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Title Operational characteristics of non-firm wind generation in distribution networks
Authors(s) Dzamarija, Mario; Bakhtvar, Mostafa; Keane, Andrew
Publication date 2012-07
Conference details 2012 IEEE Power & Energy Society General Meeting. New Energy Horizons - Opportunities
and Challenges, , San Diego, CA
Publisher Institute of Electrical and Electronics Engineers
Item record/more information http://hdl.handle.net/10197/4752
Publisher's statement © 2012 IEEE.
Publisher's version (DOI) 10.1109/PESGM.2012.6345055
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1
Abstract—Distributed wind generation is growing on power
systems across the world. It presents many well established tech-
nical issues in the distribution network, such as voltage rise, net-
work reinforcement requirements or varying power output. Non-
firm generation, i.e. one to which curtailment can apply due to
network infrastructure technical constraints, potentially holds
certain benefits for distributed wind generation. This paper will
demonstrate the operational characteristics of non-firm wind
generation, without the need for network reinforcements. It also
proposes an AC optimal power flow model used for evaluating the
maximum capacity of wind generation and time series AC optimal
power flow for time series calculation in order to determine the
energy output that this type of allocation will make during the
operation stage. Results show that a significant increase of energy
output from non-firm wind generation connected to distribution
networks can be achieved in comparison to the commonly used
firm type of allocation.
Index Terms—distribution networks, optimal power flow,
wind generation
I. NOMENCLATURE
(TS) AC OPF sets, parameters and variables are defined.
Sets
GC
W
SG
B
L
T
Set of generation capacity (indexed by gc)
Set of wind farms (indexed by w)
Set of slack generators (indexed by sg)
Set of buses (indexed by b)
Set of lines and transformers (indexed by l)
Set of time steps (indexed by t)
Variables
(V,δ)
b
(p,q)
w
(p,q)
gc
(p,q)
sg
(p,q)
l
(n,m)
i
l
(n,m)
Voltage magnitude and voltage angle at b
(P,Q) output of w
(P,Q) output of gc
(P,Q) output of sg
(P,Q) injection onto l at (start, end) bus
Current injection onto l at (start, end) bus
This work was conducted in the Electricity Research Centre, University
College Dublin, Ireland, which is supported by the Commission for Energy
Regulation, Bord Gáis Energy, Bord na Móna Energy, Cylon Controls,
EirGrid, EPRI, ESB International, ESB Power Generation, ESB Networks,
Gaelectric, Intel, SSE Renewables, SWS Energy, UTRC and Viridian Power
& Energy. M. Džamarija and A. Keane are supported by Science Foundation
Ireland under Grant Number 06/CP/E005. The authors are with University
College Dublin (e-mail: mario.dzamarija@ucdconnect.ie).
Parameters
(r,x)
l
(p,q)
b
(-,+)
(p,q)
b
V
b
(-,+)
V
ref
b
r
(p,q)
w
(-,+)
p
gc
+
β
gc
β
w
β
sg
β
l
(n,m)
i
l
MAX
t
Resistance and reactance of l
(min/max) (P,Q) demand at b
(P,Q) demand at b
(min/max) voltage magnitude at b
Voltage magnitude at b
r
Reference bus
Available active and reactive power for w
Allocated generation capacity for gc
Location of gc
Location of w
Location of sg
(start,end) bus of l
Maximum current magnitude of element l (kA)
Time step
II. INTRODUCTION
IND generation allocation is increasing in distribution
networks. Given that these resources are generally sited
in remote areas, they present well established issues in distri-
bution networks, such as network reinforcement requirements
and voltage rise. Firm connection of wind generation implies
large investments in new distribution network assets. This pa-
per proposes an alternative operation approach that might de-
lay investments in the network infrastructure.
Firm generation allocation is a traditional and prevailing
approach to power system planning. Firm generation capacity
allocation entails that a generator is allowed to output full
power at any given time, irrespective of other variables in the
network, such as demand, dynamic line ratings or network
configuration [1]. This can result in suboptimal use of distribu-
tion network capacity. The assessment of firm allocation typi-
cally focuses on maximum generation at minimum demand,
usually the worst-case condition for distribution networks.
Maximum wind generation power output occurs rather infre-
quently and coincides with minimum demand rarely. An alter-
native type of connection policy is referred to as non-firm, i.e.
one to which curtailment can apply due to network infrastruc-
ture technical constraints [2]. Although, at some stages, there
is the need for wind power curtailment, non-firm connection
would allow most of the wind energy potential to be exploited,
without network reinforcements. Nevertheless, it remains im-
portant to estimate, in a preliminary feasibility study, how
Operational Characteristics of Non-firm Wind
Generation in Distribution Networks
M. Džamarija, Student Member, IEEE, M. Bakhtvar and A. Keane, Member, IEEE
W
2
much energy curtailment may occur in order to find out if the
investment in wind farms (WF) is economically viable.
Non-firm generation capacity allocation is addressed in the
following works: [1], [3]-[5]. In [1] and [4] generation capaci-
ty is considered to be an inter-period variable, while other var-
iables are multi-period (change in between periods depending
on the generation/demand). In [1], besides the initial set of
generation capacity, a second set of generators, which are con-
nected to the same buses, introduces curtailment. Curtailed
energy is restricted by a defined curtailment factor. It is exam-
ined how the different values of curtailment factor affect the
allocated non-firm capacity. In [3] a methodology is given that
maximizes the energy from DG per euro of connection cost,
while also minimizing the voltage rise. Minimization of the
voltage rise consequently leads to minimization of curtailment
or maximization of non-firm energy. In [5] several profiles of
renewable sources (wind, wave and tidal), together with de-
mand, are considered in an OPF model. Time series OPF cal-
culations are used and OPF is deployed to allow extraction of
the maximum amount of energy from available resources while
maintaining operational limits of the network. It also examines
the economic loss due to curtailment that a renewable genera-
tor may experience.
While the work described in [1], [3] and [4] primarily deals
with the planning aspects of non-firm distributed generation,
the focus of this paper is on the operational issues of non-firm
distributed wind generation. In contrast to previously listed
works, the planning method proposed in this paper will con-
sider an artificial increase in network capacity for a non-firm
generation allocation case, by raising thermal and voltage lim-
its. As a part of this work two AC optimal power flow (AC
OPF) models are introduced. These two models, which are
used for planning and operation purposes, consider current as
the thermal limit for each network element. The time series AC
OPF (TS AC OPF) model is utilized for the operation stage in
a similar way as it is presented in [5]. The TS AC OPF model
has an asymmetrical capability diagram implemented as one of
its functionalities. The capability diagram limits, defined by
the model, can be arbitrarily modified in order to match any
symmetrical or asymmetrical piecewise linear wind turbine
capability diagram. This allows partial decoupling of the active
and reactive power dispatch in the optimization process, whilst
if using fixed power factor control, active and reactive power
dispatch is bound together. Using TS AC OPF, the effects of
network constraints on the active and reactive power dispatch
of non-firm wind generation are examined.
The planning and operation optimization models are pre-
sented in Section III, followed by the case study description in
Section IV. In Section V the results for firm and non-firm cas-
es, for the planning and operation stages, are compared. Oper-
ational characteristics of non-firm wind generation are also
discussed. A potential further research area and conclusion are
given in Section VI.
III. OPTIMIZATION MODEL
AC OPF is an industry accepted method for solving a wide
range of both technical and economic power system optimiza-
tion problems [6]-[8]. In order to find an optimal plan-
ning/operating point (minimum or a maximum of a certain
variable) for a distribution network one needs to formulate a
mathematical optimization problem that defines the power
system and includes its technical data. If an AC power system
is modeled, that calls for a non-linear programming approach,
since the equality and inequality constraints in the models are
non-linear. For the purposes of this case study an AC OPF
model for the planning stage and a TS AC OPF model for the
operation stage are utilized.
A. AC OPF Model (Planning Stage)
In the planning stage the AC OPF model is employed in or-
der to assess available headroom for generation capacity using
a single generation/demand scenario. Considering the issue of
voltage rise, which is usually the most challenging problem
when allocating distributed generation, the worst case of max-
imum generation at minimum load is studied. The allocation of
generation capacity gc is maximized in the planning stage:
1
gc
gc GC
max p .
The capability diagram considered in the AC OPF model is
defined by reactive power limits at maximum active power
output of a generator capacity according to (15).
B. TS AC OPF Model (Operation Stage)
The operation stage differs from the planning stage since it
includes time variant generation and demand. The AC OPF
model is run consecutively at each time step t in order to con-
sider time changing wind and load. This model is referred to as
TS AC OPF. Due to the time variant wind power, generation
capacity gc, used in the AC OPF model, is replaced with WF
w. Nominal power of WFs w matches allocated generation
capacity p
gc
+
, which has been determined previously in the
planning stage. Available wind power p
w
+
, as well as the de-
mand (p,q)
b
, is updated at each time step t, according to time
series data:
2
w t gc
p p , w W, t T
3
t
bb
p,q p,q , b B, t T .
At time step t, η
t
is the demand level relative to the peak
and ω
t
is the wind generation level relative to the allocated
generation capacity p
gc
+
determined in the planning stage. Pa-
rameter t is used as a time series iterations index.
The objective of the operation stage is to maximize energy
export from the WFs to the grid supply point (GSP). If there is
no wind curtailment required, then loss minimization is a sen-
sible objective function. Otherwise, if curtailment is required,
then maximization of WFs power output is a better choice for
the objective function. Depending on the situation for each
time step t, the appropriate objective function is applied. These
two approaches are described as follows.
3
1) Loss minimization objective
For the time steps t in the operation stage, during which
wind power is low, the objective function of the TS AC OPF
model is loss minimization:
4
nm
ll
lL
min p p .
Loss minimization, which is achieved by optimally dis-
patching reactive power of individual WFs according to (16),
will consequentially lead to maximum energy export from
WFs to the GSP. Active power dispatch of individual WFs is a
predetermined variable, whereby it corresponds to wind power
time series data (16).
2) Power output maximization objective
For the time steps t, that are found to be infeasible when
conducting loss minimization (4), WF power curtailment is
required, in order to solve the optimization model. For these
individual time steps t the objective function of the TS AC
OPF model is WFs power output maximization:
5
w
wW
max p .
This is achieved by optimally dispatching active and reac-
tive power of individual WFs. Active power is dispatched in
the range of 70% to 100% of available wind power p
w
+
(17).
That way up to 30% of the available wind power p
w
+
can be
curtailed at every WF. The optimization process will allocate
curtailment in a way such that only WFs violating the network
constraints are curtailed, resulting in minimum overall curtail-
ment, i.e. maximum total power output of all the WFs. The
reactive power output of WFs is within capability diagram
limits defined by (17) and is dispatched such that minimum
curtailment can be achieved.
C. Equality Constraints
The active and reactive power flow injection onto the start
bus n and the end bus m of element l is calculated according to
Kirchhoff’s Voltage Law (KVL):
6
n,m n,m
l l,KVL
p p , , l L V δ
7
n,m n,m
l l,KVL
q q , , l L. V δ
Kirchhoff’s Current Law (KCL) – conservation of real and
reactive power at bus b, used in the AC OPF model is defined:
,
||
|
,8
nm
gc sg
l
b
gc sg l b
gc GC b sg SG b
l L b
p p p p b B
,
||
|
, . 9
nm
gc sg
l
b
gc sg l b
gc GC b sg SG b
l L b
q q q q b B
KCL used in the TS AC OPF model is defined:
,
||
|
, 10
nm
w sg
l
b
w sg l b
w W b sg SG b
l L b
p p p p b B
,
||
|
, . 11
nm
w sg
l
b
w sg l b
w W b sg SG b
l L b
q q q q b B
The lower voltage side of the distribution transformer is
taken as the reference bus b
r
with the voltage magnitude
r
b ref
VV
and voltage angle
0
r
b
.
D. Inequality Constraints
Current flowing at the start and the end of the line or a
transformer l is restricted by the thermal constraint:
,
, . 12
nm
MAX
ll
i i l L
Voltage magnitude at bus b is constrained by min/max val-
ue V
b
(-,+)
:
, . 13
b b b
V V V b B
Voltage angle at bus b is constrained by min/max value:
, . 14
b
bB
The capability diagram for allocated generation capacity gc,
used in the AC OPF model, considers asymmetrical reactive
power limits:
0
0 96 15
0 98
gc
gc gc
gc gc
p
q p tan arccos . gc GC .
q p tan arccos .
Symmetrical and asymmetrical capability diagram limits for
a WF w, used in the TS AC OPF model when minimizing loss-
es:
16
ww
www
pp
w W ,
qqq
or when conducting curtailment:
07
17
www
www
. p p p
w W .
qqq
The minimum and maximum reactive power limit is defined
for each wind farm w by a variable q
w
(-,+)
which depends on the
active power dispatch p
w
, the available wind power p
w
+
and the
allocated generator capacity p
gc
+
. These reactive power limits
are defined in Appendix B as inequality constraints, and are
calculated for each time step t. These limits can also be arbi-
trarily modified in order to match any piecewise linear wind
turbine capability diagram. There are no limitations imposed
on the slack generator, connected to the GSP, since it presents
a strong transmission network.
E. Implementation and Model Validation
The (TS) AC OPF model presented is written in AIMMS
optimization modeling environment [9]. Optimization prob-
lems in this paper are solved using both versions of the
CONOPT NLP solver: 3.14G and 3.14V. CONOPT solver has
4
been developed by ARKI Consulting and Development, Den-
mark. In addition to OPF, AIMMS can also be used to solve
power flow equations with a constant objective function. The
NLP solver then looks for the only feasible solution (basic
power flow problem) and acts as a nonlinear equation solver
[10]. The AC OPF model is validated by comparing its results
with results of power system analysis software: DIgSILENT
PowerFactory [11]. The AC power flow results were found to
be identical for a range of test calculations.
IV. CASE STUDY
The (TS) AC OPF model is demonstrated on a representa-
tive Irish 6 bus 38 kV distribution network shown in Fig. 1.
Minimum and maximum allowable voltage magnitude V
b
(-,+)
at
bus b is set to 36.5 kV and 42.5 kV respectively since it is a
common practice in Ireland to operate the 38 kV network
within this voltage range. The set point for sending bus voltage
(which is also the reference bus b
r
in the two optimization
models) is 41.6 kV and this set point applies on all ru-
ral/overhead line (OHL) networks. Thermal limits for the
OHLs and the distribution transformer are set to nominal val-
ues and are as stated in Appendix C. Since the distribution
network, used for the case study, consists of OHLs that have
negligible shunt susceptance, these values are left out of (6)
and (7). The case study consists of planning and operation
stages.
2 × 31.5 MVA
110/38 kV
2
C (0.63, 0.19)
E (0.46, 0.13)
B (0.71, 0.21)
F (0.62, 0.18)
A (1.25, 0.36)
D (4.11, 1.20)
GSP
1
A Bus Name
(P, Q) Demand (MW, MVAr)
Fig. 1 Representative Irish distribution network at minimum demand
A. Planning Stage
The planning stage is divided into two separate cases: firm
and non-firm generation capacity allocation.
1) Firm generation capacity allocation
Firm capacity allocation considers thermal and voltage lim-
its in the network. It also considers an outage of one of the
distribution transformers, in keeping with the N-1 criterion
which is a standard practice in the distribution system plan-
ning.
2) Non-firm generation capacity allocation
The non-firm capacity allocation approach in this case
study considers thermal and upper voltage limits 10% higher
than the maximum allowed during normal operation as a
means of facilitating extra generation capacity. This would
imply that voltage magnitude V
b
+
at bus b is 46.75 kV. Ther-
mal limits for OHLs are set 10% higher than the value consid-
ered in the case for firm capacity allocation.
B. Operation Stage
Following on from the planning stage, historical wind and
demand time series data is used to capture the operational
characteristic of the allocated generation capacity, as shown in
Fig. 2. Wind time-series data are values recorded in May 2010
for an existing WF on the west coast of Ireland and are scaled
according to the WFs installed power. The operation stage is
run for every quarter hour period in May 2010, which totals
2976 time steps t.
0.0
0.2
0.4
0.6
0.8
1.0
Active power (pu)
May
Wind
Demand
Fig. 2 Quarter hour wind power and demand, relative to peak values, 2010
The operation stage is divided into three separate cases.
1) Loss minimization
Minimization of losses (4) is the approach taken to find the
results in this case. The nominal power of each WF w equals
their respective generation capacity gc that is calculated in the
firm allocation planning stage case. The capability diagram
applied for WFs is shown in Fig. 3b. The depicted asymmet-
rical capability diagram applies to Vestas V90 3.0 MW wind
turbine generators. It is noticeable that the capability diagram,
for higher active power output, can consume more reactive
power than it can produce.
2) Wind power curtailment without thermal constraints
The losses are minimized (4) for the time steps t that do not
require power curtailment and the output power is maximized
(5) for the time steps t that require power curtailment, i.e. no
feasible solution found for loss minimization. The nominal
power of each WF w equals their respective generation capaci-
ty gc that is calculated in the non-firm allocation planning
stage case.
In this case the following simplifications are done: 1-
thermal constraints are removed from the model, 2-capability
diagram used for the WFs is a symmetrical one (Fig. 3a).
Thermal limits are neglected in order to examine the effect of
voltage constraints in isolation. The symmetrical capability
diagram is used so that active and reactive power dispatch is
decoupled, for higher wind power values. In cases where ac-
tive power output value is higher than 22% of the rated WF
power, reactive power can take any value between -0.505 pu
and 0.505 pu (Fig. 3a).
This case is included in the case study in order to explain
how the AC OPF model controls active and reactive power
when operating non-firm wind generation.
