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Wind energy is a valuable supplement to conven-

tional energy sources, as wind power technology has

become mature. However, the maximum penetration of

wind power in electricity networks is limited by the

intermittent nature of wind energy. Fluctuations in wind

power production also makes it difficult for owners of

wind power plants to compete in the emerging electricity

markets. Energy storage devices with the ability to store

large amounts of energy for several hours or more, such

as flow cells and fuel cell systems [1], could provide the

necessary flexibility for smoothing of wind power, and

thus increase the possibilities for market operation.

Moreover, for potential wind farm sites remote from a

strong electrical connection point, energy storage could

provide an alternative to grid reinforcements.

There is a growing research interest in using energy

storage to increase the value of intermittent energy

sources in electricity markets [2,3,4]. However, impor-

tant issues such as the impact of market mechanisms,

transmission line constraints and forecasting accuracy ofwind power must be further explored to fully determine

the advantages and limitations of energy storage for this

purpose. Therefore, a method for the scheduling and

operation of such a distributed resource in a market sys-

tem has been developed and implemented in a computer

model. This paper aims to describe the proposed method,

and to show an application of the method on a case-

study, where the impact of energy storage sizing and

wind forecasting accuracy on system operation and eco-

nomics are emphasized. A list of symbols is provided in

the appendix.

The distributed resource is presented in Figure 1, and

consists of a wind power plant and an energy storage

device. The owner of the resource is assumed either to

have a demand for electricity,

, or to have contracts

with the local electricity consumers represented by an

aggregated load demand. The system is connected to the

main electricity network by a transmission line with lim-

ited capacity. Reactive power flow is neglected in the

simulations performed here, in order to keep the focus

on the scheduling and flow of real power.

The system components and the electricity market

model are presented below.

Wind power plant with local energy storage

connected to a scarcely populated grid. The direction of the

arrows refers to positive values of the variables.

The power output of the wind power plant is calcu-lated from the power curve in Figure 2. It is assumed that

the wind power plant consists of identical wind turbines,

wind power plant

Pw

transmission

line

external grid

local load

Pe

Pl

energy

storage

Ps

controllable load

Pcl

Magnus KorpsNTNU

Trondheim, Norway

[email protected]

Ragne HildrumStatkraft SF

Oslo, Norway

[email protected]

Arne T. HolenNTNU

Trondheim, Norway

[email protected]

14th PSCC, Sevilla, 24-28 June 2002 Session 31, Paper 6, Page 1

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and that the wind conditions are the same for all tur-

bines.

The wind generator input/output characteristics used

in the model.

The energy storage device is defined by its energy

capacity, charging efficiency, discharging efficiency,

charging power capacity and discharging power capac-ity. The storage equations are as follows:

(1)

(2)

(3)

where

and

are the efficiencies of charging and

discharging respectively.

Charging and discharging occurs for negative and

positive values of

, respectively. The round-trip effi-

ciency of the storage device is .

The transmission line will act as a power source or

sink, depending on the balance between local load and

generation. The power transported on the line is the

power exchanged with the marked system, and is calcu-

lated from the power balance:

(4)

(5)

Power export corresponds to positive values for

which is measured at the load side of the transmission

line. The expression for active power losses is:

(6)

The maximum allowable power exchange is equal to

the transmission line capacity, while the minimum value

is given by.

(7)

If the net power production exceeds the line capacity,

the excess power is consumed by a controllable load,

, which is used only for this purpose.

In the Nordic spot market, daily bids for sale and pur-

chase of energy in the spot market are provided to thepower pool 12 hours before the actual day. After the spot

price has been settled, the final schedule is worked out.

During the operation, if a participant does not deliver the

specified amount at the spot market, then the discrep-

ancy must be settled on the regulating power market,

which normally results in a reduced income [6].

Market operation is simplified considerably in the

model. Since the marginal cost of power produced from

a wind power plant is zero, it is presumed that wind

energy always can be sold on the market. Each day at

12.00, the owner of the distributed resource performs the

scheduling of the hourly power exchange with the mar-

ket, . The hourly income from the spot market partic-

ipation is:

(8)

Power flow in the transmission line causes losses

which are bought for spot price:

(9)

The regulating market is simplified by using average

values. The prices for sale and purchase of electricity

traded on the regulating market are assumed to be pro-portional to the spot price:

(10)

where the deviation between actual and scheduled

power exchange, , is traded on the regu-

lating market. In the Norwegian regulating market, a dis-

crepancy between the actual and planned production

could in fact lead to higher revenue, depending on the

overall power balance in the market. This could for

instance happen in the cases when the actual powerexchange is higher than scheduled at the same time as

there is a power deficit in the market. However, it is pre-

sumed that in average, deviations from the production

plan are disadvantageous, since they increase the uncer-

tainty of the overall power balance.

The operation strategy consists of three separate

parts: 1) forecasting of wind velocity 2) scheduling of

the power exchange with the market and 3) on-line oper-

ation of the storage. In the present model, the forecastsof load and spot price are assumed to have 100% accu-

racy. A flowchart of the method is shown in Figure 3,

0 5 10 15 20 25 30wind velocity, v [m/s]

Pw[MW]

Pw

S t 1+( )S t( )

1

d------Ps t( ) t Ps 0>( )

S t( ) cPs t( ) t Ps 0( )

1 crp+( ) SP Pde vt Pde v 0

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and the various steps of the algorithm are described

below.

Flowchart of the operation strategy for a wind power

plant with energy storage. The indexes for day and hour are and .

A simple algorithm for computer-generated wind

velocity forecasts has been developed. The forecasted

average wind velocity for a specified time period is cal-

culated, based on the actual wind data for the same

period. The algorithm includes the following steps:

Read wind data for t=1..tend and the coefficient

of variation for mean wind velocity prediction

Calculate

Draw a random numberfrom the normal distribu-

tion with mean and standard deviation

Return the predicted wind velocity for

t=1..tend

As an example, for a wind series with mean value 8.1

m/s and standard deviation of 4.4 m/s, the RMSE value

of prediction error is found to be 2.57 m/s using the pro-

posed method with V = 0.

The operation scheduling of the system is performed

at the specified hour

each day. The objective is to

find the scheduling plan for the next day which maxi-mizes the expected profit. Since the wind velocity fore-

cast is uncertain, and a penalty is given for trading in the

regulating market, one should consider all possible com-

binations of wind velocities in the complete optimization

problem. However, at this stage of the modelling work,

the forecasted values are treated as deterministic vari-

ables in order to reduce the computational effort to a rea-

sonable size. Trading losses due to deviations between

actual and scheduled generation are consequently omit-ted in the optimization problem.

Given the spot price, load demand and short term

forecast of wind velocity, the optimization task is to

determine the hourly trading of electricity in the spot

market which maximizes the expected profit over the

scheduling period. Mathematically, the scheduling of the

distributed resource can be formulated as:

(11)

where

(12)

subject to the system operating constraints (1)-(7) and

the initial storage level. The terms

and

are

defined in equations (8) and (9). Since there are nor-

mally large uncertainties both in the short-term and long-

term prediction of wind velocity, the optimization hori-

zon

is chosen to be 24 hours. It is therefore benefi-

cial from an economic point of view to discharge the

storage completely at the end of each day. If there were

negligible errors in wind velocity predictions, the opti-

mization horizon should be increased. Then, it could be

favorable to store energy at the end of the day, for

instance if there were a risk for long periods with no

wind.

The optimization problem is solved using a dynamic

programming algorithm, which requires discretisation of

the storage level. The optimization routine returns the

expected path for t = 1..tend, which gives the opti-

mal scheduling of power exchange from equa-

tions (1) and (4). The controllable load

is used as

dump load, and therefore its value differs from zero only

when the storage is completely filled at the same time as

the net local production exceeds the transmission line

capacity. Alternatively, one or more wind turbines could

be shut down or downregulated in order to not overload

the transmission line. The energy loss due to downregu-

lation of wind power output will be equal to

.

The operation scheduling is performed 12 hours in

advance, which means that the storage level is unknown

at the start of the optimization period. If the wind fore-

casts were 100% correct, the estimated value

from the previous optimization should be used. How-

ever, because of uncertainties in the wind forecasts, the

hourly storage levels will deviate from the estimated val-ues. To get a new estimate of the initial storage level of

day the following equation is employed:

Read system info

i = 1 , t = 1

t = tsch

?

OPERATION SCHEDULING

Estimate Si+1(0).

Find optimal Pei+1(t) for t= 1..t

end

ON-LINE OPERATION

Measure v(t), Pl(t)

Operate storage such that Pe(t)=P

e(t)

i = iend

?

TERMINATE

Read vi+1(t) , Pli+1(t) , SPi+1(t)

for t = 1..tend

Update

i , t

Y

N

N

Y

^

^

^

^

v

v v V

v t( ) x=

max F f Pe t( )( )t 1=

ten d

=

Pe t( )( ) fs pot Pe t( )( ) flos s Pe t( )( )+=

S t( )

Pe t( )

S ten d( )


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(13)

where is the storage level correction based on themeasured level at the scheduling hour

and an

improved forecast of the wind forecast for the remaining

hours of the day.

A straightforward operation strategy is used. The

energy storage is operated in order to follow the hourly

scheduling plan for power exchange with the market.

Consequently, it is presumed that the amount of electric-

ity produced by the wind power plant and consumed by

the load are continuously measured.

A case-study is used to test the proposed operation

strategy of the distributed resource. The system data for

the base case are listed in Table I. Time series for wind

velocity are computed using a synthesis algorithmdescribed in [5], and time series for load demand are

computed using the daily load curve in Figure 4. The

mean load for a certain day is obtained from a normal

distribution where is the daily mean load

and is standard deviation of the daily mean load. The

hourly values is obtained by multiplying with the corre-

sponding value of the curve in Figure 4.

Typical daily load curve for Norwegian households.

Electricity prices are shown in Figure 5, and are

assumed to be the equal for all days. The type of energy

storage is not specified, but could for instance be a

regenerative fuel cell or a redox flow cell. Such storagesystems are still under development, and the future spe-

cific costs are uncertain. Therefore, the spot prices used

in the simulations are chosen to be higher than present

values observed in the nordic power market. As a com-

parison, the actual average spot price in year 1996 and

year 2000 were 254 NOK/MWh and 103 NOK/MWh

respectively [7](1$ = 9 NOK in november 2001). Also,

the variations in simulated spot price during the day are

chosen to be higher than the relatively low variations

observed in the market today.

The simulated average price for purchase of electric-

ity in the regulating market is 17% higher than the spotprice, and the average price for sales is 12% lower than

the spot price. These values are partly based on [6],

assuming a relatively high penetration of wind power in

the market.

System data for the base case.

Simulated hourly spot price (middle) and price for

purchase (upper) and sale (lower) of electricity in the

regulating market.

In order to study the hourly system operation, a 48

hour simulation run of the base case is presented. Fore-

casted and actual values of hourly wind power produc-

tion are shown in Figure 6.

Actual,

, and forecasted, , values of wind

power production.

Figure 7 displays the scheduled and actual power

exchange with the market. The system manages to fol-

low the production plan most of the time except for

some hours at the start and at the end of the simulation

period. This discrepancy can be explained from Figure 8,

where the estimated and actual storage level are plotted.

At the start and the end of the period, the actual storage

level is empty for a longer period than expected. For

those hours, the storage cannot compensate if the windpower production is lower than predicted. This undesir-

able situation can be avoided by setting the minimum

Si 0( ) S i 1 ten d( ) S+=

N Pl l,( ) Pl

l

5 10 15 200.8

0.9

1

1.1

1.2

time [hours]

load[pu]

[MW] [MW-1] [MW] [MW] [MWh]

4.0 0.04 10 0.75 6 100

[MW] [MW] [m/s]

RMSE

[m/s]

2.6 0.52 8.2 2.0 2.6

Pema x ct Pw

ma x s Psma x Sma x

Pl l v

5 10 15 2010

20

30

40

50

time [hours]

electricityprice[$/MWh]

30 40 50 60 700

2

4

6

8

10

time [hours]

realpower[MW]

Pw

Pw

Pw


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allowable storage level, , larger than zero in the opti-

mization routine. Moreover, the actual power exchange

also deviates from the scheduling plan for . The rea-

son for this discrepancy is that the power capacity of the

storage is too low compared to the wind power produc-

tion in that hour.

Actual,

, and scheduled, , power exchange with

the market. Positive values mean export of power.

Actual, and estimated, , storage level for a

storage device with 75% round-trip efficiency.

It is important to obtain a good estimate of the initial

storage level used in the optimization routine. If the

actual storage level is higher than the estimate, the stor-

age can reach its maximum value too early by followingthe scheduling plan. Likewise, if the storage level is

lower than the estimate, the storage can be discharged

too early. The latter is observed in Figure 8, where the

estimated storage level at the start of day two () is

higher than the actual value. This causes a full discharge

of the storage at the end of the period one hour earlier

than estimated, and the system becomes less flexible.

A simple Monte-Carlo simulation technique has been

employed in order to study the impact of storage design

and wind forecasting error on the performance and eco-

nomics of the system. The parameter values in Table I

are used in the base case, and , and the RMSE

of wind speed prediction are varied in the simulations.

The stochastic variables are wind velocity and load

demand

. It should be noted that the modelling method

of wind speed and load described above does not take

into account seasonal variations. However, the error

caused by this simplification is considered to be small

for Norwegian conditions, since there is a close matchbetween the seasonal electricity demand and wind

energy in Norway [8].

The impact of storage sizing on the performance and

economics of the system. The base case parameters are used,

except for and .

Results from simulation runs with different storage

parameters and are presented in Table II. The

relative deviation from scheduled power varies

from 3% for the largest storage system to 11% for the

smallest storage system. Thus, unpredictable variations

in wind power production are smoothed by the storage

most of the time. The ratio is a measure of the

probability of line overload, since the controllable load

is only used when the net local production exceeds the

line capacity. The relative usage of the controllable load

is low for all storage designs, although there is a clear

correlation with . A two-fold increase in energy

capacity results in a four-fold reduction in the electricity

consumed by the controllable load. Moreover, an inter-esting effect is observed when comparing for

storage configurations with different power capacities,

but equal energy capacity. The usage of the controllable

load actually increases slightly for increasing power

capacity, although the opposite could be expected,

because the ability of the storage to consume excess

power also increases. However, with a higher power

capacity, it is possible to store more energy during off-

peak periods. Consequently, the storage will be com-

pletely filled more often. This is undesirable, but can be

avoided by adding a limitation on the power capacity

used in the optimization routine.Furthermore, Table II shows that the revenue

increases with increasing power and energy capacity of

30 40 50 60 70

0

1

2

3

4

time [hours]

realpower[MW]

Pe

Pe

Pe

30 40 50 60 700

10

20

30

40

50

time [hours]

stora

gelevel[MWh]

SS

S

Psma x

[MW]

[MWh]

yearly

revenue

[1000 $]

4 50 0.114 0.045 314

4 100 0.097 0.014 339

4 150 0.098 0.007 346

6 50 0.078 0.046 318

6 100 0.046 0.016 3436 150 0.043 0.008 350

8 50 0.068 0.046 320

8 100 0.033 0.016 345

8 150 0.029 0.008 352

Psma x Pde v

P

e

----------- Pcl

Pw-------

Psma x

Psm ax

Pde v Pe

Pcl Pw

Pcl Pw


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the storage, as expected. On the other hand, the storage

device is then likely to be more expensive, which is par-

ticularly true for fuel cell systems. Thus, finding an

appropriate size of the storage is not only critical for the

system operation but is also of great economic impor-

tance, due to potential high investment costs. Figure 9

displays the duration curves of charging, discharging andthe energy reserve, which provides information about

the utilization of the storage device. It is evident from

the charging and discharging curves that an energy stor-

age with separate charging and discharging devices (for

instance an electrolyser and a fuel cell) will have an

undesirable low utilization of the total installed capacity.

However, the difference between the curves implies that

storage designs with different charging and discharging

capacities should be investigated further. The usage of

the total energy capacity is also relatively low, as can be

seen from the duration curve for storage level in Figure

9. This is beneficial from a operation point of view, sincea full storage increases the risk for transmission line

overload. In the case of no transmission constraints, the

energy capacity could be considerably lower. Moreover,

the duration curve also shows that the storage is empty

for some times. As this reduces the flexibility of the stor-

age, one should consider to set the minimum allowable

storage level in the scheduling routine higher than zero.

Duration curves for charge (circles), discharge

(crosses) and the energy reserve (solid) of the storage device.

The base case parameters are used for the simulation.

The economic value of accurate wind forecasts is

illustrated in Figure 10. As expected, the revenue is

highest for perfect forecasting, since in that case all the

energy can be traded in the spot market. As the forecast-

ing error increases, it becomes more difficult to follow

the scheduled production plan. Hence, more energy must

be traded in the balancing market, and the revenue is

reduced, according to the price curves in Figure 5. This

is particularly true for the persistence method, with

RMSE equal to 4.84 m/s. The benefit of accurate wind

forecasts depends strongly on the price differencebetween spot price and regulating power prices. In this

study, the difference is relatively large, which means that

the effect of forecasting accuracy can be smaller in prac-

tice.

Yearly revenue as a function of forecast error ofwind velocity. The base case parameters are used, except for

RMSE.

The simulation results show that with a properly sized

energy storage, it is possible for owners of wind power

plants to take advantage of hourly price variations in the

spot market. Furthermore, results obtained from the sim-

ulations should ultimately be used as a part of an eco-

nomic assessment where also investment costs are

considered. It is also interesting to compare energy stor-

age with grid reinforcements in cases where the wind

power potential exceeds the capacity of the existing

transmission line. Taking into account the reduced costs

for providing the load with electricity from the distrib-

uted resource, the yearly revenue for the base case is 1.1

Mill.$. For comparison, simulations of the system with anew parallel transmission line instead of energy storage

gives a revenue of 1.0 Mill.$. Consequently, with a

period of analysis of 20 years and 7% interest rate, the

difference in investment costs of the energy storage and

the new line cannot be higher than about 1 Mill.$, if the

storage should be an economic viable alternative. With

present cost estimates [4], it is likely that electrochemi-

cal energy storage such as the hydrogen-bromine fuel

cell system will be an expensive alternative to grid rein-

forcements. On the other hand, for areas where grid

expansions lead to unwanted interference with the local

environment, energy storage should be considered as areasonable way to increase the penetration of wind

power. Another alternative is to reduce the power output

from the wind power plant in periods with high wind and

low load by either shutting down units or downregulat-

ing the output. For the system studied here, such a strat-

egy would give a yearly revenue of 0.9 Mill.$. The

energy loss due to the downregulation is 16%.

The chosen operation strategy of the energy storage is

simple, namely to follow the specified production plan.

Other, more sophisticated methods could be employed if

the spot price and regulating prices were represented as

stochastic variables, and if a more detailed model of theelectricity market were used. The optimal power

exchange with the market could then be updated each

0 20 40 60 80 1000

20

40

60

80

100

% of total time

%ofmaximumvalue

charge

discharge

energy reserve

200

250

300

350

RMSE of wind velocity prediction [m/s]

revenue[1000$]

4.840.0 2.57 3.16


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hour, by using principles of stochastic programming.

Moreover, in some cases it will be valuable to have an

energy reserve in the storage at the end of the day, for

instance if high spot prices and low wind speeds are pre-

dicted for the next days. This approach is analogous to

the so-called water value method used in hydro power

planning [9], and will be investigated further.It should also be noticed that the proposed method is

not limited to wind power, but could also be useful for

the analysis of other intermittent energy resources such

as solar, wave and small-scale hydro.

A method for the scheduling and operation of a wind

power plant with energy storage in a market system has

been presented. The method is suitable for any type of

electrical energy storage and is also useful for other

intermittent energy resources than wind. By implement-

ing the method in a computer simulation model, valuableinformation about the impact of energy storage sizing on

system operation and economics can be obtained. Simu-

lation results of a case study show that with a properly

sized energy storage, owners of wind power plants can

take advantage of variations in the spot price of electric-

ity, by thus increasing the value of wind power in elec-

tricity markets. However, with available technology and

existing price estimates, energy storage devices such as

reversible fuel cells are likely to be an more expensive

alternative than grid expansions for the siting of wind

farms in weak networks, although reducing the environ-

mental impact.A simplified representation of the electricity market is

used in the model. In order to explore further possibili-

ties for energy storage in connection with stochastic gen-

eration, further work with a detailed market description

will be carried out.

List of symbols:

[1] J. N. Baker and A. Collinson, Electrical energy stor-

age at the turn of the millennium, Power Engineer-

ing Journal, vol 13, no.3, pp 107-112, June 1999

[2] A. Cruden and G. J. W. Dudgeon, Opportunities for

Energy Storage operating with Renewable Energy

Systems, Proc. EESAT 98, Electric Energy Storage

Applications & Technologies, September 2000

[3] W. A. Amos, Economic Assessment of Wind

Energy Coupled with a Reversible Hydrogen Fuel

Cell, National Renewable Energy Laboratory,

Golden, CO, Milestone Type P report, February2000.

[4] M. Korps, R. Hildrum and A. T. Holen, Hydrogen

energy storage for grid-connected wind farms, 6th

IASTED International Conference, Power and

Energy Systems, pp 590-594, July 2001, ISBN 0-

88986-291-5

[5] D. Infield et al, Engineering tools for wind diesel

systems - Volume 6, EFI Technical Report No.

A4330, Trondheim, September 1995

[6] L. H. Nielsen and P. E. Morthorst, System integra-

tion of wind power on liberalised electricity market

conditions. Medium term aspects (in Danish), Ris-R-1055(DA), april 1998, ISBN 87-550-2396-7

[7] Homepages of Nordpool - The Nordic Power

Exchange, http://www.nordpool.no

[8] J. O. G. Tande and K-O. Vogstad, Operation impli-

cations of wind power in a hydro based power sys-

tem, EWEC99, 1999 European Wind Energy

conference, pp 425-428, August 1999

[9] O. B. Fosso et al, "Generation Scheduling in a de-

regulated system. The Norwegian case", IEEE Trans-

actions on power systems, Vol. 14, No.1, 1999

: load demand [MW]

: output of wind power plant [MW]

: power exchange with market [MW]

: power output of energy storage [MW]

: controllable load [MW]

: Deviation between actual and scheduled

power exchange [MW]

: energy storage level [MWh]

s : round-trip efficiency of energy storage

c : charging efficiency of energy storage

d : discharging efficiency of energy storage

: wind velocity [m/s]

: estimated value of variable

: mean value of variable

: hourly revenue [$/h]

x

x

: Expected revenue over the scheduling

period [$]

: transmission losses coefficient [MW-1]

: spot price of electricity [$/MWh]

: relative difference between spot price and

sales price in the regulating market

: relative difference between spot price and

purchase price in the regulating market

: standard deviation of random variables : coefficient of variation of random vari-

ables

: Weibull shape parameter

RMSE : Root-mean-squared error of wind fore-

cast [m/s]

: index for time

: time step [hours] : index for day


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