IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 3, AUGUST 2007 1259

Optimizing a Battery Energy StorageSystem for Primary Frequency Control

Alexandre Oudalov, Daniel Chartouni, and Christian Ohler, Member, IEEE

AbstractThis paper presents a method for the dimensioningof a battery energy storage system (BESS) to provide a primaryfrequency reserve. Numerical simulations based on historic fre-quency measurements are used to determine the minimum possiblecapacity, i.e., the lowest possible cost, which fulfills the technicalrequirements of the grid code. We implement a novel control al-gorithm with adjustable state of charge limits and the applicationof emergency resistors. At current European market prices, an op-timized lead-acid BESS can be a profitable utility solution for theprimary frequency control.

Index TermsAncillary service market, battery energy storage,net present value, primary frequency control.

I. INTRODUCTION

POWER systems currently undergo considerable changein operating requirementsmainly as a result of dereg-ulation and due to an increasing amount of discontinuousdistributed generation. Additionally, continuing load growthand increasing regional power transfer in interconnected net-works lead to stressed and less secure power system operation.This has triggered interest both from transmission system op-erators and power utilities in large-scale battery energy storagesystems. While battery energy storage technologies can cover awide spectrum of applications, ranging from short time powerquality support to hours-long energy management, the supplyof primary control reserve has been identified as the applicationwith the highest value for the owner of the battery energystorage system (BESS) [1]. The profitability of this applicationwas established by comparing frequency control reserve priceson ancillary service markets with realistic installation andmaintenance costs of BESS units.

Previous research and practical installations [2][8] havetechnically shown that a BESS can provide frequency regula-tion indeed. The BESS unit absorbs energy when the systemfrequency is above a nominal value and discharges this energyback into the grid when the frequency is below the nominalvalue. The main driving forces for these BESS prototypes,however, were either special system reliability requirementsor the testing of new technology. The batteries were usuallyover-dimensioned, so that the total BESS cost was too high toallow a monetary payback for the installations. In contrast tothis, we treat here BESS units that are commercially viable atcurrent market conditions. This paper provides a method for

Manuscript received January 17, 2007. Paper no. TPWRS-00029-2007.The authors are with ABB Switzerland Ltd., Corporate Research Center,

CH-5405 Daettwil-Baden, Switzerland (e-mail: alexandre.oudalov@ch.abb.com).

Digital Object Identifier 10.1109/TPWRS.2007.901459

Fig. 1. Principal diagram of the BESS.

minimizing the BESS capacity and as a result for minimizingthe BESS installation cost. The method is based on historic fre-quency data, and the BESS capacity is minimized with a novelcontrol algorithm that has adjustable state of charge limits.

Emergency resistors are an essential component of an op-timal BESS for primary frequency control. They dissipate en-ergy during rare events when an extreme over-frequency ex-cursion occurs while the BESS happens to be fully charged: itwould be uneconomic to size the batteries for such a rare eventof extreme over-frequency excursion. Because there is a con-flict between the objective to minimize the BESS cost and theobjective to minimize the use of the emergency resistors, thelatter condition enters as a side constraint (sometimes called abudget constraint) in the optimization procedure.

The outline of this paper is as follows: Section II gives abrief overview of commercially available BESS technologies;Section III describes principles of primary frequency control inEurope; Section IV explains the economic valuation of a BESSunit for such application. Section V presents the BESS capacityminimization and corresponding BESS operating strategy.

II. BATTERY ENERGY STORAGE SYSTEM

All commercially available BESS have a similar systemdesign: batteries are connected to a power conversion system(PCS) that converts a variable dc voltage of the battery to athree-phase ac voltage of the utility (see Fig. 1). Four types ofbatteries have been considered in this study (see Table I).

The cost of BESS units per power unit is a strong functionof their (energy) capacity, i.e., the maximum discharge time. Tocalculate the total BESS cost (over the complete lifetime of 20years), we add the cost of PCS to the net present value (NPV)of costs of each BESS type, including needed cell replacements.

0885-8950/$25.00 2007 IEEE

1260 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 3, AUGUST 2007

TABLE ICHARACTERISTICS OF DIFFERENT BATTERIES

Fig. 2. NPV of cost for different types of 10-MW BESS and PHS versus vari-able capacity and NPV of profit (dashed horizontal line) obtained by sellingprimary reserve in Germany.

Fig. 2 shows the NPV of cost for 10-MW BESS units as a func-tion of BESS capacity.

The NPV of cost for a pumped hydro storage (PHS) plant isplotted on the same diagram for comparison. PHS is the unbeat-able storage solution for a discharge time higher than 0.75 h incomparison to any BESS technology; however, its application isvery limited due to geographical and environmental constraints.Among batteries, lead-acid BESS is the most economic solutionfor a discharge time up to 1.25 h.

Fig. 2 anticipates results for the market price for the primaryreserve service and results for the capacity minimization to bediscussed below.

III. PRIMARY FREQUENCY CONTROL RESERVEThe electric power system is unique in that power production

and consumption must be matched instantaneously and contin-uously. Disturbances in this balance cause a deviation of systemfrequency from a set-point value and reduce the quality of powersupply. Therefore, each power system operator is obliged tomaintain a sufficient amount of active power in reserve to com-pensate for the worst credible contingency (loss of the largestgeneration or transmission facility).A. Frequency Control Reserves in UCTE

Three types of reserves performed in different successivesteps are maintained to help Central European transmission

Fig. 3. Deployment of frequency control reserves in UCTE.

TABLE IIREQUIREMENTS FOR PRIMARY FREQUENCY CONTROL RESERVE IN UCTE

system operators (TSOs) members of the Union for the Co-or-dination of Transmission of Electricity (UCTE) (synchronousinterconnection of central European countries) to achieve therequired generation-load balance (see Fig. 3).

A deviation of system frequency will cause primary con-trollers of all generators subject to primary control to respondwithin a few seconds to stop frequency drop/rise. Requirementsfor primary reserve in UCTE are shown in Table II [13]. Sincethe early days of UCTE, the primary frequency control was amandatory service organized through the vertically integratedelectrical utilities making all large thermal and hydro units( MW) available for the provision of primary reserve.

During the last decade, markets for ancillary services havebeen established in many European countries. Under freemarket conditions, the control philosophy is still respected, butthe TSOs do not exercise direct authority over the power plants.Other entities such as loads, distributed generation, and energystorage have the right, not an obligation, to offer frequencycontrol reserves as long as they fulfill technical and commer-cial requirements set by the TSO. Currently, primary reservemarkets are local; cross border reserve markets, however, arebeing discussed and will be established in the near future [14].

B. Primary Frequency Control Market MechanismIn case of primary frequency control, the TSO pays for the

mere availability of control power. There is no utilization pay-

OUDALOV et al.: OPTIMIZING A BATTERY ENERGY STORAGE SYSTEM FOR PRIMARY FREQUENCY CONTROL 1261

Fig. 4. Prices for primary frequency control reserve in Germany in 2001-2007.

ment proportional to the actual amount of energy supplied orconsumed. All suppliers are paid a fixed price for the wholetendering period per kW of standby reserve. Thus, the reserveavailability payment can be calculated as a product of contractedreserve power in kW, the primary reserve price (Euro/kW/pe-riod), and the tendering period (1). The primary reserve price isbased on the final accepted bid submitted to the TSO as follows:

Payment Reserve Price Period (1)The German market for primary frequency reserve has been es-tablished in 2001 and has the longest historic records in UCTE.Awarding of contracts for the provision of primary reserve isrealized in a nondiscriminatory manner on the basis of publictenders. Fig. 4 illustrates the results of tenders in four GermanTSOs starting from 2001. The current average price for primaryreserve is about 60 Euro/kW/six month. Thus, the annual pay-ment for keeping a primary reserve of MW in Germany is120 k Euro.

IV. ECONOMIC VIABILITY OF BESS APPLICATIONFOR PRIMARY FREQUENCY CONTROL RESERVE

To determine the economic viability of BESS applicationfor primary frequency control, the total revenue from sellingreserve must be compared with capital, operating,and maintenance (O&M) costs over the BESS life cycle

Profit (2)Revenue (3)

Cost (4)

In these equations, is the BESS life cycle and the dis-count rate (here years, %). Revenue and Costare annual values. The revenues depend on the primary reserveprices and are subject to uncertainty. In this work, we use rev-enues of 120 Euro/kW/year. Looking back to Fig. 2 provides afirst impression on the potential benefit of the BESS application.

from selling MW of primary reserve during 20

years in Germany is slightly less than 14 million (Euro). Com-paring this figure to the total cost over 20 years, of thebattery technologies, we note that the 10-MW lead acid BESSis a profitable solution ifand only ifthe BESS capacity canstay smaller than 9 MWh.

The owner of the BESS unit would attempt to minimize theBESS capacity in order to maximize his profit. It is the mainobject of this paper, and in particular the next section, to cal-culate the minimum size neededsuch that the BESS is nevercompletely discharged and 100% of the time able to provide thecontracted primary reserve power.

V. BESS DIMENSIONINGTo determine the minimal BESS capacity, we have modeled

the actual BESS operation and adapted the operating algorithmto measured frequency data of the UCTE grid. The minimal con-ceivable BESS capacity for the contracted primary reserveis limited to 0.25 hours, since the BESS has to furnish pri-mary reserve for at least 15 min (see Table II). The realistic min-imum will be higher because primary control events can followeach other at short intervals so that there is not enough time torecharge the BESS. For this reason, the recharge strategy hasa strong influence on the optimization result. Another issue isthe use of emergency resistors. While they help to reduce theneeded capacity of the BESS unit by dissipating energy duringrare events when an extreme frequency excursion occurs whilethe BESS happens to be fully charged, we propose to use themas infrequently as possible. This goal enters as a side conditioninto the optimization. It would be neither an environmental noran economic optimum to avoid emergency resistors completely.

A. UCTE Frequency ProfileThe measured UCTE frequency for several months of 2005

has been obtained from the Swiss coordinatorETRANS. Mea-surements have 1 Hz of sampling with less than 1 mHz of accu-racy. Fig. 5 shows the measured UCTE frequency in April 2005.

The UCTE rules [13] specify the nominal frequency 50 Hzand noncritical frequency window of mHz. This windowallows avoiding a calling up of primary control at near nominalfrequency.

The main observation from this data is that the frequencyquality in UCTE is maintained very well. Most of the time(70%), the frequency in UCTE stays within the noncriticalwindow of mHz. There are only few frequency excursionsoutside of mHz per month. A frequency deviation of

mHz was never reached throughout the year 2005. Highand low frequency deviations are symmetrical over the longperiod (month).

In the short term, however, there are many deviations, andthey are not necessarily balanced. They can occur at randompoints in time with random amplitude and random repetitionrates. As the frequency deviates to values higher than 50.020Hz, the primary frequency controller has to absorb power; as thefrequency deviates to values below 49.980 Hz, it has to supplypower (see the left-hand side of Fig. 6).

The power-frequency (p-f) characteristic of the primaryfrequency controller is linear outside the noncritical frequencywindow (see then right-hand side of Fig. 6). It is defined in the

1262 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 3, AUGUST 2007

Fig. 5. Measured frequency in UCTE, April 2005. From a frequency qualityperspective, April 2005 was an average month.

Fig. 6. Power-frequency (p-f) characteristic of the BESS primary frequencycontroller in accordance to the UCTE requirements [13].

grid code [13], which states that the full primary reservehas to be activated when the frequency deviation reaches

mHz. As an example, we choose a contracted primaryreserve Pn (nominal power of the BESS) of 2 MW, which is0.06% of the total UCTE primary reserve. The BESS followsthe frequency profile; however, its influence on the frequencyis neglected.

The p-f characteristic permits the transformation of the mea-sured frequency deviations into a required output/input powerfor every second (see Fig. 7). The duration, the maximum power,and the energy of each discharging/charging pulse have been an-alyzed in Table III.

B. Simulation of BESS Supplying Primary Reserve in UCTE1) BESS With No Additional Charging: We start the analysis

with an unrealistic case for illustration purposes only: a BESSwith an efficiency of 70% that is charged and discharged only infunction of the frequency variation with no additional charging.At the beginning of the month, the BESS is 100% charged, andthen, it supplies/absorbs power depending on the system fre-quency variation (see Fig. 7).

With the given p-f characteristic, the operating rules are verysimple:

Discharge the battery when mHz. Charge the battery when mHz.

Fig. 7. Primary reserve power curve, April 2005. Power supplied to the grid isbelow zero (BESS in discharge mode). Power absorbed from the grid is abovezero (BESS in charge mode).

TABLE IIIRESULTS OF STATISTIC ANALYSIS OF PRIMARY RESERVE POWER CURVE

The curve named No recharge in Fig. 8 shows the changein the BESS state of charge (SoC) upon furnishing primary fre-quency control reserve in April 2005. Due to the limited BESSefficiency, the overall SoC trend leads to a continuous dischargeof the BESS in the long run. In this case, the minimum requiredBESS capacity for one month (April 2005) is 1.62 hours, alarge and costly BESS capacity. This is of course not a prac-tical operating strategy; the BESS must rather be recharged atcertain time periods in order to maintain a reasonable state ofcharge during the course of operation.

2) BESS With Additional Charging: In a second stage, weappended the operating rules in the following way:

Recharge the battery up to 100% when the frequency isinside the noncritical window .

Use a small recharge power (a few percent of ). If the battery is full (100%), absorb power with auxiliary

resistors.The required minimum BESS capacity is drastically reducedwith an increase in BESS recharge power. Fig. 8 shows the stateof charge of the BESS with efficiency 70% as a function oftime and recharge power 1%, 3%, and 5% of . The higher

OUDALOV et al.: OPTIMIZING A BATTERY ENERGY STORAGE SYSTEM FOR PRIMARY FREQUENCY CONTROL 1263

Fig. 8. SoC of the BESS with efficiency 70%, no recharge, and recharge with1%-5% of BESS nominal power, April 2005.

Fig. 9. Impact of recharge power on the BESS design and operation.

the recharge power, the higher the deepest state of charge andthe smaller the needed battery capacity.

There are, however, also disadvantages with a high rechargepower. With the high recharge power, the BESS is fully chargedmost of the time and is not able to absorb power from the gridin the case of a frequency rise above the noncritical window.We use auxiliary resistors to dissipate power under these cir-cumstances. This costs money. Energy has to be bought on themarket that could be obtained for free during the high frequencyperiods.

Fig. 9 puts together two plots that demonstrate the impact ofthe recharge power percentage on BESS design and operation.The black line shows how the BESS capacity depends on therecharge percentage. The BESS capacity is the minimum valuein Fig. 8 plus 0.25 hours to ensure a further maximum dis-charge event (15 min full nominal power) at the lowest statisti-cally occurring level of charge.

The grey line in Fig. 9 shows how the total energy losses inthe auxiliary resistors during one month depend on the rechargepercentage.

3) BESS With Additional Charging and SoC Max/Min Limits:If the target level for the state of charge is chosen slightly below100%, we keep some charging reserve, and most of the eventscan be avoided where energy would be dissipated in the resis-tors. Based on this idea, we have improved the BESS operatingstrategy. The goal is now not to keep the battery 100% chargedbut to keep it in a range between two defined SoC levels. This

enables the BESS to absorb more power if needed and reducesthe use of resistors. Additionally, there is a procedure incor-porated into the control algorithm that allows selling relativelysmall amounts of excessive energy on the intra-day market. Themain goal of the selling procedure is not to gain a profit but againto keep the SoC parameter of the BESS between the two limits

and .The complete set of operating rules is the following: Discharge the battery when mHz. Charge the battery when mHz. Discharge the battery (sell energy on the market) when

actual (maximum discharge power %of ).

Recharge the battery when and. (maximum recharge power % of ).

Dissipate energy in emergency resistors whenmHz and %.

Idle the battery when and.

Operating rules with SoC limits allow a considerable decreasein utilizing resistors to only a few times per month comparedto typically 10 000 operations (pulses) of the BESS during thatmonth, hence justifying the term emergency resistors.C. Optimizing BESS Capacity

The main objective is to maximize the profit for the potentialBESS owner acting at the ancillary service market. Becausethe main cost driver is the battery capacity, the optimizationwill be essentially equivalent to a minimization of the batterycapacity.

On the other hand, the use of emergency resistors is usuallyconsidered negative because it means wasting useful energy.This is a requirement that is opposed to our main optimizationgoal and that constitutes conceptual difficulties. We let it enteras a side condition. In this way, it is possible to express anypossible preference in that regard. The extremes may rangefrom putting no value to the resistively dissipated energy otherthan its purchase price to putting a very high penalty factor(e.g., 100) on this price to squeeze out the resistor use almostcompletely. In our opinion, it is neither an environmental nor aneconomic optimum, to avoid emergency resistors completely.

The annual values Revenue and Cost in (3) and (4) may beexpressed as (5) and (6), respectively

Revenue Payment (5)

Payment is the primary reserve availability payment (1). isthe revenue from selling energy on intra-day market. Sold en-ergy is the additional source of profit for the owner of the BESS,although its monthly amount of energy will rarely exceed 0.1hours

Cost (6)

where is the BESS installation and O&M cost. is thecost of recharge energy bought from the grid.

All parameters and variables used in the optimization aregrouped in Table IV.

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TABLE IVBESS PARAMETERS AND VARIABLES FOR OPTIMIZATION

The objective function is to maximize the profit (2)

Profit Revenue - Cost

Payment

(7)The method provides the optimal BESS capacity and can bedivided in two steps.

At the first step, the NPV of profit is calculated for each setof combinations of the variables in the parameter range (seeTable IV). Simultaneously, for each set of combinations, we ad-ditionally calculate the battery capacity and resistor losses.

Fig. 10 shows a contour plot of the required battery capacityin as a function of the variables sell power and the upperlevel . For example, with a sell power of % anda level of 0.04 , the required battery capacity is0.625 . In this example the other variables (see Table IV)are fixed to recharge power % and

.

It can be seen from Fig. 10 that the smaller the parameterssell power and in other words the smaller the amountof sold energythe smaller the required battery capacity. Thisis good for the total BESS cost because the battery capacity isthe main cost diver.

We indicate in the same plot contours of a fixed amount ofenergy dissipated in the emergency resistors. It is clear that thesmaller the parameters sell power and the higher , thehigher the resistor losses.

The second step is the search for the optimal BESS capacitytaking into account the energy losses in the resistors. Having nomathematical formulation for penalty factor of using resistors,we restricted the resistor losses to maximum 10% of the totalenergy uptake into the BESS.

Fig. 10. Contour plot of the required battery capacity inP h as a function ofthe variables sell power and the upper level SoC . The lines that are schemat-ically shown in addition correspond to resistor losses of 5%, 10%, and 20% ofthe total energy uptake into the BESS. Frequency data: April 2005.

TABLE VRESULTS OF BESS CAPACITY OPTIMIZATION

Fig. 11. Monthly SoC variation of the 2-MW BESS with adjusted SoCmax/min limits. Frequency data: April 2005.

The corresponding optimal BESS capacity is 0.62 h. Othervariables and outputs are listed in Table V. The correspondingBESS state of charge profile is depicted in Fig. 11.

Fig. 12 illustrates the BESS operation algorithm for a periodof 32 h during April 2005. At the beginning of time interval,the BESS SoC is at Pn*h within the interval

. Next, there is a period with prevailing positivefrequency deviations so that the SoC moves above the

OUDALOV et al.: OPTIMIZING A BATTERY ENERGY STORAGE SYSTEM FOR PRIMARY FREQUENCY CONTROL 1265

Fig. 12. Provision of primary reserve by the BESS in April 2005.

and a certain portion of energy is sold on the intra-day market.This energy is delivered as constant power (Sell power inTable IV) during one hour. It has to be scheduled at least 30min in advance.

During this period, the frequency remains high, and the SoCreaches 100%. Therefore, excessive energy is dissipated inemergency resistors. Shortly after that period, the scheduledpower delivery starts, and it brings the SoC back into the SoCtarget operating range. Then, there is a long interval with theprevailing low system frequency. The SoC progressively goesdown and passes the limit after some hours. At thismoment, the BESS control system issues a charging commandwith an appropriate value (3% of ) during periods when thefrequency stays inside a noncritical window .Toward the end of the period, the system frequency is high, sothat the SoC comes back into the operating range by primarycontrol action itself.

D. Multi-String Operating AlgorithmThe well-known operating rules for multi-string BESS units

can be applied to our control algorithm in a straightforwardmanner (see Fig. 13). The BESS monitoring and control systemuses the frequency measurement and the SoC level as inputsignals. The BESS is composed by a large number of batterycells grouped into parallel strings. Each string is connected toa common ac bus via an individual power conversion system.Cells operate in two symmetric groups; one is used for the down-ward frequency regulation and another one for the upward fre-quency regulation. The two groups shift their roles at convenientpoints in time. The consistent charging direction for each cell re-duces the battery aging and prolongs the battery lifetime.

E. Dynamically Adjustable SoC-LimitsThe BESS operating strategy might be further improved by

introducing dynamically adjustable SoC limits. Rules for theadjustment of SoC min/max limits can be derived by the statisticanalysis of frequency measurements. Here we see trends in thedaily, weekly, and seasonal frequency variations.

Fig. 13. BESS multi-strings layout and operating principle.

Fig. 14. Average daily frequency variation during April 2005.

Fig. 14 represents the average daily frequency variationduring April 2005. It can be observed that the frequency variessubstantially during a transition from one hour to another, dueto a change in the electricity production schedule. This infor-mation can be used for a dynamic adjustment of SoC min/maxlimits just before the change of the hour.

As another example, the can be decreased duringthe night hours because the system frequency is expected to berather high (see Fig. 14). The values of recharge and sell powercan also be adjusted dynamically in function of market condi-tions.

VI. CONCLUSION

The supply of a sufficient frequency control reserve is impor-tant to balance power system load and generation at any instantfor a secure and high-quality power supply. BESS are able tosatisfy the technical requirements for primary frequency con-trol.

This paper provides a method for the dimensioning of a BESSto provide primary reserve based on historic frequency measure-ments. A lead-acid BESS can be a profitable utility solution at

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current battery system costs and current market prices for theprovision of primary reserve capacity.

With rare use of emergency resistors, the optimum capacity is0.62 h multiplied by the nominal power rating. For a cost-effec-tive sizing, it is essential to use adjustable maximum and min-imum state of charge limits, to recharge at moderate rate whilethe system frequency is within the noncritical window, and tosell some power to the intra-day market if the state of charge ison the high side. An economically optimum BESS for primaryfrequency control includes emergency resistors to dissipate en-ergy during rare events when an extreme over-frequency excur-sion occurs while the BESS is fully charged.

ACKNOWLEDGMENTThe authors would like to thank G. Linhofer (ABB Switzer-

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Alexandre Oudalov received the Ph.D. degreein electrical engineering in 2003 from the SwissFederal Institute of Technology of Lausanne (EPFL),Lausanne, Switzerland.

Since 2004, he has been a Research Engineer inthe Information Technologies Department at ABBSwitzerland, Corporate Research, Daettwil-Baden,Switzerland. His research interests include powersystem control, distributed generation, energystorage, and distribution automation.

Daniel Chartouni received the Ph.D. degree in solidstate physics from the University of Fribourg, Fri-bourg, Switzerland.

He joined ABB Switzerland, Corporate Research,Daettwil-Baden, Switzerland, in 2000 and is a ProjectLeader in the Electro-technologies Department. Hisareas of interest are devices for energy storage andthermal management of power devices.

Christian Ohler (M06) received the Ph.D. degree insemiconductor physics from the Technical Universityof Aachen, Aachen, Germany.

He joined ABB Switzerland, Corporate Research,Daettwil-Baden, Switzerland, in 1998 and is GroupLeader in the Electro-technologies Department. Hisareas of interest are devices for energy storage andswitchgear.