IEEE Power Electronics Magazine - June 2019 - 23

MPC
This control is used to minimize the error between the reference and the predicted control variables in the next
sampling time [25], and it requires extensive calculations
and is sensitive to parameter variation. MPC offers several
important advantages, such as the constraints on both
inputs and outputs, which can be considered in the calculations. The predictions can provide early warnings of
potential problems.

P=

V 2com
Vcom E
Z cos(i - d) - Z cos(i)

(5)

Q=

V 2com
Vcom E
Z sin (i - d) - Z sin (i).

(6)

The conventional droop method assumes a highly inductive effective impedance between the converter circuit and
the ac bus that means i = 90°, which in turn changes (7)
and (8) into
Vcom E
Z sin (d)
2
Vcom E cos (d) - V com
Q=
.
Z

Power-Sharing Control

P=

This is the second stage of the primary control level that is
responsible for system reliability and performance and
ensures proper sharing of the power between grid distributed units within an MG. In this stage, the control approach
can be based on the droop characteristics or centralized
power-sharing control.

Droop-Based Techniques
Droop-based techniques aim to control the output active
power and regulate the output voltage, which can be
achieved through different approaches, such as the conventional [26] and nonconventional droop methods. The
conventional droop method assumes highly inductive
effective impedance between the converter circuit and
the ac bus. This is to tune the voltage reference of the
converter and control the active and reactive power,
neglecting the frequency harmonics. The relation
between the active power (Po) and the angular frequency
(~ o) related to the reference values of the power (P *) as
well as the relation between reactive power (Q o) and the
DER output voltage (E *) related to the reference value of
the reactive power (Q *) [20] is shown in (2) and (3):
~ o = ~l - D P P
E = E l - D Q Q,

Conventional droop is simple and reliable for the
traditional system because it assumes a high inductive
impedance between the voltage source converter and
the ac bus. Nevertheless, it still cannot be applied for
MG applications, which involve a low-voltage transmission system that is represented as a resistive impedance. To improve conventional droop control, adjustable load sharing is used [27]. This method depends on
adjusting the time constant of the active and reactive
power controllers without any difference in voltage or
frequency. This method is simple for implementation
and robust against system parameter variation. However, this simplicity becomes complexity when nonlinear loads are used. The voltage active power droop
(VPD) and frequency reactive power boost (FQB) methods [26] are implemented mainly for transmission lines,
represented as a resistive effective line impedance load,
which means i = 0, and d can be assumed to be very
small, giving sin (d) . d. With these assumptions, (5) and
(6) become

(2)
Vcom E - V 2com
Z
Vcom E
Q . Z d.

(3)

P.

where
P = Po - P *
Q = Qo - Q* ,
and D P and D Q are the droop factor coefficients that can
be determined based on the steady-state performance condition by adding a PI reactive power compensator in the
grid-connected mode where the PI compensator forces the
DER reactive power output to track its desired value. The
delivered power to the ac bus can be calculated from (4) as
follows [26]:
S = Vcom I * =

Vcom E+i - d V 2com +i
,
Z
Z

(7)

(4)

where (E+d) is the voltage source converter, (Z+i) is the
effective line impedance connected to a common ac bus
voltage (Vcom +i), and active power (P ) and reactive power
(Q) are achieved as in (5) and (6), respectively:

(8)

The VPD/FQB characteristics are shown in Figure 6.
This approach controls the low-voltage MG performance.
However, this system is strongly dependent on system

E

ω

E∗

ω∗

O

Pmax P
(a)

Qmin

O

Qmax

(b)

FIG 6 The droop/boost characteristics for MGs. The (a) VDP
characteristic and (b) FQB characteristic. max: maximum;
min: minimum.

June 2019

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IEEE Power Electronics Magazine - June 2019

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