Reactive power sharing in microgrid using virtual voltage

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 11, No. 4, August 2021, pp. 2743~2751
ISSN: 2088-8708, DOI: 10.11591/ijece.v11i4.pp2743-2751  2743
Journal homepage: http://ijece.iaescore.com
Reactive power sharing in microgrid using virtual voltage
Eder A. Molina-Viloria1
, John E. Candelo-Becerra2
, Fredy E. Hoyos Velasco3
1
Tecnologico de Antioquia, Institución Universitaria, Facultad de Ingeniería, Medellín, Colombia
2
Universidad Nacional de Colombia-Sede Medellín-Facultad de Minas-Departamento de Energía Eléctrica y Automática,
Medellín, Colombia
3
Universidad Nacional de Colombia-Sede Medellín-Facultad de Ciencias-Escuela de Física, Medellín, Colombia
Article Info ABSTRACT
Article history:
Received Feb 5, 2020
Revised Nov 9, 2020
Accepted Nov 17, 2020
The traditional droop control strategy has been applied previously in
microgrids (MGs) to share accurately the active power. However, in some
cases the result obtained when sharing reactive power is not the best, because
of the parameters related to the distances from distributed generators (DGs)
to the loads and the power variations. Therefore, this paper proposes a
reactive power control strategy for a low voltage MG, where the unequal
impedance related to the distances between generators and loads requires
adjustments to work with the conventional frequency and voltage droop
methods. Thus, an additional coefficient is calculated from parameters of the
network that relate the location of elements. The test is perfomed by
simulations in the MATLAB-Simulink software, considering a three-node
MG with three DGs and a load that can change power at different periods of
time. The results show that it is possible to improve reactive power sharing
between the DGs located in the MG according to the load changes simulated
and to improve voltages with this method.
Keywords:
Microgrid
Power transfer
Reactive power sharing
Virtual voltage
Voltage control
This is an open access article under the CC BY-SA license.
Corresponding Author:
Fredy E. Hoyos Velasco
Facultad de Ciencias-Escuela de Física
Universidad Nacional de Colombia, Sede Medellín
Carrera 65 Nro. 59A-110, Medellín, 050034, Colombia
Email: fehoyosve@unal.edu.co
1. INTRODUCTION
Microgrids (MGs) help relieve the stress of the main transmission systems, reduce electrical losses,
and improve power quality of the systems as it is very effective to integrate renewable energy sources [1].
Some studies have been carried out in MGs considering different perspectives such as the need of
compensation to improve power quality [2], power management and control [3, 4], protection [5],
programming [6], and communication [7]. An MG can combine several renewable energy units, loads, and
energy storage system [8]. Compared to the conventional distribution system, an MG can be operated
connected to the power grid or island mode [9]. However, in low voltage MGs, the low capacity of reactive
power supply from generation sources and compensators does not allow an exact distribution of reactive
power to avoid overloads [10], because the impedance of the distribution feeder is mainly resistive [11]; in
this case the droop control method is subject to poor transient stability, due to the poor coupling of reactive
power between DG units when no additional inductance is present [11].
Line impedances and DG output impedances significantly affect the sharing of reactive power
during the operating mode connected to the network and during the island mode, due to voltage drops [11].
Consequently, the concepts of droop control have been widely adopted to provide decentralized power,
without relying on communications [12]. Although the frequency droop control technique can be used to

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Int J Elec & Comp Eng, Vol. 11, No. 4, August 2021 : 2743 - 2751
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achieve accurate real power distribution, voltage droop control commonly results in poor reactive power
distribution [13]. This is due to the lack of coincidence in the voltage drops across the DG, which is induced
by the mismatch in the impedance feeder and/or the differences in the powers of the units [14].
At present, the voltage controllers in the MGs are unable to share the reactive power demand among
even identical inverters operating in parallel [15]. Some researchers have previously worked on this issue, as
in [16], which propose an alternative controller for reactive power sharing between parallel inverters with
nominal voltages. The method requires that each unit have a common load voltage measurement, which
limits its applicability in more complex MG scenarios with multiple loads. In [17], the method improves the
distribution of reactive power by changing the voltage bias based on conventional slope control, which is
activated by a sequence of synchronization events through the communication network. In [18], it is
illustrated the control strategy to improve the distribution of reactive power and decrease in a single-phase
MG on the island. In [19], a distributed secondary control strategy is proposed, in which each generator uses
the measurements of other DGs at each sample time for the control of frequency, voltage and reactive power.
In [20], the restoration of frequency and voltage is presented as the secondary control in a hierarchical control
of the MG. In these methods the nominal value of the frequency and voltage deviation is determined in the
central control and then transmitted to the other DGs of the MG to restore them. Therefore, MG control is
assumed centralized in this method.
In [21], a resistive capacitive output impedance (RC-Inverter) is proposed. This equivalent output
impedance of the RC inverter is designed by the introduction of capacitive-resistive virtual impedances. This
usually provides rapid reactive power for low MGs voltages and maintains system voltage stability.
However, the method works by estimating the voltage drops with the virtual impedance, so the error in the
estimate makes the method not work well and accurately. In [22] a voltage source inverter based on servo
system is proposed, which is designed as a reference tracker. A new control is proposed to determine the set
point of reactive power in each inverter to make its contribution in the distribution of reactive power; but it presents
the problem of communication, which makes it very impractical when implemented in industrial cases.
In [23], a new decentralized model is proposed for distribution of reactive power and frequency
restoration in an island system. The proposed method does not need communication link between the DG,
synchronization between each DG is achieved by detecting load change with the Wavelet transform; but this
model is very flawed, since it uses two compensators which act one after the other, after a certain time when
a load change occurs a condition is necessary for the second compensator to act and it is necessary that at that
time there is no another load change, which would be obsolete in the face of major changes as in real
systems. In [24], a novel droop control method for voltage and frequency in autonomous MGs is proposed,
by incorporating predictive mechanisms in the DG. However, this method fails to share reactive power
between the different DGs.
Therefore, the references consulted show that the previous work has focused on the control of active
and reactive powers in MGs in island mode and how the virtual voltage has not been considered based on the
variable load voltage that is connect to the MG as part of the solution. Therefore, the objective of this work is
to share reactive power in an MG using the concept of virtual voltage and how it improves voltage regulation
better than the droop control. Therefore, the contributions in this article are: the virtual voltage variables that
are calculated for each inverter based on the RMS value of the node voltage where the loads are connected.
The exchange of reactive power is achieved in several nodes of a network, once there are some variations in loads.
2. MATERIAL AND METHOD
The P-ω and Q-V droop controls have been used successfully in MGs [25]. This method is simple
and can perform the 'plug-and-play' feature without communication. The P-ω droop control is used to control
and regulate the frequency of the electrical network to share efficiently the active power. In order to control
and track the reference voltage, the voltage control loop uses a PI controller, where the reference voltage is
given by the virtual voltage controller, and the current controller loop uses a P controller to adjust the
inductance low pass filter current, more details can be seen in [26].
Consider the diagram presented in Figure 1, where we can calculate active and reactive powers
flowing to the load from DGs. The active power and the reactive powers transferred from the inverter to the
load is given by (1) and (2). The term P is active power, Q is reactive power, E is the voltage at the terminals
of the DG, R is the resistive part of the line impedance, X is the inductance of the line impedance, and V is
the voltage in the load node. These two equations consider the active and reactive power losses due to the
inductanace associated to the network.
𝑃 =
1
𝑅2+𝑋2
(𝑅𝐸2
− 𝑅𝐸𝑉 𝑐𝑜𝑠 𝛿 + 𝑋𝐸𝑉 𝑠𝑖𝑛 𝛿) (1)

Int J Elec & Comp Eng ISSN: 2088-8708 
Reactive power sharing in microgrid using virtual voltage (Eder A. Molina-Viloria)
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𝑄 =
1
𝑅2+𝑋2
(𝑋𝐸2
− 𝑋𝐸𝑉 𝑐𝑜𝑠 𝛿 − 𝑅𝐸𝑉 𝑠𝑖𝑛 𝛿) (2)
Figure 1. Simplified diagram of the MG
The controlled system has been presented in [26, 27]. Therefore, a small signal model is derived for
the proposed controller, in which the virtual voltage that is based on the RMS voltage of the load node
V_rms, it is considered as the variable controller. By considering small disturbances around the equilibrium
state defined by (∆δe,E,V), equations (1)-(2) can be linearized around this point, then we have:
∆𝑃(𝑠) = (
𝜕𝑃
𝜕𝐸𝑉
) ∆𝐸𝑉(𝑠) + (
𝜕𝑃
𝜕𝛿
) ∆𝛿(𝑠) (3)
We can express this last equation in terms of 𝑘𝑝𝑒 and 𝑘𝑝𝑠 as ∆𝑃 = 𝑘𝑝𝑒∆𝐸𝑣(𝑠) + 𝑘𝑝𝑠∆𝛿(𝑠).
Similarly, the small disturbances around the equilibrium point are defined by (∆𝛿𝑒, 𝐸, 𝑉) and the reactive
power equation can be linearized around this point as expressed in (4).
∆𝑄(𝑠) = (
𝜕𝑄
𝜕𝐸𝑉
) ∆𝑋𝑉(𝑠) + (
𝜕𝑄
𝜕𝛿
) ∆𝛿(𝑠) (4)
In terms of 𝑘𝑞𝑒 and 𝑘𝑞𝑠, this last equation can be expressed as ∆𝑄(𝑠) = 𝐾𝑞𝑒∆𝐸𝑉(𝑠) + 𝑘𝑞𝑠∆𝛿(𝑠);
where the term ∆ indicates the small-signal deviation of the variable around the equilibrium point and theses
variations are expressed as ∆𝑊 = −𝑘𝑝∆𝑝 and ∆𝐸 = 𝐾∆𝑉
𝑟𝑚𝑠. The terms 𝑘𝑝𝑒, 𝑘𝑝𝑠, 𝐾𝑞𝑒 , and 𝑘𝑞𝑠 are
calculated around the equilibrium point, which is the sensitivity of the power flow to the virtual voltage and
voltage angle regulation. Thus, the partial derivative of the active power based on the virtual is shown in the
term as 𝑘𝑝𝑒.
𝑘𝑝𝑒 = (
𝜕𝑃
𝜕𝐸𝑉
) =
(2𝑅𝐸𝑉− 𝑅𝑉 𝑐𝑜𝑠 𝛿+𝑋𝑉 𝑠𝑖𝑛 𝛿)
(𝑅2+𝑋2)
(5)
Similarly, we can obtain the partial derivative of the active power with respect to the angle and it is
expressed as 𝑘𝑝𝑠.
𝑘𝑝𝑠 = (
𝜕𝑃
𝜕𝛿
) =
1
𝑅2+𝑋2
(𝑅𝐸𝑉𝑉 𝑠𝑖𝑛 𝛿 + 𝑋𝐸𝑉𝑉𝑐𝑜𝑠 𝛿) (6)
Now, the partial derivative of the reactive power with respect to the virtual impedance is presented
in (7) as 𝑘𝑞𝑒.
𝑘𝑞𝑒 = (
𝜕𝑄
𝜕𝐸𝑉
) =
(2𝑋𝐸𝑉−𝑅𝑉 𝑠𝑖𝑛 𝛿−𝑋𝑉 𝑐𝑜𝑠 𝛿)
(𝑅2+𝑋2)
(7)
From the partial derivative of the reactive power with respect to the virtual impedance, (8) is
obtained:
𝑘𝑞𝑠 = (
𝜕𝑄
𝜕𝛿
) =
1
𝑅2+𝑋2
(𝑋𝐸𝑉 𝑠𝑖𝑛 𝛿 − 𝑅𝐸𝑉 𝑐𝑜𝑠 𝛿) (8)

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Now, supposs that the real power and the reactive power are measured using a first-order low-pass
filter, the cut-off frequency 𝑊𝑓 of the active power droop controller and the reactive power controller can be
linearized around the same point [26].
∆𝑃𝑚𝑒𝑑 =
𝑊𝑓
𝑆+𝑊𝑓
∆𝑃(𝑠) (9)
∆𝑄𝑚𝑒𝑑 =
𝑊𝑓
𝑆+𝑊𝑓
∆𝑄(𝑠) (10)
Therefore, it follows from (9), (10) that:
∆𝑊(𝑠) =
− 𝐾𝑚𝑊𝑓
𝑆+𝑊𝑓
(𝑘𝑝𝑒∆𝐸𝑣(𝑠) + 𝑘𝑝𝑠∆𝛿(𝑠)) (11)
∆𝐸(𝑠) =
− 𝐾𝑣𝑊𝑓
𝑆+𝑊𝑓
∆𝑉
𝑟𝑚𝑠(𝑠) (12)
We can use the last term in (12) to replace it in (11), and obtain:
∆𝑊(𝑠) =
− 𝐾𝑝𝑊𝑓
𝑆+𝑊𝑓
[𝑘𝑝𝑒 (
𝑆+𝑊𝑓
∆𝑉
𝑟𝑚𝑠(𝑠)) + 𝑘𝑝𝑠∆𝛿(𝑠)] (13)
Using (3)-(6), equation (14) can be obtained:
∆𝑉
𝑟𝑚𝑠(𝑠) = [
∆𝑤(𝑠)−𝑘𝑝𝑘𝑝𝑑∆𝛿(𝑠)
𝑘𝑝𝑘𝑝𝑒𝑘𝑣
] (14)
when we replace the term ∆𝑉
𝑟𝑚𝑠(𝑠) in (13) and we reorganize again, we obtain the expression (15):
∆𝑊(𝑠) =
− 𝐾𝑝𝑤𝑓
𝑆+𝑤𝑓
[𝑘𝑝𝑒 (
𝑆+𝑊𝑓
[
∆𝑤(𝑠)−𝑘𝑝𝑘𝑝𝑑∆𝛿(𝑠)
𝑘𝑝𝑘𝑝𝑒𝑘𝑣
] ) + 𝑘𝑝𝑠∆𝛿(𝑠)] (15)
Finally, by considering that ∆𝑊(𝑆) = 𝑆∆𝛿(𝑆), we can obtain a homogeneous equation that describes
the free movement of the system for small disturbances around the equilibrium point (𝛿, E, V). Equation (16)
considers that 𝑎 = 𝑘𝑝𝑘𝑝𝑒𝑘𝑣, 𝑏 = 2𝑤𝑓𝑘𝑝𝑘𝑝𝑒𝑘𝑣, 𝑐 = 𝑘𝑝
2
𝑘𝑝𝛿𝑤𝑓𝑘𝑝𝑒𝑘𝑣, and 𝑑 = 2 𝑤𝑓
2
𝑘𝑝
2
𝑘𝑝𝑠𝑘𝑝𝑒𝑘𝑣.
𝑎𝑆3
∆𝛿(𝑠) + 𝑏𝑆2
∆𝛿(𝑠) + 𝑐𝑆∆𝛿(𝑠) + 𝑑∆𝛿(𝑠) = 0 (16)
3. RESULTS AND DISCUSSION
The DGs presented in the MG of Figure 1 deliver active power to the loads including the effects of
line impedances. Figures 2(a), 2(b) and 2(c) show the active power delivered by each DG (DG1, DG2, DG3),
based on the strategy used, which are the strategy of droop control vs the virtual voltage RMS. The graphs
show the comparison of the two control strategies and their behavior in the case of a load change in the MG node.
The active powers increase depending on the amount of electric load that are connected to the node.
We can observe how the new proposed controller responds faster and better than the droop controller. It can
be seen that both controllers manage to share the active power precisely, according to the connection and
disconnection of different loads. We can also detail that the proposed control strategy manages to stabilize
the active power much faster than the fixed value strategy. Furthermore, we can see how generators DG1,
DG2 and DG3 share the active power with two different controllers in their inverters.
Figure 3(a) shows the proposed control strategy of the RMS voltage and Figure 3(b) the droop
control strategy. We see that these strategies manage to share the active power precisely in the face of
different load changes. So during the first 12 seconds we observe the active power consumption of
approximately 2100 W, as a result of which a load of (10+j0.05) Ω is connected. In the 12-second period a
load of (15+j0.05) Ω is connected, in this period the active power consumption of the load in the node is
increased based on the consumption of the previous period, and it is possible to see that both control
strategies respond very well to the connection of the new load, only that the proposed strategy manages to
stabilize at a fixed value the active power much faster than the droop.

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(a) (b)
(c)
Figure 2. Active power obtained with the virtual voltage and droop control strategies; (a) DG1,
(b) DG2, and (c) DG 3
(a) (b)
Figure 3. Active power of DGs obtained with the; (a) virtual voltage and (b) droop control strategies
In the 24-second period a load of (20+j0.08) Ω is connected to the MG node, in this period an
increase in power consumption is generated, but the control strategy acts immediately and recover the active
power of the load at a stable value. In the course of 36 seconds a load (25+j0.10) Ω is connected, in this
period a considerable increase in the active power consumption in the node is generated, but it is possible to
see how the control strategy Proposal responds quickly and manages to stabilize the power value at a fixed
value. In the course of 48 seconds, a load of (50+j0.20) Ω is connected, which causes the active power
supplied by the three generators to increase based on the previous period. At this point we observe how both
controllers respond exceptionally to the load change.
Moreover, two different control strategies in their respective inverters are presented in Figure 4(a)
the proposed RMS voltage control strategy and Figure 4(b) the droop control strategy. We see that only the

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proposed control strategy manages to share the reactive power quickly and it is stable for different load
changes and this is not achieved by the droop control. During the first 12 seconds we can see how a load of
(10+j0.05) Ω is connected in this period of time and the proposed control strategy responds very well to the
connection of the load, delivering a reactive power in proportion to the distance. In the period of 12 seconds
to 24 seconds a load of (15+j0.05) Ω is connected, and the reactive power consumption of the load in the
node is increased based on the consumption of the previous period. In this period of time DG1, DG2 and
DG3 deliver different reactive powers that depend on the distance from the load to each generator.
(a) (b)
Figure 4. Reactive power of DGs obtained with the; (a) virtual voltage and (b) droop control strategies
A load of (20+j0.08) Ω is connected to the MG node in the period of 24 seconds to 36 seconds. In
this period of time it is observed that DG1, DG2 and DG3 increase the reactive power delivered to the MG in
different proportions, as a result of the new load on the MG. Over a period of 36 seconds to 48 seconds a load
(25+j0.10) Ω is connected, which generates an increase in the consumption of reactive power in the MG,
showing that the proposed control strategy responds quickly and manages to stabilize the power at a fixed
value. In the course of 48 seconds the load (50+j0.20) Ω is connected, which causes the reactive power
supplied by the three generators to increase based on the previous period. In this period of 48 to 60 seconds,
we can observe how the proposed control strategy responds much faster and manages to stabilize at a fixed
value much faster than the droop control strategy.
In Figures 5(a), 5(b) and 5(c), we observe the reactive power of the three generators that conform
the MG with the proposed controller and the droop controller, when different electrical loads are connected.
Over the course of the simulation, we can see that the proposed control responds faster and stabilizes in less
time and better than the droop control. Figure 6(a) shows the behavior of how the proposed and the droop
controls response to the connection of different electrical loads over a period of time. Figure 6(b) shows the
behavior of the RMS voltage at the node where the five electrical loads of the MG are connected.
The figure shows the RMS voltage of the proposed control strategy in blue and the droop control
strategy in red. We can observe how the new proposed control responds faster and better than the droop
control, to different load changes. The proposed control strategy allows the frequency of the three generators
to stabilize at a single value, a few seconds after the load changes. Besides, the controller maintains the
frequency close to a reference value and closer than the droop controller after load variations. These results
show that when the connection of the second load is made, the node voltage drops sharply, but immediately it
recovers the voltage to a close original value. Therefore, the proposed control maintains a stable value during
all periods in which the electrical loads are connected and disconnected. However, when the droop control
strategy is used, the voltage drops below the value obtained with the proposed control strategy, which is why
we can conclude according to what has been observed as the proposed new control strategy responds faster
and better than the droop controller.
Figures 7(a) and 7(b) show the active and reactive powers when multiple loads are connected and
disconnected at different periods of time in a node of the MG. The active and reactive powers increase
depending on the amount of loads that are connected to the node. We can observe that the active power and
reactive power consumed by the loads is the same, independent of the control strategy used to regulate and
keep the voltage stable in the node where the loads are connected and disconnected.

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(a) (b)
(c)
Figure 5. Reactive power of DGs obtained with the virtual voltage and droop control strategies; (a) DG1,
(b) DG2, and (c) DG3
(a) (b)
Figure 6. Results obtained with the virtual voltage and droop control strategies; (a) frequency and
(b) load voltage
(a) (b)
Figure 7. Response of the MG node for different load changes; (a) active power and (b) reactive power

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4. CONCLUSION
This paper presented a control strategy using a virtual RMS voltage to share the reactive power
between different DGs in an MG, when electrical loads are connected at different periods of time. Results
were obtained for a system with three DGs, with which it was possible to share reactive power between the
DGs of the MG according to the different load changes. Therefore, at each moment the active power and the
reactive power supplied by the DG increase, and this control strategy based on an adaptive virtual RMS
voltage works successfully when it is related to the load node. The proposed control strategy effectively
regulates the frequency close to the reference value and it also maintains the balances of the active and
reactive powers.
ACKNOWLEDGEMENTS
The authors thank COLCIENCIAS, the Universidad Nacional de Colombia, and the Tecnologico de
Antioquia, Institución Universitaria.
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