power
point tracking. The results confirmed the
excellence of the adopted approach. In [14], an
adaptive feed-forward control strategy is applied
to solve the jumping disturbance issue at the input
voltage of the DC-DC boost converter. The
adopted approach combined feedback and adaptive
feed-forward control techniques. The obtained
results showed the effective performance of the
explored approach. In [15], the researchers
proposed the feed-forward/feedback technique to
tune the classical pole placement controller for the
single Input Single Output (SISO) system. The
control strategy was tested on both mathematical
and physical models of the plant. The results
recommended that the adopted approach achieved
excellent responses with zero steady state error
under the load variation. In [16], the author
proposed the feed-forward/feedback control
strategy depending on the Deep Q-learning
Network (DQN) for liquid level regulation under
various disturbances. The adopted approach was
compared with the conventional PID feedback
system. The obtained results showed the
supremacy of the proposed strategy.
In [17], the authors introduced a dual control
method to regulate the voltage of multi-micro grid
inverters. The adopted approach utilized the feed-
forward/feedback control structure to enhance the
transient response, to reduce the steady state error
and to optimize the performance of the controller.
The feedback system was converted into an
optimization problem with linear objective
functions. The experimental results proved the
effective performance of the proposed approach in
terms of voltage regulation, harmonics rejection,
and fault condition operation.
The importance of this paper relies on
developing a new merged control method based on
feedback and a feed-forward controller for input
disturbance disposal of a single-phase voltage
source inverter (VSI-H bridge). The mathematical
model of the VSI-H-bridge has been built. Then,
the DC disturbance mathematical model has been
established in the case of static and dynamic loads.
To show the effectiveness of the proposed new
control method, its results are compared with the
DC input voltage of the VSI-H bridge when using
a conventional PID with feedback. The results and
discussion show the superior of the new control
method.
This paper is organized as follows: section 1
introduces the literature review. The mathematical
model of single phase VSI is presented in section
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2. Section 3 proposes the FFFB system of single
phase VSI under different loads. The simulation
results and discussion are presented in section 4.
Finally, the paper is concluded in section 5.
2 VSI-H Bridge Inverter
Mathematical Modelling
In this section, the VSI-H bridge inverter design
will be illustrated along with control structures of
feedback and feed-forward/feedback control
systems. The inverter filter circuit will be
explained as well.
2.1 VSI-H Bridge Implementation
The VSI-H bridge as shown in Figure 1 comprises
two arms, each with two switching devices and
antiparallel freewheeling diodes for discharging
the inverse current. The inverse load current flows
through these diodes in the case of dynamic load.
These diodes offer an alternative direction for
inductive current, which continues to flow even
though the switch is turned off.
Fig. 1: VSI-H bridge inverter.
T1, T2, T3, and T4 are switching devices. The
switches in each branch are switched alternately
such that they are not in the same state (ON / OFF)
at the same time. In operation, they are both turned
off for a brief amount of time known as blanking
time (dead time) to prevent cross-through of the
operation. To obtain the output, the switches T1
and T2 or T3 and T4 must be operated
simultaneously. Table 1 showed the switching
state of the half-bridge inverter.
Table 1. Full bridge inverter switching states
T1
T2
T3
T4
Vo
ON
ON
OFF
OFF
+Vdc
OFF
OFF
ON
ON
-Vdc
ON
OFF
ON
OFF
Zero
OFF
ON
OFF
ON
Zero
The PWM VSIs are the most appropriate ones
in the industry. It is used to retain the inverter's
output voltage at the rated voltage independent of
the output load. PWM is a technique that generates
constant amplitude pulses by altering the pulse
duration by controlling the duty cycle. Analog
PWM control necessitates the generation of both
fundamental and carrier signals, which are fed into
the comparator and the final output is generated
based on some logical output. The fundamental
signal is the target signal source, which may be a
sinusoidal or square wave, while the carrier signal
is either a saw-tooth or triangular wave of a much
higher frequency than the fundamental signal,
[23], [24], [25], [26].
To reduce harmonics produced by the pulsating
modulation waveform, a low pass LC filter is
necessary at the VSI-H bridge output terminal.
The cut-off frequency of an LC filter is selected so
that the majority of the low order harmonics are
omitted. To operate as an ideal voltage source with
no additional voltage distortion under load
variations or nonlinear loads, the inverter's output
impedance must be held at zero. Therefore, the
capacitance and the inductance of the selected
filter should be maximized and minimized
respectively, [18], [19], [20], [21], [22]. See Figure
2.
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Fig. 2: VSI-H bridge with resistive load.
2.2 VSI-H Bridge State Space
Implementation
The full bridge single phase inverter with resistive
load will be modelled by deriving the operation
states equations as follow the state space
representation for state (1) will be:
(1)
(2)
(3)
(4)
The state space representation for state (1) will be:
(5)
Where
(6)
(7)
For State (2): at the negative half cycle, T2 and T4
are ON, applying KVL, then:
(8)
(9)
(10)
(11)
(12)
The state space representation for state (2) will be:
(13)
Where
(14)
State space averaging technique is used to
combine both of the two operation states in one
state space representation as follows:
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The averaging state space for resistive load will
be:
(15)
Then, the VSI-H bridge inverter is loaded with
resistive - inductive load. This load change is
modeled by deriving the operation states equations
as follows:
For State (1): at the positive half cycle, T1 and T3
are ON, and by applying KVL, then:
(16)
(17)
(18)
(19)
(20)
(21)
The state space representation for state (1) will be:
(22)
Where
(23)
For State (2), at the negative half cycle, T2 and T4
are ON, by applying KVL, then:
(24)
(25)
(26)
(27)
(28)
(29)
The state space representation for state (2) will be:
(30)
Where
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State space averaging technique is used to
combine both two operation states in one state
space representation as follows:
Averaging the state space for Ohmic -
inductive load will be:
(31)
2.3 Feedback Control Structure
When the inverter output reaches the load voltage,
the output voltage on the load side is sensed by the
voltage sensor and fed back to a subtractor which
compares the load output to the reference signal
(desired signal) and generates the voltage error
signal. A proportional-integral (PI) controller
receives this instantaneous error. The integral term
in the PI controller enhances tracking by
decreasing the instantaneous difference between
the reference and the actual voltage. The error is
forced to stay within the range specified by the
triangular waveform's amplitude (modulation
index). The controller signal will calculate the
proper magnitude of the sine wave to be compared
with a triangular carrier signal and the
intersections will decide the switching frequency
and pulse width, [20]. See Figure 3.
Fig. 3: Feedback control system of VSI-H bridge
inverter.
Fig. 4: Feedforward/Feedback control system
of VSI.
2.4 Feed-forward/Feedback Control
Structure
The feed forward control responds to change in
command or measured disturbances in a pre-
defined way. Based on the prediction ability of the
plant behavior, it can react be-fore error takes
place. On the other hand, the system response
must be predictable to implement the feed forward
structure. Moreover, it may not generalize to other
conditions and will not be accurate if the system
changes. Combining feed-forward with feedback
control system is often used to provide the
optimum response behavior of the plant due to
merged advantages
of both control structures, [16]. In this paper, the
combined control system is utilized to reject the
DC input disturbance of VSI-H bridge and keep a
stable voltage waveform at its terminal under load
variations as shown in Figure 4.
3 The Proposed Feedforward /
Feedback Control Implementation
There are many control systems for a single-phase
voltage inverter to enable it to drive the required
loads as efficiently as possible. However, due to
the possibility of disturbances at more than one
side of these systems, there is a need to merge two
control systems. In the presented paper, the Feed-
forward/Feedback (FF/FB) control system is pro-
posed to control the generated output voltage and
to reject the DC link voltage disturbance under
various loads. This section illustrates the detailed
model of VSI and the proposed control approach
under disturbance - load variation.
3.1 Model Parameters
The feedback control structure is applied on the
VSI-H bridge based on the parameter listed in
Tables 2-7. Figure 6 illustrates the full details of
the Simulink model. The inverter block is a H-
bridge circuit with IGBT/diode as power switches.
The controller tracks only the reference voltage
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and is totally ignored to measure the DC link
voltage disturbances. The model shows the
Sinusoidal Pulse Width Modulation (SPWM)
pulses generation and the low pass LC filter.
Then, the implementation of the combined
control systems occurred using the parameter
values in Tables 2 to 7. As shown in Figure 6, the
static Feedforward control is used to reject the DC
link disturbances and along with the feedback
controller (PID), the output voltage is kept
constant under load fluctuations. On the other
hand, the total modulation index is determined by
two values including the PID controller and the
static gain which provides the better attenuation to
the input disturbances.
Table 2. Inverter bridge design data
Parameter
Value
DC input (Volt)
200
Number of arms
2
Snubber resistance RS (ohm)
1e7
Snubber capacitance CS (F)
Inf
Power electronics device
IGBT with diode
RON (ohm)
1e-3
Fig. 5: Implemented feedback control with VSI-H bridge inverter.
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Fig. 6: Implemented FF/FB control with VSI-H bridge inverter.
Table 3. LC filter design data
Parameter
Value
Inductor (H)
5e-3
Capacitor (F)
50e-6
Table 4. SPWM pulse generation
Signal
Specifications
Fundamental wave
Sine wave
50 HZ
Table 5. Feedback system design data
Parameter
Value
Reference voltage (rms)
100 V
Proportional controller
1e-5
Integral controller
0.28
Derivative controller
1e-5
PID structure
Parallel
Output limitation
0.2 – 1
Table 6. Feedforward/Feedback controller data
Parameter
Value
Reference voltage (rms)
100 V
Proportional controller
1e-5
Integral controller
0.28
Derivative controller
1e-5
PID structure
Parallel
Output limitation
0.2 – 1
Static gain
0.001667
Carrier Wave
Zero phase shift
Triangle wave
5000 HZ
90o phase shift
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Table 7. Variable load data
A full comparison will be made on both control
systems (feedback and combined one) to
investigate the inverter behavior. 15% of DC link
disturbances as shown in Figure 7. For each case
the load will be changed three times to engage the
inverter with static load (Ohmic, Ohmic-inductive)
or dynamic load such as induction motor.
Fig. 7: DC link voltage with 15% disturbance
3.2 The Proposed Control Process
The combined control structure is used to reject
the DC link fluctuations and to regulate the
generated voltage of the VSI-H bridge inverter
model in Figures 6 and 7. The proposed control
strategy estimated the required modulation index
to generate the proper SPWM pulses to the
inverter bridge switching devices. The merged
control criteria utilized the closed loop of classical
PID controller, which uses a three mathematical
operation to the produced error signal in order to
apply accurate and optimal control of VSI-H
bridge. Moreover, it applied the static feed-
forward controller with the existing PID
manipulator in order to improve the ability of the
DC disturbance rejection. The control process can
be explained as follows:
The feedback controller (PID) will
regulate the generated output voltage by
measuring it and feeding it back to the
error detector, which estimates the error
between the reference and the produced
voltages.
The PID will produce a proper modulation
index in order to generate the switching
pulses.
The static feed-forward controller will
modify the modulation index value
according to the DC link Disturbance.
The modulation index value will be
limited at the boundary of (0.2 - 1) using
the saturation block, this step will ensure
the linear behavior of the proposed
controller.
The modulation index value will specify
the fundamental wave magnitude to be
compared with the carrier signal and thus
the generation of SPWM pulses.
The generated pulses will be distributed on
the four-switching device of the inverter
bridge.
The low pass LC circuit will filter the
bridge output voltage before applying it to
the load.
Different load types were connected to the
VSI output terminal to investigate its
response.
The same power system was controlled by
only a feedback controller to com-pare its
results with the proposed approach.
The proposed control method can be summarized
by the flow chart, illustrated in Figure 8.
Load
Specifications
Resistor
10 ohm.
Inductor
10e-3 H.
Single phase
induction
motor
Nominal voltage (rms) = 100 V.
Capacitive Start.
Nominal power = 186.5 VA.
Frequency = 50 HZ.
Torque = 1 p.u.
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start
Set Vref, static gain,
fundamental frequency, carrier
frequency, filter inductor, filter
capacitor, load type and DC
disturbance value.
Measured the output volatge
Calculate the Error
Perform PID on the Error to
estimate (mi)
DC link
Disturbance
Static Feed-forward
controller
+/-
SPWM pulses generation
mi
Inverter bridge switches
Low pass LC filter
Stable output voltage
End
Fig. 8: Control process flow chart
4 Results and Discussion
Tables 8, 9, and 10 display the results for the
system under different loads, R, RL, and induction
motor. The results compare between using a
feedback controller only and the proposed FFFB
controller under disturbance. It can be seen that the
merged control approach FFFB scores better
performance than the feedback control in terms of
overshoot, minimum settling, maximum settling,
and peak values. However, it records close results
to the feedback system in terms of rise and settling
times. It can be shown that the proposed approach
can handle disturbance rising and provide a more
efficient response compared to the feedback
system.
Table 8. Step responses of both control systems
with ohmic load under 15% disturbances
Ohmic load results under 15% disturbance
Parameter
Feed back
Feed forward +
Feedback
Rise time (sec)
0.000361
0.000545
settling time
(sec)
0.103576
0.103807
Settling Min
(volt)
99.457572
99.749542
Settling Max
(volt)
112.447286
105.619826
Over shoot
12.447286
5.619826
Peak (volt)
112.447286
105.619826
Peak time (sec)
0.021750
0.021712
Table 9. Step responses of both control systems
with RL load under 15% disturbances
Resistive - inductive load results under 15%
disturbance
Parameter
Feed back
Feed forward +
Feedback
Rise time (sec)
0.000376
0.000554
settling time
(sec)
0.176280
0.103146
Settling Min
(volt)
99.592600
99.817048
Settling Max
(volt)
112.523055
105.925001
Over shoot
12.523055
5.925001
Peak (volt)
112.523055
105.925001
Peak time (sec)
0.021550
0.021550
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Table 10. Step responses of both control systems
with induction motor load under 15% disturbances
Induction motor results under 15% disturbance
Parameter
Feed back
Feed forward +
Feedback
Rise time (sec)
0.004629
0.001873
settling time
(sec)
0.200000
0.200000
Settling Min
(volt)
99.779150
99.955386
Settling Max
(volt)
100.350549
100.314212
Over shoot
12.965064
6.546617
Peak (volt)
112.965064
106.546617
Peak time (sec)
0.020750
0.020750
Fig. 9: Output RMS voltages of the conducted
control systems under ohmic load
Fig. 10: Modulation indices responses of the
conducted control systems under ohmic load
Fig. 11: Inverter RMS voltages of ohmic load
under 15% disturbance.
Fig. 12: Inverter RMS voltage errors of ohmic
load under 15% disturbance.
Fig. 13: Modulation index responses with ohmic
load under 15% disturbance
The effectiveness of the proposed controller FFFB
is shown for ohmic load only, the other loads RL,
and the induction motor proves the same effective
results. Figures 9 and 10 show the simulation
results for RMS output voltages and the
modulation index of VSI fed different loads using
three different control types, the Open Loop (OL),
the feedback (FB) and the proposed FFFB systems
under disturbance of 15% of DC link value. It is
notable that the open loop control is the fastest one
with respect to rise and settling times, but it
provides the worst response under disturbance. It
can be seen that the remaining approaches
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overcome the disturbance, but the merged system
FFFB leads to more stable RMS voltages.
Fig. 14: Speed responses under full load with 15%
disturbance.
Fig. 15: RMS inverter voltages at 15% disturbance
for different loads
Figures 11 to 13 show the simulation results for
RMS output voltage, error, and the modulation
index of closed loop control system using ohmic
load only. It is notable that the proposed system
FFFB provides minimum oscillation and overshoot
and thus more stable voltage compared to the FB
controller. The increment of disturbance can be
handled as well with the superior proposed FFFB
approach. For more convenience, a dynamic
response for the proposed system is simulated.
Figure 14 illustrates the speed response of
dynamic rated load. It can be seen that applying
more disturbance increases the motor speed.
Moreover, the superior performance of the
proposed approach is proved in stabilizing the
motor speed under rated load conditions. Figure 15
shows the performances of both control systems
under variable loads as well as disturbance
conditions. The proposed FFFB system shows the
best performance in disturbance rejection
regarding the load type and the fluctuation level.
On the other hand, the overshoot values of voltage
vary from one load type to another. It is notable
that it is high in case of induction motor, and it is
low in case of ohmic load.
5 Conclusion
In this paper, a new combined feedback/feed-
forward FFFB controller for single-phase VSI is
proposed under different loads and disturbance
conditions. The mathematical and MATLAB
models of the system are presented. The response
and behaviour of the system under sudden change
of DC link voltage of 15% are studied. Different
scenarios are presented to prove the effectiveness
of the proposed FFFB to enhance system stability
and performance parameters such as overshoot,
settling time, and rising time. The performance of
the combined control system FFFB is assessed and
compared with the other two control strategies, the
open-loop, and the closed-loop feedback control
systems. The proposed FFFB system enhances the
behaviour and the performance parameters
compared to other controllers. The proposed
closed-loop controller (FFFB) can reduce the
overshoot by 50% less than the feedback controller
only. Also, the settling time has been improved by
41%, and 61% for RL and induction motors,
respectively.
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Mohammad A. Obeidat, Mustafa Alzghoul,
Khaled A. Mahafzah, Hesham Al Salem
E-ISSN: 2224-2856
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
“All authors contributed to the study conception
and design. Material preparation, data collection
by Mustafa Alzghoul, analysis of the results was
performed by Mohammad Obeidat, Khaled
Mahafzah, Mustafa Alzghoul, and Hesham Al
Salem. The first draft of the manuscript was
written by Mustafa Alzghoul, then it was reviewed
by Mohammad Obeidat, Khaled Mahafzah and
Hesham Al Salem. All authors commented on
previous versions of the manuscript. All authors
read and approved the final manuscript”.
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This article is published under the terms of the
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WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2022.17.61
Mohammad A. Obeidat, Mustafa Alzghoul,
Khaled A. Mahafzah, Hesham Al Salem
E-ISSN: 2224-2856
570
Volume 17, 2022
