Distribution Network Reconfiguration with
Aggregated Electric Vehicle Charging Strategy Hantao Cui, FangxingLi, Xin Fang
RunshaLong
Dept. of Electrical Engineering and Computer Sci.
School of Electrical and Computer Engineering
The University of Tennessee
The University of Oklahoma
Knoxville, USA
Norman, USA
Contact:
[email protected]
Abstract-With a higher level of electric vehicle load penetrated
earliest research addressed this problem with branch exchange
in the distribution network, reconfiguration could be employed
procedures
to
algorithms
minimize
energy
losses.
Based
on
a
second-order
conic
[3] and is followed by numerous heuristic [8]. Recent research aims to reformulate the
programming formulation, an improved set of network radiality
problem as mixed-integer quadratic programming (MIQP) or
constraints
second-order
is
proposed
using
power-flow
based
network
connectivity conditions. This proves to be a computationally more efficient method compared to the spanning tree constraints.
conic
programming
(SOCP)
to
availability of high-efficiency commercial solvers
utilize
the
[9,10].
To incorporate electric vehicle charging in the reconfiguration
One concern of the SOCP-based reconfiguration model is
model, two aggregated charging strategies are proposed: the
that, in order to ensure radiality, considerable amounts of
arbitrary delay and the peak-avoiding delay. The decision of
binary variables have to be used as branch status indicator,
delay hours is formulated as constraints and co-optimized into
which is the main cause of long computational time. This paper
the reconfiguration model.
Case study on the IEEE 33-bus
system illustrates the performance of the proposed model and the effectiveness of the proposed charging strategy.
Index
Terms-Distribution
network
reconfiguration;
proposed an improvement to the SOCP model in reduced
second
order conic programming; network radiality constraints; electric
model
they are powered by pure electric motors and have zero emissions on road. The increasing penetration of EV charging load into the distribution network is bringing in challenges for the network operations. For example, free and unmanaged EV
[1], increasing power line losses and increasing [2].
Reconfiguration is an approach to maintain operational economy of distribution systems through opening and closing network
topology.
Network
reconfiguration has been adopted to reduce network loss
[3],
balance power between phases generation host capacity
[3] , and increase distributed [4]. Reconfiguration can be employed
to reduce network losses from excess EV charging load under smart grid paradigm
Extensive research has been carried out on the optimization distribution
network
reconfiguration.
The
This work was supported primarily by the Engineering Research Center Program of the National Science Foundation and the Department of Energy under NSF Award Number EEC-1041S77 and the CURENT Industry Partnership Program.
978-1-4673-8040-9/15/$31.00 ©2015 IEEE
second-order
conic
delay hours are co-optimized in the modified reconfiguration bus distribution system of the proposed model and method. 11.
DISTRmUTION NETWORK RECONFIGURATION
This convex model to solve the problem of distribution network reconfiguration is to minimize the energy losses over the network based on AC power flow. Power balance, line current limit and some other constraints are considered. The solution would be a radial configuration of the network indicating the on/off status of the switches on branches.
A.
Problem Formulation - Objective: Energy loss minimization over time
[5 -7], which has not been studied yet. The
strategies are used and co-optimized with the reconfiguration.
for
on
model. Section IV shows the numerical study on the IEEE 33 -
min
performance could be further enhanced if proper EV charging
techniques
based
presents the methodology of the arbitrary delay and the peak
and operation of the distribution system such as overheating
the
model
avoiding delay charging strategies, where the decisions of
charging may have significant impacts on the infrastructure
alter
delay-based,
programming and the connectivity-based radiality. Section III
INTRODUCTION
Electric vehicles (EVs) are gaining popularity worldwide as
to
proposed
This paper is organized as follows. Section 11 describes the
I.
switches
Two
optimized in the reconfiguration model.
reconfiguration
the peak load
complexity.
aggregated EV charging strategies are also formulated and co
vehicle charging strategy
transformers
[10] by
formulating the connectivity-based radiality constraints and
F
nt
=
n
p; :1 x!J.t II 1=1 i=O
(1)
Subject to: - Active power injection constraint lit
I aij.l[gijVi� - Vi.IVj•1 x(gij cosBij +bij sin Bij )] P;:I =I 1=1 jEC(i) (2) =p; � - p; � , i=I, ... ,n
- Reactive power injection constraint
The spanning constraints generate a radial network by
nt
enforcing the following conditions. Equation
QI =" � " � a [-(b.. + b .. /2) xV2t t=1 jEC(i) +Vi,tVj,t x( bij coseij -gij sinei)] =Qi� - Qi�' i=I, ,,., n tj,(
t.l
t)
SI}
node. Every node except for the substation should have one
(3)
- Line current limit
I'�t = at,t [AyVi� + BijVL - 2Vi,tVj,t ( C ij cos eij - Dij sin e)] (5) � It2max ' I = I, . , Aij =gJ + (bij +bsij /2)2 (6) (7) Bij =gi� +bJ Cij =gJ +bij (bij +bSij 12) (8) Dij =gijbsij 12 (9) m
- Spanning tree radiality constraints
fJji +fJji=�'
1=1 .. "m
(10)
I fJ = I , jEC(i) ij
i =1 ,. ,. ,n
(11)
,
.8;j E {O,I}, where
j E C( k)
i = I,... ,n,
O:S:at:S:l,
(12) (13) (14)
j E C(i) 1=1,,,. ,m
and
QL
are the injection of active and reactive
i at time t. aij, also denoted as a" is the switch i and j, indicating the switch status to be open ( a ij 0) or closed (aij I). gij and b ij are the conductance and susceptance of line i-j, respectively. power on bus
status variable of the line-l connecting bus =
concern in its implementation. B.
Second-order Conic Programming Formulation The AC power flow based network reconfiguration model
is non-linear with the presence of power injection equations. A
second-order conic (SOC) reformation is used in the following new variables:
Ui =y;2, i=I,,,.,n R;j,t =Y;,tVj,t COSB;j,t Tj; ,t =Y;,Yj,t sin eij,t
respectively.
i.
Vi•t, Vi.ruin
CU) is the set of buses able to be connected to bus
and
Vi•max
are the voltage magnitude, minimum
tolerable voltage, and maximum tolerable voltage of bus and
t, respectively.
Bj,t is the corresponding voltage
i at
li,t li max are the current and the maximum tolerable current on line (at time t, respectively. fJij is the status variable of whether bus i is the parent node of bus j (flij I) or not (flij 0). time
=
The objective function
angle.
=
(1) is to minimize the total network
losses over the whole simulation period, which is equivalent to
the total active power injections on all buses. Equation (2) and (3) are the active and reactive power injections as a function of
In
where
Q/t =I I Qij =Qi� - Qi�' t=1 jEC(i)
i =I, ,,,, n
(19) (20) (21) (22)
In the process of minimizing energy losses, it is observed
optimum. Note that in the network model
(18)-(22), the new
Ui,t, Rij,t and Tij,t are treated as the decision variables instead of Vi,t and Bij,t. When the model is solved, Vi,t and Bij,t can be obtained by solving (15)-(17). Also note that Rij,t and Tij,t are defined by lines while Ui,t is defined W.r.t. nodes. That variables
means even if line
l connecting nodes i and j is open, the i and j may still be non-zero. Thus the
physical voltage of bus
voltage variables should be redefined by lines equal to the
nodal voltage with the line connected, and to be zero otherwise. Define subsidiary variables
U;,t
and
U;,t
2 Ui,t t < - a, Virnax ' 0< 2 - at Vjrnax - Uj,t
