Edinburgh Research Explorer
Minimising Energy Losses: Optimal Accommodation and Smart
Operation of Renewable Distributed Generation
Citation for published version:
Ochoa, LF & Harrison, G 2011, 'Minimising Energy Losses: Optimal Accommodation and Smart Operation
of Renewable Distributed Generation', IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 198-205.
https://doi.org/10.1109/TPWRS.2010.2049036
Digital Object Identifier (DOI):
10.1109/TPWRS.2010.2049036
Link:
Link to publication record in Edinburgh Research Explorer
Document Version:
Peer reviewed version
Published In:
IEEE Transactions on Power Systems
Publisher Rights Statement:
(c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other
users, including reprinting/ republishing this material for advertising or promotional purposes, creating new
collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this
work in other works.
General rights
Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)
and / or other copyright owners and it is a condition of accessing these publications that users recognise and
abide by the legal requirements associated with these rights.
Take down policy
The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer
content complies with UK legislation. If you believe that the public display of this file breaches copyright please
contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and
investigate your claim.
Download date: 11. Aug. 2022
1
Abstract—The problem of minimising losses in distribution
networks has traditionally been investigated using a single,
deterministic demand level. This has proved to be effective since
most approaches are generally able to also result in minimum
overall energy losses. However, the increasing penetration of
(firm and variable) Distributed Generation (DG) raises concerns
on the actual benefits of loss minimisation studies that are limited
to a single demand/generation scenario. Here, a multi-period AC
Optimal Power Flow (OPF) is used to determine the optimal
accommodation of (renewable) DG in a way that minimises the
system energy losses. In addition, control schemes expected to be
part of the future Smart Grid, such as coordinated voltage
control and dispatchable DG power factor, are embedded in the
OPF formulation to explore the extra loss reduction benefits that
can be harnessed with such technologies. The trade-off between
energy losses and more generation capacity is also investigated.
The methodology is applied to a generic UK distribution network
and results demonstrate the significant impact that considering
time-varying characteristics has on the energy loss minimisation
problem and highlight the gains that the flexibility provided by
innovative control strategies can have on both loss minimisation
and generation capacity.
Index Terms—Distributed generation, energy losses, wind
power, optimal power flow, smart grids, distribution networks.
I. INTRODUCTION
NERGY LOSSES have been and will remain as one of the
metrics used to assess distribution network performance.
In liberalised electricity markets (e.g., UK) regulators provide
economic incentives to those distribution network operators
(DNOs) that outperform targets set for a given period (e.g.,
allowed loss percentages). Even where targets vary according
to the specific geographical or legacy circumstances of each
DNO, underachievers are subject to economic penalties.
Incentive-based regulation, towards higher performance
networks, is the main driver for minimising losses in
distribution systems.
Traditionally, loss minimisation has focussed on optimising
This work is part-funded through the EPSRC Supergen V, UK Energy
Infrastructure (AMPerES) grant in collaboration with UK electricity network
operators working under Ofgem’s Innovation Funding Incentive scheme – full
details on http://www.supergen-amperes.org/.
The authors are with the Institute for Energy Systems, School of
Engineering, University of Edinburgh, Edinburgh, EH9 3JL, U.K. (e-mail:
luis_ochoa@ieee.org, gareth.harrison@ed.ac.uk)
network (re)configuration [1, 2] or reactive power support
through capacitor placement [3, 4]. However, the transition
from passive distribution networks to active, low-carbon ones
presents opportunities. Although planning issues, the
regulatory framework, and the availability of resources limit
DNOs and developers in their ability to accommodate
(renewable) Distributed Generation (DG), governments are
incentivising low-carbon technologies, as a means of meeting
environmental targets and increasing energy security. This
momentum can be harnessed by DNOs to bring network
operational benefits through lower losses delivered by
investment in DG. The unbundling rules in liberalised markets
preclude ownership of DG by DNOs and prevent the DNO
from directly planning the location and size of DG units.
However, through the provision of information and incentives
DNOs can indirectly steer third party investment in DG
towards technically and economically beneficial locations.
The optimal accommodation and operation of DG plants to
minimise losses has attracted the interest of the research
community in the last fifteen years. The studies found in the
literature can be classified into two approaches: minimisation
of power losses, and minimisation of energy losses.
Minimisation of Power Losses
. Although extensively used
when considering passive networks (without DG), this
approach only caters for a single load level making it
impossible to determine the actual impact of variable forms of
DG (wind, photovoltaics, etc.). This is particularly true with
significant reverse power flows (and losses) occurring during
rated output and minimum load conditions. The inherent
variability of loads means the reduction of losses brought
about by the ‘optimal’ size and location of a firm (e.g., gas)
DG unit during maximum demand might not occur at other
loading levels, resulting in non-optimal energy losses for a
given horizon. This approach has been tackled using impact
indices [5, 6], metaheuristics [7, 8], analytical methods [9-12],
classical methods [13-15] and other techniques [16-18].
Minimisation of Energy Losses
. Capturing the effects that
the variability of both demand and (renewable) generation has
on total energy losses for a given horizon is essential as it
considers the actual metrics used by DNOs [19]. Modeling
DG plants as firm generation (to some extent a less complex
optimisation problem) was adopted for loss analyses using
Tabu Search [20] or Genetic Algorithm (GA)-based
multiobjective approaches [21]. As for variable (renewable)
Minimising Energy Losses:
Optimal Accommodation and Smart Operation
of Renewable Distributed Generation
Luis F. Ochoa, Member, IEEE, and Gareth P. Harrison, Member, IEEE
E
2
generation, the optimal allocation of DG plants based on
impact indices (including losses) was previously proposed by
the authors in [22], and extended to a GA-based
multiobjective formulation in [23]. Energy losses were also
considered in reference [24], where it was presented a multi-
resource GA-based multiobjective technique that catered for
some aspects of active network management through the use
of a linearised Optimal Power Flow (OPF). Energy loss
minimisation was also studied in [25] through the optimal mix
of statistically-modelled renewable sources considering a
passive approach to network management.
Overall, few studies properly investigate the energy loss
minimisation problem (as single or multiple objectives)
considering time-varying demand and generation.
Additionally, the potential advantages of adopting real-time
control and communication systems as part of the future Smart
Grid [26] for loss reduction have been largely neglected. Here,
a multi-period AC Optimal Power Flow technique is adopted
to minimise energy losses by optimally accommodating
variable DG and employing innovative control schemes. It
employs the same computational framework originally
developed to determine the volume of DG that can be
accommodated within distribution networks [26-28].
However, it has a distinct and separate contribution through its
application to loss minimisation particularly with regard to the
potential benefits of Smart Grid technologies. The method
effectively captures the time-variation of multiple renewable
sites and demand as well as the effect of innovative control
schemes within the OPF.
This paper is structured as follows: first, a simple test
feeder is used to contrast the power and energy loss
minimisation approaches. Section III presents the loss-
minimising multi-period OPF and its embedded Smart Grid-
based schemes. In Section IV, the method is applied to a
generic UK distribution network using real demand and wind
speed data: the findings demonstrate the significant impact of
time-variation on energy losses and highlights the benefits of
Smart Grid strategies for both loss minimisation and
renewable penetrations. Finally, section V concludes the work.
II. P
OWER LOSSES VS ENERGY LOSSES
The ‘optimal’ accommodation and sizing of DG units
where the time-varying characteristics of demand are
neglected is very likely to lead to sub-optimal results. Fig. 1
presents a simple 4-bus test feeder with a total peak demand of
7.5MW (network parameters are given in Table II, Appendix).
A 1.01pu target voltage at the grid supply point (GSP)
secondary busbar is assumed. In order to investigate the
impact of DG on losses three cases are evaluated:
1. Maximum Demand – a ‘power only’ snapshot at fixed
maximum DG output and fixed maximum demand;
2. Variable Demand – an energy analysis at fixed
maximum DG output and an annual load curve presented
in Table I (Appendix), and;
3. Variable Demand and DG – an energy analysis where
DG output is driven by wind power data and demand
varies as in case 2.
Operating the DG unit at unity power factor, Fig. 2 shows
the resulting percentage losses relative to the power and
energy delivered (to consumers). In all cases a distinct u-shape
[5, 19] is evident as DG capacity initially lowers losses before
higher capacities see losses rise. The loss benefits vary
between the approaches and the maximum demand ‘power
only’ analysis may be over- or under-estimating losses
depending on the size of the DG. The maximum demand
analysis results in a larger capacity at which minimum losses
occur (see the arrows in Fig. 2) but the losses are lower than
the more realistic ‘energy’ analyses. When the variability of
wind power is introduced the reduction in energy losses is less
significant as most of the time the actual power injection is
lower than the nominal capacity.
The impact of DG units on energy losses will depend on
the specific characteristics of the network, such as demand
distribution and behaviour, topology, as well as the relative
location of the generators and whether their output is firm or
variable. Incorporating these complexities into an optimisation
framework for energy loss minimisation is a challenge that has
only been (partially) addressed by a few studies.
Fig. 1. One-line diagram for the 4-bus test feeder at maximum load.
Fig. 2. Percentage power losses (peak demand) and annual energy losses
relative to the delivered power and energy, respectively.
III. FORMULATING THE ENERGY LOSS MINIMISATION
PROBLEM USING A MULTI-PERIOD AC OPTIMAL POWER FLOW
Optimal Power Flow [29] is widely accepted and mainly
used to solve the economic dispatch problem. It can be
adapted for different objectives and constraints with, e.g., an
OPF-like (reduced gradient) method applied to a (power) loss
minimisation problem [13]. A similar formulation with the
objective of maximising DG capacity has also been adopted in
[30-33]. However, in these OPF-based approaches, only peak
demand and passive operation of the network were considered.
Here, the OPF framework previously developed in [26-28]
is tailored to minimise energy losses across a given time
horizon. The process is designed for balanced distribution
systems such as those in operation in the UK and could be
GSP
(5MW, 1.64MVAr)
OLTC
1 2 3
2 x 30MV
A
15.5MVA
132/33 kV
(2.5MW, 0.82MVAr)
DG
4
15.5MVA
Unity p.f.
0
1
2
3
0246810
Maximum
Demand
Variable
Demand
Variable
Dem&DG
Losses (%)
Nominal DG Capacity (MW)
3
combined with capacitor placement using a method similar to
[34]. Thermal and voltage constraints are accounted for while
catering for the variability of both demand and generation and
the use of Smart Grid-based control schemes. The framework
for handling the variability of, and inter-relationships between,
demand and generation as well as the salient points of the
mathematical formulation are briefly outlined.
A. Framework for Handling Variable Resources and Demand
In networks with significant volumes of variable DG robust
assessment of power flows are often best based on hourly
historic demand and resource time series covering at least a
year [35, 36]. For optimisation applications and depending on
the size of the network, number of DG units, control schemes,
etc., analysis of a whole year’s time series imposes a
significant computational burden. To diminish the number of
periods to be evaluated whilst preserving the behaviour and
inter-relationships between resource and demand, Ochoa et al.
[26] used a process of discretisation and then aggregation
according to the characteristics of ‘similar’ periods. To
illustrate this, Fig. 3 (top) presents a week-long snapshot of
hourly demand and wind power data for central Scotland in
2003 [37]. Fig. 3 (bottom) shows the discrete values following
the allocation of the original data into a series of 7 bins
covering specific ranges ({0}, (0,0.2pu], (0.2pu,0.4pu],…,
(0.8pu,1.0pu), {1.0}) in which the mean values (e.g., 0.3pu for
the (0.2pu,0.4pu] range) characterise each new hour. The
aggregation process groups hours in which the same
combination of demand and generation occur. For instance,
the arrows point to hours where demand is 0.7pu and wind is
zero; these conditions occur for a total of 18 hours in this
particular week. This will constitute a period to be evaluated
along with other combinations each with different overall
duration in the optimisation problem. Ochoa et al. [26]
provides a more detailed treatment of the framework.
Fig. 3. (Top) Winter week hourly demand and wind power for central
Scotland, 2003 [37]. (Bottom) Discretised data processed before aggregating
the coincident hours of each demand-generation scenario.
B. Multi-Period AC Optimal Power Flow
The objective function of this loss analysis-focussed AC
OPF is the minimisation of the total energy (line) losses over a
given time horizon. The multi-periodicity, in terms of
demand/generation combinations is achieved by providing
each combination, m, with a different set of power flow
variables with a unique, inter-period set of generation capacity
variables is used throughout the analysis [26].
The basic multi-period AC OPF formulation minimises the
total energy losses of the network over a time horizon
comprising m periods,
mM
. Using the elements of the
OPF, the objective function is formulated as:
min
1, 2,
,,
PP
lm lm m
mM lL
ff
(1)
where
1,
,
P
lm
f
and
2,
,
P
lm
f
are the active power injections at each
end (denoted 1 and 2) of branch
l, lL ; and,
m
is the
duration of period
m. The difference between the net
injections at each end of the branch defines the energy loss.
The objective is subject to a range of constraints including bus
voltage and branch thermal limits but security, voltage step
and fault level constraints, which can be implemented within
the same framework [31-33], are not considered here to ensure
clarity. No capacity constraint is placed on the new DG units
since the aim is to accommodate as much capacity as is
required to minimise the energy losses. A full mathematical
specification is given in [26].
C. Incorporating Smart Control Schemes
Traditional (passive) networks specify fixed values for
substation secondary voltages and operate DG units at
constant power factors over all load conditions. While DNOs
may vary the substation voltage seasonally or specify power
factors on a time-of-day basis, neither is actively dispatched.
To facilitate understanding of the potential influence of Smart
Grid-based control schemes on loss reduction, a series of
variables and constraints are incorporated in the method. Here,
coordinated voltage control (CVC) and adaptive power factor
control (PFc) have been implemented but generation
curtailment is not, as its main purpose is to allow the
connection of DG capacity beyond firm energy limits which
tends to raise energy losses [26]. This planning orientated
analysis assumes the measurement and control infrastructures
to support the control schemes are in place, and that response
delays are negligible.
1) Coordinated Voltage Control
Dynamic control of the substation transformer tap changer
(OLTC) may allow more DG capacity to be connected by
selecting the OLTC secondary voltage to allow maximum
export from DG whilst ensuring upper and lower voltages are
respected [26]. In each period the OLTC secondary voltage,
mOLTC
b
V
,
, is treated as a variable (not fixed) parameter, varying
within the statutory range (
(,)
b
V
):
,
OLTC
bbmb
VV V
(2)
The OLTC model follows standard OPF practice in
allowing the ‘best’ tap setting to be chosen. This differs from
the strict voltage constraints applied in power flow and in the
OLTC OPF models used in [30]-[33]. In effect OPF’s choice
is mimicking the decision process of the coordination system
in selecting the voltage that delivers most benefit.
0.0
0.2
0.4
0.6
0.8
1.0
1 254973971211451
6
(p.u.)
Wind Demand
0.0
0.2
0.4
0.6
0.8
1.0
1 254973971211451
6
Winter: 1st Week of January
(p.u.)
d0.7-w0.0
4
2) Adaptive Power Factor Control
Many DG technologies can operate at a range of power
factors. It is envisaged that DG can provide a scheme in which
the power angle of each generator,
,
g
m
, is dispatched for each
period within a given range (
(,)
g
):
,
g
gm g
(3)
D. Implementation
The method was coded in the AIMMS optimisation
modelling environment [38] and solved using the CONOPT
3.14A NLP solver. Simulations carried out on a PC (Intel
Core2 2.13GHz, 2GB RAM) were delivered in around 3
seconds for firm generation cases (subsection IV.B) and 3 to 5
minutes for variable generation cases (subsections IV.C and
D),depending on the analysis.
IV. CASE
STUDY
A generic UK medium voltage distribution network is used
to demonstrate the multi-period AC OPF technique. The
characteristics of the network and the corresponding demand
and (renewable) generation data are presented first. In order to
evaluate the impact not only of the optimal accommodation of
variable generation, the loss minimisation problem also
considers the Smart Grid control schemes presented earlier. In
the sequence, the trade-off between energy losses and more
renewable energy is investigated. Finally, the computational
performance is briefly discussed.
A. Network
Fig. 4 shows the EHV1 Network, a 61-bus 33/11kV radial
distribution system available in [39]. The feeders are supplied
by two identical 30MVA 132/33kV transformers. The GSP
voltage is assumed to be nominal while in the demand-only
case (no DG), the OLTC at the substation has a target voltage
of 1.045pu at the secondary. A voltage regulator (VR) is
located between buses 304 and 321, with the latter having a
target voltage of 1.03pu. The OLTCs on the 33/11kV
distribution transformers have a target voltage of 1.03pu (to
ensure supply on the rural 11kV feeders within voltage limits).
Voltage limits are ±6% of nominal, reflecting UK practice.
The total peak demand is 38MW.
Six wind generation sites are available considering two
different wind profiles: WP1 and WP2. The group of buses
1105, 1106 and 1108 are considered to be sufficiently close
geographically to all use the WP1 profile. The second profile
is used by the remaining sites (1113, 1114, 1115) located in
the island connected by the subsea cable (line 318-304). While
in the same geographic area, these two groups are far enough
apart to have different, if related, wind profiles.
Demand and generation data correspond to central Scotland
in 2003. The wind production data was derived from the UK
Meteorological Office measured wind speed data and have
been processed and applied to a generic wind power curve
[37]. The discretisation and aggregation process presented in
section III.A is applied to the 2003 hourly data. The extra
wind profile means each scenario has an extra generation
element, i.e., demand-generation-generation (e.g., 1.0pu-
0.3pu-0.5pu). The 8760 hours are reduced to an equivalent 56
periods. The aggregation process resulted in a load factor of
0.639, and capacity factors of 0.415 and 0.483, for WP1 and
WP2, respectively. The error relative to the actual data is less
than 1% in all cases, indicating that the method preserves the
original behaviour. Table III (Appendix) presents the number
of aggregated hours for each of the considered multi-periods
(i.e., demand/generation/generation scenarios). The extra wind
profile requires the inclusion of a set of new generators with
associated variables and parameters within the appropriate
constraints.
Fig. 4. UK GDS EHV1 Network [39] and potential locations for distributed
wind power generation.
B. Firm Generation
Considering the original configuration without DG, at peak
demand (38MW) power losses are 6.94% while in annual
energy terms the aggregated demand profile from Table I
implies an annual consumption of 214GWh and energy losses
of 4.7% (comparable with typical UK rural networks).
First, the impact of firm (constant) generation on losses is
studied for both the peak and variable demand scenarios. The
network is operated as business as usual (BAU) without Smart
Grid control schemes. The total DG capacity (at three different
fixed power factor settings) and the corresponding losses
found by the analysis are presented in Fig. 5. The energy
analysis, able to evaluate the losses at every demand scenario,
produces very different results from the peak analysis. Indeed,
for this network, the annual energy losses can be reduced with
a much smaller capacity than that found when only peak load
is considered. Nonetheless, in both cases the technique is able
to accommodate DG units such that losses are significantly
reduced. For instance, unity power factor operation of
generators (with 14.6MW total capacity) can decrease annual
energy losses by 60%. For peak demand only, the reduction is
more than 70% but requires more than 22MW total capacity.
The corresponding breakdown of capacities for each DG
GSP
305
OLTC
1113
Node Inde
x
LEGEND
100
302
303
1102
306
1103
307
1104
1105
308
309
1106310
312
1107
313
314
1108
315
1101301
316
317
1109
1110319338
341
340
339
318
304
1111321
320
311
subsea cable
322
1114
1115326
1112324
328
1113325342
331
327
1116328
329
1117
330
337
335
332
333
1118334
336
interconnector
V
R
DG
DG
DG
DG
DG
DG
