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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 11 Issue: 09 | Sep 2024 www.irjet.net p-ISSN: 2395-0072
© 2024, IRJET | Impact Factor value: 8.315 | ISO 9001:2008 Certified Journal | Page 396
Optimal designing and parameter selection of voltage source inverter
for real-time performance analysis in weak grid and standalone mode
Harendra Pal Singh1*, Anurag K. Swami1
1Department of Electrical Engineering
College of Technology, Pantnagar
Uttarakhand, 263145, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - This study aims to enhance inverter stability for
lower-voltage distribution networks by focusing on grid
impedance-based stability. Additionally, it suggests
considering IEEE Standard-519 when selecting the ideal filter
and controller parameters for weak grids. Two techniques are
used to improve inverter stability: (A) altering the grid-side
inductance, and (B) changing the VSI's output impedance. The
goal is to optimize the VSI controller's and filter design's
parameters. To obtain the optimized Current Control Loop
(CCL) parameters to maintain the Total Harmonic Distortion
(THD) level at the Point of Common Coupling (PCC) and
ensure VSI stability during parametric uncertainty, Ziegler-
Nichols (ZN), Particle Swarm Optimization (PSO), and a real-
coded Genetic Algorithm (GA) are utilized. To validate the
effectiveness of the optimized CCL parameters, a real-time
simulator, Typhoon HIL, is used to simulate a VSI-based system
connected to a weak grid and operating in standalone mode.
Various conditions, such as filter inductance variation, grid
Short Circuit Ratio (SCR), output power regulation, and
sudden load changes in a standalone distribution network, are
tested. The VSI-based system's controller model simulation
and parameter optimization are performed using
MATLAB/SIMULINK with m-files. Regardless of whether the
inverter is connected to the grid or not, this paper provides an
extensive review of how to select the optimal inverter
component parameters and their impact under various real-
world conditions
Key Words: Controller stability criterion, Heuristic
optimization technique, Power quality, Total Harmonic
Distortion, Weak grid condition, Impedance-based stability,
Standalone microgrid system.
1.INTRODUCTION
Grid Connected Inverters (GCIs) have become a critical
component of modern power systems, enabling the
integration of various Distributed Energy Resources (DERs)
into the main utility grid. These DERs encompass a range of
capacities, categorized as lower/small level (less than 10
kW), medium level (10 – 1000 kW), and higher level (1 - 10
MW), each with distinct operational requirements [1]. To
ensure the reliable and safe operation of these systems, a set
of international and national standards, including those
governing operational principles, power quality, safety
measures, and responses under abnormal conditions, have
been established, offering valuable guidance for application-
specific practices, as noted by [2],[3]. Across the globe,
widely recognized standards, such as IEEE – 1547 [4], IEC –
61727 [5], IEEE – 929 [6], along with region-specific
standards like VDE-AR-4105 (Germany) [7] and RULE-21
(California, USA) [8], play a pivotal role in governing the
interconnection of DERs with the grid, ensuring a seamless
transition towards cleaner and more sustainable energy
systems.
For systems rated at 69 kV and below, IEEE Std. 519
recommends specific limits to ensure the quality of power at
the PCC. According to [9], it stipulates that the total
harmonic distortion should not exceed 5%, and individual
voltage distortion should be within 3%. Additionally, it
provides guidelines for limiting the current distortion
concerning the short circuit current (Isc) to load current
ratio (IL), emphasizing the attenuation of higher-order
harmonic components. To gauge the strength of the grid
connection, [10] points out that the percentage of current
ripples in the inverter output current is a crucial indicator.
For weaker grid connections, the standard allows for 0.3%
current ripples, while in the case of stronger grid
connections, this tolerance can be higher. This approach
defines the smoothness of the output current, ensuring
compliance with the specified grid connection conditions.
The research work’s primary objective is to thoroughly
investigate the design of a VSI and its impact on operational
performance, particularly under conditions of a weak grid,
while simultaneously upholding established power quality
standards. In order to attain this goal, it is imperative to gain
a comprehensive understanding of how the inverter
functions within a distribution network. A weak grid is more
susceptible to voltage drops, harmonic distortion, and
equipment failures. This is because the higher impedance
can cause the voltage to drop more as the current flows
through the grid. It can also amplify the effects of harmonic
distortion and make it more difficult for equipment to
operate reliably. Also, weak grids can undermine
sustainability by increasing energy losses, reducing
reliability, increasing the cost of electricity, and limiting the
integration of renewable energy.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
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The stability of grid-connected inverters can be
comprehensively assessed by examining their response to
both small and large-scale disturbances within the control
signal, as discussed in [11][12]. The small-scale disturbances
may not significantly disrupt VSI synchronization with the
grid but can manifest their effects during grid feeding,
potentially leading to the generation of harmonics and
voltage instability at the PCC [13]. To evaluate instability
arising from small signals, two distinct methods have been
proposed: one based on eigenvalues and the other based on
impedance. Furthermore, in such operating conditions, the
interplay between the Phase Locked Loop (PLL) and CCL can
introduce current distortion, emerging as a key factor in
potential system instability, as outlined by [11]. Effective
damping mechanisms play a pivotal role in preserving system
equilibrium during transient network conditions. This
research, therefore, conducts a comprehensive exploration of
inverter stability issues, particularly when operating in weak
grid scenarios and amidst dynamic conditions.
Traditionally, impedance-based system stability
criteria have solely relied on network impedance, regardless
of variations in the current reference [14]. In reality, the
current reference can also affect the stability of a power
system. For example, if the current is measured at a point on
the grid where the impedance is high, then the system is
more likely to become unstable. Therefore, the impedance-
based stability approaches have been outlined, including (a)
designing control strategies that enhance adaptability to
changes in grid impedance, (b) adjusting the output
impedance of the VSI when it’s connected in parallel with
other devices or passive components, and (c) considering
impedance variations in filter design and VSI control, where
parameters are determined based on grid-side impedance
changes to prevent instability conditions [15], [16]. However,
it’s important to note that in weak grid conditions, the grid
impedance can interact with the CCL, potentially leading to
system instability. This paper explores all three of these
methods in experimental scenarios.
Microgrid management strategies are designed to
attain optimal power scheduling through the implementation
of controller actions. Two distinct approaches have been put
forth: the Rule/Reference-based approach and the Predictive
optimization-based approach. The Tunable- Rule/Reference-
Based-Heuristic (TRBH) approach offers a notable advantage
by inherently furnishing a re-setting strategy. This is achieved
by computing a specific outcome based on a particular
illustration conforming to the optimal tuning dispatch rule.
Consequently, predictive optimization is not recommended
as the primary controlling method [17].
1.2 Literature Review
In grid-connected mode, the grid is the dominant factor,
connected to the main grid, the main grid is the primary
source of power and control, and it is typically expected to
be in a stable and reliable state. However, when confronted
with weak grid scenarios, the primary focus shifts toward
evaluating the controller’s performance and its adaptability
to impedance variations. For lower and medium-level VSIs,
improvements in the inverter switch control, combined with
well-designed filters, have proven advantageous in
enhancing the quality of the output current, discussed in [18]
and [19]. Nevertheless, these enhancements may impact the
control bandwidth and the variation in grid-side impedance.
To achieve better performance and power supply quality, it
is imperative for the current control loop to exhibit higher
control band- width and swift dynamic response. Prior
studies [20],[21], underscore the importance of judiciously
selecting controller gain values based on filter design and
power-sharing criteria, necessitating precise specification of
the control range. Controller parameters must be
meticulously designed to minimize errors resulting from
anticipated input values. However, the core concept of
current regulation entails comparing reference and
measured output current values, enabling error utilization to
modulate power electronic converters’ switching for the
attainment of desired output [22].
Throughout history, various methods have emerged to
efficiently tune PID/PI controllers, particularly for systems
with complex, inverse responses. These methods, like
Ziegler-Nichols (1942) [23], Cohen-Coon (1953), and
Tyreus-Luyben (1997), rely on inherent process
characteristics and involve oscillatory approaches. While
established, these methods are known for being time-
consuming and imprecise due to their reliance on trial-and-
error. In contrast, the Internal Model Control (IMC) method,
introduced by Rivera (1986) [24], utilizes a fitness function
to determine optimal controller parameters directly, offering
a more efficient and accurate solution.
Within the realm of computational intelligence
algorithms, including Artificial Neural Networks (ANN),
Genetic Algorithms (GA), Particle Swarm Optimization (PSO),
Predictive Model Control (MPC), and others, these
techniques offer promising solutions for accurately
determining controller gain values [25],[26]. PSO, in
particular, has gained widespread acceptance owing to its
simplicity, computational efficiency, and robustness, as it
was originally introduced by Kennedy and Eberhart in 1995
[27], [28]. Over time, through a trial-and-error procedure,
various algorithm parameters have been refined for ease of
implementation across diverse applications, as seen in
Eberhart, Simpson, and Dobbins (1996). The PSO algorithm
can accommodate different fitness functions tailored to
specific objectives. For instance, the Integral of Time
multiplied by Absolute Error (ITAE) performance index
criteria for control system design was introduced by Graham
1.1 Motivation
and it is generally assumed that the operation is stable under
these circumstances. This means that when a microgrid is
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Table -1: COMPARISON OF REAL CODED GA AND PSO
and Lathrop in 1953 [29]. The PSO algorithm’s
implementation shares similarities with Genetic Algorithms
(GA), initializing with a population of random solutions [30].
Table 1 compares real-coded GA and PSO, and shows that
real-coded GA are better suited for implementation in this
case, especially in terms of representation and robustness to
noise. Also, real coded based GA is a better suited for the
problems with real variables. To ensure closed-loop
performance and system stability, the Routh-Hurwitz (R-H)
criteria can be employed to define the boundaries of the
search space based on the closed-loop characteristic
equation [31]. Advanced Digital Signal Processors (DSPs)
play a vital role in reducing control delay time and enhancing
system responsiveness, thus bolstering overall system
reliability. Additionally, Field Programmable Gate Array
(FPGA) circuits and the Space Vector Pulse Width
Modulation (SVPWM) technique prove valuable for
addressing issues like signal delay, dead-time, and mitigating
output current harmonics [32].
Ensuring the stability and reliability of a distribution
network requires the design of a robust VSI, with careful
consideration of critical factors like grid impedance
variations and the maintenance of power quality. However,
in situations where generation systems are situated in
remote areas, the medium-voltage transmission lines may be
extended, resulting in a significant inductive grid impedance
[33]. High grid impedance characterizes what is commonly
referred to as a weak grid. In accordance with IEEE Std.
1204-1997 [34], a grid is typically deemed weak when the
Short Circuit Ratio (SCR) is less than three. Weak grids are
often encountered in remote or rural areas that rely on
lengthy feeder lines for their power supply.
Based on the preceding discussions, we have prepared a
comprehensive comparison, as presented in Table 2. This
table is instrumental in highlighting the unique contributions
of this paper by contrasting it with various prior works from
the literature. It not only aids in gaining a fundamental
comprehension of VSI component design and parameter
selection but also provides practical insights for real-world
validation.
1.3. Contribution
A comprehensive discussion on VSI design and parameter
selection for the lower voltage network level is presented
here. The primary focus revolves around addressing two key
challenges: managing impedance variations at the PCC and
enhancing the tracking performance of the CCL. Regarding
this, the paper shows the validation and main contributions
of this work as follows:
(i). The paper’s primary contribution is an improved
controller for VSIs, enhancing dynamic response in low
voltage networks, especially during transients. It emphasizes
the need for controller stability to prevent instability in weak
grid conditions. The paper also introduces a method to select
VSI filter parameters, aiming to minimize stored energy in
components while improving THD levels at the PCC.
(ii). The paper examines the robustness of the proposed
single loop controller in regulating the VSI's behavior under
diverse operational conditions.
(iii). Through simulations on a real-time simulator, Typhoon
HIL, the study validates the effectiveness of optimized CCL
parameters. These parameters are assessed under varying
conditions such as changes in grid-side inductance, grid SCR,
and abrupt load changes, both in a VSI-based system
connected to a weak grid and in a standalone distributed
network. This analysis serves to confirm the controller’s
Factors
Real-coded GA
PSO
Representation
Chromosomes (strings of genes)
Particles (position and velocity)
Search mechanism
Particles (position and velocity)
Velocity and position updates based on
individual and social learning
Strengths
Global search, good at finding diverse solutions
Fast convergence, efficient for problems
with continuous decision variables
Weaknesses
Can be slow to converge, prone to getting stuck
in local optima
Can be sensitive to parameter settings
Robustness to noise
More robustness to noise than PSO
Less robust to noise than GA
Data types
Can be binary, integer, or real
Can be binary, integer, or real
Ability to solve multi-objective
problems
Can solve multi-objective problems
Typically only used to solve single-
objective problems
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tracking performance in real-time scenarios, ensuring its
reliability and adaptability across different conditions.
(iv). The two methods are employed to enhance inverter
stability: (a) changing the output impedance of the VSI by
adjusting the grid-side inductance, and (b) optimizing the
parameters for filter design and VSI controller.
The paper additionally introduces the
implementation of a Proportional-Resonant (PR) con- troller
in the proposed VSI approach. This addition aims to enhance
harmonic attenuation at the PCC, particularly in the presence
of weak grid conditions, with the ultimate goal of improving
the THD level.
The paper presents a comprehensive analysis of
plant model-based tuning rules and outlines various factors
to consider for optimizing the current controller gain values
of VSI to address varying production rates and different grid
scenarios. This flexibility enables the controller to be fine-
tuned to specific operating conditions, thereby enhancing its
overall performance and adaptability in practical scenarios.
This paper is described in the following sections: Section 2
details the system description, Section 3 describes filter
designing and parameters selection, Section 4 elaborates
controller modeling; PSO algorithm and real coded based GA
implementation, and sensitivity/fitness function, Section 5
gives results and discussion of the different scenario analysis,
and Section 6 concludes the work done in the paper.
TABLE – 2:
COMPARATIVE ANALYSIS ACROSS VARIOUS REFERENCE SOURCES IN THE LITERATURE.
2. SYSTEM DESCRIPTION
Fig -1: VSI System in GFL mode
In a grid-feeding mode, a VSI-based system functions as a
controlled current source, as shown in Fig. 1, and plays a vital
role in meeting power supply and demand requirements
[18],[20]. Moreover, the grid-feeding (GFL) VSI-based system
injects output current while closely tracking the PCC voltage.
It also offers higher impedance to grid disturbances and
noise, contributing to the overall enhancement of power
quality within the system. Voltage-oriented control is the
common choice in VSI-based systems for synchronization and
control purposes [40]. Notably, power to the grid can be
effectively regulated by controlling the output current of the
VSI-based system, especially when the grid voltage remains
relatively constant. Fig. 2 illustrates a grid-connected VSI with
an LCL filter, taking 3-ϕ output voltage and current as inputs
for the controllers. The switching signals for the VSI are
generated using the SVPWM scheme.
Fig -2: Schematic diagram of grid connected VSI with LCL
filter
The objective of the controller is to adequately control the
output current of the VSI by following the active power
command given by the operator. As the controller follows the
grid voltage and injects the current to the PCC, hence, power
quality issues present in the PCC voltage worsen the power
Items
References
This paper
Standards and regulations
[1],[2],[3],[4],[9],[10][34]
✓
Different modeling methods
[18],[20],[35]
SRF and SF
Filter designing
[10],[36],[37],[38],[39]
with minimum energy storage
Different control techniques
[21],[22],[17],[40].[41]
VOC with PI and PR controllers
Controller tuning techniques
[23],[24]
ZN, PSO and GA implementation
Optimization techniques
[25],[26],[27], [28],[29],[30]
heuristic approach
Stability analysis
[31],[12],[42]
in grid following and forming modes
Impedance based stability
[33],[11],[13],[14],[16],
✓
Real-world implementation
[32],[12],
with consideration of different conditions
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quality of the output current of the VSI. However, the output
current’s power quality can also be improved by
appropriately designing the filter components and the control
parameters. Here, the designing purpose parameters
associated with the VSI are to improve the system efficiency
in terms of reliability, resiliency, and redundancy and the
power delivered to the utility with improving the power
quality. The inverter output voltage and current from Fig. 2
can be written as,
(1a)
(1b)
where Vinv{.} , iinv{.} , ig{.} , i{.} , ic{.} and Vg{.}
represents inverter output voltage, inverter output
current,
grid feeding current, inductor current, capacitor current and the
grid voltage of {a, b, c}
phase respectively. The
R = (Rf
+
Rg), and
LT = (Lf +
Lg) where
Rf
, Rg,
Lf
and Lg are the
inverter side and grid side filter resistance and inductance
respectively. Rd is a damping resistor.
The
Cf
is the filter
capacitance and ω is the grid frequency.
3. FILTER DESIGNING AND PARAMETERS
SELECTION
The filter acts as an intermediary between the VSI and
PCC, enhancing the quality of the out- put current in
compliance with IEEE Std.519 guidelines. IEEE Std.519-2022
[43], also concerned for harmonic control in electric power
systems, which was updated from IEEE Std.519-2014 [44] to
include more stringent harmonic limits at the PCC between
the utility and the customer. This is necessary to
accommodate the increasing number of non-linear loads on
the power system, such as variable frequency drives, and
switch-mode power supplies. In grid-connected mode, the
proper selection of the filter and power-sharing parameters
ensures the power quality within the regulated range and
enhances the system performance against the transient
conditions. The percentage of current ripple limits and
harmonic distortions in output current recommendations
are given in Table 3, which helps to design the filter
components for the VSI-based system.
The higher switching frequency operation inverter
applications avoid the use of only inductive components in
the filter for the medium and higher power rating inverters
because of the bigger size requirement which turns into
costly and higher voltage drop across it [36]. Compared to
first and second-order filters, the third-order LCL filter has a
lower cost and is smaller in size which makes it more
suitable for the inverter output connection with the main
utility at medium and higher voltage levels. LCL filter
provides excellent attenuation of bode 60 dB to the
switching frequency Fig. 3. But, in case the grid side
impedance is lower, resonance can be triggered, leading to
system instability [10]. Moreover, this resonance effect can
subsequently cause voltage and current instability in
proximity to the resonance frequency. The purpose of
applying the resistive damper is to reduce the attenuation
and increase the damping (Q - factor) at the characteristic
resonance frequency with the minimum power loss.
TABLE-3: CURRENT HARMONIC LIMITS IN THE
PERCENTAGE OF RATED CURRENT AMPLITUDE
ACCORDING TO IEEE 519.
Fig - 3: L, LC and LCL filter bode plot.
In summary, the design of the LCL filter concerns the
following points;
• Overall filter size, cost, losses
• Current distortion in different components
• Resonance and dynamic performance of the overall system
• Low voltage drops across the filter
• Higher power factor.
The parameter selection, according to the recommended
maximum current distortion limit in the output current set
the percentage of current ripples in the inverter output
current is the primary concern to describe the lower limit of
the filter inductance value. Similarly, the filter capacitance is
chosen based on the energy stored in the capacitor. The
selection for the filter capacitor is a trade-off between the
energy stored in the capacitor and the inverter-side
inductance (Lf )[39]. The higher value capacitance uses more
reactive power to flow into the capacitor and more load
current demand from the Lf and the inverter switches. As a
consequence, the system efficiency will be decreased. The
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filter inductive reactance should be lower than the capacitive
reactance, so the lower the voltage drop across Lf . Generally,
the reactive power for the capacitor is chosen between 5 -
15% of the rated capacity as per the requirement.
(a)
(b)
Fig - 3: (a).Equivalent circuit diagram of LCL filter
connected between VSI and grid, (b). Phasor diagram for
the unity power condition.
The following equations represent the circuit shown in
Figure 4 (a) and (b). These equations will be employed to
compute the transfer function of the LCL filter:
(2a)
(2b)
(2c)
(2d)
where, Vinv is the inverter output 3 − ϕ voltage vector, S
represents the switching space vector, Vdc is the DC - link
voltage, ic is the capacitor current, iinv and ig are the inverter-
side and grid-side currents.
The transfer function of the LCL filter network Gp(s) is
considered as a plant for the controllers and calculated from
the ratio of output grid current ig(s) to the inverter output
voltage Vinv.(s) is represented in (3);
(3)
where, a1 = RdCf , b3 = Lf LgCf , b2 = C[(Lf + Lg)Rd + LgRf + Lf Rg],
b1 = RdRgCf + RdRf Cf + Rf RgCf + Lf + Lg, b0 = Rf + Rg. Here, b3, b2,
b1 are the grid-side inductance dependent coefficients, which
affect the grid connection (stiff/weak grid) requirements.
The resonance frequency of LCL filter is calculated by using
(4);
(4)
Generally, the initial operating conditions of VSI should
be determined before selecting the filter parameters, like
rated power (Prated), rated iinv, output voltage Vinv, inverter
switching frequency, fsw, fundamental frequency, f0. The
steps for choosing the LCL filter parameters are as follows:
Step 1. Determine the maximum value for the inverter-side
inductance, Lf, based on the maximum value of current
ripples in the output current as follows:
(5)
where Vdc is the input DC voltage, that can obtain from
(2√3V(g,rms)/M) here M is the modulation index, D is the
duty cycle, ∆i|max is maximum current ripple, that is
generally set to be 20 - 30%. As given in [10], to calculate
the minimum inductance value based on switching
frequency is given as;
(6)
Step 2. As discussed earlier, determine the filter capacitor
value based on the maximum reactive power stored in the
capacitor as given below;
(7)
where Prated is the VSI power rating, ω0 is fundamental
angular frequency.
Step 3. Based on selection of switching frequency, fsw,
determine the filter cut-off frequency as (1/10th) of (fsw).
Step 4. Determine the minimum inductance value at selected
fsw according to the IEEE std. as defined in table II current
distortion and harmonic limits, as given in (6).
Step 5. The maximum and minimum value of inductance
provides a selection range for the inverter-side and grid-side
inductors to choose the suitable values based on harmonic
attenuation and the inductance ratio aL (i.e., aL =Lf/Lg). The
resonance frequency decreases as the grid-side inductance
increases with respect to the inverter side. The ratio aL = 1,
i.e., Lf = Lg, corresponds to the minimum capacitance
requirement and lower harmonic attenuation [10].
Step 6. The THD level of the output current must be below
5%. If THD is higher than 5% then decrease the attenuation
rate and design the new filter parameters.
Generally, the filter parameters selection includes
filtering and controlling issues, which is a trade-off between
better filter action (minimum current distortion) and fast
dynamic performance. Selected filter parameters are given in
the Table 5. The trade-off is shown in the result, Section
5.1.1, and minimum current distortion, means better
tracking of the reference value.
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Fig - 5: 3ϕ SRF Controller for VSI in GFL mode
4. CONTROLLER MODELLING
In situations where a weak grid connection exists, there is
a risk that the controllers may struggle to accurately follow
the grid’s voltage or angle as a reference, potentially leading
to instability in the system. To mitigate this, it’s essential to
configure the gain values within the CCL according to the
characteristics of the plant model to ensure precise tracking
performance. Consequently, in order to optimize the
performance of Local Control Units (LCUs), it is imperative to
meticulously design and fine-tune the control parameters.
This is especially critical for maintaining system stability
across a wide spectrum of operating conditions, particularly
in low voltage distributed networks [12].
The adaptive control scheme is built upon a cascaded
feed-forward control structure, featuring two control loops,
the inner and outer loops, operating in the Synchronously
Rotating Frame (SRF) and the Stationary Frame (SF). In this
context, the primary focus of controller modeling is on the
inner loop, which is meticulously designed to minimize
settling times during power regulation and to enhance
system dynamic performance. It is important to highlight
that a single-loop control scheme while offering a
compromise between fast control dynamics and stable
steady-state performance, is typically less robust due to its
sensitivity to grid noise (such as harmonics, voltage sags, or
transients) [41]. However, it’s essential to acknowledge the
interdependence between active and reactive powers, and
the existence of filters and source inductance can lead to the
occurrence of a non-unity power factor current. This, in turn,
introduces a cross-coupling term linking the d-axis and q-
(8a)
(8b)
From the above equations, the active and reactive powers
can be calculated as:
(9a)
(9b)
The current injected into the grid is expected to be in
phase with grid voltage which makes the operation at unity
power factor. Therefore, Vq = 0, in eq. (9a) and (9b), we get;
Pi = 1.5 Vdid and Qi = -1.5Vdiq, which provides decoupling for
the better controlling between the active and reactive power
flow to the grid.
4.1 Current Controller Structure
The adaptive current control scheme is deliberately
designed with relatively lower complexity to accommodate
the challenges posed by varying system parameters. In this
axis within the SRF, which can have a detrimental effect on
controller performance and power regulation.
In the context of GCI systems, employing decoupling
techniques is essential for mitigating sensitivity to load
changes, enhancing disturbance rejection capabilities, and
reducing the output current THD, particularly when dealing
with non-linear loads. It’s evident that the controller plays a
pivotal role in shaping the quality of the current supplied to
the primary utility, ensuring a sinusoidal output with
minimal THD.
The most widely used PI and PR controllers are considered
controllers for the inverter output current regulation. The
relationship given for the system in equation 1(a), is
converted into the synchronous frame as;
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approach, the grid-side voltage (Vg) and current (ig)
variables serve as key input parameters for the CCL. The
direct axis current (id) component is computed using the
measured output current, and the necessary phase angle for
this conversion is generated by the PLL. The id component is
then compared with the reference value id* to generate
modulating voltage signals as per equations (10a), (10b).
From Fig. 5, the operation of the current controller in SRF
can be expressed as :
(10a)
(10b)
where KP is the proportional and KI is the integral gain
values of the PI controller.
The PI controller in dq frame exhibits a single pole at zero
frequency, resulting in infinite gain. However, it is incapable
of eliminating steady-state error at the fundamental
frequency. In a positive sequence SRF, the PI controller
behavior is equivalent to the PR controller in SF [21].
Alternatively, the PR controller in αβ frame is advantageous
due to its high gain at the resonant frequency. As per the IMC
principle, it can eliminate the steady state error while
tracking the sinusoidal signal and provides better harmonic
attenuation. The additional damping factor in the ideal
resonant term makes the PR controller more reliable for
practical applications and can be represented as expressed
in (11);
(11)
where ω0 is system fundamental angular frequency, ωc is
cut-off frequency, ξ is damping factor.
To maintain the robustness of the PR controller, the ωc
bandwidth must be close enough to the system frequency. If
the system frequency varies significantly, the ωc can be
adjusted accordingly. Therefore, in comparison to PI
controller, the PR controller has an advantage in closed-loop
performance for frequency variations.
As depicted in Fig. 5, it’s evident that the reference
voltage and current are derived from the PCC. These
reference signals can be distorted due to the weak grid
conditions. This distortion has an impact on the CCL
performance, which needs to be enhanced to improve the
overall performance of the VSI. When using a single-loop
control system in the presence of grid noise, such as
fluctuations or disturbances in the electrical grid, the
stability of the VSI is compromised. Grid noise may introduce
unpredictable variations in the electrical parameters that the
control system relies on, leading to instability in the VSI's
operation. As a result, the effectiveness of the single-loop
control system in regulating the VSI's behavior is limited or
constrained. Determining the appropriate controller gain
values is critical in control system design. It ensures the
system stability while achieving the desired level of tracking
performance and meeting the safety and performance
requirements. The controller tuning purpose is to minimize
the overshoot and time response for transient conditions.
When the parametric uncertainty and performance
specifications are fixed, controller parameters can be
optimized for any possible case.
Problem Formulation
To enhance the stability of a VSI, the controller gain
values, filter parameters, and power- sharing parameters
must be kept within the prescribed limits. The optimization
of controller parameters is synthesized with the offline
procedure, ensuring the operating range of the other
components. The performance index is based on error (e)
minimization and used for further optimization
implementation as given in the following equation;
(12)
s.t., KP max > KP > KP min , KI max > KI > KI min
Where, KP max and KP min are the maximum and minimum
values of the proportional gain and KI max and KI min are the
maximum and minimum values of the integral gain of the PI
controller.
4.2 Fitness Function
The ITAE performance index criteria to design a control
system is derived by using a set of 2nd- order to 8th-order
normalized transfer function coefficients to minimize the
ITAE index criteria for a step signal [29]. Since it can provide
high disturbance rejection capability to the controllers and
minimize the overshoot during transients. This index is also
often used for small data sets or data obtained from the step
response. ITAE performance index trades-off between error
magnitude and settling time [45]. In this paper, the fitness
function for the controller tuning is based on minimizing the
ITAE, which is calculated by using Simpson’s 1/3 rule. The
expression for the ITAE performance index is given by (13);
(13)
where, t is the time and e(t) is the error produced by the
difference between reference and measured value.
4.3 PSO Implementation
PSO is an iterative method that depends on the problem
searching space to determine the optimal solution for the
fitness function shown in Fig. 6. This algorithm is evaluated
based on the movement of each particle and the swarm
experience. Each particle movement is based on its own
experience and collaboration of the swarm. It attracts
towards the best local position (X(p,best)) experienced by its
own and best global position (X(g,best)) by the swarm. The
basic rules of the PSO algorithm can be briefly described in
the following stages; (a). Finding out the fitness value of each
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particle, (b). Updating the best local and global positions, (c).
Updating velocity and best global position.
(14a)
(14b)
where, i represents the index of the particle; Xik and Vik
defined as the position and velocity of the particle i at kth
iteration, respectively; w represents the inertia weight which
can set between [0-1] (a small inertia weight helps in explore
the search space while a large inertia weight facilitates in
exploit the search space), and also provides the balance
between local and global explorations and exploitations
which results in fewer iterations on average to find a
sufficiently optimal solution; c1 and c2 are the acceleration
constants used to guide the particle’s movement to the pbest
and gbest positions; r1 and r2 are the random number variable
between [0-1].
Bounded searching space provides fast solutions, but in
case the optimum global value is located outside of the
boundary conditions, it influences the optimality of the
solution [25]. However, the boundary conditions can be
extended but this would increase the calculation time and
can affect the optimal solution. Therefore, sufficient
information about the system parameters limit is beneficial
to set the boundary conditions for the search.
4.4 GA Implementation
The implementation of GA is the same as the PSO
algorithm and a search mechanism to find out the optimal
solution from the given problems, which is inherently based
on its natural selection. GA provides a solution based on the
chromosomes that can adapt to the change in the
surrounding environmental conditions and are able to
reproduce crossover and mutation. In other words, GA
simulation is based on the “survival of the fittest” among
individual steps of consecutive generations for solving a
problem. So, the solution for each successive generation is
more adaptable for their search space. The simulated binary
crossover (SBX) operator uses a parameter (known as
distribution index, ηc) to maintain the positive integer value
during the overall running time of the simulation. This
parameter has a direct effect on controlling of generation of
offspring solutions [46]. The generation of offspring
and from the parent and is defined as;
(15)
where, βi is called as the spread factor. The probability
distribution index (ηc) plays a crucial role in single-point
crossover (SPX) by influencing the "search power" of the
offspring solution. The probability distribution index allows
to control the “spread”, which affects the diversity of
offspring solutions around the parents. Higher values of ηc
(closer to 20) lead to offspring with values closer to the
parent's average, limiting exploration. Lower values of ηc
(closer to 2) generate offspring with values further away
from the average, encouraging exploration. The probability
distribution index is used to create an offspring with similar
search power in single point crossover, which can be
represented as in (16);
(16)
By using the random number and the probability
distribution function, helps to select a new value “βqi” for a
specific characteristic of the offspring in the evolutionary
algorithm. This value is chosen in a way that reflects the
desired distribution of characteristics in the population,
guiding the algorithm towards promising solutions. From a
defined probability distribution index, the ordinate “βqi” is
found which is helpful for the offspring generation as given
in the following eqns.;
(17a)
(17b)
Crossover is performed with a higher probability (Pc),
whereas the mutation is performed with a low probability
(Pm), see Table 5. If the mutation probability is kept very low,
then no element would be mutated by the mutation
operator.
Generally, when the fitness function is provided to GA, it is
used to observe the behavior of the function in the given
criterion of the problem. So, in the case of the minimization
of objective function value, the lowest value would be the
most suitable solution for the given situation. The developed
algorithm is proposed to find out the optimal controller gain
values based on the minimum error.
The finally designed VSI components’ parameters are
tested under dynamic operating conditions in standalone
mode for stability analysis. In standalone mode, three VSI
sources are considered to create an isolated microgrid
environment with critical and non-critical loads, as shown in
Fig. 7. The main purpose of this standalone network system
Fig – 6: Block diagram of controller tuning using PSO
algorithm.
Mathematically, the search process can be represented by
the simple equations with concerning position vector Xi =
(xi1, xi2, . . . , xin) and velocity vector Vi = (vi1, vi2, . . . , vin) within
the specified selection range. The optimality of the solution
depends on each particle’s velocity and position which is
updated as equation 14 in the algorithm.
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is to evaluate the stability and performance of the designed
VSI in terms of frequency and voltage stability during the
transient condition. It is crucial to investigate any potential
disturbance in microgrids, particularly in the islanded mode,
because the inertia is low. When operating in the droop
control mode, the bus frequency and voltage amplitude
reflect, respectively, the output active and reactive power
that satisfies the P-f and Q-V droop characteristics. The
droop characteristic equations can be expressed as;
(18a)
(18b)
where, m and n are the droop coefficients, fref and V ref are the
bus frequency and voltage amplitude at the PCC and Pref and
Qref are the active and reactive power of the DG units.
Fig -7: Circuit diagram of three VSI based standalone
microgrid system.
5. RESULTS AND DISCUSSION
The proposed GCI system power rating is 10 kW with 3Φ-
inductive load, as shown in Fig. 1, which is designed and
tested in MATLAB/SIMULINK with m-files. The SIMULINK
block diagram is given in Fig. 5. This paper validates the
designed LCL filter for harmonic attenuation and verifies the
stability conditions of the controller using the TYPHOON HIL
emulator for real-time performance. The controller’s design
is primarily oriented towards enhancing tracking
performance, especially in situations characterized by a less
stable grid.
TABLE - 5: SELECTED PARAMETERS FOR THE
EXPERIMENTAL SET-UP
Parameters
Values
VSI Power rating
10 kW
AC Voltage
400 V
rated AC Current
20 A
Input DC voltage (Vdc)
850 V
Inverter-side inductance (Lf )
2.53 mH
Grid-side inductance (Lg)
2.53 mH
Filter Capacitance (Cf )
10.03 µF
Damping resistor (Rd)
1.588 Ω
3Φ Inductive load
1 kVA, 0.9 pf
Switching frequency (fsw)
20 kHz
AC frequency (f0)
50 Hz
Sampling Time (Ts)
10 µs
Cut-off frequency (ωc)
31.41
P − f droop gain (mp)
3.93e-4
Q − V droop gain (nq)
4.08e-3
Resistance line - 1 (Rline1)
0.23 Ω
Inductance line - 1 (Lline1)
0.31 mH
Resistance line - 2 (Rline2)
0.35 Ω
Inductance line - 2 (Lline2)
1.85 mH
Load - 1
7 kVA, 0.9 pf
Load - 2
8 kVA, 0.9 pf
Parameters for Optimization
algorithm
Values
Population size (Np)
50
No. of iteration
100
Inertia constant (w)
0.9
Acceleration constant (c1 = c2)
2
Distribution index for crossover (ηc)
20
Distribution index for mutation (ηm)
20
Crossover Probability (Pc)
0.8
Mutation Probability (Pm)
0.2
Lower bound (KP min, KImin)
1.5, 1500
Upper bound (Kpmax, KImax)
3, 3000
The poles and zeros of the designed filter are in the left
half of the s-plane, which represents the filter stability. By
additional damping in the filter, the system stability is
enhanced, shown in Fig 8 (a). As we increase the switching
frequency, the filter becomes more effective at eliminating
higher-order harmonics. To evaluate stability
comprehensively, we have analyzed the gain and phase
margins through the plant’s transfer function and Bode plots,
depicted in Fig. 8 (b). This analysis provides valuable
insights into the filter’s stability and its ability to suppress
harmonics, essential for assessing its performance.
LOAD - 3
DG - 1
Vl1
Rf 1
Lf 1
Rg 1 Lg 1
il1
C1
Vo1 io1
V*
i1
i*
o1
V*
o1
Rline 1
CURRENT
VOLTAGE
POWER
CONTROLLER CONTROLLER CONTROLLER Lline 1
DG - 2
Vl2
Rf 2
Lf 2
Rg 2 Lg 2
il2
C2
Vo2 io2
V*
i2
i*
o2
V*
o2
CURRENT
CONTROLLER
Rline 2
VOLTAGE POWER
CONTROLLER CONTROLLER
Lline 2
DG - 3
Vl3
Rf 3 Lf 3
Rg 3 Lg 3
il3
C3
Vo3
io3
V*
i3
i*
o3
V*
o3
CURRENT VOLTAGE
CONTROLLER CONTROLLER
POWER
CONTROLLER
LOAD - 2
LOAD - 1
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(a)
(b)
Fig - 8: Stability analysis(a). Pole and zeros of the closed
loop system with (red) and without (blue) damping, (b).
Bode plot of the plant transfer function with(red) and
without(blue) damping
A higher switching frequency (refer to Table 5) is
employed throughout the simulation. This higher frequency
assists in the precise tracking of time-varying signals,
compensating for dead time, and reducing current ripples in
the output current.
The simulation parameters used for the system design are
given in Table 5.
Table - 6: COMPARISON OF CONTROLLER GAIN VALUES
AND STEADY-STATE RESPONSE WITH DIFFERENT
CONTROLLER TUNING TECHNIQUES
Items
Gain values (Kp,
KI)
Mp
Tss
(sec)
ZN method
1.6821, 1587.06
12%
100
PSO
2.5, 2944.6
19%
89
Real coded based
GA
2.2, 2316.3
15%
95
Fig - 9: PI controller gain response comparison with ZN,
PSO and GA
The selected controller parameters are detailed in both
Table 5 and Table 6. To initiate the optimization processes,
the initial parameters for the PSO and GA are derived from
the ZN method, which assists in establishing the upper and
lower limits. In Fig. 9, a comparative analysis of the PI
controller’s settling time (Tss) and maximum peak overshoot
(Mp) is conducted across different tuning methods, including
ZN, PSO, and GA, and the results are summarized in Table 6.
Notably, GA outperforms the other methods by achieving Mp
value and Tss that aligns with the desired criteria.
Consequently, the GA tuning method is selected for further
experimental validation, as it meets all the specified criteria.
The exploration into the controller’s performance under
weak grid conditions is prompted by the intermittent nature
of renewable sources and variations in load-side impedance.
In this context, the figures, specifically Fig. 10, 11, and 12,
illustrate the dynamic response of the PI controller under
various conditions during power regulation. These figures
underscore the controller’s efficacy in the nonlinear time
domain, particularly when there are changes in current from
15A to 20A, demonstrating its dynamic response and its
capability to control reactive power effectively.
The experiment aims to verify the obtained
controller parameters from real-coded based GA, see Table
6, with the PI and PR controllers’ performance for weak grid
operating conditions based on Lg variation and (X/R)
variation, fault occurrence at the PCC and also tested for
sudden load change in the standalone distributed network.
5.1 Parameter Variation Impact Analysis
5.1.1 Effects due to Lg variations
In general, Lg is kept lower than Lf as suggested in many
works of literature [36],[37]. Therefore, here the CCL
performance is tested for the lower Lg values to achieve the
considered objective for the designed filter. The controller
performance is responsible for controlling the active and
reactive power supply to the utility, as shown in Fig. 10 (a)
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and (b). The figure implies that the controller achieves the
steady state within the standard time (Tss = 3 - 5 ms) and Mp
within 5% for the CCL. We find the Lg variation for the
transient condition in CCL, which could be responsible for
the system’s stability. The minimum Lg value has the
maximum Mp and Tss. The best controller tracking
performance is obtained when Lg is set to 2.53 mH, the Mp
and Tss are within the desired criteria, see in Fig. 10 (a). At
this value, the inductance ratio (aL) would be one, and the
capacitor requires minimum energy storage, which also
fulfills our filter design objective. From the above
demonstration it is clear that as the controller performs
worse as the Lg value decreases, so it is important to
maintain the grid impedance according to the connection
requirements. In weak grid scenarios, it is better to consider
equalizing the value of Lf to reduce harmonics and current
distortion at the load side.
(a)
(b)
Fig - 10: (a). Comparison of Id current with Lg variation,
(b). Comparison of Iq current with Lg variation.
5.1.2 Effect on (X/R) variation
(a)
(b)
Fig - 11: (a). Comparison of Id current with (X/R)
variation, (b). Comparison of Iq current with (X/R)
variation.
5.1.3 Effect of fault occurrence at PCC
Generally, a three-phase fault is considered for the controller
performance and the system withstands capacity for the
short circuit current analysis during transient conditions.
Because the maximum fault current occurs in 3-phase fault.
To study dynamic conditions, two types of disturbances are
considered; a sudden change in power demand and a change
in the line impedance. In a low voltage distribution network,
the lower line impedance at the grid side, in case of sudden
load changes, creates a severe problem that affects the
controller performance and overall system efficiency
(especially lower SCR value systems due to over-current). In
Fig. 11 (a) and (b), the current is stepped up at 0.5 seconds
to increase the power supply. The weak grid characteristics
are defined as, SCR < 3 and (X/R) < 5 [11]. Where The SCR
specifies the maximum amount of power that the power
system can handle without compromising power quality at
the PCC. As shown in Fig. 11 (a), the controller is quite
robust to avoid the instability condition in the system and
track the reference value with minimum oscillations. The
best controller tracking performance with minimum ripple
current (based on Tss, Mp) is achieved when the (X/R) is
equal to 2.5, which is within weak grid condition at the grid-
side.
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When any fault occurs, the protection relay operating time is
about 0.22 seconds [11]. The Critical Clearing Time (CCT) is
a typical criterion for evaluating the transient stability limits.
As we can see in Fig. 12, the fault is cleared within CCT, and
the current signal is back on the track set by the controller.
The controller limits the fault current during the fault
condition and does not allow it to exceed the desired value. It
shows the robustness of the controller and fault ride-
through capability for lower strength systems to recover the
voltage stability after the fault.
Fig -12: (a). Id current, (b). Iq current, (c). VSI output 3ϕ -
current during the fault condition, (d). Output 3ϕ - voltage
during the fault condition.
Fig - 13: THD analysis of VSI output current(a).for PI
controller, (b). for PR controller.
5.1.5 Standalone Mode Controller Performance
Analysis
In Fig. 7, the designed three VSIs (10kVA each) are
connected to a distributed network in standalone mode for
testing the stability and reliability performance. The
eigenvalue spectrum of the consider network in Fig. 14
demonstrates the effectiveness of the designed controller
system. The negative eigenvalues indicate that the system
remains stable during standalone operation. The different
cluster positions show the different modes in the microgrid
system, such as distribution line, filter, power, voltage, and
current controller state variables. Fig. 15 demonstrates the
effectiveness of the controller tracking performance when
there is a sudden 20% increase in load-1 at DG-1. The small
load variation at a particular DG in the network, while here
the load increase occurs at 0.5 seconds, leading to changes in
5.1.4 THD Analysis
PI controller operates on a fixed frequency of the system, so
its output could be unstable under weak grid conditions. But
the PR controller has cut-off frequency bandwidth (ωc)
around the system frequency, as discussed earlier in the
current controller structure. For this experiment, the
frequency variation is considered ±2Hz. The parameters are
determined similarly to the PI controller to obtain the
required closed-loop response from the PR controller. The
cut-off frequency bandwidth can be extended by tuning the
ωc. The higher value of ωc is responsible for the increase in
peak magnitude at the system frequency, which corresponds
to a higher gain value and better current ripple attenuation.
The lower value of ωc corresponds to wider bandwidth at the
system frequency [47]. The comparison for THD analysis by
using PI and PR controller is shown in Fig. 13. The output
current THD levels are below 3% as per requirements for
the weak grid applications, which shows the quality of the
output current.
(a)
(b)
active power sharing and consequently affecting the VSI
frequency shown in the figure. However, active power
oscillations may occur between parallel inverters during the
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Fig - 15: Stability analysis of the three VSI standalone system when sudden load increased at 0.5 sec.
load fluctuations, but here the power flow is smooth without
using any external damping techniques.
Fig - 14: Eigenvalue spectrum of three VSI in standalone
mode
5.1.6 Controller Performance Validation
The plant function, considering all aspects outlined in
section III, and tested it in MATLAB/SIMULINK. This testing
helps us select accurate parameters in line with standard
requirements [4], [9]. The controller gain values have been
diligently calculated using three distinct methods to
optimize controller performance during operation. These
optimization algorithms have been implemented in custom
m-files. The effectiveness of the controller loop optimization
has been rigorously tested and verified using the Typhoon
real-time emulator model-604, which provides an
impressive 20-nsec sampling resolution. In Fig. 16, the
schematic editor is used for VSI modeling purposes, which is
compiled with the real-time hardware emulator set-up, and
the SCADA (Supervisory Control and Data Acquisition) panel
is used for monitoring and visualization of the output results.
The Typhoon set-up is connected through the Ethernet
connection mode to the desktop system. The validation on
Hardware-In-Loop implementation is completely reliable for
the coordinated power feeding to the utility from different
power generation sources through the connected power
converter.
Fig - 16: HIL set-up :- Typhoon-Hil emulator 604 set-up in
real-time mode.
5.1.7 Discussion
According to the findings in [9], the parameter optimization
has yielded satisfactory results, as the THD level of the VSI
output current remains consistently below 3%. In direct
comparison to the results presented in [19], it is evident that
the filter and controller parameters, as well as the resulting
THD levels, are improved and better than the given results in
the mentioned paper for the same inverter rating. Moreover,
weak grid stability issues discussed in references such as
[14] and [15] have been successfully addressed through the
application of universal control modeling and various
operating conditions tailored to weak grid scenarios. To
mitigate the impact of grid- side impedance variations on
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CCL, this study has systematically tested different controller
tuning methods, meticulously documented in Table 6. The
stability of the impedance variation-based controller
performance is demonstrated in Fig. 10 and 11. The study’s
rigor extends to testing the VSI’s performance during a
three-phase fault occurrence at the PCC, as illustrated in Fig.
12. Furthermore, the VSI’s performance was assessed in a
standalone distributed network subjected to sudden load
changes, revealing its robust controller tracking capabilities
in parallel operation, which is vividly depicted in Fig. 15. The
results collectively demonstrate that the designed VSI
parameters are versatile and adept at handling a spectrum of
scenarios, particularly in less stable conditions. The
Comprehensive CCL tracking performance underscores the
VSI’s reliability even in challenging real-time conditions.
6. CONCLUSION
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In this paper the grid impedance-based stability is concerned
and improve the inverter stability for lower-voltage
distribution networks. The calculated filter and controller
parameters show their best performance for weak grid
conditions. The GA results are the best option for the
controller considerations for controller performance. Finally,
it investigates the designed system parameters for controller
tracking performance. The variations in Lg and (X/R) shows
the impact on controller performance during grid-side
impedance variations. The controller tracking performance
is satisfactory for weak grid impedance scenarios. The
performance at fault occurrence and sudden load change
conditions shows the robustness of the system. To improve
the THD level in the output current of the VSI, a PR controller
is implemented, which shows an improved THD level
compared to a PI controller. For future work on GCIs with
weak grid conditions, two promising avenues for exploration
include frequency stability or rate of change of frequency
(ROCOF) of the VSI for grid synchronization and reactive
power sharing management at the PCC.
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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 11 Issue: 09 | Sep 2024 www.irjet.net p-ISSN: 2395-0072
© 2024, IRJET | Impact Factor value: 8.315 | ISO 9001:2008 Certified Journal | Page 412
BIOGRAPHIES Harendra Pal Singh received his
B.Tech degree in Electrical and
Electronics Engineering from
Uttarakhand Technical University ,
India. His M.Tech in Power System
Engineering from Uttarakhand
Technical University , India. Currently,
he is perusing PhD in Electrical Engineering from GBPUA&T,
College of Technology, Pantnagar, India. He worked with UI-
ASSIST project at IIT Kanpur, as Research Associate. He also
has industrial experience.
His research interest includes microgrids, distributed power
generation, application of power electronics in power system
fields, optimization applications.
Anurag K. Swami is working as a
professor at College of Technology,
Pantnagar, Uttarakhand. His area of
specialization is control applications in
renewable energy systems and
controller designing applications in
different areas.