1118 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, …best.eng.buffalo.edu/Publication/IEEE_Storage...

1118 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 3, AUGUST 2011

Optimal Planning to Include StorageDevices in Power Systems

HyungSeon Oh, Member, IEEE

Abstract—It is difficult to forecast renewable energy resourcesdue to their variability. High uncertainty of the resources in-creases the concern about the reliable operation of the electricpower system. Storage devices have been considered a candidate tocontrol variable energy resources, and most studies on storage de-vices are performed in the economic dispatch. Therefore, electricpower adequacy may be an issue. In this paper, a new approachin the optimal power flow framework is proposed for deployingstorage devices, and the feasibility and economic impact analysesare discussed.

Index Terms—DC power flow, optimal power flow (OPF), powertransfer distribution factor (PTDF), storage devices, variable en-ergy resources.

NOMENCLATURE

Branch impedance matrix.

Bus impedance matrix.

C Grand offer/operation cost of generators.

GA Group of generators with high ramp rate so thatsuch generators have the capability to change theiroutput after realizing the renewable outputs.

GB Group of generators that do not have the capabilityto change their generation according to therenewable outputs.

H PTDF matrix with cardinality of -by- .

Identity matrix with cardinality of -by- .

L Generator location matrix with cardinality of-by- .

LL Storage device location matrix with cardinalityof -by-

Number of states of the output from the variablegenerators at time .

Pg Power injection vector.

Probability that variable generators’ output is inth state at time .

Manuscript received November 24, 2009; revised February 11, 2010, May26, 2010, and July 14, 2010; accepted September 08, 2010. Date of publicationDecember 17, 2010; date of current version July 22, 2011. This work was sup-ported by the U.S. Department of Energy. Paper no. TPWRS-00913-2009.

The author is with the National Renewable Energy Laboratory, Golden, CO80401 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRS.2010.2091515

X Line reactance.

Recovery period in years.

a Construction cost related to rated power in $/MW.

b Construction cost related to rated energy in$/MWh.

Load profile at time .

diag(x) Diagonal matrix with the diagonal elements of x.

th unit vector.

f Power flow on the transmission network.

g Generation vector.

Index of realization of the output from variablegenerators at a time slice.

Index of location in the power system.

Number of lines.

Number of buses.

Number of storage devices.

Number of generators.

Index of time slices (i.e., time ).

Maximum value of v.

Minimum value of v.

x Vector of (i.e., ).

Vector of (i.e., ).

Vector of (i.e., ).

Variable x at location , realization of thevariable generators’ output at time .

Effective discharge of the storage devices, .

Number of time slices.

Frequency that a cycle of the time slicerepeats in a year.

Yearly cost recovery factor.

Efficiency of storage devices during charge.

Efficiency of storage devices during discharge.

Discharge rate of storage devices in MW.

Charge status of storage devices in MWh.

Ratio of energy stored initially to rated energy.

U.S. Government work not protected by U.S. copyright.

OH: OPTIMAL PLANNING TO INCLUDE STORAGE DEVICES IN POWER SYSTEMS 1119

Interest rate.

Charge rate of storage devices in MW.

Duration of time slice .

-by-1 voltage angle vector.

Minimum discharge duration of storage devicesin h.

Rated energy of storage devices in MWh.

Rated power of storage devices in MW.

I. INTRODUCTION

R ENEWABLE energy resources are being explored as ameans of reducing global greenhouse gas emissions. Be-

cause many renewable energy resources are remotely locatedfrom a load center, supporting the transmission network is nec-essary. The integration of resources into the power system alsobecomes important with the use of renewable energy resources.The recent development of efficient expansion-planning algo-rithms [1]–[5] helps simultaneously optimize the transmissionnetwork and generation.

Renewables such as solar energy and wind are variable en-ergy resources. The forecast error of wind is typically 30% fora single location and 10% for an aggregate large area [6]–[8]. Ifthe transmission network has no congestion, the error may notbe a problem as increasing reserve margin can cover 10% error.However, the transmission networks are not up-to-date in mostof the world. With congestion, the difference between forecastand actual output must be covered locally, and therefore, theforecast error is too large to reliably operate the power systemwhen the penetration of variable energy resources is high.

Suggestions for mitigating the effect of the variability in-clude using 1) demand-side management, 2) generators withhigh ramp rates, and 3) energy storage devices.

Demand-side management has been proposed for relievingmarket volatility and for improving market efficiency [9]–[12].The net injection (defined as the difference between generationand demand) at a location determines the operation set point.Therefore, the forecast error of the injection is the geometricsum of the error in the forecast on demand and generation; i.e.,the overall error is the mean square error from demand forecastand generation forecast. If demand can be managed efficientlyso that the net injection remains in the proximity of the forecast,the variability of renewable energy resources will not affect thepower system operation.

Reducing locational marginal pricing (LMP) is the aim of de-mand-side management. Because LMP is an incremental cost tothe system by an additional demand, the management is mainlyfocused on marginal reduction. For a system with a high pene-tration of variable energy resources, demand-side managementalone may not be enough to mitigate the impact of the resourcevariability. If a system can adjust an operation set point whenneeded, the forecast error may not have a large impact on thereliability. A generator with a high ramp rate can provide flex-ibility to the system. Hydroelectric power plants have a highramp rate, but they are built in limited locations and their opera-tion may be limited due to environmental constraints. There are

other types of generators with a high ramp rate, but their fuelcosts are high because their fuel is mainly gas. If the fractionof these generators should increase according to the penetrationof renewable generators, the resulting system may be highly in-efficient. Storage devices, which can provide enough flexibilityto mitigate the impact of variable output of the variable gener-ators, become attractive candidates to control the resource vari-ability. Presently, a high construction cost is the main hurdle toinstalling storage devices in the system.

Studies have assessed the economic impact and the deploy-ment of storage devices [13]–[16]. The studies in [13]–[15] eval-uate the benefit of storage devices by load shifting. The idea isthis: When energy is purchased, stored, and then sold at a higherprice than was paid for it, the value of the storage devices is di-rectly related to the difference in price. The operation scheduleof the storage devices depends on LMP that is assumed to beavailable in advance. Therefore, the studies assume that LMPis invariant to utilizing the devices. With [16], which assumedLMP to be a linear function of demand, it was possible to con-struct a function relating the charging/discharging of the storagedevices with LMP. However, the study does not consider thetransmission network, and the linear function is based on empir-ical data. With a high penetration of renewable energy resources,the congestion pattern is likely different from that in the currentsystem, and so is LMP as a result. Therefore, the linear equationis not guaranteed valid in a system with a high renewable en-ergy penetration. Even if the congestion pattern stays the same,LMP can change according to the amount of energy stored andconsumed because the amount affects dispatch. It is thereforenecessary to apply these studies in the power system operationand planning.

In this paper, a modeling of storage devices is proposed in theoptimal power flow (OPF) framework to take the transmissionnetwork into consideration, and the simulation results are dis-cussed.

II. STORAGE DEVICE MODELING

A storage device is characterized by its rated energy , ratedpower , and efficiencies ( and ). In the OPF framework,the storage devices provide a path for power flow from one timeto the next at the same location; i.e., energy can be stored forfuture use and discharged when needed. Because the efficien-cies are less than unity, utilizing the devices is not efficient un-less they are charged at a low LMP and discharged at a highLMP. The future charging status of the storage devices varies ac-cording to the charging and the discharging rates and accordingto the duration in the current time slice:1

(1)

Equation (1) holds if there is no variability. For variable in-jections, the variation in charge and discharge rates according tothe actual output of the variable generators must be considered.Because the status of the storage devices depends on the history,multiple realizations of the output of the renewable generatorsat time may need to be considered as well. Additionally, in

1A time slice represents a typical seasonal load. For example, a time slice fora peak period is summer between 12 p.m. and 4 p.m.


power system operation and planning, multiple scenarios at dif-ferent time slices for optimal use of the devices must be consid-ered. Therefore, in considering multiple routes to reach the caseat the last time slice, many different cases between time slicesand must be considered. For example:

(2)

The future charge status depends only on the last observedvalue of the status and not on the history of the process beforethe time. Then, the status is

(3)

With (3), the number of cases to consider becomes

(4)

Note that the storage devices may be able to adjust their out-puts (discharge rate and charge rate ) in a short time, andtherefore, the values of and can change in different realiza-tions of the output from renewable generators.

At the time slice , discharge rate and charge rate behaveas effective generation and effective load, respectively. There-fore, they enter into the power balance equation:

(5)

After a cycle of time slices, charge status of the storagedevices must return the initial values for serving the next cycle:

(6)

The following are limits on discharge rate , charge rate ,charge status , rated energy , and rated power :

(7)

(8)

(9)

(10)(11)(12)(13)(14)

Equations (7) and (8) indicate that the energy to be consumedor stored is limited to the available energy or to the space tostore in the devices. Constraints (9), (10), and (11) are appliedbecause the charging and discharging rates and the charge statusare constrained by the properties of the storage devices. Equa-tions (12) and (13) indicate that the rated power and energyof the storage devices are limited by the storage technologies.Equation (14) shows that the storage devices should operate fora certain minimum duration.

III. PROBLEM FORMULATION

A. Objective Function

It is possible to minimize the yearly system cost using sto-chastic programming (i.e., the sum of both operation and con-struction costs for a year). The operation cost is the cost to gen-erate electricity, . In general, construction cost includes thecost to build generators and to upgrade the transmission net-work. However, the scope of this study includes the storage de-vices in the optimization process, and therefore, only the costto add storage devices is considered. In this study, a linear con-struction cost is considered in terms of the rated power and therated energy. Reference [3] contains the general setup for powersystem planning to consider the addition of generators and thetransmission upgrade in the OPF framework:

(15)

Because multiple time slices are involved, C is not the offer/operation cost in a time slice. Instead, C is a grand offer/opera-tion cost:

...

(16)

B. Constraints

In addition to the constraints related to the storage deviceslisted in (3) and (5)–(14), there are the following constraints:

(17)

(18)

(19)

Equation (17) is the constraint defining the operation range ofgeneration; (18) is the power balance equation for the system;and (19) shows the upper and the lower limits for the flow overthe transmission network, which obeys Kirchhoff’s laws.

Instead of using H and Pg in (19), it is desirable to use, and as in [3] because doing so yields a sparser con-

straint matrix. For a full AC OPF model, (18) and (19) shouldbe replaced with highly nonlinear equations, and additionalconstraints associated with voltage and reactive power mustbe added. (The equations and the constraints in a formal ACOPF formulation can be found in [19].) Finding a solution tothe full AC OPF for a large-scaled system is computationallyexpensive. In this study, a lossless linear approximation is usedto simplify the problem.

The output from generators with high ramp rates can be ad-justed after the realization of the output from variable gener-ators in the same way as the storage devices. The set of suchgenerators is termed GA, and the complementary set is calledGB. Then, only the generation from the generators in GA can


be changed for different realizations among generators. For ex-ample:

(20)

where and stand for the location matrix of generatorsin GA and in GB, respectively.

Because the output from the generators in GB cannot changefor different realizations, a unique output should be determinedin dispatch. Therefore, the cost C in (15) and (16) can be classi-fied into two groups—GA and GB—so that the number of con-trol variables remains minimal. Note that the offers/operationcosts do not change with different realizations. Without the lossof generality, the constant in the objective function can bedropped. By dropping , the objective function is the sum ofoperation and construction cost for one cycle of the time slices,i.e., instead of a year. To summarize, the optimizationproblem is

(21)

where equality constraints from (3), (6), (18), and (20) (see theequation at the bottom of the page): and inequality constraintsfrom (7)–(14), (17), and (19):

Note that the problem is formulated using a lossless DC OPFmodel. Therefore, losses, voltage, and reactive power are notconsidered in this study.

In this setup, the outputs from the renewable generators areinjected to the system, and therefore, they are identical to nega-tive demand with the same magnitude. It is also possible to op-timally accept the fraction of outputs from the renewable gener-ators. In order to find the optimal fraction, the renewable gener-ators are added in , as a part of GA. All the outputs are offered

Fig. 1. Three-bus system of which reactance values are all 0.1 . R and S standfor variable renewable generator and storage devices, respectively.

at a generation cost so that the system operator can optimallydispatch the output. Note the generation costs of the renewablegenerators and the storage devices are assumed negligible in thisstudy. If nonzero operation costs exist for the renewable gener-ators and for the storage devices, their costs can be included inC, and their dispatches should be included in . For , theoutput from renewable generator is constrained by the avail-ability of :

(22)

By adding (22) to (21), the system operator can optimallydispatch conventional and renewable generators, as well as thestorage devices. This problem finds the optimal solution with apossible construction of the storage devices by minimizing thesum of the construction costs of the devices and the operationcosts.

Because (21) is a linear problem and the objective function isnot parallel to any constraints, the solution from the optimiza-tion problem is the unique global optimizer [17]. Therefore, allthe solutions that will be presented in Sections IV, V, and VIare global optimizers that include the global optimal scheduleof the storage devices.

IV. SIMPLE ILLUSTRATIVE EXAMPLE

A. Simulation Environment

For a simulation, a three-bus example is used as illustratedin Fig. 1. For the system, all reactance values are identical. Thecapacities of the lines connecting Bus 1–2, Bus 2–3, and Bus3–1 are 250, 120, and 250 MW, respectively. While G1 is anatural gas generator, G2 is a coal generator.

Demand and the outputs from renewable generator R at eachtime slice are listed in Table I. Three different time slices are


TABLE IDEMAND AND THE OUTPUTS FROM THE RENEWABLE

GENERATOR AT VARIOUS TIME SLICES

considered, and for the second time slice, there are three pos-sible outputs from R. For the first and third time slices, it is cer-tain that R does not generate any output. For the second timeslice, the output from R may be 200, 100, and 0 MW with theprobabilities of 20%, 50%, and 30%, respectively.

In this simulation, it is assumed that three time slices arerepeated for -years (30 years). For example, there are threetime slices, , and . The sequence of the time slices,

, takes 100 h, and it is repeated for 30 years(i.e., ,approximately 2603 cycles). The block offers/operation costsfrom G1 are $10/MWh for [0 200 MW) and $30/MWh for [200300 MW], and those for G2 are $20/MWh for [0 70 MW) and$40/MWh for [70 100 MW]. In this study, the threshold for ahigh ramp rate is set to the capability to adjust the generation in15 min, and therefore, coal generators do not belong to GA. Inthis simulation, G1 belongs to GA, and therefore, its dispatchesat (first realization at the second time slice), , and canbe different while the dispatches of G2 at the time slices shouldbe the same regardless of the realization of the output from re-newable generators. The construction costs to build the storagedevices (a and b) are $160/kW and $240/kWh, respectively [18];

is 87.6 . The efficiencies of S1 andS2 are 90% for both discharging and charging processes.

The values are chosen for simulations, and therefore, the ef-ficiency data may not reflect actual technology. Note that onlyround-trip efficiency is available, which is the product of twoefficiencies ( and ). According to the data from a vender[20], the round-trip efficiencies are 87% for pumped hydro, 90%for battery, and 125% for compressed air energy storage. Be-cause efficiency data during discharging and charging processesare unavailable, both efficiencies are assumed to be identicalin this study. In that sense, the efficiencies are above 90% forthe above technologies. However, any values for the efficien-cies would work in this formulation.

Without the storage devices, only the first case is feasible, andLMP is $10/MWh for all the buses. The cases at the second andthird time slices are not feasible due to generation limits andcongestion.

B. Simulation Result With Storage Devices

The problem described in (21) is solved with the data pre-sented in the previous subsection by using MATPOWER [19],and the result is presented in Table II. With the storage devices,

TABLE IIGENERATION DISPATCHES AND THE EFFECTIVE DISCHARGE

FROM THE STORAGE DEVICES AT THE TIME SLICES

TABLE IIILMP IN $/MWH AT THE TIME SLICES

all the cases are feasible and the system cost is $14 000/h. Inboth cases, the same dispatch results were observed whetherthe system accepted all or part of the output from the renewablegenerator. It is necessary to construct the storage devices thatrated power and rated energy equal: [77.1; 112.6 MW] and[2857; 10 000 MWh], respectively. Because G1 has the abilityto change its output in a short time, its outputs are different forthe second time slice according to the different realizations ofthe renewable generators. The charge rate is effectively de-mand, while the discharge rate is generation. Therefore, therealization from Table I, generation dispatch g, and the effectivedischarges from Table II are the electric power outputs thatsupport the total loads in Table I from the renewable generators,the generators (G1 and G2), and the storage devices (S1 andS2), respectively. As shown in the tables, the storage devicesare charged at the first time slice so that they can fulfill demandat the second and third time slices. Consequently, LMP with thedevices is higher than it is without the devices at the first timeslice (Table III).

There are three different routes to the last time slice in a cycle( , or ). Becauseeach route contains three cases, nine cases (

) must be considered to optimize the system. The number ofroutes increases as the number of time slices increases and/or thenumber of realizations per time slice increases. For comparison,only five cases were considered ; this effect will bediscussed in detail in the next sections.

V. IEEE 30-BUS SYSTEM


Fig. 2 shows the one-line diagram of the modified IEEE30-bus system [19]. The capacities of tie-lines between Areas 1and 2 and Areas 2 and 3 are 10 MVA and 20 MVA, respectively.The values of the reactance are listed in Table IV.

The offers/operation costs of generators are given in Table V,and the generators located at Bus 13, Bus 22, and Bus 23 havea high ramp rate (i.e., GA). Because of the high costs of Firm 5and 6, high demand, and limited capacity of the tie-lines, Area


Fig. 2. Modified IEEE 30-bus system. An R next to a diamond and an S nextto a square are renewable generators and storage devices, respectively.

TABLE IVLINE REACTANCE X DATA

TABLE VPIECE-WISE BLOCK OFFERS/OPERATION COSTS OF GENERATORS

2 is termed a load-pocket. The values of construction costs andefficiencies are the same as those listed in Section IV.

TABLE VIDEMAND AND RENEWABLE OUTPUT REALIZATION IN MW FOR SEVENTIME SLICES. 5 AND 7 SUBSCRIBED WITH R STAND FOR THE LOCATION

WHERE THE RENEWABLE GENERATORS ARE LOCATED

In this simulation, seven time slices and three outputs foreach time slice are considered. Table VI lists the detailed datafor demand and outputs. As discussed in the previous section,there are routes to the last time slice. For opti-mizing the system by considering all the routes, one has 15 309

cases that should be considered becausethere are seven time slices in one route. It is clear that the ap-proach becomes computationally expensive for a large system.With the setup represented in (20) and (21), the system containsonly 21 cases.

The solutions to the cases at the first, second, sixth, and sev-enth time slices include no congestion with either renewablegenerators or storage devices. The cases at the third and fifthtime slices yield solutions with congestion; the tie-line betweenAreas 1 and 2 is congested on both cases and that between Areas2 and 3 is only congested at the fifth time slice. The case at thefourth time slice is not feasible. Due to the renewable genera-tors, a case at the fourth time slice becomes feasible only forthe first realization. However, it is noteworthy that many casesbecome infeasible if all the outputs from the renewable gener-ators are injected into the network. In other words, some of therenewable output must be curtailed for the reliable operation ofthe power system when the system does not include the storagedevices.


Certain sites are preferred for the storage devices such as thecompressed air energy storage [21] and pumped hydroelectricgenerators. In this case, the locations of the storage may be pre-determined. Sections V-B and C list the simulation results forthe given locations of the storage devices. Some storage devices,such as batteries, can be installed anywhere. Sections V-D andE present the simulation results when there is no restriction toconstructing the storage devices.

B. Storage Devices With Locational Constraints: All theOutputs Accepted From Renewable Generators

In the case that the system accepts all the outputs from re-newable generators, the construction of the storage devices is:

MW and MWh. Thesystem cost is $6172/h, and the computation time to find theoptimal solution is 1.4 s by using a laptop with 2.53-GHz IntelCore™ 2 Duo Processor and 4-GB 1067-MHz DDR3 memory.For 100 h, total energy generated from the renewable genera-tors is 8.7 GWh on average. Table VII presents the dispatchesand the effective discharge of the storage devices. The effectivedischarge of the storage devices is listed in Table VII. Fig. 3illustrates the charge status of the storage devices at the var-ious locations. One might predict from the studies in [13]–[15]that energy is stored when electricity is less expensive and dis-charged at a peak period. The results in Fig. 3 show the trend aswas expected. Clearly, during the low-demand periods (the firstand the second time slices), the devices are charged so they canprovide electricity during the high-demand periods (the third,fourth, and fifth time slices). Because of the variation of localdemand around the devices, the charge/discharge behaviors varywith each other.

C. Storage Devices With Locational Constraints: Outputs ofthe Variable Generators Are Optimally Dispatched

In the case where the system operator optimally dispatchesthe renewable outputs, the construction of the storage devicesis: rated power MW and rated energy

MWh. It takes 1 s to find the optimal solution.Because the system operator can curtail the renewable outputand the cost to construct the storage devices is high, the storagedevices with smaller capacities are constructed in comparisonto those referenced in the previous section; the system cost is$5564/h. All the cases are feasible with the curtailment of theoutput. Over the same period (100 h), total energy generatedfrom the renewable generators is on average 7.5 GWh, and thecurtailed energy is therefore 1.2 GWh. The dispatches and ef-fective discharge of the storage devices are listed in Table VIII.The optimal charge status of the storage devices at the variouslocations is illustrated in Fig. 4.

By storing energy at off-peak periods and selling at peak pe-riods, the capabilities of generators and the transmission net-work are fully utilized.

D. Storage Devices With No Locational Constraints: All theOutputs Accepted From Renewable Generators

In this simulation, the system accepts all the outputs fromrenewable generators, and the locations of the storage de-vices are determined during the optimization process. Thecomputational time using the same laptop is 4 s. The op-timal locations for the storage devices are Buses 4, 12,

TABLE VIIDISPATCHES OF GENERATORS AND THE EFFECTIVE DISCHARGE RATES

OF THE STORAGE DEVICES WHERE ALL THE OUTPUT FROM THERENEWABLE GENERATORS IS ACCEPTED. B IN THE FIRST COLUMN

STANDS FOR THE LOCATION OF THE STORAGE DEVICES

Fig. 3. Charging status of the storage devices located at Bus 14, Bus 19, andBus 21.

13, 16, 17, and 23. The construction of the storage de-vices are MW and

MWh. The system costis $5807/h. Fig. 5 illustrates the charge status of the storagedevices at the various locations. The storage devices located atBuses 12, 13, 16, and 17 have a similar charging/dischargingschedule because they are closely located in the load pocket.Because of the big load at Bus 23, it is optimal to construct a


TABLE VIIIDISPATCHES OF GENERATORS AND THE EFFECTIVE DISCHARGE RATESOF THE STORAGE DEVICES WHERE THE SYSTEM OPERATOR OPTIMALLY

DISPATCHES THE OUTPUT FROM THE RENEWABLE GENERATORS

Fig. 4. Charging status of the storage devices located at Bus 14, Bus 19, andBus 21.

Fig. 5. Charging status of the storage devices optimally located at Bus 4, Bus12, Bus 13, Bus 16, Bus 17, and Bus 23.

TABLE IXDISPATCHES OF GENERATORS AND THE EFFECTIVE DISCHARGE RATESOF THE STORAGE DEVICES WHERE THE SYSTEM OPERATOR OPTIMALLY


large storage device at the location. The dispatches and effectivedischarge of the storage devices are listed in Table IX.

E. Storage Devices With No Locational Constraints: Outputsof the Variable Generators Are Optimally Dispatched

The simulation environment of this section is that the op-timization process determines both optimal dispatches fromthe renewable outputs and the locations of the storage devices.The computation time using the same laptop is 4 s. The op-timal locations for the storage devices are Buses 4, 12, 13,16, 17, and 23, which are the same results as in Section V-D.The constructions of the storage devices are rated power

MW and rated energyMWh. The system cost is

$5405/h. Because the solution in Section V-D is in the feasibleregion of this problem and the optimization process finds thebest solution among feasible ones, the system cost from thissolution is less than that found in Section V-D. A similarresult was observed in Sections V-B and C, where the systemcost from Section V-C is less than that found in Section V-B.Fig. 6 illustrates the charge status of the storage devices at thevarious locations. The storage devices located at Buses 12, 13,16, and 17 have a similar charging/discharging schedule. The


Fig. 6. Charging status of the storage devices optimally located at Bus 4, Bus12, Bus 13, Bus 16, Bus 17, and Bus 23.

dispatches and effective discharge of the storage devices arelisted in Table X.

VI. IEEE 118-BUS SYSTEM


Fig. 7 shows the one-line diagram of the modified IEEE118-bus system [19]. The capacities of tie-lines connectingAreas 1–2, Areas 2–3, and Areas 2–4 are modified. The of-fers/operation costs of generators at Area 2 are higher thanthese costs in other areas. The generators located at Bus 10,Bus 30, and Bus 89 have a high ramp rate (i.e., GA). Becauseof the high costs of the generators in Area 2, high demand inthe area, and limited capacity of the tie-lines, Area 2 is termeda load-pocket. The values of construction cost and efficienciesare the same as those listed in Section IV.

Because of the limits on the number of variables imposedon MATPOWER, one is constrained to choose a large systemand the numbers of GA and renewable generators to considerall the locations as possible sites for the storage devices. In thissimulation, eight time slices and five outputs for each time sliceare considered. The variability of the outputs is larger for therenewable generator in Area 1 than that in Area 3.

In each time slice in this simulation, all loads can be fulfilledusing the existing generators with neither renewable generatorsnor the storage devices. The system cost without the renewablegenerators and the storage devices is $116 334/h. The systemcost is $109 530/h with the renewable generators whether all ora fraction of the outputs of the variable generators are accepted.Generators located at Buses 10, 30, and 89 are classified as theGA. All the locations are considered as a site for the construc-tion of the storage devices. As discussed in the previous section,there are routes to arrive at the last time slice. Ifone wants to optimize the system by considering all the routes,one has 3 125 000 cases. With the setup represented in(21) and (22), the system contains only 40cases.

B. Simulation Results

Fig. 8 illustrates the simulation results when the electricitymarket accepts all the outputs of the variable generators, re-

TABLE XDISPATCHES OF GENERATORS AND THE EFFECTIVE DISCHARGE RATESOF THE STORAGE DEVICES WHERE THE SYSTEM OPERATOR OPTIMALLY


spectively. The computation time to find the optimal solutionis 1010 s, and the system cost is $109 490/h. The construc-tions of the storage devices at Buses 8, 9, 10, and 31 are: ratedpower MW and rated energy

MWh.Fig. 9 shows the simulation results for a market that optimally

dispatches the output of the variable generators. It is optimal toconstruct a storage device at Bus 31, and the rated power and


Fig. 7. Modified IEEE 118-bus system. The green circles indicate the locationof the renewable generators.

Fig. 8. Charging status of the storage devices optimally located at Bus 8, Bus9, Bus 10, and Bus 31.

Fig. 9. Charging status of the storage device optimally located at Bus 31 only.

energy are MW and MWh, respectively. Thesystem cost for the solution is $109 330/h, and it takes 890 s tofind the solution.

The red square in Fig. 7 indicates the location of Bus 31. Thestorage device at Bus 31 is located in the load pocket. Energy

Fig. 10. Charging status of the storage devices optimally located at Buses 8, 9,10, 30, 31, and 113.

Fig. 11. Charging status of the storage devices optimally located at Buses 30,31, and 113.

is stored and discharged according to the expected profiles ofthe load and the output of the variable generators. The storagedevices at Buses 8, 9, and 10 are located in Area 1. When theoutput of the variable generators are all accepted, the devices atBuses 8, 9, and 10 are useful to mitigate the impact of the vari-ability of the renewable generator in the same area that is morevariable than the other renewable generator. When the output ofthe variable generators can be curtailed, it is more economicalto not construct multiple storage devices. However, it is cost ef-fective to include the devices even though all the output of thevariable generators can be accommodated without the devices.

The outputs from the renewable generators are doubled to seehow the solution changes when they will not be accommodatedwithout the storage devices. Figs. 10 and 11 illustrate the simu-lation results when either all the outputs or a fraction of the out-puts from the renewable generators are accepted, respectively.The results are listed in Table XI.

The locations of Buses 30, 31, and 113 are indicated by thered oval in Fig. 7. They are near Area 2, which is a load pocket.As the variability of the outputs from the variable generatorsincreases, a larger amount of energy needs to be stored, and as aresult, the larger capacities of the storage devices are required.


TABLE XICOMPUTATION RESULTS FROM THE SIMULATIONS

Due to high computation cost, it is not practical to use thisapproach with a full-detailed system model. The problem dis-cussed in this study is linear programming. Therefore, the com-putation cost is in the order of , where N is the number ofvariables. Because storage devices are considered at each bus, Nis proportional to the number of buses in the system. Recently,a new network reduction methodology is developed for plan-ning studies [22]. With the combination of the methodology, itwould be possible to apply this approach at the national levelin a reasonable time. Future study is undergoing to include theoperation and construction planning for transmission, genera-tors, and storage devices. In this study, only a limited numberis selected for the number of different time slices per year andrealizations per time slice for showing the applicability of theproposed model. For a planning study, a larger number would beappropriate for reflecting reality. The size of this dimension willincrease the complexity in computation to apply the proposedmodel for a planning study. Parallel computation with variousdecomposition methods is under consideration for reducing thecomputational expense.

VII. CONCLUSION

Securing the reliability of power systems while implementingvariable energy resources is challenging. Storage devices repre-sent one candidate to control the variability; however, the lackof proper modeling makes optimally dispatching the storage de-vices difficult. In this paper, a new method to model the storagedevices is proposed and tested in certain scenarios.

Because storage devices provide a way to utilize the powersystem elements including the transmission network and gen-erators efficiently, they mitigate the impact of the variability ofthe renewable generators. From the economic point of view, theoutput from renewable energy resources does not need to be cur-tailed, and consequently, the deployment of the storage devicesimproves system efficiency. In conjunction with a network re-duction method, the storage device modeling described in thispaper provides an efficient way to accommodate the storage de-vices in the OPF framework and can therefore be used in a plan-ning study to consider the high penetration of variable energyresources and storage devices into the power industry.

In this study, the method proposed is tested using the DC OPFapproximation—a linear, lossless OPF. However, implementingthis method in the AC OPF framework should be straightfor-ward and is the focus of a subsequent analysis. Further workto efficiently solve a large-scaled system to include the reliablegenerators and transmission upgrades, as well as the storage de-vices, is also underway.

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HyungSeon Oh (M’07) received the Ph.D. degree in electrical and computerengineering from Cornell University, Ithaca, NY, in 2005.

He is an Engineer II at the National Renewable Energy Laboratory, Golden,CO. His research interests include energy systems economics, power systemplanning, smart grids, storage, computer simulation, and nonlinear dynamics.

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