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IEEE TRANSACTIONS ON POWER SYSTEMS 1
Droop-Controlled Inverters as Educational Control
Design Project
Jimmy Chih-Hsien Peng, Senior Member, IEEE, Gurupraanesh Raman, Member, IEEE,
John Long Soon, Member, IEEE, and Nikos D. Hatziargyriou, Fellow, IEEE
Abstract—Electric grids are seeing increasing adoption of
renewables interfaced with power electronics. As the share of
renewable generation increases, the inverters are expected to
operate in grid-forming mode to replace large conventional
synchronous generation. Further, in geographical islands and
isolated/rural areas, inverters interfacing renewable generators
and storage are used to form the grids and share the loads. Given
the expected presence of grid-forming inverters in future power
systems, there is an urgent need to revise education curricula
about the stability issues arising from these interconnected invert-
ers. Existing training is overly reliant on numerical simulation or
on expensive tools such as real-time simulators. In this paper, we
present a laboratory hands-on project dealing with small-signal
stability in droop-controlled inverters. It entails simulation and
hands-on experimentation for which an inexpensive microgrid
set up was developed in-house at the National University of
Singapore. The design project can be integrated into power
engineering courses offered to senior and postgraduate students.
Index Terms—droop control, education, inverter-based sys-
tems, microgrid, power systems, stability and control.
I. INTRODUCTION
MODERN power systems are increasingly equipped with
power electronic converters such as inverters to in-
terface renewable generation and FACTS devices to provide
network compensation. Traditionally, power electronics are
studied at the device/equipment level, whereas the dynamic
stability between power converters is rarely touched upon. This
topic has gained industry attention in recent years (e.g., [1]).
In particular, the oscillatory interactions between inverters to
resolve power imbalances in AC grids have been demonstrated
to trigger network instability [2]–[4]. Since present educational
curricula do not include training power engineers to address
these new dynamic phenomena, this task is left to the industry.
To close this gap, the motivation of this paper is to present
Manuscript received April 15, 2021; revised June 30, 2021; accepted August
11, 2021. This work was supported in part by the Singapore Ministry of Edu-
cation Academic Research Fund Grant R-263-000-D10-114. (Corresponding
author: Jimmy Chih-Hsien Peng).
J. C. -H. Peng, G. Raman, and J. L. Soon are with the Department of
Electrical and Computer Engineering, National University of Singapore, Sin-
gapore 117583. (email: gurupraanesh@u.nus.edu, jpeng@nus.edu.sg, soon-
johnlong1998@gmail.com).
N. D. Hatziargyriou is with the National Technical University of Athens,
Athens 15773, Greece. (email: nh@power.ece.ntua.gr).
This is a post-print version of the paper: J. C. -H. Peng, G. Raman, J.
L. Soon and N. D. Hatziargyriou, ”Droop-controlled inverters as educational
control design project,” IEEE Trans. Power Syst., published Aug. 2021. DOI:
10.1109/TPWRS.2021.3106005. Paper accessible at https://ieeexplore.ieee.
org/document/9519514/.
a teaching curriculum that engages students (particularly se-
nior and postgraduate) to understand the control of inverter-
based systems used to manage renewable distributed energy
resources.
Controlling inverters to regulate the voltage/frequency and
provide stable power sharing within an autonomous grid, i.e.,
microgrid, or within a broader distribution system is of high
interest to the grid-edge revolution—empowering prosumers
to provide grid services to low-voltage power networks [5].
Different to classic electromechanical oscillations witnessed in
conventional grids, inverter-generated oscillations are largely
triggered by the designed power controllers [6]. As syn-
chronous generators are being replaced by renewables, such
oscillatory dynamics will be evermore dominant in future
grids. Among the various power sharing approaches, droop
control is perhaps the most widely recognized solution given
its analogous behavior to the classic synchronous generator
[7]. Thus, the design of droop-controlled inverters is identified
as the logical application to train young engineers regarding
the stability and control of inverter-based power systems.
Hands-on implementation of taught concepts is consid-
ered as the best teaching pedagogy in engineering courses
[8]. However, safety concerns and cost considerations often
constrain the instructor’s ability to demonstrate theoretical
knowledge using practical examples in educational institu-
tions. For instance, developing an educational microgrid in
the laboratory would require the acquisition of expensive
equipment such as programmable loads, real-time emulators,
and protection devices [8]. Furthermore, safety certifications
need to be obtained from the institution and the local power
utility, which can be a lengthy bureaucratic process along with
costly annual upkeep expenses. These deterring factors lead
many institutions to resort to numerical simulations, despite
the abstractness of the virtual environment [9], [10]. In fact, the
use of simulations is not the ideal pedagogy for teaching power
electronics to young engineers as reported in [11]. One cannot
fully appreciate the concepts without building/working with
the actual physical components. Recognizing this issue, the
power electronics society has developed pedagogical hardware
experience over the last few decades [12]. In contrast, little
has been done in the power systems community. Although
attempts have been conducted in the recent years, they gen-
erally demand significant initial hardware investment; this is
discouraging to most academic institutions, especially those
in the developing countries. It should be noted that rural
electrification in developing countries, often based on micro-
grids and renewable integration, rely on the deployment of
IEEE TRANSACTIONS ON POWER SYSTEMS 2
power electronics technologies. However most of the targeted
communities do not have the financial capability to procure
those expensive equipment for training their engineers [13]–
[15]. Many community projects have consequently failed in
the long-term due to the lack of proper maintenance and
inadequate operation [16]. There is a need for a practical
solution to train engineers about inverter control without costly
investments, which defines the scope of this paper.
The contribution is the development of a student project
consisting of a set of tasks in the context of inverter control
and stability analysis. In our case, the design project has been
integrated into a graduate module at the National University
of Singapore entitled EE5702—Advanced Power Systems
Analysis. Students are first lectured on the operating princi-
ples of inverters and in modeling their dominant dynamics.
Subsequently, they build droop controllers that satisfy a set of
given specifications outlined by the project tasks. The design
and analysis stages rely on numerical simulations, while the
validation is performed using an experimental microgrid. The
experimental microgrid constructed for this project focuses on
the dominant dynamics of interconnected inverters while ne-
glecting load dynamics, as these have been proven to have little
contribution to the small-signal stability [4], [17]. It comprises
of 3 three-phase inverters sharing constant impedance loads,
and is capable of capturing the oscillatory dynamics witnessed
at various ratings. The inverters are supplied by a DC power
supply representing an ideal source. Details regarding PCB
fabrication and codes are made available for teaching instruc-
tors at [18]. Overall, this paper puts forth a holistic approach
to train power engineers on the stability of inverter-based
generations in an electric grid in a relatively cost-effective
manner. As a result, the proposed project can reach a much
broader audience than just well-funded institutions.
The learning outcomes for the design project are as follows:
1) Design closed-loop voltage control for a three-phase
inverter using current and voltage PI controllers.
2) Implement decentralized power sharing among multiple
grid-forming inverters using droop control.
3) Design and implement generalized droop control and
lead-lag compensators for guaranteeing stability for all
droop gains and network configurations.
The layout of the upcoming sections is as follows. Theoret-
ical concepts, simulation approaches, and experimental setup
are described in Section II. Subsequently, project tasks and
their expected results are presented in Section III. Finally,
conclusions are drawn in Section IV.
II. CO NC EP TS A ND ANA LYSIS
The design project demands students to apply theoretical
concepts into working solutions and resolve the small-signal
instability within a microgrid. Students are first asked to model
the microgrid, and then verify their inverter droop controller
designs using MATLAB/Simulink. Finally they implement
their design in the experimental microgrid for validation. Upon
completion of the project, students are expected to become
familiar with inverter modeling, control design, and stability
analysis in addition to gaining hands-on experimentation skills.
P
f
f0
-kf
Q
Vref
V0
-kv
Pmax Qmax
fmin Vmin
Fig. 1. Frequency and voltage characteristics for conventional droop control.
Details of the required theoretical knowledge, simulation mod-
els, and the experimental microgrid setup are discussed in the
forthcoming subsections.
A. Droop Control Fundamentals
Droop control is one of the most commonly implemented
methods of decentralized power sharing among different power
electronic inverters. A droop-controlled inverter mimics the
behavior of a synchronous machine by reducing its output
frequency and voltage in a linear proportion to the active and
reactive power drawn from it [7]. The steady-state f-Pand V-
Qcharacteristics for the conventional droop control are shown
in Fig. 1, and can be mathematically represented as:
f=f0−kfP
Vref =V0−kvQ, (1)
where Pand Qare respectively the active and reactive power
outputs of the inverter, f, its output frequency, and Vref ,
its terminal voltage. The subscript ‘0’ indicates the no-load
or nominal value. The parameters kfand kvare the droop
coefficients or gains. Based on (1), the conventional droop
control can be more precisely referred to as the P-f/Q-V
droop.
The working of droop control is explained as follows.
Considering a system with ndroop-controlled sources, the
frequency of each source should be equal in the equilibrium
state. As a result, the active power outputs must satisfy:
kf1P1=kf2P2=· · · =kfnPn(2)
which yields the relation:
Pi∝1
kfi
∀i∈[1, n](3)
Therefore, each source takes up a fraction of the total active
load inversely proportional to its frequency droop coefficient.
Conversely, the droop coefficients of each inverter must be
chosen in inverse proportion to its capacity, so that its steady-
state power output is proportional to the capacity. Note that this
type of droop control does not enable accurate reactive power
sharing along similar lines as active power because the steady
state voltages of the sources depend on the interconnection
topology and load locations, and are therefore not always equal
[19].
IEEE TRANSACTIONS ON POWER SYSTEMS 3
Pmeas
1.5 (vdid+ vqiq)
1.5 (-vdiq+ vqid)Qmeas
vd, vq, id, iq
Power measurement V
-
kv
V0
Qmeas
1
𝑇
𝑐𝑠 + 1
-
kf
f0
Pmeas
f1
𝑠δ
2𝜋ω
1
𝑇
𝑐𝑠 + 1
Droop control
ω0Lf
ω0Cf
-
vd
vd*
vd
--
iL,d
iL,d*
vq
-
iL,q
iL,q*
ω0Cfω0Lf
-
vq*
0
2
V
δ
2/Vdc SPWM Firing
pulses
dqabc
vinv,d
vinv,q
𝑘𝑝𝑖 +𝑘𝑖𝑖
𝑠
𝑘𝑝𝑣 +𝑘𝑖𝑣
𝑠
𝑘𝑝𝑣 +𝑘𝑖𝑣
𝑠𝑘𝑝𝑖 +𝑘𝑖𝑖
𝑠
Voltage control Current control
-
+
_
Six-switch
inverter
LfRf
Cf
Vdc
vdq
idq
vinv,dq iL,dq
Fig. 2. Detailed model of a three-phase inverter with cascaded droop, voltage and current control loops.
B. Modeling a Three-Phase Inverter
A droop-controlled three-phase inverter entails a DC source
connected to a three-legged bridge, whose outputs are fed
through an LC filter designed to meet THD requirements.
The frequency and RMS voltage set points for the inverter
output are dictated by the droop controller, based on the
measurements of the active and reactive power drawn from
the inverter. Typically, the measured power values in the droop
controller are first passed through a first-order low pass filter,
whose time constant Tcdetermines the inertial behavior of
the inverter. The output frequency set point is tracked by
changing the rate of change of the phase angle reference δ,
and the voltage magnitude, using cascaded voltage and current
PI controllers along the dand qaxes.
The current and voltage controllers should be designed such
that the droop, voltage, current, and pulse-width modulation
controllers have bandwidths in increasing order, with each
stage significantly faster than its preceding one. This time-
scale separation ensures that the different stages do not interact
which could reduce the stability margin of the entire cascade
[20], [21]. It also conveniently enables the independent design
of the controllers in each loop. Given the inverter switching
frequency fsw, the filter inductance Lfand internal resistance
Rf, the current PI controller (kpi+kii /s)can be systematically
designed as per the above principles as:
kpi =LfωBi
kii =RfωBi ,(4)
where ωBi = (2πfsw )/α is the bandwidth of the current
controller, and αis the bandwidth ratio, typically selected
between 3 to 10. Similarly, given the filter capacitance Cfand
the expected load resistance Rload, the voltage PI controller
(kpv +kiv/s)can be designed as:
kpv =CfωBv
kiv =ωBv
Rload
,(5)
where ωBv = (2πfsw )/α2is the bandwidth of the voltage
controller. Finally, the slowest controller, i.e., the droop con-
troller, is typically designed with a bandwidth of 2 to 15 Hz
by appropriately selecting Tc.
Considering the above cascaded control structure, the “de-
tailed model” of the droop-controlled inverter shown in Fig.
2 considers all the hardware components including switches
(treated to be ideal) and the LC filter (ignoring parasitic
elements), in addition to the software components– the droop,
voltage and current control loops. As such, it is the most
accurate representation of the physical inverter. However, the
detailed model requires significant computational resources for
simulation due to the relatively higher-bandwidth dynamics
of the inner voltage and current loops considered, as well as
the switches and the LC filter. To aid in faster simulation
while preserving the system-level dynamics, a “simplified
model” can be used, where the voltage and current control
loops are assumed to be stable and infinitely fast. This is a
justifiable assumption given the time-scale separation between
the dynamics of the cascaded controllers [22]. As a result, the
inverter can then be conveniently modeled as an ideal voltage
source with the same droop controller as before. This is shown
in Fig. 3.
C. Ensuring Stability under Droop Control
The small-signal instabilities arising in multi-inverter micro-
grids under conventional droop control (1) can be attributed
IEEE TRANSACTIONS ON POWER SYSTEMS 4
Ideal three-phase
voltage source
V
∠
δ
V
-
kv
V0
Qmeas
1
𝑇
𝑐𝑠 + 1
-
kf
f0
Pmeas
f1
𝑠δ
2𝜋ω
1
𝑇
𝑐𝑠 + 1
Droop control
Pmeas
1.5 (vdid+ vqiq)
1.5 (-vdiq+ vqid)Qmeas
vd, vq, id, iq
Power measurement
Fig. 3. Simplified model of a three-phase inverter, represented as an ideal voltage source operated under droop control.
ΔP
ΔQ
Δf
ΔV
ΔP
ΔQ
Δf
ΔV
φ
(a) (b)
φR
X
Fig. 4. Illustrating droop control action under (a) conventional droop control
and (b) generalized droop control.
to the following two factors pertaining to power flow in the
interconnection network.
1) P-V/Q-f cross-coupling: In transmission systems where
the conventional droop control is originally borrowed from, the
power lines are predominantly inductive in nature. Therefore,
the active power flow through a line is strongly coupled to
the phase angle difference and the reactive power, on the
voltage magnitude difference across the terminal ends. The
conventional droop control reflects this relationship, with the
droops in frequency and voltage dependent on the active
and reactive power, respectively. However, in the distribution
level, the lines have non-negligible resistances. This introduces
cross-coupling between the active power and voltage, and
between the reactive power and frequency, which increases
with the R/X ratio of the network.
2) Distribution system lag: The behavior of the intercon-
nection network is resistive-inductive, which means that the
power flows are subject to a phase lag dependent on the R/X
ratio. For lower values of R/X, the phase lag can be high,
reducing the phase margin, and potentially destabilizing the
medium- as well as low-frequency modes of the system [3].
The destabilizing influence of the cross-coupling effect can
be nullified by using generalized droop control, where the
power measurement frame of each inverter is rotated so that
the power flow dynamics appear inductive in the rotated frame
(see Fig. 4). The droop control equations in the steady-state
therefore become:
f=f0−kf(Pcos φ−Qsin φ)
V=V0−kv(Psin φ+Qcos φ),(6)
with φ= tan−1ρ,ρbeing the R/X ratio of the network.
On the other hand, the effect of distribution system lag can
be addressed by modifying the power measurement filter in the
droop control loop, such that it provides an equivalent phase
Fig. 5. The developed three-inverter microgrid setup used for experimental
verification of stability concepts.
lead. The filter now takes an improved lead-lag compensator
form
F(s) = s2/ω2
0+ 2ρs/ω0+1+ρ2
(ρ2+ 1)(Tcs+ 1)(τs + 1) ,(7)
where ω0is the nominal grid frequency (here, 2π(50) rad/s),
and the time constant τshould satisfy τ << Tc(typically
selected as 0.001 s).
Overall, for a given network R/X ratio ρand droop
controller time constant Tc, the generalized droop controller
(6) and lead-lag compensator (7) has no parameters that
require tuning, making control design very convenient. For
detailed proofs on how these control modifications guarantee
the stability, the reader is referred to [3] and the accompanying
lecture slides in [18].
D. Experimental Design
The educational microgrid is pictured in Fig. 5, and consists
of 3 three-phase inverters interconnected in the topology
shown in Fig. 6. Each inverter is controlled by TI-F28335 DSP,
and is fed by a full-bridge rectifier whose input is obtained
from the 400 V three-phase AC mains. The interconnection
lines are implemented as lumped resistors and inductors, which
can be flexibly adjusted. Two resistive loads are connected
at the output of Inverter-1, one of which can be switched
to create real time disturbances. Furthermore, protection cir-
cuits, i.e., fuses and relays, are installed to prevent hardware
IEEE TRANSACTIONS ON POWER SYSTEMS 5
+
_
+
_
+
_
Inverter-1
Inverter-2
Inverter-3
LfRf
Cf
Cf
Cf
LfRf
LfRf
Z12
Z23
Load-1 Load-2
Fig. 6. Single-line diagram of the microgrid case study used for the project.
failure and ensure the safety of the students. Detailed design
specifications, e.g., component models and PCB designs, and
micro-controller codes are made available in [18]. These codes
are programmed in C language and contain all the necessary
functions to operate the three-phase inverter required for
this design project. They are executed using Code Composer
Studio, and users can modify the controller gains and calibrate
the sensors as required for their individual microgrids. Overall,
the construction cost of this educational microgrid is around
USD 1,000 [23].
III. PROJ EC T TASKS AND EXECUTION
In the project, the students are expected to simulate an
islanded microgrid consisting of inverter-based generation.
More specifically, they are trained to systematically develop
and implement droop controllers such that the grid stability is
guaranteed for any droop gain values and network impedances.
Note that the theoretical background for the topic, e.g., design
of cascaded controllers with appropriate time-scale separation,
small-signal models and stability analysis, should be first
delivered through lectures prior to issuing the project. Lecture
slides designed for this project can be accessed at [18].
The project tasks are designed to evaluate the students’
ability to 1) collect, select, and use the given information from
a datasheet to simulate an islanded microgrid consisting of
inverter-based generation, 2) undertake independent research
and inquiry, and 3) integrate theory and practice. They are
divided into three stages. First, students will focus on modeling
the inverter and microgrid. Second, they will proceed to design
the inverter control and perform stability analysis. Finally, the
developed controllers will be validated by numerical simu-
lations and laboratory tests. In order to expose the students
to various design issues, they can easily experiment with
different control parameters using simulations, and observe
their corresponding time-domain dynamics and analyze eigen
plots. During this design phase, students are also encouraged to
discuss the outcomes of the numerical simulations—a process
that helps strengthen their understanding and trains their
design skills. On the other hand, hardware validation is only
conducted at the final stage of the project for safety considera-
tions. Since students will be deliberately operating the inverters
near instability, the hardware experiment is recommended to
be conducted at low voltage, i.e., de-rated values, to ensure
TABLE I
MICROGRID PARAMETERS (SIMULATION)
Inverter parameter Value
Power rating 10 kVA
Voltage rating, V0230 V per phase
Nominal frequency, ω02π(50) rad/s
Power filter cut-off frequency, ωc= 1/Tc2π(5) rad/s
Switching frequency 10 kHz
LC filter parameters (Lf,Rf,Cf) 0.5 mH, 0.2 Ω, 50 µF
Nominal droop gains (kf,kv) (0.1%,5.0%)
Network parameter Value
Line impedances Z12 =Z23 (0.1 + j0.1) Ω
Load-1 31.74 Ω
Load-2 158.7 Ω
TABLE II
MICROGRID PARAM ET ERS ( EX PER IM ENTA L)
Inverter Parameter Value
Power rating 200 VA
Voltage rating, V021 V per phase
Nominal frequency, ω02π(50) rad/s
Power filter cut-off frequency, ωc= 1/Tc2π(5) rad/s
Switching frequency 10 kHz
LC filter parameters (Lf,Rf,Cf) 1 mH, 0.2 Ω, 50 µF
Nominal droop gains (kf,kv) (0.1 %,5.0%)
Network parameter Value
Line impedances Z12 =Z23 (0.3 + j0.34) Ω
Load-1 13.23 Ω
Load-2 66.15 Ω
hardware safety, with accompanying simulations carried out
additionally to validate the results. The microgrid rating can
be increased to match the simulation parameters if permitted
by the available infrastructure, technician credentials, and
with appropriate safety precautions. We also note that if the
hardware setup is not pushed to instability limits, then it can
be safely operated at the full rating.
A. Project Tasks
The design project consists of a total of 9 tasks. Tasks 1 to 8
are simulation-based using typical distribution ratings outlined
in Table I, while the experimental Task-9 is conducted using
settings listed in Table II. The tasks are detailed below.
•Task-1: Consider a single inverter with no droop control,
connected to two loads, Loads 1 and 2. For the parameters
from Table I, implement cascaded current and voltage
control loops to achieve closed-loop voltage control.
Design the current and voltage PI controllers such that
the voltage settling time is at least 5 times smaller than
the time-constant of the droop controller (i.e., Tc). The
peak overshoot of the voltage should be no more than
5%. Verify these requirements by switching ON Load-2
to create a step disturbance and observing the inverter
RMS output voltage.
IEEE TRANSACTIONS ON POWER SYSTEMS 6
•Task-2: Add the conventional (P-f/Q-V) droop con-
troller using the settings outlined in Table I to the
inverter constructed in Task-1. Create a load disturbance
by switching Load-2 ON. Observing the steady states
before and after the disturbance, verify that the voltage
and frequencies of the inverters conform to the desired
P-fand Q-Vdroop characteristics.
•Task-3: Connect the droop-controlled inverter to an infi-
nite bus through an impedance (0.1 + j0.1) Ω. Observe
its time response to a step change in Load-2 ON at the
inverter bus. Next, construct a simplified model of the
same inverter that considers only the droop controller.
That is, the LC filter, the voltage and current controllers
will be removed by assuming the voltage control to be
infinitely fast. Connect this model to an infinite bus and
validate it against the detailed model by comparing the
transient waveforms of P,Q,f, and Vwhen subjected
to the same step change in load.
•Task-4: Use the simplified inverter model obtained in
Task-3 for all the remaining tasks. Construct the three-
inverter setup shown in Fig. 6. Using a load step-change,
i.e., Load-2 ON, observe the active and reactive power
shared by each inverter before and after the disturbance.
Comment on the power sharing accuracy under conven-
tional droop control.
•Task-5: Increase the frequency droop gain (kf) of each
inverter separately, while retaining the other inverters’ kf
at the nominal value. Determine the point of marginal
stability corresponding to each inverter, i.e., the kf
value where the damping ratio of the overall system
becomes ζ= 0. Present the time response (Pand Q
waveforms) of the multi-inverter system when the droop
gains are separately changed from the nominal value
to the above instability limit. Referring to the kflimit
for each inverter, comment on the relation between the
interconnection impedance and stability margin.
•Task-6: Replace the conventional droop controller of
each inverter by a generalized droop controller with the
appropriate rotation angle. Also replace the conventional
first-order filter with a lead-lag compensator using the
appropriate phase gain at the grid frequency ω0= 2πf0.
Plot the Bode diagram of the new compensator along
with that of the original first order filter, and measure
their respective phase gains at grid frequency. Finally,
use a load step disturbance, e.g., Load-2 ON, to discuss
whether/how the power sharing accuracy is affected by
the proposed control modifications in reference to con-
ventional droop control.
•Task-7: Determine the time response of the modified
system for the three different droop gain combinations
as obtained from Task-5. Verify that the proposed design
modifications make the system stable for the same droop
gain values that made the original system oscillatory. In
other words, demonstrate that the stability region has
expanded for the modified droop controller.
•Task-8: The lead-lag compensator is parameterized by
the term ρ. From theoretical analysis, this value should
be the same as the R/X ratio of the network, which
Fig. 7. Response of closed-loop voltage control for Task-1 for a step
disturbance in load. Here, the voltage overshoot is measured as 1.04%.
for the given system is 1.0. Now, keeping the network
impedances (i.e., R/X) fixed, investigate how the system
damping changes if the designed ρis changed. Take the
droop gains (kf,kv) for all the inverters as (0.5%, 5%),
and compare the time domain power outputs for ρ= 1.0
(normal case), 0.1 (too small), and 7.0 (too large).
•Task-9: Repeat Tasks 5, 6, and 7 for the experimental
microgrid whose parameters are listed in Table II. Subse-
quently, verify the expansion in stability region with the
conventional droop controller with first-order filter and
the generalized droop control with lead-lag compensation.
Discuss the possible causes of the variations between the
experimental and numerical results.
B. Task Execution
The steps and expected results for each project task are
summarized below.
•Task-1: The purpose of this task is to assess the students’
knowledge on inverter modeling and control implemen-
tation. They will first develop a detailed three-phase
inverter model shown in Fig. 2 using the parameters
listed in Table I. The internal control loops, i.e., voltage
and current controls, are then implemented. The expected
time-domain voltage plot when subjected to Load-2 ON is
given in Fig. 7, where the PI controllers are parameterized
as kpi = 10.47,kii = 4188.8,kpv = 0.35, and
kiv = 4399.1. Note that the exact dynamics may vary
based on the selected control gains.
•Task-2: This is an extension of the previous task in
which the droop controller (1) will now be added to the
developed model in Task-1. Since the droop coefficients
are indicated in Table I as percentages, they should be
duly converted into absolute values based on the rated
power and voltage of the inverter. The inverter ratings
of 10 kVA, 230 V (per phase) are also conveniently
taken here as the bases for per-unit calculations and for
displaying results. Students will validate their designs
using a simple load step change, and record the steady-
state voltage and frequency at the inverter bus. The
correct values are listed in Table III. The droop-controlled
inverter is now ready to be integrated into a microgrid.
•Task-3: The aim of this task is to guide students towards
system-level analysis, starting with a simple two-bus
configuration. Notably, the inverter oscillating against the
infinite grid is the simplest system where instability due to
IEEE TRANSACTIONS ON POWER SYSTEMS 7
TABLE III
EXP ECT ED STE ADY STATE VALU ES F OR TAS K-2
Parameter Before load step After load step
P0.5 pu 0.6 pu
Q0 pu 0 pu
f49.975 Hz 49.970 Hz
V230 V per phase 230 V per phase
Fig. 8. Comparing the response of the detailed and simplified inverter models.
droop control can be potentially observed. Here, students
will be exposed to practical issues such as resolving the
trade-off between simulation time and accuracy, leading
them to make design choices based on analytical thinking.
The noticeable issue in the task is the long computing
time to execute one simulated case study, which will
become intolerable when simulating more inverters. Stu-
dents should be able to identify the root cause being the
use of the detailed inverter model, which is not scalable
for simulating multi-inverter dynamics. To resolve this
problem while retaining the accuracy of the results, the
detailed model should be modified into reduced-order
variant shown in Fig. 3. A properly-reduced model will
exhibit a distinct simulation speedup while preserving
the accuracy of the dominant power sharing dynamics,
i.e., the power oscillations should have similar amplitudes
TABLE IV
EXP ECT ED STE ADY STATE POW ER MEASUREMENTS FOR TAS K-4
Inverter Before load change After load change
P(pu) Q(pu) P(pu) Q(pu)
1 0.1667 0.032 0.2 0.038
2 0.1667 -0.006 0.2 -0.008
3 0.1667 -0.024 0.2 -0.029
and oscillatory frequencies as the case of detailed model.
Further, this task enables students to observe the impact
on the internal control loops on the system stability,
and appreciate that well-designed inner loops do not
significantly affect the dominant droop-control dynamics.
The expected time-domain performance is illustrated in
Fig. 8.
•Task-4: The objective of this task is to strengthen the
theoretical understanding of power sharing under the
conventional droop control law. Students will analyze
the performance of their designed droop controllers for
two different load configurations. Referring to the steady-
state power contributed by each inverter listed in Table
IV, they should conclude that the conventional droop
control always ensures active power sharing in inverse
proportion to the frequency droop gain. In contrast, the
reactive power is not necessarily proportionally shared if
the network topology and loads are asymmetrical with
respect to the inverters. Moreover, although the loads are
purely resistive, some inverters generate non-zero reactive
power which leads to wasteful circulating currents. This
task therefore provides the opportunity to study inequities
in the reactive power sharing performance and highlights
the need for secondary control to correct them.
By now, students should have become familiar with
inverter modeling, control design, and numerical valida-
tions using MATLAB/Simulink.
•Task-5: In this task, students will observe that an increase
in the droop gains leads to instability. They are also
expected to appreciate the effect of the frequency and
voltage droop gains (kfand kv), on the system stability
upon completion of this task. Specifically, the students
can determine through simulations that the voltage droop
gain does not have a significant impact on the dominant
dynamics.
For the given design specifications, the system becomes
unstable when kf1= 0.81%, kf2= 0.56% and kf3=
0.81% (see Figs. 9(a)-(c) respectively). In each case,
the frequency droop gains of the other inverters are
maintained at 0.1%. The above limits signify the stability
margin of the system at the different nodes, from which
students should identify that the node with the lowest
stability margin is the one that has the most interconnec-
tions and thereby the highest Th´
evenin admittance. This
finding is a critical concept in stability analysis under
droop control.
•Task-6: The conventional droop controller provides a
limited stability region, which may not be sufficient if the
grid operator demands faster time responses, or when the
network impedances change. Here, the students will now
proceed to formulate solutions that improve the damping
ratio using a generalized droop controller summarized by
(6) and Fig. 4. Furthermore, the compensator based on
(7) will replace the original first-order filter in the droop
controller. The students are also encouraged to pursue
other designs along these conceptual lines, e.g., through
virtual impedance control.
For the task at hand, we have the R/X ratio ρ= 1,
IEEE TRANSACTIONS ON POWER SYSTEMS 8
(a) (b) (c)
P1and P3
overlap
Fig. 9. Active and reactive power waveforms for the three-inverter microgrid as the frequency droop gains of each inverter are increased one by one to
identify the point of critical stability, which is: (a) Inverter-1 kf1= 0.81%, (b) Inverter-2 kf2= 0.56%, and (c) Inverter-3 kf3= 0.81%.
Frequency (rad/s)
Magnitude (dB)
Phase (deg)
ω0=100π
rad/s
-84.3 ̊
-38.2 ̊
F0(s)
F(s)
Fig. 10. Bode plots for the conventional power measurement filter F0(s)and
the designed lead-lag compensator F(s).
TABLE V
EXP ECT ED STE ADY STATE POW ER MEASUREMENTS FOR TAS K-6
Inverter Before load change After load change
P(pu) Q(pu) P(pu) Q(pu)
1 0.1855 0.0212 0.2221 0.0257
2 0.1599 -0.0044 0.1914 -0.0052
3 0.1481 -0.0162 0.1771 -0.0193
from which the generalized droop rotation angle should
be determined as φ= 0.79 rad. The lead-lag com-
pensator can be designed with τ= 1 ms (say). The
Bode characteristics of the compensator are compared
with that of the original filter in Fig. 10. Students are
also expected to compare the steady state outputs of
their generalized droop controllers against the original
ones from Task-5, for the same three-inverter microgrid
system. Specifically, the generalized droop control does
not enforce proportional active or reactive power sharing,
as seen from the steady-state readings from Table V.
Students are then instructed on the need for secondary
control in order to mitigate the inequity in power sharing.
•Task-7: Here, students will adopt the same design ap-
proach outlined in Task-5 by finding the new maximum
droop gains that make the three-inverter microgrid crit-
ically stable. The objective of this task is to provide
compelling arguments that justify the superiority of their
developed generalized droop controllers from Task-6.
The anticipated outcome is that larger droop gains can
be utilized without causing power sharing instability as
shown in Fig. 11. This extended region is defined as the
improved stability. In addition, the use of larger droop
gains enable the system to reach the steady state at a
faster rate after a disturbance. With the tasks heretofore,
students should have developed a detailed understanding
of inverter control and power sharing stability within a
microgrid.
•Task-8: In this task, students will study the impact of
improper design of the lead-lag compensator on the
system stability. The system stability is theoretically guar-
anteed when the phase lead of the compensator exactly
cancels the lag of the inductive line dynamics. Here, the
students will attempt to violate this condition and verify
that the stability is indeed compromised. Specifically, the
expected results from Fig. 12 show the system becoming
marginally stable when the value of the designed ρ
significantly deviates from the actual R/X ratio on either
side. Note that the actual damping of the system depends
on the value of τselected. Overall, this task contributes to
a better appreciation of the effect that the line dynamics
have on stability.
•Task-9: In order to verify the accuracy of the waveforms
obtained from the hardware setup, the students will first
obtain simulation results considering the new ratings and
system parameters taken from Table II. Note that these
new power and voltage ratings–respectively 200 VA and
21 V (per phase)–should be taken as the per-unit bases
for parameterizing the droop controllers and for scaling
the measured waveforms. On successfully demonstrating
their numerical results to the teaching assistants, they
will be permitted to insert their designed values and
conduct practical experiments. The first purpose of this
approach is to examine students’ ability to relate theory
to practice and train their experimental skills. Second,
IEEE TRANSACTIONS ON POWER SYSTEMS 9
(a) (b) (c)
Fig. 11. Performance of the designed generalized droop controllers when subjected to the same frequency droop gain variations as those from Fig. 9. The
droop gains are: (a) Inverter-1 kf1= 0.81%, (b) Inverter-2 kf2= 0.56%, and (c) Inverter-3 kf3= 0.81%.
(a) (b) (c)
Fig. 12. Active and reactive power waveforms for the three-inverter microgrid for (a) ρ= 1.0, (b) ρ= 0.1, and (c) ρ= 7.0. The damping performance
worsens as the mismatch between the designed and true ρvalue increases.
due to the difference in system parameters between the
simulation and experimental case studies, this task also
allows students to verify that the droop controller design
can be readily adapted for the experimental system by
plugging in the appropriate R/X value. The anticipated
design values of the improved droop controller are ρ=
0.88,φ= 0.72 rad and τ= 1 ms. The students are
expected to identify the individual frequency droop gain
at each node that makes the system unstable (5.11%,
2.27% and 5.11% respectively), and show that the same
droop gains are stable when generalized droop control
is used. The expected waveforms are shown in Fig.
13. The experimental results should be similar to the
corresponding numerical waveforms. Minor differences
between the two can arise depending on the calibration
of the sensors, as well as tolerances in the line and load
impedances.
C. Student Performance and Feedback
The subject of AC microgrids with droop-controlled invert-
ers was included as one of six topics in a graduate module
at the National University of Singapore entitled EE5702—
Advanced Power System Analysis in Fall 2020. The associated
theory aspects were tested during the final examination and
contributed to 12.5% of the final marks in the module. The
assignment described in this paper was one of two design
projects for the module, and contributed an additional 15%
to the final marks. Of the 38 enrolled students, 22 were part-
time students from the industry. The fundamentals of inverter
modeling, control, and simulation were first taught in 6 hours
of lectures. Subsequently, students had four weeks to complete
the design project and submit a detailed report. Two teaching
assistants and one postdoctoral researcher were assigned to the
module.
The distributions of the total marks and the marks scored
per task can be found in Section S1 of the Supplementary File.
Overall, the students did moderately well, with a class average
score of 60% and a median of 69%. The top mark was 98%
and the lowest 2%. It should be noted that the students were
not able to execute Task-9 owing to the COVID-19 pandemic.
At that time, the National University of Singapore was under
partial lockdown, and students were not allowed to work on
campus. Nevertheless, experiments were carried out by the
instructors and the results shared with the students.
A survey was administered at the completion of the module,
the results of which are given in Section S2 of the Supplemen-
tary File. Of the 38 enrolled students, 21 responded. Students
generally appreciated the holistic approach in teaching power
IEEE TRANSACTIONS ON POWER SYSTEMS 10
Simulation
Conventional droop with first-order filter
Generalized droop with lead-lag compensator
Experiment
kf1 increased kf2 increased kf3 increased
kf1 increased kf2 increased kf3 increased
Simulation
Experiment
P1and P3
overlap
Fig. 13. Experimental and corresponding simulation results when the frequency droop gain of each inverter is individually changed from the nominal value
to its stability limit. The nominal droop gains of the inverters are kf= 0.1% and kv= 5.0%, and the stability limits for the individual frequency droop
gains are as follows: kf1: 5.11%, kf2: 2.27%, kf3: 5.11%.
system dynamics with practical case studies and solutions,
with 67% of the respondents expressing positive feedback.
Further, 81% of the respondents reported that the module had
enhanced their critical thinking and interest in power systems.
Based on informal feedback received during the course such
as email exchanges and from office hours, one common
issue was the lack of available textbooks on the topic of
droop-controlled inverters. Although there are published books
in the literature, many are collections of technical papers.
As such, they demand extensive prerequisite knowledge in
power electronics and power systems, and lack illustrative
examples with detailed working steps. Recognizing this issue,
we then presented additional numerical examples to strengthen
students’ learnings along with tutorial sessions on developing
simulation models. This experience clearly raises the need for
a step-by-step textbook targeting beginners regarding system-
level analysis of inverter-based power systems. Against this
background, nearly 95% of the respondents rated the module
to be either difficult or very difficult. At the same time,
the students also agreed that the project helped them better
appreciate the practical applications of such topics that are
traditionally purely research oriented.
At the end of the project, most were able to apply the
abstract control theory into controller design, and validate
the inverter performance through numerical simulations and
hardware-based experimentation. Despite the omission of sev-
eral practical design considerations such as inverters’ inter-
action with synchronous generators and secondary control
functionality, this project trains students with the core skill
sets required to manage inverter-based renewable generation.
Specifically, part-time students found the taught skills to be
useful in their daily engineering jobs. From this viewpoint,
this educational project is arguably a success.
IV. CONCLUSION
An educational project consisting of step-by-step procedures
for inverter modeling, control design, and performance vali-
dation was presented in this paper. The objective is to train
students/engineers on the mathematical concepts of stability
and control using numerical tools and an experimental testbed.
This project was tailored for postgraduate students with prior
experience in power systems and power electronics. Specif-
ically, the project tasks address control design both at the
power electronic converter level and power systems level.
While completing these tasks, students are exposed to the
modeling of a single inverter as well as that of a microgrid
consisting of multiple inverters. The development of droop
controllers enables students to appreciate the importance of
system stability when inverters are increasingly interconnected
in future electric grids. An educational microgrid testbed
has been developed, which enables students to validate their
inverter controllers in a laboratory environment. Based on
the student feedback from Fall 2020, many found the project
both challenging and inspiring. The students understood the
practical benefits of the skills they have mastered during the
IEEE TRANSACTIONS ON POWER SYSTEMS 11
lectures, and have become more passionate about contributing
to a more power-electronic future grid.
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Jimmy Chih-Hsien Peng (S’04-M’12-SM’21) re-
ceived the B.E. and Ph.D. degrees in electrical
and computer engineering from the University of
Auckland, Auckland, New Zealand, in 2008 and
2012, respectively. He is currently an Assistant Pro-
fessor in electrical and computer engineering with
the National University of Singapore, Singapore.
Previously, he was an Assistant Professor with the
Masdar Institute (now part of the Khalifa Univer-
sity), Abu Dhabi, United Arab Emirates. In 2013, he
was appointed a Visiting Scientist with the Research
Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge,
MA, USA, where he became a Visiting Assistant Professor in 2014. His
research interests include power system stability, cyber security, microgrids,
and high-performance computing. He is currently the Secretary of the IEEE
Power and Energy Society Working Group on High-Performance Computing
for Power Grid Analysis and Operation. He is also a member of the Electrical
and Electronics Standards Committee of the Singapore Standards Council.
Gurupraanesh Raman (S’16-M’20) received the
B.Tech. degree in electrical and electronics engi-
neering from the National Institute of Technology,
Tiruchirappalli, India in 2016 and the Ph.D. degree
in electrical and computer engineering from the Na-
tional University of Singapore, Singapore in 2021.
He is currently a Research Fellow at the Singa-
pore ETH Centre and the National University of
Singapore, working on the Future Resilient Systems
programme. His research interests include modeling
data corruption in active distribution systems and
stability analysis of microgrids.
John Long Soon (S’15–M’19) received the Mas-
ter’s and Ph.D. degrees in electrical engineering
from the University of Sydney, NSW, Australia, in
2015 and 2019, respectively. From 2018 to 2019,
he was a Professional Laboratory Officer at the
School of Electrical and Information Engineering
in the University of Sydney, NSW, Australia. Since
2019, he is a Research Fellow at the Department of
Electrical and Computer Engineering at the National
University of Singapore where his focus is on fault-
tolerant converters, reliability of power electronics,
and converter topologies.
Nikos D. Hatziargyriou (S’80-M’82-SM’90-F’09)
is professor in Power Systems at the National Tech-
nical University of Athens. He has over 10 years’
industrial experience as Chairman and CEO of the
Hellenic Distribution Network Operator (HEDNO),
and as executive Vice-Chair and Deputy CEO of
the Public Power Corporation (PPC), responsible
for the Transmission and Distribution Divisions. He
was chair and vice-chair of the EU Technology and
Innovation Platform on Smart Networks for Energy
Transition (ETIP-SNET). He is an honorary member
of CIGRE and past Chair of CIGRE SC C6 “Distribution Systems and
Distributed Generation”. He is Life Fellow Member of IEEE, past Chair of
the Power System Dynamic Performance Committee (PSDPC) and currently
Editor in Chief of the IEEE Transactions on Power Systems. He is the
2017 recipient of the IEEE/PES Prabha S. Kundur Power System Dynamics
and Control Award. He has participated in more than 60 RD&D projects
funded by the EU Commission, electric utilities and industry for fundamental
research and practical applications. He is the author of the book “Microgrids:
Architectures and Control” and of more than 250 journal publications and 500
conference proceedings papers. He is included in the 2016, 2017 and 2019
Thomson Reuters lists of the top 1% most cited researchers and he is a 2020
Globe Energy Prize laureate.
