1
The optimal operation of energy storage in a
wind power curtailment scheme
S. Gill, G. W. Ault Member IEEE, I. Kockar, Member IEEE
Abstract—Generator curtailment allows Distribution Network
Operators to increase the maximum capacity of distributed
renewable generation connections to their networks, but
curtailment means lost revenue for generators. Energy Storage
Systems (ESS) can mitigate curtailment by time-shifting
generation away from congested periods and can combine this
with other tasks. This paper develops a linear-programming
optimization to maximize the revenue generated by an ESS
connected to a wind farm in a curtailment scheme. The storage is
used for curtailment reduction and price-arbitrage in an external
market. A case study is developed and the optimization applied
for storage devices with a range of efficiencies and penetrations.
The effect of storage efficiency on revenue is shown to be
stronger in price arbitrage than in generation-curtailment. An
economic analysis is carried out for a Sodium Sulphur battery
store and it is clear that, at current costs, more valuable revenue
streams are required to achieve economic viability.
Index Terms— Distributed Power Generation, Energy
Storage, Power System Management, Wind Energy.
I. NOMENCLATURE
Network Setup
Local network power demand
PD
Capacity of firmly connected generation
Pfirm
Capacity of non-firmly connected generation
Pnf
Network export / import capacity
Pin/out
Curtailment during period 1 with no store,
Pcurt
referred to as ‘curtailed power’
Storage Device Setup
SOC
State of Charge
Maximum State of Charge (Energy capacity)
SOCmax
Maximum rate of charge
Pcmax
max
Maximum rate of discharge
Pd
εin ,εout ,εrt Charging, discharging and round trip efficiency
Optimization variables
Eic
Energy charging store from grid during period i
Energy discharging store to grid during period i
Eid
Curtailed energy charging store in period i
Eicurt
Spot market price
pi
Price of curtailed energy
picurt
n
Number of time steps
Δt
Length of time step in hours
This work is partly funded through the Centre for Doctoral Training in
Wind Energy Systems at the University of Strathclyde. EPSRC
EP/G037728/1.
Computing provided by the EPSRC funded Faculty of Engineering and
Institute of Complex Science High Performance computer at the University of
Strathclyde.
Economic Analysis
NPV
Net present Value
R
Revenue
C
Costs
r
Discount rate
II. INTRODUCTION
The growth in renewable generation and the challenges this is
placing on power systems means that Energy Storage Systems
(ESS) are an active area of research. As well as pumped
hydro storage, a few newer technology energy storage
installations are now in trial and operation around the world
[1], [2]. Technologies available for energy storage now
include compressed air storage, flywheels and a range of
chemical batteries. Applications of ESS include pricearbitrage, load-leveling and the provision of ancillary services
such as spinning reserve. They also have the ability to assist in
the integration of intermittent renewable generators such as
wind power [3], [4].
The growth in renewable power generation is raising
challenges for the operation of powers systems at all scales.
These include the stochastic and unpredictable nature of the
renewable resources and the geographic distribution of wind
farms, often in remote areas with weak electrical grids. The
location of renewable resources and the relatively small size of
many renewable generators are leading to an increase in
connections at distribution level. In many cases this provides
the only grid connection option, for example in Scotland some
wind farms on the UK grid are located over 50 miles from the
nearest transmission substation [5]. In other cases, the costs of
connecting at high voltages are prohibitive [6].
Under traditional operational arrangements there are strict
limits on the capacity of distributed generation that can
connect to a particular location or distribution network [6]. In
simplified terms, this limit is set by the export capacity from
the location and the minimum local demand level. This ‘firm
capacity’ is available under all normal operating conditions
without requiring any operational management from the
Distribution Network Operator (DNO). To raise the capacity
of generation further requires operational management of
generators and other network components through Active
Network Management (ANM) schemes. One such ANM
approach is generation curtailment where distributed
generators are required to reduce their output under specified
conditions. This is of particular use with low capacity factor
generation such as wind where, a large fraction of time, the
firm generation output and demand level provides adequate
network capacity to operate additional generation. Generation
2
curtailment schemes can allow a significant increase in the
capacity of distributed renewable generation connecting to a
network and can raise the amount of renewable electricity
generated [7], [8]. Whilst this is advantageous in terms of
increasing renewable generation, curtailment represents lost
revenue to the distributed generator owner.
The use of ESS in these situations has an obvious benefit to
the non-firm generator as it can reduce curtailment by storing
otherwise curtailed renewable energy and discharging this
when network capacity is available. But the financial viability
of ESS is likely to hinge on the fact that it can access more
than this one revenue stream from curtailment-reduction.
This paper investigates the optimal scheduling of ESS
cooperating with wind farms and connected to a distribution
network. The work studies the use of ESS in two modes:
curtailment-reduction and price-arbitrage though buying and
selling to a spot market. As both the wind farms and ESS are
small they are modeled as price takers on the spot market and
do not influence prices. The paper develops a linearprogramming optimization problem and uses historical data to
find the maximum revenue that an ESS could make over a 1
year period. Results are developed for a range of efficiencies
and penetrations of ESS. An economic analysis is carried out
for a Sodium Sulphur battery as an example of an ESS
technology to assess the economic viability based on the two
revenue streams and the specific technical and cost parameters
of Sodium Sulphur batteries.
This method finds the upper bounds on revenue in a given
historical period. It provides a useful tool for benchmarking
real-time operational strategies as well as providing useful
information to DNOs about potential power flows in a
network with energy storage included and the potential
opportunities that ESS presents.
Section III provides a summary of the literature in this area.
Section IV lays out the optimization problem. Section V
describes the case studies and presents results. Section VI
carries out an economic analysis on a Sodium Sulphur battery
and sections VII and IX respectively discuss and conclude the
study.
III. LITERATURE REVIEW
The development of curtailment schemes for distributed
generation is relatively new. A number of papers study the
effect of curtailment on the maximum capacity of distributed
generation and on energy generated. Allowing up to 10%
curtailment of generation across a year can, together with
power factor control and coordinated voltage control, more
than double the capacity that can connect [7]. The set up of a
generation curtailment scheme on the Orkney Islands
distribution network in Scotland is described in [9]. The
economic viability of such a scheme will depend on the level
of curtailment experienced, and the principles of network
access applied to the non-firm generation. In [10] a method of
determining the economic feasibility of curtailment is
developed and in a case study it shown that curtailment has the
ability to triple the ‘firm capacity’ level of connection. This
result includes the addition of some generation that will be
curtailed only during network faults as well as ‘Regulated
Non-Firm’ generation which experiences curtailment during
normal operating conditions and corresponds to ‘non-firm’
generation in this study. The study shows that significant
levels of non-firm generation are likely to connect to
distribution networks in the future. The role of distributed
generation curtailment in conjunction with heat-energy storage
and a district heating network is investigated in [11].
The operation of ESS with distributed renewable generation
depends on the market arrangements for the generators. If
generators are penalized for deviating from their bid positions
posted at gate closure a storage device can mitigate the
uncertainty. In [12] control strategies are developed to
minimize penalties applied to a wind farm for deviations from
bid positions. Whilst this is likely to be useful to network
operation, it requires a market mechanism that penalizes
generation for variation from bid positions.
In generation curtailment schemes storage can reduce
curtailment, a strategy that is investigated in [13]. This study
assumes that curtailment occurs at night when demand is low
and it schedules storage on a daily cycle of charging and
discharging. A cost-benefit analysis shows that only ZincBromine flow-batteries are likely to be economically feasible.
The assumption of daily cycling used here will be invalid with
high non-firm generation penetration as curtailment will not
be confined to the night time.
A linear programming optimization solution is proposed in
[14] to maximize the revenue from a wind farm and ESS. No
curtailment is applied and the ESS is only used to time-shift
energy output from the wind-farm and not to buy from the grid
as in an arbitrage strategy. The optimization is extended to a
multi-objective fuzzy-optimization including a risk
management objective. The linear programming algorithm is
similar to that developed in this study but here it is extended to
include curtailment and full price arbitrage.
In [15] an heuristic optimization process is used to maximize
revenue for an ESS connected to a wind-farm in a curtailment
scheme. The problem combines time-shifting of wind-farm
output to avoid curtailment with price-arbitrage on the spot
market. Whilst the method is shown to solve the problem it is
computationally and conceptually complex.
IV. PROBLEM DESCRIPTION
This section develops a linear-programming based
optimization algorithm for the maximization of revenue from
a distribution network connected storage device. The store can
time-shift generation from a wind farm with a non-firm
connection to avoid curtailment and it can carry out pricearbitrage with an external market. Throughout this paper the
term ‘curtailed generation’ is used to refer to the potential
generation that would have been curtailed because of network
constraints when no energy-storage is present.
The problem consists of a network model, storage model and
input time series; data from these are collated into the linear
3
Fig 1. Simple network model off curtailment sch
heme with energ
gy
storage.
opptimization prroblem. Thesee components are describ
bed
sepparately and are followed by a description of how the
alggorithm is implemented
A. Network Mod
del
n
scenarrio modeled is shown in Fig
g. 1.
Thhe simplified network
Thhe components of the schemee are:
- Local demand time series
- An import / export circuiit to an extern
nal network with
w
fixed power carrying
c
capability.
- Firmly connected wind geeneration up to the maxim
mum
capacity calculated from th
he annual minim
mum demand and
a
the import / export
e
capacity
y by:
=
/
+
Fig 2. Generic model oof an energy storaage system.
med that all
For the purposes of this case studdy, it is assum
model sees thee same wind
distributted wind geneeration in the m
profile and as such tthere is perfecct correlation bbetween the
potentiaal output of firm
m and non-firm
m wind generattion.
D. Settiing up the optim
mization
The opptimization is constructed tto maximize tthe revenue
generateed by the ennergy store. T
The problem is initially
formulaated with threee variables forr each period in the timeseries: C
Charging energgy from the ggrid, discharginng energy to
the gridd and charging from curtailedd energy. For aany period, i,
the channge in the statte of charge off the store is reelated to the
energy vvariables via:
∆
(1)
- Non-firmly connected wind generation
n which will be
curtailed wheen the total geeneration on th
he network wo
ould
otherwise ex
xceed the sum of export cap
pacity and currrent
local demand
d.
- Energy Storaage with the ability to trad
de with the spot
s
market and access
a
the curttailed generation from the nonn
firm wind farrm.
B. Storage Modeel
A generic energy
y storage modeel is shown in Fig. 2 and can
n be
used to model most
m forms of en
nergy storage device.
d
It conssists
off an energy con
nversion unit fo
or charging and for dischargiing.
w be the sam
me unit and may
m
Foor many appliccations these will
reppresent, for ex
xample, the po
ower electroniic convertor on a
baattery. Other sy
ystems such ass hydrogen sto
orage will requ
uire
sepparate energy
y conversionss systems fo
or charging and
a
disscharging. Botth charging and discharging will incur lossses,
annd the produ
uct of the efficiencies
e
fo
or charging and
a
disscharging givee the round trip
p efficiency off the energy sto
ore.
Thhe Energy store itself has a maximum
m
and a minimum sttate
off charge.
C. Input time-seeries data
Thhe method requires the use of
o time-series data for netw
work
deemand, wind geeneration produ
uction and spo
ot-market price. In
ann open electriciity market the most appropriate time steps are
thee trading perio
ods, for examp
ple half-an-hou
ur in the UK. The
T
deemand and gen
neration time-seeries will conssist of the averrage
poower level across a single trad
ding-period.
=
(
+
(2)
) + The objeective functionn is formulatedd as:
−
−
,
(3)
,
The pricce that the stoore pays to usee curtailed eneergy is set to
zero in this study too reflect the ffundamental ffact that the
energy that would oth
therwise be cuurtailed is avaiilable to the
storage system at no ccost.
Three s ets of constraiints apply to tthe objective: tthose due to
the consstruction of thhe energy storee itself, those imposed by
the avaailability of ccurtailed generation and thhose due to
networkk constraints.
The connstraints due too the storage deevice are:
0<
0<
0<
0<
+
∆
∆
<
;∀ = 1. .
(4)
<
;∀ = 1. .
(5)
∆
+
∆
(
<
;∀ = 1. .
(6)
<
;∀ = 1. .
(7)
+
(
) −
,
+
,
) +
<
; = 1. .
=0
(8)
(9)
4
Equations 4-7 represent the power limits and equation 8
imposes the constraint that the SOC be within bounds at all
times. In addition, equation 9 ensures that the final state of
charge is the same as the initial state of charge.
The availability of curtailed energy constraint is:
0<
<
;∀ = 1. .
∆
(10)
Finally, the network constraints are:
∆
∆
<
;∀ = 1. .
(11)
<
;∀ = 1. .
(12)
Equations 3 – 12 provide the full formulation of the linear
programming optimization problem.
E. Implementing the optimization
A number of simplifications can be applied to the problem laid
out above. The full problem is an optimization in 3
unknowns. For large problems, a reduction in the size of the
size of the problem leads to significant reductions in the
computational resources required. A number of observations
can be used to reduce the number of variables:
1.
2.
3.
Periods with curtailed energy available: the
network link will be at full export capacity otherwise
curtailment would not occur. There is no capacity to
discharge the store and is therefore constrained to
0. These variables can be removed from the problem.
Periods with more curtailed energy available than
the storage can absorb: If the curtailed energy is
larger than the maximum energy the store can absorb,
and the cost of curtailed energy is 0 or less than the
market price of electricity, the optimization will
choose to use curtailed energy and not to buy from
will therefore be
the spot market. The value of
zero and can be removed from the optimization.
No curtailed energy available: the value of
,
is constrained to 0 and can be removed from the
optimization.
These observations reduce the maximum size of the
optimization to 2 , and the actual size will be smaller than
this by the number of periods during which observation 2 is
valid.
The implementation is carried out in Matlab and makes use of
the optimization toolbar and the interior point solver. The
maximum size of the problem that can be solved on a standard
32-bit machine is approximately 1000 time periods. The limit
is set by the maximum size of the matrix generated during the
optimization. Use of 64-bit Matlab allows up to approximately
8000 time periods to be solved. With half-hour time periods
this solves to an approximately 5 month time-horizon. In this
study a full 1 year time series is split into four 3 month
sections and each is solved as a separate optimization.
V. CASE STUDY
A. Case Description
The case study modeled is based on data for a typical 33kV
distribution network. Demand ranges from 6-30MW and there
is a 35MW circuit to the higher voltage network; there is 41
MW of firmly connected wind generation. Four scenarios are
modeled:
1. No non-firm wind. This is used as a base case; the ESS in
this scenario only operates in arbitrage mode as there is no
non-firm wind curtailment.
2. Low non-firm wind penetration: 10MW capacity
3. High non-firm wind penetration: 20MW capacity
4. Curtailment-reduction only: 20MW non-firm wind power
capacity connected, but the ESS is only able to time-shift
curtailed generation and cannot participate in price
arbitrage. This is implemented by setting all values of Eic
to zero.
The network characteristics and the curtailment applied to
non-firm wind in scenarios 2 and 3 are shown in Table 1.
TABLE 1: CHARACTERISTICS OF THE CASE STUDY NETWORK.
CURTAILMENT AND GENERATION VALUES FOR NON FIRM GENERATION
ARE FOR THE SITUATION WITH NO STORAGE.
Demand
6 – 30 MW
Import / Export Capacity
35 MW
Firm Wind Capacity
41MW
Scenario
Low (2)
High (3)
Non- Firm Capacity
10MW
20MW
Non Firm Generation
306GWh
647 GWh
Curtailed Energy
0.840 GWh
251GWh
Fraction curtailed
0.0267
0.28
No. of periods with curtailment
1020
5839
(out of 17520)
Supply and demand data is taken from a representative UK
distribution network, the time series consist of half-hourly
average demand and generation values for 2009. Fig. 3 (a)
shows a two week period of the normalized data. Demand
displays regular daily, weekly and annual variations. High
demand periods occur during winter months and early
evening, lowest demand occurs during summer nights. By
contrast, the wind generation does not display regular
variations.
The curtailment applied to non-firm wind for the same two
week period is illustrated in Fig. 3 (b) for the high and low
penetration scenarios. With 10MW of non-firm wind installed
only 3.38GWh is curtailed across the year, compared to
250GWh when 20MW is installed. These figures represent
7.5% and 28% of the total available non-firm generation
respectively. The high levels of curtailment seen in the 20MW
scenario will only be viable if the wind farm has a high uncurtailed capacity factor (> 0.45), such wind-farms will be
located in areas of high wind-resource where distribution
networks are likely to be at their most stretched. As well as
increasing the fraction of energy curtailed, the increased
penetration of non-firm wind changes the time structure of
curtailment. With 10MW of non-firm generation 89% of all
curtailment occurs between midnight and 6am. This means
daily cycling algorithms can be applied. But with 20MW of
5
Demand
firm Gen
neration
Normalised Power
1
0.8
0.6
0.4
0.2
0
0
2
48 96 144 192 240 288 336 384 432 480 528 576 624 672
time ( 1/2
2 hour periods)
(a))
demand
10MW
20MW
25
Fig. 4. Example resu
ults from simulaation. A 7 day perriod with (a) the
origginal wind-farm curtailment, (b)) the prices shown and (c) the
opti mal schedule. The shaded section identifiess periods with
curttailment.
power (MW)
20
15
and with the pow
wer to energgy capacity raatio kept at
1MW
W:6MWh.
10
5
0
1 192 240 288 336
3 384 432 480 528 576 624 672
48 96 144
time (Half hour periods)
(b))
Figg. 3. (a) Time seeries of normalizeed demand and generation
g
for tw
wo
weeeks during Octo
ober 2009; (b) cu
urtailment of non
n-firm generation
plootted with netwo
ork demand for the
t same two weeeks. Curtailmen
nt
witth 10MW and 20M
MW are plotted together.
t
0
noon-firm wind only
o
43% of cu
urtailment occu
urs during thesse 6
hoours. In thesee cases the optimization
o
problem
p
is more
m
coomplex and daiily cycling of the
t energy storre would not be
b a
viaable control strrategy.
Ass the UK doess not operate a ‘pool type’ electricity
e
systtem
wiith a true spott market, the spot
s
market iss simulated ussing
daata from the UK
U balancing mechanism
m
[16]. This takes an
avverage of all trades
t
carried out on the op
pen market fo
or a
paarticular period
d over the threee days leading up
u to gate clossure
forr the period [17
7].
ES
SS devices are modeled ass 1MW, 6MW
Wh units and the
folllowing investiigations are conducted:
- The effect off storage efficciency. Stores with round trip
efficiencies ranging from 55
5% to 95% aree modeled.
- Storage charrge cycling. The size and nu
umber of storrage
cycles is inv
vestigated for comparison with fixed cy
ycle
operating sttrategies. Estiimates of liffetimes rely on
knowledge of
o the number and Depth of Discharge (Do
oD)
of storage cycles. The optim
mal schedule fo
or a 75% efficiient
store is used to investigate storage
s
cycling
g.
- Total storag
ge penetration.. The margiinal revenue and
a
marginal curttailment reducction curves fo
or the network are
found in ordeer to show the effect of increeased storage size.
A network iss modeled with
h 77% efficien
nt storage deviices
connected wiith storage cap
pacity ranging from 1 to 20M
MW
B. Resuults
The onee year long prroblem is solvved using the ooptimization
algorithm
hm and splittiing the time series into tthree month
segmentts. Each segmeent is solved seeparately in appproximately
2 hourss on the Univversity of Stratthclyde Enginneering High
Perform
mance Computeer which is a 1000 core SUN
N Fire X2270
based m
machine with Inntel Xeon X55570 CPUs. Thee simulations
use a c omputing nodde with 8 2.933GHz cores annd 12GB of
RAM. T
The sum of thee results of thee four segmentts is used for
the annuual revenue andd curtailment rreduction.
A sectioon of the optim
mized results are shown in Fig. 4 for a
77% effficient ESS witth 20MW of nnon-firm wind. The shaded
vertical areas crossinng all three grraphs highlight periods of
networkk congestion tthat lead to ccurtailment. D
During these
periods the store is onnly able to charrge. Outside off these times
the storaage charges annd discharges w
with the aim off making the
best posssible use of the price variation. The sm
mooth curves
seen onn the charging graph during curtailment is a feature of
the opttimization alggorithm and is an artiffact of the
mathem
matical methodoology applied w
when there is an excess of
equally priced curtaileed energy.
1) Sttorage Efficiency
Fig. 5 ((a) shows the storage revennue generated for the four
scenarioos and how thiis varies with ESS round tripp efficiency.
The ES
SS makes mosst revenue in sscenario 3 (high non-firm
penetrattion) with higgh ESS efficieency and leastt revenue in
scenarioo 1 (no non-firrm wind) and low ESS efficciency. In all
scenarioos the revenuue increases with efficienccy, but the
increasee is most pronnounced when the ESS is onnly carrying
out pricce-arbitrage (sccenario 1). In tthis scenario thhe ESS must
buy all its energy from
m the market iincluding enouugh to cover
losses hhence an incrrease in efficiiency decreasees the costs
requiredd to charge the energy store. Secondlly increased
efficienccy provides m
more opportunnities to engaage in price
6
1: 0MW
W
4: 20M
MW no arbitrage
80
70
60
50
40
30
20
10
0
55
60
1.5
65
70 75 80 85 90
round trip efficiency
(a))
3: 20MW
W
2: 10M
MW
95
10
00
Fig. 6. Histogram of th
he depth of disccharge associated
d with a 75%
efficient sstorage device.
1
M. Rev enue
0.5
0
50
60
70
0
80
90
10
00
round trip
t efficiency (%)
(b)
Figg. 5. The effectt of round trip efficiency on (a)) storage revenu
ue
(sccenarios 1 -4) and (b) curtailment-rreduction (scenarrios 2-3).
arbbitrage. To in
ncrease revenu
ue across a charge/discharrge
cyycle the price-d
differential must be high eno
ough to cover the
t
coost of the lossess. With low effficiency this means
m
trading will
w
onnly occur acrross high prrice differentiials, with hiigh
effficiencies add
ditional trading
g opportunitiees – those with
w
low
wer price diffeerentials – beccome availablee and, of course,
proofitable.
In contrast, wheen the ESS is only carrying
g out curtailmeentredduction (Scen
nario 4) the energy
e
to chaarge the storee is
avvailable at zero
o price (in linee with the assu
umptions madee in
thiis case study
y) so addition
nal charging does not in
ncur
addditional costs. Revenue will still increase with
w efficiency
y as
seeen in Fig. 5 (a)); the increase is now only due
d to the increease
in the energy sold to the market.
Unnlike revenue, the curtailm
ment-reduction
n decreases with
w
stoorage efficienccy as shown in
n Fig. 5 (b) forr scenarios 2 – 4.
Ass storage devicces become more
m
efficient they
t
required less
l
ennergy to chargee them as the ch
harging losses are lower.
2) ESS cycling
g
In many investig
gations storage is operated in a fixed cycle, for
exxample fully ch
harging and diischarging across each 24 hour
h
peeriod. As this optimization do
oes not apply su
uch a constrain
nt it
is useful to meaasure the distrib
bution of the DoD
D
of cycless to
mating the lifettime of the en
nergy store and
d to
asssist with estim
beegin to open up
p asset managem
ment issues forr energy storag
ge.
mber of cycles of different siizes from a tim
meFinnding the num
serries generated from stochastiic data requiress a cycle-countting
alggorithm. Rain--flow counting
g is used for structural
s
fatig
guedaamage analysiss and providees a method of
o estimating the
nuumber of cycles of particular sizes in a time-series [1
18].
60
M. Curtailment R
Reduction
1.4
50
1.2
1
40
0.8
30
0.6
20
0.4
10
0.2
M Revenue (£1000/MW)
Curtailed Energy Reduction
(GWh)
50
M. Curt' reduction (GWh/MW)
Revenue (£1000)
3: 20MW
2: 10MW
0
0
20
10
15
Storage Capcaccity (MW)
Marginal Revenuee and marginal cu
urtailment reducttion curves for
Fig. 7. M
75% efficcient storage in sccenario 2 with 20M
MW of non-firm wind.
0
5
Applyinng rain-flow coounting to the S
SOC time-seriees for a 75%
efficientt device givess the distributiion of cycle ssizes. Fig. 6
shows thhe results to be bi-modal witth the two peakks occurring
at the exxtremes: most cycles are of eeither less thann 10% Depth
of Disccharge (DoD) or greater thaan 90% DoD. As a first
estimatee, the number of cycles for uuse in lifetime calculations
is assum
med to be the nnumber greater than 90%, in tthis case 199
cycles inn the one year analysis periodd.
3) Sttorage penetrattion
The maarginal effect oof energy storrage as a functtion of total
installedd storage capaacity is shownn in Fig. 7 forr scenario 3.
Marginaal revenue annd marginal curtailment-reeduction are
estimateed by finding tthe change in tthe relevant quuantity as the
total cappacity is increaased by 1MW//6MWh blocks. The results
show a law of diminnishing returnss: when storaage capacity
equals non-firm winnd capacity inn this scenario marginal
revenuee has fallen by m
more than 40%
% and marginall curtailment
reductioon by more than
an 60%.
S capacity for ttwo reasons:
Marginaal revenue willl fall with ESS
the limiited availabilityy of zero-priceed curtailed eneergy and the
finite neetwork capacityy. This secondd effect is impoortant during
periods of high markeet-price as onlyy a limited pow
wer output by
the storaage can be acccepted by the nnetwork. Once the network
capacityy is fully utilizzed during theese periods andd the ESS is
using thhe residual network capaciity up to thiss limit then
additionnal stored enerrgy will only be able to be sold during
other peeriods at a loweer price. E
7
VI. ECONOMIC ANALYSIS
This section carries out a calculation of the Net Present Value
(NPV) of an ESS system installed in the UK for scenarios 1 3.
A key difficulty in analyzing the economics of ESS is the
large variability in cost estimates. Estimates of the capital cost
vary widely, particularly for novel ESS technologies currently
in development and early trial deployment. Table 2 gives
ranges of costs estimates and other characteristics for one ESS
technology: Sodium Sulphur batteries (Na-S). One detailed
analysis of a Na-S battery available in the literature estimates
that expected costs will be in the region of $2500 / kW
installed [2]. The values used in this analysis are listed
separately in Table 2.
TABLE 2: CHARACTERISTICS OF ESS TECHNOLOGIES, RANGES REFLECT
THE VARIETY OF ESTIMATES AVAILABLE. [19], [20]
Na-S (range)
Estimated used in
this study
0.77
1610
Efficiency (%)
0.75 – 0.8 (0.77)
Total upfront capital cost
1340 – 2580
for 1MW/6MWh
(£1,000)
O-M (£1,000/yr)
12.9
12.9
Cycles at 100% DoD
2000 – 3200
2500
Figures converted to Pounds Sterling at: £1 = US$1.55 [21]
One particular difficulty is in estimating the expected lifetime
of an ESS device. The upper limits for the number of life-time
cycles varies depending on the operational strategy and
particularly the Depth of Discharge and, as with cost there are
a wide range of estimates. The total number of lifetime cycles
is significantly affected by the depth-of-discharge. One study
looking at Na-S batteries gives 2,500 cycles at 100% DoD
compared to 4,500 at 90% and 40,000 at 20% [22].
The revenue generated by the ESS includes the direct revenue
as calculated in the simulations, and any subsidy for which the
ESS itself or the additional renewable generation is eligible. In
the UK wind farms receive either feed-in tariffs for small scale
generators or Renewable Obligation Certificates (ROCs) for
large generators. In this analysis it is assumed that every MWh
of renewable electricity generated receives a payment at the
average ROCs rate for December 2010 – October 2011 which
is £48.34 [23].
The NPV is a measure of the financial viability of a project
spread across time. It includes a discount rate applied to future
cash flows which favors the present over the future. If the
NPV of a project is greater than 0 it will make a return on
investment over and above the discount rate. Two important
discount rates are the social time-preference rate; the UK
treasury suggests a value of 3.5% to be used [24]; and a
discount rate based on opportunity costs, often estimated at or
assumed to be 10% [25].
=
−
(1 + )
(13)
The sum in (13) runs over the lifetime of the project including
the initial capital investment which occurs here in year 0. For
a battery with 77% efficiency the number of cycles in a year is
199 giving a lifetime of approximately 12 years.
The NPVs for a single Na-S battery connected under scenario
1 and 3 is shown in Table 3. All NPV results are negative and
it can be concluded that Na-S batteries are not economically
viable operating in the scenarios modeled. The NPV for
scenarios with high curtailment-reduction are significantly
higher than those where no curtailment is available, this is due
to the additional revenue from renewable subsidies.
TABLE 3: NET PRESENT VALUE OF NA-S BATTERY STORAGE
Non-Firm wind capacity
(MW)
20
20
0
0
Discount Rate (%)
NPV
3.5
10
3.5
10
-£680,000
-£937,000
-£1,290,000
-£1,380,000
VII. DISCUSSION
The economic analysis shows that the high capital cost of ESS
devices makes them uneconomic in the studied case. To
change this result either the investment and operational cost
needs to be reduced, or the revenue streams enhanced.
If operations and maintenance costs remain fixed then the
capital cost of a Na-S battery would need to be reduced to
£930,000 (from the £1,610,000 assumed in the analysis) to
allow an investment to break even under the social-time
preference discount rate. Using the 10% discount rate the
capital cost would need to be £670,000. Both of these capital
cost values are well below the cost lower bounds of the cost
estimates currently available.
Increasing the revenue could be achieved by accessing other
revenue streams and including these in the optimization. In
[26] the value of a range of benefits from energy storage is
estimated. The high value benefits of storage are concentrated
in the reserve and response markets and in investment-deferral
for both transmission and distribution networks. Access to
revenue from these is likely to be problematic for privately
owned distribution-connected storage. Reserve and response
markets are often set up for large participants: in the UK the
minimum unit size of a unit that can participate in the fast
reserve market is 50MW [27]. Accessing revenue from
investment deferral is difficult for private storage owners,
although an ownership model based on storage as a network
asset may be more suitable.
VIII. CONCLUSION
The NPV of a project is given by:
This paper has developed and tested a linear-programming
method to optimize the revenue of an ESS connected with a
wind farm in a curtailment reduction scheme. The
8
optimization allows the combination of more than one revenue
stream, in this case curtailment-reduction and price-arbitrage.
General optimization methods such as this will be important in
situations where there are high levels of non-firm generation
curtailment. The method has the potential to be extended to
more revenue streams should they be able to be enumerated in
a robust manner.
[14]
The case study results show the relative importance of storage
efficiency when operating in price-arbitrage mode compared
to curtailment-reduction. A cycle-counting method is used to
estimate the depth of discharge of a device optimized using
this method and the asset management implications of this are
noted. Finally an economic analysis suggests that the two
analyzed revenue streams will not be sufficient for economic
viability of a Na-S battery ESS. Research is urgently required
into the ability of ESS to access revenue related to higher
value benefits. Other future research suggested by this
analysis includes the extension of the optimization to include
network effects with wind and storage distributed in a realistic
distribution network model.
[17]
IX.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
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Simon Gill is currently a PhD candidate in the Wind Energy Doctoral
Training Centre at the University of Strathclyde. He obtained a Masters
degree in Astrophysics from the University of Edinburgh in 2003, and spent
four years teaching physics. His research interests include energy storage,
active management of distribution networks and the integration of renewable
energy into power systems.
Graham Ault (M’1998) received his Bachelors in Electrical and Mechanical
Engineering (1993) and PhD in Electrical Power Systems (2000) from the
University of Strathclyde, Glasgow, UK. Since 1996 has been researching
power system planning and operations issues relating to distributed energy
resources in distribution systems. He is currently a Professor in the Institute
for Energy and Environment at the University of Strathclyde
Ivana Kockar received the B.Sc. degree from the University of Belgrade.
After 4 years in industry, she obtained the M.Eng and PhD degrees in
electrical engineering from McGill University, Montreal, Canada. She spent a
year at University of Manchester, UK, and then joined Brunel University.
Currently, she is with the Institute of Energy and Environment, University of
Strathclyde, Glasgow, UK.
Her research interests include power system operation planning, and
economics of energy systems including market modelling, network access and
pricing, active demand participation, as well as implications of environmental
issues on system operation and planning.