MIMO design of voltage controllers
for Distributed Generators
Anna Rita Di Fazio, Giuseppe Fusco, Mario Russo
Department of Electrical and Information Engineering
University of Cassino and Southern Lazio
Cassino, Italy
{a.difazio, fusco, russo}@unicas.it
Abstract—A large penetration of Distributed Generation (DG)
may severely impact on the voltage profiles along LV distribution
feeders. The first, cheapest and simplest step that can be
undertaken is to involve DG units in the voltage control of the LV
distribution networks, adopting a fully-decentralized architecture
and avoiding any additional communication infrastructure. The
paper proposes a design methodology for voltage control of
DG units: a local controller measures and regulates the voltage
at the node to which each DG unit is connected by acting
on the DG reactive power injections and without any need
for data or measurement exchange with other controllers. The
controller design is based on a structural MIMO model of
the distribution system and ensures a satisfactorily regulation,
while avoiding any operation conflict among DG units. Stability
analysis is also presented. The results of numerical simulations
in PSCAD/EMTDC environment are discussed to validate the
proposed approach.
Index Terms—Distributed Generation, Distribution Systems,
Voltage Regulation, Reactive Power Control, MIMO model
I. I NTRODUCTION
The inflexible structure of existing distribution systems
is inadequate to sustain a large penetration of Distributed
Generation (DG). In particular, LV distribution systems often
lack of monitoring and automated control systems, and are
designed to deliver strictly-unidirectional power flows from the
secondary substation through radial feeders to the consumers.
In this frame, voltage control represents a fundamental issue
when connecting a large amount of DG to LV distribution
systems [1]–[3]. In fact, the connection of large amount of
DG causes inverse power flows and possible over-voltages
along the LV feeders. Consequently, maintaining the nodal
voltages within the required limits is a challenge for the LV
distribution system operators. At the same time, the large
number of nodes along LV feeders and the large number
of existing LV networks push for finding cheap solutions to
the voltage control problem, avoiding the installation of new
measurement and control equipment and of highly-performing
communication infrastructures.
The first, cheapest and simplest step that can be undertaken
is to involve DG units in voltage control of the LV distribution
networks, adopting a fully-decentralized architecture, that is
adopting local DG control systems which do not exchange any
data or measurements. A technique that has been proposed in
literature is based on the partial curtailment of the DG active
power injection in the case of over/under voltages [4]–[6].
Unfortunately, this technique impacts on the active powers
which represent the value added product for the DG owners.
An alternative solution is to act on the reactive powers which
can be injected by some DG units. The advantages of such a
solution are represented by the limited modifications required
to the existing DG control systems and by the absence of
a production cost related to reactive power. As a drawback,
acting on reactive powers has a weaker impact on nodal
voltages with respect to active powers in LV distribution
systems. Within this latter approach, decentralized Volt/Var
control [7]–[9] is adopted in some distribution networks. Such
a control determines the DG reactive power to be injected as
a function of the voltage at the DG terminals, according to a
piecewise linear relationship Q(V ).
The decentralized Volt/Var control presents some stability
problems: the contemporary presence of multiple DG unit
controllers without coordination poses problem of mutual
interactions which may lead to the instability of the system [8],
[10], [11]. For example, if the controller of a DG increases
the reactive power injection so as to support voltage profile
in response to a load increase, then the effects of its action
are viewed by other controllers as a voltage increase and,
consequently, they will act reducing their reactive power
injections. Reversely, these reductions are viewed by the
former controller as a further load increase and consequently
a “hunting” instability among the controllers is established.
Keeping the decentralized architecture and using local reactive power control, the present paper proposes a design
methodology for voltage control of DG units. The idea is to
realize a secure plug and play connection of the DG units to
the distribution system without any need of data exchange with
other control systems but, at the same time, to improve the
nodal voltages by acting on the DG reactive power injections.
A local controller measures and regulates the voltage at the
node to which each DG unit is connected. Its design is based
on a structural MIMO model of the distribution system and
ensures a satisfactorily regulation, while avoiding operation
conflicts among DG units. Stability analysis is also presented.
The results of numerical simulations are discussed to validate
the proposed approach.
0
1
MV/LV
MV distribution
system
L1
lmg
lm1
L2
mg
m1
2
l2
Lm1
n
ln
Lmg
Vj−1
Vj
Rj
Pj−1, Qj−1
Xj
Ln
Pj , Q j
PL,j
QL,j
P̄DG,j
Q̄DG,j
Figure 2. Electric equivalent circuit for the j − th branch.
PV
PV
Figure 1. Distribution feeder with PV units.
II. S YSTEM
B. Network modelling
MODELLING
The aim is to derive a structural MIMO model of the LV
distribution system suitable for decentralized voltage control
design of DG units. Firstly, the DG models are derived. Then,
the network model is developed based on the linearization of
the classical DistFlow equations and on the enforcement of
the border conditions for each feeder. Eventually, the network
model is combined with the model of the DG units, yielding an
accurate MIMO model that accounts for the interaction among
the DG units along a feeder.
Let a LV distribution system be considered with a radial
feeder composed of n nodes; the feeder is supplied by a
secondary substation and other feeders supplied by the same
MV/LV transformer are included in L1 as equivalent active and
reactive powers. Along the feeder, g DG units are connected
to different nodes: the i − th DG unit is connected to the
mi − th node and the ordered set of indexes {m1 , . . . , mg }
denotes the nodes to which the DGs are connected, as shown in
the one-line diagram in Fig. 1. Various types of DG units can
be connected; in the present paper, without loss of generality,
reference is made to PhotoVoltaic (PV) systems which are the
most-widely spread in LV distribution systems.
The aim is to model the network in terms of nodal voltage
amplitude variations in response to the reactive power injections by the DGs. The model of the feeder in Fig. 1 is based
on the steady-state DistFlow equations [12].
The generic j − th branch of the feeder is represented
by the electric circuit shown in Fig. 2. The branch model is
characterized by: three variables at the supplying node, namely
the voltage amplitude Vj−1 , the in-flowing active Pj−1 and
reactive Qj−1 powers; three variables at the receiving node,
namely the voltage Vj , the out-flowing active Pj and reactive
Qj powers; four branch parameters, namely, the resistance Rj
and reactance Xj , the shunt load active PL,j and reactive QL,j
powers. Two additional external variables are included, namely
e DG,j powers related to the DG
the active PeDG,j and reactive Q
which may be connected to the j − th node.
The DistFlow equations for the j − th branch are
Pj = Pj−1 −Rj
2
Pj−1
+ Q2j−1
e DG,j
− QL,j + Q
2
Vj−1
−2 Rj Pj−1 + Xj Qj−1
Qj = Qj−1 −Xj
2
Vj2 = Vj−1
+
A. PV system modelling
The aim of this subsection is to model the PV systems by
identifying the input command that can be used to control
the output injected reactive power and the related input-output
transfer function.
The PV systems are static generators with power electronic
interface to the distribution network. The interface inverter is
typically equipped with a reactive power control loop: on the
basis of a reactive power set-point, the inverter pulses are generated so as to inject the desired reactive power. Then, the DG
reactive power closed-loop response can be characterized by a
simple time constant τDG of few milliseconds. Consequently,
the transfer function referred to the i − th DG is
QDG,i (s) =
1
Ui (s)
1 + s τDG,i
(1)
where QDG,i is the injected reactive power, τDG,i is the time
constant and Ui is the input command, that is the reactive
power set-point to the inverter.
2
+ Q2j−1
Pj−1
− PL,j + PeDG,j
2
Vj−1
(2)
2
(Rj2 + Xj2 ) (Pj−1
+ Q2j−1 )
2
Vj−1
standing for j = 1, . . . , n with
e DG,j = 0
PeDG,j = 0
Q
e DG,j = QDG,k
PeDG,j = PDG,k Q
∀j ∈
/ (m1 , . . . , mg )
∀j ∈ (m1 , . . . , mg )
being k : mk = j
Since (2) are non linear, they are linearized around an initial
point. Let the vector of nodal variables be defined as
T
(3)
xj = Pj Qj Vj2
and let the operating condition in which the DG power
injections are null be considered as initial point and indicated
as
2 T
x0,j = P0,j Q0,j V0,j
Linearizing the DistFlow equations (2) around such an
initial operating condition yields the following branch model
e DG,j 0 T
(4)
∆xj = Jj ∆xj−1 + PeDG,j Q
2
V0,m
1
being
∆xj = xj − x0,j = ∆Pj ∆Qj ∆Vj2
and Jj the Jacobian matrix related to (2)
∂xj Jj =
∂xj−1 x0,j−1
T
(5)
(6)
The linear set (4), (6) can be analytically solved and its
solution can be partitioned yielding the following matrix
relationship [13]
∆V = Γ Q
(7)
T
∆V = ∆Vm2 1 ∆Vm2 2 . . . . . . ∆Vm2 g
QDG,1 QDG,2 . . . . . . QDG,g
∆Vm2 1
1
1+sτDG,1
[Γ]
2
∆Vdes,g
Cg (s)
+
Ug
∆Vm2 g
1
1+sτDG,g
Figure 3. MIMO control scheme for the design.
and the transfer function Ci (s) represents the voltage con2
troller for the i − th DG unit. It is worth noting that V0,m
i
can be interpreted as a bounded bias which depends on the
operating conditions of the feeder, and the dimension of the
plant square matrix P0 (s) is equal to g, independently from
the number of nodes of the distribution system.
III. C ONTROL
DESIGN AND STABILITY ANALYSIS
The control design aims at ensuring a satisfactorily voltage
regulation at nodes at which the DGs are connected while
guaranteeing system stability. Without loss of generality let
the case of two DGs (g = 2) connected at nodes m1 and m2
be considered. The proposed control matrix is
n
1 + τzi s o
C(s) = diag Ci (s) = kci
1 + τpi s
i = 1, 2
where kci , τzi and τpi are design parameters with τzi < τpi .
The open loop matrix F(s) = P0 (s)C(s) takes the form
 kc1 γ11 (1+τz s)

kc2 γ12 (1+τz s)
T
1
and Γ ∈ IRg×g a non singular matrix of known scalars.
C. MIMO modelling for design
By combining the DG and the network modelling, see (1)
and (7), the MIMO model can be written in matrix form as
∆V(s) = Γ G(s) U(s) = P0 (s)U(s)
U1
2
V0,m
g
∆Qn = 0
C1 (s)
+
+
∆V02 = 0
∆Pn = 0
Q =
2
∆Vdes,1
+
2
Vref,g
In (4), for j ∈
/ (m1 , . . . , mg ) the last term is trivially null
and, consequently, can be skipped.
The model for the whole feeder is composed of n sets of
equations of type (4) in n + 1 variables ∆xj for j = 0, . . . n.
Then, to obtain a defined problem, 3 scalar variables must
be fixed by forcing the border conditions of the feeder: the
squared voltage amplitude V02 at the supplying station, which
is assumed to be fixed as slack bus, and the active and reactive
powers, Pn and Qn , flowing out of the last node which are
assumed to be always null. The border conditions can be
expressed in terms of variations as
with
2
Vref,1

F(s) = 
2
(1+τp1 s)(1+τDG1 s)
(1+τp2 s)(1+τDG2 s)
kc1 γ11 (1+τz1 s)
(1+τp1 s)(1+τDG1 s)
kc2 γ22 (1+τz2 s)
(1+τp2 s)(1+τDG2 s)

 (11)
with γiℓ (ℓ = 1, 2) elements of matrix Γ2×2 . Each transfer
function Fiℓ (s) satisfies the condition
(8)
lim Fiℓ (s) 6= 0
s→0
being
T
∆Vm2 1 (s) ∆Vm2 2 (s) . . . . . . ∆Vm2 g (s)
1
G(s) = diag GDG,i (s) =
1 + s τDG,i
T
U(s) = U1 (s) U2 (s) . . . . . . Ug (s)
Choosing kci such that
∆V(s) =
kci >>
(12)
it results
Fii (s)|s=0 >> 1
with U(s) the input vector. From (5) specified for j = mi ,
the voltage output Vm2 i can be written as
2
+ ∆Vm2 i (s)
Vm2 i (s) = V0,m
i
1
γii
(9)
Defining the i − th regulation error
Ei (s) = ∆V 2des,i − ∆Vm2 i (s)
(13)
Then, the voltage control scheme shown in Fig. 3 is derived,
where the variational set-point is defined as
the expression of the steady-state regulation error ess can be
approximated as follows
2
2
2
∆Vdes,i
(s) = Vref,i
− V0,m
i
ess ≈ [F(s)|s=0 ]−1 ∆V des
(10)
(14)
2
2
with ∆V des = (∆Vdes,1
∆Vdes,2
)T the vector of desired
set-points. From (14) using (11) one obtains


1
2
2
γ22 ∆Vdes,1
− γ12 ∆Vdes,2
 kc1 γ11

1


ess ≈

γ22 − γ12 
1
2
2
−∆Vdes,1 + ∆Vdes,2
kc2
(15)
Given ∆V des , for a suitable choice of gains kci satisfying
condition (12) it is possible to guarantee from (15) a limited
steady-state regulation error in terms of variational quantities.
By using (9), (10) and (13), from ess it is possible to
determine the error in terms of voltage amplitudes, as shown
in Sect. IV-A.
The study of the closed-loop system stability can be approached using the Gershgorin theorem [14]. It affirms that if
matrix I + F( ω) is a row or column dominant diagonal the
number N of encirclements of vector det(I + F( ω)) around
the origin for all ω ∈ IR is given by the sum of the numbers ν1
and ν2 of the encirclements of vectors representatives of the
functions 1 + F11 ( ω) and 1 + F22 ( ω), respectively. Hence
N = ν1 + ν2
(16)
According to the Rosenbrok procedure, matrix I + F( ω)
is a row dominant diagonal if
|1 + F11 ( ω)| >
|F12 ( ω)|
(17)
|1 + F22 ( ω)| >
|F21 ( ω)|
(18)
Conditions (17)-(18) are satisfied if the Gershgorin circles,
built on the Nyquist plot of F11 ( ω) and F22 ( ω), respectively, do not encompass the critical point (−1 +  0) for all
ω ∈ IR. For each ω, the radius of the circle is given by the
quantity at the right-hand side of (17) in the case of F11 ( ω),
while in the case of F22 ( ω) by the quantity at the right-hand
side of (18). From a practical point of view, it is sufficient to
draw the Gershgorin circles only for a finite number of values
of ω, in particular at low frequency, since the radius decreases
when frequency increases.
At this point, according to the Nyquist criterium, the closedloop is asymptotically stable if
N = pol
(19)
being pol the number of positive real part roots of the open
loop characteristic polynomial cpol (s).
Parameters τzi and τpi are then designed so as to ensure
that conditions (17), (18) and (19) are satisfied.
IV. C ASE
STUDY
A 0.4 kV − 50 Hz distribution system is considered composed of a three-phase feeder with eight nodes and supplied
by a 20/0.4 kV substation. The 20 kV supplying system is
represented by its Thevenin equivalent seen from the MV/LV
substation, assuming a 1000 M V A short-circuit power and
an open-circuit voltage in the range 0.95 ÷ 1.05 p.u.. The
MV system supplies the 20/0.4 kV 0.25 MVA transformer
TABLE I.
B RANCH ELECTRICAL PARAMETERS
Branch
from node to
1
2
3
4
5
6
7
TABLE II.
Node
number
1
2
3
4
5
6
7
8
node
2
3
4
5
6
7
8
R
[Ω]
0.067
0.038
0.073
0.051
0.061
0.033
0.026
X
[Ω]
0.016
0.009
0.017
0.009
0.009
0.005
0.004
R ATED NODAL LOADS
PL
[kW ]
64.0
0.58
21.0
1.5
0.0
4.4
1.5
4.4
QL
[kV Ar]
32.0
0.26
9.45
0.68
0.0
2.0
0.68
2.0
with 6% short-circuit voltage. The electrical parameters of the
seven lines composing the feeder and of the eight loads are
reported Tables I and II, respectively. Two 20 kW − 25 kVA
PV systems are connected at nodes m1 = 5 and m2 = 7. The
interface inverter is equipped with active and reactive power
control systems. In the remainder, firstly, the proposed design
is described and the stability analysis performed and, then, the
voltage controllers are validated by numerical simulations.
A. Numerical design
Referring to the model of the DG, the values assumed by the
parameters are τDG,1 = 0.05 and τDG,1 = 0.06. Concerning
Γ, it is obtained
!
0.0289 0.0294
Γ=
(20)
0.0289 0.0334
Matrix Γ is calculated assuming the following initial operating
condition: all loads equal to the 60% of their rated values, the
nominal voltage for MV Thevenin equivalent supplying system
and no active and reactive power injection by the DGs. Matrix
Γ in (20) presents a peculiar structure: the elements lower the
main diagonal belonging to the same column have all the same
value.
Starting from Γ the gains of the controllers which satisfy
condition (12) are set equal to kc1 = 300 and kc2 = 250,
respectively. Assuming Vref,1 = Vref,2 = 1.0 p.u., V0,5 =
0.945 p.u. and V0,7 = 0.937 p.u., from (10) it is obtained
2
2
∆Vdes,1
= 0.1070 and ∆Vdes,2
= 0.1220. Then, using (15)
−4
−2 T
it is ess ≈ (−4e
1.51e ) . From (13) with s = 0, it is
obtained ∆V52 = 0.1065 and ∆V72 = 0.1079; finally, from (9)
it is V5 = 0.9998 p.u. and V7 = 0.9929 p.u.. These latter
values, compared with the unitary references Vref,1 and Vref,2 ,
give evidence of the quite small regulation error achieved in
terms of voltage amplitudes.
1
Imaginary Axis
Imaginary Axis
5
0
-5
0.5
0
-0.5
-10
5
10
Real Axis
15
-1
-2
20
10
1
5
0.5
Imaginary Axis
Imaginary Axis
0
0
-1
0
Real Axis
1
2
-1
0
Real Axis
1
2
0
-5
-0.5
-10
0
5
10
Real Axis
15
20
-1
-2
Figure 4. Nyquist plot of F11 ( ω) and Gershgorin circles (top-left). Nyquist
plots of F22 ( ω) and Gershgorin circles (bottom-left). Zoomed view of
F11 ( ω) around the critical point (top-right). Zoomed view of F22 ( ω)
around the critical point (bottom-right).
As concerns the parameter’s value of each controller it is
set τz1 = 0.03, τp1 = 7, τz2 = 0.02 and τp2 = 6. Substituting
in (11) the values of all parameters it results
 8.67(1+0.03 s)

7.35(1+0.02 s)

F(s) = 
(1+7 s)(1+0.05 s)
(1+6 s)(1+0.06 s)
8.67(1+0.03 s)
(1+7 s)(1+0.05 s)
8.35(1+0.02 s)
(1+6 s)(1+0.06 s)


The Nyquist plots of F11 ( ω) and F22 ( ω) together with
four Gershgorin circles drawn at ω1 = 1e−4 (red), ω2 = 1e−3
(green), ω3 = 1e−2 (magenta) and ω4 = 1e−1 (black) are
built and reported in Fig. 4. In particular the two plots at the
right-hand side of Fig. 4 report a zoomed view which show
that the Gershgorin circles do not encompass the critical point.
Conditions (17)-(18) are satisfied and matrix I+F( ω) is then
row dominant diagonal. Moreover, from the analysis of the
Nyquist plots reported in Fig. 4 it is trivial to recognize that
ν1 = ν2 = 0; then N = 0. At this point, since the roots of
polynomial cpol (s) are
{−20, −50/3, −1/6, −1/7}
it results pol = 0. Then condition (19) is fulfilled and the
closed-loop system is asymptotically stable.
B. Numerical simulations
The distribution system under study has been simulated in
PSCAD/EMTDC environment, including the PV systems and
the designed voltage controllers. To validate the performance
and the stability of the system the transients in both unsaturated and saturated operation have been analyzed.
1) Unsaturated operation: The analyzed perturbations are
small so that the DG voltage controllers respond in the linear
range of reactive power variations, without the intervention
of any saturation. Two types of perturbations are considered:
the connection of a load at node 6, in between the two PV
systems, and the step increase (from 1.0 p.u. to 1.005 p.u.)
of the voltage amplitude at the MV busbar of the secondary
substation. In addition two different operating conditions of
the system are assumed:
• Case A: all the loads are equal to half of their rated values
and both the PV systems generate 20 kW of active power;
• Case B: all the loads are increased of the 50% with
respect to their rated values and both the PV systems
generate 0.5 kW of active power.
These cases are considered because they represent extreme
operating conditions that are far from the ones assumed at the
voltage control design state.
To keep the DG reactive power injections in the linear range
of variation, adequate voltage reference set-points are set, in
particular,
• Case A: Vref,1 = 1.023 p.u. and Vref,2 = 1.029 p.u.,
• Case B: Vref,1 = 0.942 p.u. and Vref,2 = 0.935 p.u..
In Figs. 5 and 6 the time evolution of the voltages at nodes
5 and 7 and of the reactive powers injected by the two PV
systems are reported in the Case A, respectively, for the load
insertion and for the step increase of the voltage at MV busbar.
In all figures, the electrical quantities are expressed in p.u. of
the PV systems rated powers. From these figures, it apparent
that the response to both the small perturbations is stable and
that the nodal voltages recover their value near to the set-point
in few seconds, whereas the reactive power injections have a
smooth variation and settle in few tens of seconds. Similar
considerations can be made for the Case B from the Figs. 7
and 8, which report the time evolution of the same quantities
in response to the same two same small perturbations.
2) Saturated operation: The analyzed perturbations are
large so that the DG voltage controllers respond leaving or
entering saturation on reactive power injections. Two perturbations of the voltage amplitude at the MV busbar of the
secondary substation are considered by applying firstly a step
increase from 1.0 p.u. to 1.01 p.u. and then a step decrease
back from 1.01 p.u. to 1.0 p.u. Concerning the operating
conditions of the system, it is assumed that all the loads are
equal to their rated values and both the PV systems generate
12.5 kW of active power. The voltage reference set-points of
both the DG controllers are equal to 1.0 p.u.
In Figs. 9 and 10 the time evolution of the voltages at
nodes 5 and 7 and of the reactive powers injected by the
two PV systems are reported respectively for the step increase
and decrease of the voltage at MV busbar. From the time
evolution of the reactive powers, it is evident that after the first
perturbation both the voltage controllers leave the saturated
operation, in which the reactive power injection is fixed at its
maximum value, that is 0.5 p.u.. After the second perturbation
the controllers leave the linear range of operation and reactive
power is saturated again. It apparent that the response to both
the perturbations is stable in spite of the saturation effect on
reactive powers. Concerning the time evolution of voltages,
it is apparent that, as expected, when the reactive power
saturates, the voltages remain far from voltage reference setpoints.
DG reactive power injections
DG reactive power injections
0.150
0.100
0.360
Qdg1
0.050
Qdg1
0.340
0.000
0.320
-0.050
0.300
-0.100
0.280
Qdg2
-0.150
0.260
-0.200
-0.250
0.240
-0.300
0.220
sec
Qdg2
90.0
95.0
100.0
105.0
110.0
115.0
120.0
125.0
130.0
135.0
140.0
90
100
110
Feeder nodal Voltages
1.0300
130
140
Feeder nodal Voltages
0.9420
Vdg2
1.0290
0.9410
1.0280
0.9400
1.0270
0.9390
1.0260
0.9380
1.0250
0.9370
1.0240
Vdg1
0.9360
Vdg1
1.0230
0.9350
1.0220
0.9340
1.0210
0.9330
1.0200
Vdg2
0.9320
98.0
99.0
100.0
101.0
102.0
103.0
104.0
105.0
106.0
107.0
108.0
Figure 5. Time evolution of the reactive powers injected by DG and of the
voltages at the nodes where DG units are connected – Case A, load variation
98.0
99.0
100.0
DG reactive power injections
102.0
103.0
104.0
105.0
106.0
107.0
108.0
DG reactive power injections
0.400
0.050
0.350
0.000
101.0
Figure 7. Time evolution of the reactive powers injected by DG and of the
voltages at the nodes where DG units are connected – Case B, load variation
0.100
0.300
Qdg2
-0.050
Qdg2
0.250
-0.100
0.200
Qdg1
-0.150
0.150
-0.200
sec
120
Qdg1
0.100
140
150
160
170
180
190
140
150
160
Feeder nodal Voltages
170
180
190
Feeder nodal Voltages
1.0320
0.9440
1.0310
0.9430
1.0300
1.0290
Vdg2
0.9420
Vdg1
0.9410
1.0280
0.9400
1.0270
0.9390
1.0260
0.9380
1.0250
0.9370
1.0240
1.0230
0.9360
Vdg1
0.9350
1.0220
148.0
Vdg2
0.9340
149.0
150.0
151.0
152.0
153.0
154.0
155.0
156.0
157.0
158.0
Figure 6. Time evolution of the reactive powers injected by DG and of the
voltages at the nodes where DG units are connected – Case A, MV voltage
variation
148.0
149.0
150.0
151.0
152.0
153.0
154.0
155.0
156.0
157.0
158.0
Figure 8. Time evolution of the reactive powers injected by DG and of the
voltages at the nodes where DG units are connected – Case B, MV voltage
variation
V. C ONCLUSION
DG reactive power injections
Qdg1
A design methodology for voltage control of DG units in
LV distribution systems has been developed. A local controller
measures and regulates the voltage at the node to which each
DG unit is connected by acting on the DG reactive power
injection. According to a decentralized architecture, no data or
measurement exchange with other controllers is needed. The
design of the local controller is based on a structural MIMO
model of the distribution system. The results of numerical
simulations have shown the effectiveness of the proposed
approach: the designed controllers improve the nodal voltages
by ensuring a satisfactorily regulation. An important feature of
the proposed design methodology is that it avoids operation
conflicts among DG units and system instability, which is the
main limitation of the Volt/Var controls that have previously
been proposed for DG units in LV networks.
Qdg2
0.500
0.480
0.460
0.440
0.420
0.400
0.380
sec
45.0
50.0
55.0
60.0
65.0
70.0
75.0
80.0
85.0
90.0
95.0
Feeder nodal Voltages
Vdg1
1.0000
Vdg2
0.9990
0.9980
0.9970
0.9960
0.9950
R EFERENCES
[1] P. Ferreira, P. Carvalho, L. Ferreira, and M. Ilic, “Distributed energy resources integration challenges in low-voltage networks: Voltage control
limitations and risk of cascading,” IEEE Trans. on Sustainable Energy,
vol. 4, no. 1, pp. 82–88, June 2013.
[2] P. Chen, R. Salcedo, Q. Zhu, F. de León, D. Czarkowski, Z. Jiang,
V. Spitsa, Z. Zabar, and R. Uosef, “Analysis of voltage profile problems
due to the penetration of distributed generation in low-voltage secondary
distribution networks,” IEEE Trans. on Power Delivery, vol. 27, no. 4,
pp. 2020–2028, Oct. 2012.
[3] R. Tonkoski, D. Turcotte, and T. El-Fouly, “Impact of high pv penetration on voltage profiles in residential neighborhoods,” IEEE Trans. on
Sustainable Energy, vol. 3, no. 3, pp. 518–527, July 2012.
[4] S. Conti, A. Greco, N. Messina, and S. Raiti, “Local voltage regulation in
lv distribution networks with pv distributed generation,” in International
Symposium on Power Electronics, Electrical Drives, Automation and
Motion, May 2006, pp. 519–524.
[5] E. Demirok, D. Sera, R. Teodorescu, P. Rodriguez, and U. Borup,
“Evaluation of the voltage support strategies for the low voltage grid
connected pv generators,” in Energy Conversion Congress and Exposition (ECCE), 2010 IEEE, Sep 2010, pp. 710–717.
[6] S. Chalise, B. Poudel, and R. Tonkoski, “Overvoltages in lv rural feeders
with high penetration of wind energy,” in IEEE Power and Energy
Society General Meeting, July 2013, pp. 1–5.
[7] M. Juamperez, G. Yang, and S. Kjaer, “Voltage regulation in lv grids
by coordinated volt-var control strategies,” Journal of Modern Power
Systems and Clean Energy, vol. 2, no. 4, pp. 319–328, Dec. 2014.
[8] P. Jahangiri and D. Aliprantis, “Distributed volt/var control by pv
inverters,” IEEE Trans. on Power Systems, vol. 28, no. 3, pp. 3429–
3439, Aug. 2013.
[9] P. Esslinger and R. Witzmann, “Experimental study on voltage dependent reactive power control q(v) by solar inverters in low-voltage
networks,” in CIRED, Jun 2013, pp. 1–4.
[10] M. Kashem and G. Ledwich, “Multiple distributed generators for distribution feeder voltage support,” IEEE Trans. on Energy Conversion,
vol. 20, no. 3, pp. 676–684, Sept. 2005.
[11] A. R. Di Fazio, G. Fusco, and M. Russo, “Decentralized control of
distributed generation for voltage profile optimization in smart feeders,”
IEEE Trans. on Smart Grid, vol. 4, no. 3, pp. 1586–1596, Sept. 2013.
[12] M. Baran and F. Wu, “Optimal capacitor placement on radial distribution
systems,” IEEE Trans. on Power Delivery, vol. 4, no. 1, pp. 725–743,
Jan. 1989.
[13] A. R. Di Fazio, G. Fusco, and M. Russo, “Decentralized voltage control
of distributed generation using a distribution system structural mimo
model,” Control Engineering Practice, vol. 46, pp. 81–90, 2016.
[14] H. Rosenbrok, Computer aided control systems design. Academic Press,
1974.
0.9940
0.9930
0.9920
0.9910
49.0
50.0
51.0
52.0
53.0
54.0
Figure 9. Time evolution of the reactive powers injected by DG and of the
voltages at the nodes where DG units are connected – Case C, MV voltage
step increase
DG reactive power injections
Qdg1
Qdg2
0.500
0.480
0.460
0.440
0.420
0.400
0.380
sec
99.0
100.0
101.0
102.0
103.0
104.0
103.0
104.0
Feeder nodal Voltages
Vdg1
1.0000
Vdg2
0.9980
0.9960
0.9940
0.9920
0.9900
99.0
100.0
101.0
102.0
Figure 10. Time evolution of the reactive powers injected by DG and of the
voltages at the nodes where DG units are connected – Case C, MV voltage
step decrease