1
Assessing the Potential of Network Reconfiguration
to Improve Distributed Generation Hosting Capacity
in Active Distribution Systems
Florin Capitanescu, Luis F. Ochoa, Senior Member, IEEE, Harag Margossian, and
Nikos D. Hatziargyriou, Fellow, IEEE
Abstract—As the amount of distributed generation (DG) is
growing worldwide the need to increase the hosting capacity of
distribution systems without reinforcements is becoming nowa-
days a major concern. This paper explores how the DG hosting
capacity of active distribution systems can be increased by means
of network reconfiguration, both static, i.e., grid reconfiguration
at planning stage, and dynamic, i.e., grid reconfiguration using
remotely controlled switches as an active network management
(ANM) scheme. The problem is formulated as a mixed-integer,
nonlinear, multi-period optimal power flow (MP-OPF) which
aims to maximize the DG hosting capacity under thermal and
voltage constraints. This work further proposes an algorithm to
break-down the large problem size when many periods have to be
considered. The effectiveness of the approach and the significant
benefits obtained by static and dynamic reconfiguration options in
terms of DG hosting capacity are demonstrated using a modified
benchmark distribution system.
Index Terms—active distribution system, distributed genera-
tion, hosting capacity, network switching, optimal power flow,
smart grids.
NOMENCLATURE
List of Acronyms
ANM active network management.
APFC adaptive power factor control.
DG distributed generation.
DSO distribution system operator.
MHC maximum hosting capacity.
MINLP mixed integer nonlinear programming.
NLP nonlinear programming.
OLTC on load tap changing transformer.
OPF optimal power flow.
MP-OPF multi-period optimal power flow.
RCS remotely controlled switches.
Sets
N set of nodes.
G set of DG units.
F. Capitanescu is an independent researcher (e-mail: fcapi-
tanescu@yahoo.com). L. Ochoa is with the University of Manchester,
UK (e-mail: luis
ochoa@ieee.org). H. Margossian is with both SnT,
University of Luxembourg, Luxembourg, and K.U. Leuven, Belgium,
(e-mail: harag.margossian@uni.lu). N. Hatziargyriou is with NTUA, Greece
(e-mail: nh@power.ece.ntua.gr). F. Capitanescu and H. Margossian are partly
supported by the Fonds National de la Recherche, Luxembourg, as a part
of the “Reliable and Efficient Distributed Electricity Generation in Smart
Grids” (REDESG) project (C11/SR/1278568).
E set of substations interconnecting the distribution
network with the upstream network.
T set of OLTC transformers.
L set of lines.
S subset of lines with remotely controlled switches.
M set of periods.
Continuous optimization variables
P
gi
installed active power capacity of DG unit at a
predefined location i.
P
curt,m
gi
amount of curtailed generation at node i in period
m.
P
m
ei
active power of the substations interconnecting with
the upstream grid in period m.
Q
m
ei
reactive power of the substations interconnecting
with the upstream grid in period m.
φ
m
gi
phase angle between voltage and current in period
m which defines DG power factor cos(φ
m
gi
).
e
m
i
the real component of complex voltage at bus i in
period m.
f
m
i
the imaginary component of complex voltage at bus
i in period m.
Binary optimization variables
s
ij
binary variable that models the on/off status of a line
switch over all periods (in static reconfiguration).
s
m
ij
binary variable that models the on/off status of a line
switch in period m (in dynamic reconfiguration).
Parameters
g
ij
conductance of the branch linking nodes i and j.
b
ij
susceptance of the branch linking nodes i and j.
b
sh
ij
shunt susceptance of the branch linking nodes i and
j.
P
ci
peak load active power.
Q
ci
peak load reactive power.
ω
m
gi
scalar (ω
m
gi
∈ [0; 1]), allowing to define the genera-
tion level in period m relative to the installed power,
as ω
m
gi
P
gi
and ω
m
gi
P
gi
tan(φ
m
gi
), respectively.
η
m
scalar (η
m
∈ [0; 1]), allowing to define the load
level in period m relative to the peak, as η
m
P
ci
and
η
m
Q
ci
, respectively.
V
i min
minimum voltage limit.
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V
i max
maximum voltage limit.
I
max
ij
maximum current of line linking nodes i and j.
K
I
“bigM”-type constant.
φ
min
gi
minimum phase angle between voltage and current.
φ
max
gi
maximum phase angle between voltage and current.
τ
m
duration of the period m.
γ scalar (γ ∈ [0; 1]) defining the maximum allowed
amount of curtailed energy relative to the uncon-
strained energy harvest over all periods.
˜s
ij
switches status in DSO “business as usual” topology.
∆s
sta
maximum allowed number of topology changes in
static reconfiguration.
∆s
dyn
maximum allowed number of topology changes in
dynamic reconfiguration.
I. INTRODUCTION
T
HE increase of the amount of distributed generation
(DG) (e.g., wind, photovoltaic, etc.) at both medium and
low voltages is encouraged worldwide as a means to meet
today’s stringent environmental constraints. DG installations
are mainly limited by operational constraints, like thermal
limits, voltage rise, or protection issues. The adoption of
the “fit-and-forget” principle, i.e., allowing accommodation
of DG only if it does not lead to constraint violation un-
der the worst-case scenario, leads, in many cases, to costly
network reinforcements or limited DG capacity allowed to
be connected. Furthermore, where unbundling rules apply
(as in Europe), distribution system operators (DSOs) have
generally little or no control over DG placement and size,
provided that grid operational constraints are satisfied. In
this context, non-optimal DG locations may have negative
consequences in several respects: (i) failure to achieve green
energy targets, especially in countries with modest renewable
energy resources, and (ii) limited harvesting of the potential
DG benefits (e.g., deferral of load-led network reinforcements,
reduction in losses and carbon emissions, etc.).
To overcome the drawbacks of the “fit-and-forget” ap-
proach, active network management (ANM) schemes have
been proposed as a solution to significantly increase the
amount of DG capacity, while exploiting DG benefits. Within
this new paradigm, centralized [1] or distributed [2] control
schemes have been proposed, together with additional com-
munication, monitoring and control infrastructure, so as to
manage DG output and other potentially controllable network
elements (e.g., on-load tap changing transformers, etc.).
Although DG location and size is decided by the DG
owner according to the site climatic conditions, gas supplies
and other techno-economic criteria, differentiated connection
charges and regulatory rules can influence DG location de-
cision. Therefore, appropriate tools to determine the most
suitable locations and corresponding penetrations are very
useful [3]–[5]. The assessment of the distribution system DG
hosting capacity and the closely related problem of optimal
DG siting and sizing have become a major research focus [3]–
[5]. Several approaches have been investigated in this context
including: linearized OPF [6], [7], snapshot-based NLP OPF
with additional constraints (e.g., on fault level [8]), multi-
period NLP OPF [9], [10], multi-period MINLP OPF [11], and
snapshot-based metaheuristics (e.g., genetic algorithm [12]–
[14]).
However, these previous works did not explore available
options to increase DG hosting capacity by network reconfigu-
ration. This idea has been articulated recently [15], [16] and its
potential benefits have been illustrated, on a snapshot-basis, by
simple topology enumeration [15] or genetic algorithm [16].
Network reconfiguration is a major DSO control means
which is used for various purposes such as: loss minimization
[17], [18], load balancing [18], post-fault service restoration
[19]–[21], reliability improvement [22], or multi-criteria anal-
ysis [22]. According to the distribution system operation time
frame network reconfiguration can be classified as:
• static reconfiguration which considers all (manually or
remotely controlled) switches and looks for an improved
fixed topology at the planning stage (e.g., from an
yearly/seasonal basis up to operational planning);
• dynamic reconfiguration which considers remotely con-
trolled switching (RCS) in a centralized active network
management (ANM) scheme to remove grid congestions
in real time.
Static network reconfiguration has been very extensively
investigated so far, for snapshot-based loss minimization, rely-
ing on approaches such as: mathematical programming (e.g.,
MINLP with complex voltages expressed in polar coordinates
[23], Benders decomposition approach applied to MINLP
formulation [24], mixed-integer conic programming [25], [26],
mixed-integer linear programming [25], [27], mixed-integer
quadratically constrained programming [28], etc.) or heuristic
techniques (e.g., branch exchange [18], [22], [29], [30], genetic
algorithm [21], [31], memetic algorithm [21], informed search
[20], harmony search algorithm [17], etc.).
Dynamic network reconfiguration has comparatively re-
ceived much less attention and has been studied using ap-
proaches such as: linear programming [32], dynamic program-
ming [19], [33], or branch exchange-based heuristics [22],
[29].
The work described in this paper builds upon the NLP multi-
period OPF framework proposed in [9] by which centralized
ANM schemes are considered to cope with voltage rise and
thermal overload issues. The main contribution of this work
is that it further investigates, by means of a MINLP MP-OPF
formulation, the extent of the potential benefits from adopting
static and dynamic network reconfiguration as options to
increase the ability of distribution systems to host DG. Another
contribution of this work is that it proposes an algorithm for
reducing the size of the MP-OPF for a large number of periods.
It is important to emphasize that, compared to most related
works in network reconfiguration, the proposed approach
considers: a different optimization goal, distributed generation,
the inherent time-varying (renewable) generation patterns and
load behavior which are aggregated into multi time periods,
ANM schemes, and both static and dynamic reconfiguration
options. Given these salient features and the adoption of
rectangular coordinates for voltages, the proposed problem
formulation differs fundamentally from other MINLP-based
works on network reconfiguration such as [23], [24].
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The remaining of this work is organized as follows. Section
II presents the mathematical model of the MP-OPF problem.
Section III describes an algorithm to reduce the problem
size. Section IV provides extensive numerical results with the
method from the application of the approach on the widely
used 34-bus system from [18]. Section V discusses different
implementation aspects of the method. Finally, conclusions are
drawn in Section VI.
II. PROBLEM FORMULATION
The optimization problem is formulated relying on rectan-
gular coordinates of complex voltages to alleviate problem
nonlinearity:
V
i
= e
i
+ jf
i
, V
i
=
q
e
2
i
+ f
2
i
, i ∈ N,
where e
i
and f
i
are the real and imaginary components
respectively, and V
i
is the voltage magnitude.
A. Objective function
The goal of the optimization problem is to maximize the
overall amount of DG that can be hosted by the distribution
system. The corresponding objective function is called here-
after maximum hosting capacity (MHC):
MHC = max
X
i∈G
P
gi
(1)
where P
gi
denotes the installed active power capacity of DG
unit at a predefined location i.
Although this formulation can account for discrete DG
capacities [11], these are modelled as continuous variables.
This is due to the fact that this formulation aims to model the
hosting capabilities of the network rather than actually allocat-
ing DG plants. In addition, this also reduces the computational
burden of the problem.
B. Constraints
1) Power flow equations: the active/reactive power balance
equations at bus i ∈ N in each period m ∈ M are:
P
m
ei
+ ω
m
gi
P
gi
− P
curt,m
gi
− η
m
P
ci
=
X
j∈N
s
m
ij
P
m
ij
=
X
j∈N
s
m
ij
g
ij
(V
m
i
)
2
−
X
j∈N
s
m
ij
[(e
m
i
e
m
j
+ f
m
i
f
m
j
)g
ij
+ (f
m
i
e
m
j
− e
m
i
f
m
j
)b
ij
], (2)
Q
m
ei
+ ω
m
gi
P
gi
tan(φ
m
gi
) − η
m
Q
ci
=
X
j∈N
s
m
ij
Q
m
ij
= −
X
j∈N
s
m
ij
(b
sh
ij
+ b
ij
)(V
m
i
)
2
+
X
j∈N
s
m
ij
[(e
m
i
e
m
j
+ f
m
i
f
m
j
)b
ij
− (f
m
i
e
m
j
− e
m
i
f
m
j
)g
ij
], (3)
where, P
m
ij
and Q
m
ij
denote the active and reactive power
flows between nodes i and j. Although the optimization
model adopts a constant power load model, other load models
(e.g., voltage dependent load model) can be incorporated
straightforwardly.
2) Active/reactive powers on the substations interconnect-
ing with the upstream grid:
P
min
ei
≤ P
m
ei
≤ P
max
ei
, i ∈ E, m ∈ M (4)
Q
min
ei
≤ Q
m
ei
≤ Q
max
ei
, i ∈ E, m ∈ M (5)
3) Branch current limits:
(I
m
ij
)
2
= (g
2
ij
+ b
2
ij
)
(V
m
i
)
2
+ (V
m
j
)
2
− 2(e
m
i
e
m
j
+ f
m
i
f
m
j
)
≤ K
I
(1 − s
m
ij
) + s
m
ij
(I
max
ij
)
2
, ij ∈ L, m ∈ M, (6)
where K
I
is a “bigM”-type constant properly chosen to relax
constraints (6), if line ij is open at the optimal solution, a fact
which is obtained as a result of the solution.
4) Voltage limits:
V
2
i min
≤ (e
m
i
)
2
+ (f
m
i
)
2
≤ V
2
i max
, i ∈ N, m ∈ M. (7)
5) Static reconfiguration:
X
ij∈L
|s
ij
− ˜s
ij
| ≤ ∆s
sta
, (8)
where ˜s
ij
models the DSO “business as usual” topology and
s
ij
models an improved fixed topology over all periods. This
constraint expresses the fact that the DSO is not willing to
perform static grid reconfiguration by using more than ∆s
sta
actions on manually or remotely controlled switches.
6) Radiality: Because most distribution systems operate
radially as a trade-off between investment cost (mainly in
protection systems) and reliability, radiality is considered a
constraint, which is modeled in the following way:
X
ij∈L
s
ij
=
X
ij∈L
˜s
ij
. (9)
The above constraint models the fact that the sum of statuses of
all lines must not change after static reconfiguration. However,
this constraint may be insufficient to ensure radiality in grids
where there are some zero-injection nodes [28]. Actually,
the presence of zero-injection nodes could lead to tricky
cases because, at the optimal solution, these nodes can be
isolated whereas the network remains in a weakly meshed
configuration if this leads to a better objective and satisfies
the problem constraints. A practical solution is adopted by
which each zero-injection bus is replaced with a very small
reactive power load (of value slightly above the power flow
convergence tolerance), enforcing thereby that, in order to
satisfy power flow equations, the node is never isolated. As
the number of zero-injection nodes in a distribution system
is generally small, this change does not affect practically the
result of the optimization.
C. Active network management
To assess the MHC improvement in the presence of ANM
schemes the corresponding constraints are modeled as follows.
1) Voltage control (VC): The control of the secondary
voltage of the OLTC transformers can be incorporated into
the model by choosing properly the bounds V
i min
and V
i max
in constraints (7) for the corresponding busbar.
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2) Adaptive power factor control (APFC): Control of the
DG power factor cos(φ
m
gi
) within some agreed range (e.g.,
between 0.95 lagging and 0.95 leading) can be modeled as:
φ
min
gi
≤ φ
m
gi
≤ φ
max
gi
, i ∈ G, m ∈ M (10)
3) Energy curtailment (EC): Curtailment of DG power
output can be limited to avoid economic unviability. This is
modelled with the following constraint:
X
m∈M
P
curt,m
gi
τ
m
≤ γ
X
m∈M
ω
m
gi
P
gi
τ
m
, i ∈ G (11)
where τ
m
is the duration of the period m, γ is a scalar manag-
ing the amount of curtailed energy relative to the unconstrained
energy harvest over all periods
P
m∈M
ω
m
gi
P
gi
τ
m
.
Furthermore the active power curtailment of DG units is
upper bounded by the DG plant production in period m:
P
curt,m
gi
≤ ω
m
gi
P
gi
, i ∈ G, m ∈ M. (12)
4) Dynamic reconfiguration: The ability of the DSO to
actively operate RCS to remove constraints in real-time can
be modeled by the following constraint:
X
ij∈S
|s
m
ij
− s
m−1
ij
| ≤ ∆s
dyn
, ij ∈ S, m ∈ M. (13)
This constraint models the DSO practical requirement to per-
form a limited number of switching actions ∆s
dyn
to transfer
from one state to another, where s
m
ij
models the possibility to
act on RCS in period m .
Note that this constraint is different from the static reconfig-
uration (8), as it considers only RCS and is period-dependent.
Furthermore, this constraint imposes additional radiality
constraint:
X
ij∈S
s
m
ij
=
X
ij∈S
s
ij
, m ∈ M, (14)
This models the fact that the sum of statuses of lines with
RCS must not change after reconfiguration at every period m.
D. Summary of control variables
The set of control variables of this optimization problem
comprises continuous variables (P
gi
, P
curt,m
gi
, φ
m
gi
, P
m
ei
, Q
m
ei
,
and e
m
i
, f
m
i
at nodes where voltage is controlled) and binary
variables (s
m
ij
and s
ij
), whereas e
m
i
and f
m
i
at all nodes are
optimization variables.
E. Overview of the proposed method
An overview diagram of the proposed method in terms of
data inputs and operational options is given in Fig. 1.
III. REDUCING THE PROBLEM SIZE
The MP-OPF formulation (1)-(14) is a very challenging
MINLP problem due to the incorporation of network reconfig-
uration. Indeed, this, in combination with the number of peri-
ods to be considered, may lead to a very large combinatorial
space. As a consequence, the size of the problem becomes
significantly large and potentially unmanageable by current
commercial solvers. An effective reduction of periods is hence
yes
static reconfiguration ?
dynamic reconfiguration ?
OLTC voltage control ?
power factor control ?
DG adaptive
DG energy curtailment ?
yes
yes
yes
yes
no
grid data
time periods
generation/load
compute maximum
DG hosting capacity
input dataoptions to increase hosting capacity
ANM schemes
Fig. 1. Overview of the proposed method
essential in order to render the problem manageable and reduce
the computational burden of the MINLP MP-OPF problem.
Here, this is done by identifying the potentially binding (or
critical) periods which actually trigger network constraints.
Network reconfiguration (both static and dynamic) is inves-
tigated using the following iterative algorithm:
1) Initialize the set of potentially binding periods by select-
ing only the worst-case demand/generation scenario.
2) Solve the MP-OPF model (1)-(14) by considering only
the current set of potentially binding periods.
Note that if dynamic reconfiguration is allowed, it is
assumed that the network topology change in a given
period impacts all subsequent periods, which keep there-
fore the same topology, as long as a new topology
change in another period occurs
1
.
3) At the solution of the problem (i.e., new topology and
DG nominal capacity) check, using a classical power
flow program, whether there are operational constraints
violations in the remaining periods.
If the operational constraints of any period are satisfied,
then an acceptable solution of the MP-OPF problem is
obtained.
Note that if dynamic reconfiguration is allowed the
feasibility of every period m which presents violated
constraints is further individually checked by a special
1
Assume for instance the following set of k periods
{m
1
, m
2
, m
3
, . . . , m
i−1
, m
i
, . . . , m
k
} and that topology changes occur
in periods m
3
and m
i
. According to the periods processing in dynamic
reconfiguration, the grid operates in three different topologies between
periods: m
1
to m
2
(the original topology), m
3
to m
i−1
, and m
i
to m
k
,
respectively.
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case of MP-OPF model, which is formulated as follows:
min
X
ij∈L
r
ij
+
X
i∈N
(r
i min
+ r
i max
) (15)
s.t. (2) − (5), (9), (13), (14) (16)
(I
m
ij
)
2
≤ K
I
(1 − s
m
ij
) + s
m
ij
(I
max
ij
)
2
+ r
ij
, ij ∈ L
(17)
V
2
i min
− r
i min
≤ (e
m
i
)
2
+ (f
m
i
)
2
, i ∈ N (18)
(e
m
i
)
2
+ (f
m
i
)
2
≤ V
2
i max
+ r
i max
, i ∈ N (19)
r
i min
, r
i max
≥ 0, i ∈ N (20)
r
ij
≥ 0, ij ∈ L (21)
In this formulation constraints (17), (18), and (19)
are relaxations of original operational constraints (6)
and (7), obtained by means of additional non-negative
continuous variables r
ij
, r
i min
, r
i max
. This optimization
problem looks for optimal switching actions on RCS that
minimizes the degree of relaxation (or infeasibility) of
the problem.
Note that if dynamic reconfiguration is needed to remove
violated constraints in a given period, the grid topology
is switched back in the next period to the safe topology
computed by MP-OPF in step 2, since the new topology
resulted after dynamic reconfiguration may not ensure
feasibility of subsequent periods.
4) For periods which lead to violated operational con-
straints build up three period rankings according to
the maximum violation of: lower voltage limit, upper
voltage limit, and thermal limit, respectively. Pick up
the top period
2
from each ranking and add it to the set
of potentially binding periods.
Go to step 2.
Although not described explicitly, the ANM schemes can
be incorporated straightforwardly in this algorithm.
IV. CASE STUDY
In this section, different cases involving potential DG sites,
reconfiguration strategies and the use of the ANM schemes
are studied considering a modified benchmark distribution
system. First, the network’s maximum hosting capacity (MHC)
is assessed adopting static reconfiguration. Then, the benefit of
dynamic reconfiguration as a single ANM scheme is assessed.
The combined benefits of static reconfiguration and classical
ANM schemes are explored next. Finally, the computational
aspects of the proposed technique for reducing the problem
size are discussed.
A. Test system
The proposed approach is applied on the widely used 34-bus
12.66 kV distribution system [18], see Fig. 2. This benchmark
system was modified to consider eight potential sites for DG.
2
Note that if DG curtailment option is allowed, the curtailment may spread
over a significant number of periods, depending on the value of parameter γ.
Consequently, the algorithm performance requires further tuning regarding the
choice of the number of periods to be selected for inclusion into the MP-OPF
problem.
TABLE I
CHARACTERISTICS OF TEST DISTRIBUTION SYSTEM
nodes lines sectionalizing tie feeders potential
switches switches DG sites
34 37 31 5 1 8
Fig. 2. One line diagram of the modified 34-bus distribution grid [18].
A summary of the characteristics of the test system is given
in Table I. In the business as usual network operation, the
normally closed switches (s2 to s32) are called sectionalizing
switches, and the normally open switches (s33 to s37) are
called tie (or emergency) switches.
The peak load is 3.715 MW and 2.3 MVar. The minimum
load is 40% of the peak. Eight potential sites for the deploy-
ment of DG units (G1 to G8) are considered as shown in
Fig. 2. A mix of locations (mid and end points of feeders) for
these generators were chosen in order to mimic different types
of connections.
B. Considerations
Unless otherwise specified, a set of 146 (aggregated) load
periods and two wind profiles (WP1 and WP2) from [9], and
shown in Fig. 3, are considered (i.e., historic demand and wind
data corresponds to central Scotland in 2003). Generators G1,
G2, G7, and G8 are assumed to follow WP1 whereas G3, G4,
G5, and G6 are assumed to behave according to WP2.
Three cases for the deployment of DG are considered:
• Case A: only two sites are available (G5 and G8);
• Case B: only six sites are available (G1, G2, G3, G4, G7,
and G8);
• Case C: all eight sites (G1 to G8) are available.
The minimum and maximum voltage limits are set to 0.95
p.u. and 1.05 p.u. at all nodes, respectively, aligned with MV
limits common in Europe. The voltage controlled by the OLTC
at bus 0 has a deadband
3
of 1.02 p.u. to 1.045 p.u.. The thermal
3
The lower bound has been chosen so that to ensure that all voltages in all
periods are above minimum limit.
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![Fig. 3. Number of coincident hours during one year for 146 aggre ated demand/generation periods and two different wind sites [9]. The shaded cells indicate the set of periods which have been found binding in the optimization problems solved in the paper.](/figures/fig-3-number-of-coincident-hours-during-one-year-for-146-9u3prpac.webp)
