Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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Sizing and Siting of Battery Energy Storage Systems: A Colombian Case  PDF

  • Alvaro Avendaño Peña
  • David Romero-Quete
  • Camilo A. Cortes
Department of Electrical and Electronics Engineering, UniversidadNacional de Colombia, Bogotá, Colombia,

Updated:2022-05-11

DOI:10.35833/MPCE.2021.000237

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Abstract

This paper presents a mixed-integer linear programming (MILP) formulation for sizing and siting of battery energy storage systems (BESSs). The problem formulation seeks to minimize both operation costs and BESS investment. The proposed model includes restrictions of the conventional security-constrained unit commitment problem, a piece-wise linear approximation to model power losses, and a linear model of hydro generation units. The proposed model is tested in a 6-bus test system and a 15-bus system representing the Colombian power system. For the two studied systems, simulation results show that the reduction of operation costs due to the installation of BESSs compensates the investments, under some of the considered technical cost cases. Additionally, results show that adequate sizing and siting of BESSs reduce renewable energy curtailment in the Colombian power system with high penetration of fluctuating renewable generation.

A. Avendaño Peña, D. Romero-Quete, and C. Cortes (corresponding author) are with the Department of Electrical and Electronics Engineering, Universidad Nacional de Colombia, Bogotá, Colombia (e-mail: aaavendanop@unal.edu.co; dfromeroq@unal.edu.co; caacortesgu@unal.edu.co).

I. Introduction

BATTERY energy storage systems (BESSs) are increasingly used in electric power system applications, as quickly as their costs are decreasing. For instance, the Tranquillity project, with a capacity of 72 MW/288 MWh, was commissioned in California, USA as a support for the Tranquillity Solar Facility, as well as a support for future integration of new renewable sources [

1]. Another important project is the Hornsdale Power Reserve, with a capacity of 100 MW/129 MWh, constructed in Jamestown, South of Australia. In this project, 70% of the capacity was used for reliability purposes and the rest for market participation in ancillary services [2]. However, the use of BESSs for electric power system applications in developing countries has a considerable delay compared with developed countries, mainly because of the capital cost of these kinds of projects.

In Colombia, for instance, only until 2018 did the CREG (the system regulator in Colombia) consider BESSs as an option to mitigate the delays in the expansion of the transmission system [

3]. Later, between years 2020 and 2021, the UPME (energy planning unit in Colombia) published the first public call to select an investor for the construction, operation, and maintenance of a 45 MW/45 MWh BESS to be located in the north of the country [4], [5]. To take part in the public call and in future projects, some important players such as the case of Grupo Energia Bogota (an important transmission system operator in Colombia) that supported the present work were interested in studying the optimal sizing and siting of BESSs in the Colombian network, as these elements become a potential choice for addressing different issues of modern power systems, e.g., integration of renewable sources.

As a way to optimize different objectives, sizing and siting of BESSs play an important role in determining future investments in new elements of electrical networks. For instance, in [

6], the column and constraint generation (C&CG) algorithm was used, and a method termed robust optimization of storage investment on networks (ROSION) was proposed to minimize investments in BESSs, while guaranteeing a feasible system operation and reducing load/renewable power curtailment. In [7], the power system planning was formulated as a mixed-integer linear programming (MILP) problem, seeking to find an optimal combination of new transmission lines and BESSs that maximizes social welfare, while including the effect of power losses in the formulation. However, these studies considered the new BESS energy capacity as a constant value in the objective function, thus limiting the search space for the optimization problem.

In [

8], BESSs was also included as a decision option in transmission expansion planning (TEP). The problem was solved using C&CG algorithm, which converted the original problem to a four-level problem. Three of the sub-problems included binary variables, while the last one was converted to a linear programming (LP) problem. The formulation aimed to minimize investment and operation cost by seeking optimal sizing and siting of BESSs and new transmission lines. Although both power and energy capacities of BESSs were included as variables in the objective function in [8], no power losses were considered in the constraints of the problem, i.e., the costs of power losses were neglected in the decision-making.

In [

9], the minimization of both operation costs and renewable power curtailment was proposed, using BESSs as a decision option. The problem was modeled as an LP problem, thus resulting in a reduction of a computational burden compared with MILP formulations. BESS locations were selected by searching overloaded lines of the system and choosing the buses connected to lines linking wind farms. The capacity of lines where BESSs were connected determined the size of BESSs. Additionally, as an improvement of the previous paper, the methodology suggested in [10] proposed the use of BESSs as a part of support in the integration of renewable sources and as an option to replace generation by fossil fuel as much as a possible. However, those studies did not take into account unit commitment (UC) and hydro plant constraints that might affect the decision results, especially in power systems with high penetration of hydro plants.

Considering different stages of the traditional electricity supply chain and their unique features, models can represent the features of power systems with a great degree of accuracy. For instance, two different methods were proposed in [

11] to determine the optimal sizing and siting of BESSs. The first method was based on the complex-valued neural networks (CVNVs) and time domain power flow (TDPF) and was used to determine the optimal location of BESSs, while the size of BESSs was determined by running TDPF and economic dispatch (ED). This method was applied to transmission networks. The second method was applied to distribution networks and considered distribution network services of BESSs, like peak load shaving or load curve smoothing, to improve the performance of the distribution network by finding the optimal size of BESSs. Similarly, considering transmission and distribution systems, a bilevel program (BP) problem was proposed in [12], where the upper level was for the distribution system and the lower level was applied in transmission system. The upper-level problem was modeled as an AC power flow model based on second-order cone programming (SOCP), with the advantage of having more accuracy in AC power flow of radial systems. The objective function was to minimize investment and operation costs. The lower-level problem used a DC power flow model and its objective function was to maximize the social welfare. The duality-based approach was used to solve the BP problem. However, these studies did not take into account hydro power constraints and power losses in the transmission system.

In this paper, an MILP formulation is used as a tool to determine the sizing and siting of BESSs to minimize investment and operation costs in a system with an energy mix heavily dominated by hydro power or non-conventional renewable sources in the near future, such as the Colombian power system [

13]. The model takes into consideration the behavior of different kinds of energy sources. For this reason, UC constraints, hydro power dispatch constraints, and renewable source constraints are included. The model also includes DC power flow constraints and an approximation for power losses, thus loss cost is considered in the analysis. Finally, the model includes decision variables to represent both power and energy capacities of BESSs, which allows finding an optimal energy/power ratio. Therefore, the proposed methodology which integrates different elements presented in previous works contributes to the state of the art in this field, since such a comprehensive model has not been studied in the literature.

The rest of the paper is organized as follows. Section II describes the mathematical formulation of the optimization problem. Section III explains case studies that are used to test the mathematical model, and the results are also discussed in this section. Section IV presents the main conclusions.

II. Mathematical Formulation of Optimization Problem

The optimization problem aims to find the optimal sizing and siting of BESS units to minimize the overall operation cost in a power system. The mathematical formulation is partially based on [

8] but includes UC and hydro power constraints based on [14]-[16], to accurately model the generator behaviors. Power losses are taken into account using a very popular linear approximation suggested in [17] to consider their effect on the decision-making. Finally, the behavior of BESS units is based on the formulation in [8], [12].

A. Objective Function

The objective function of the model is to minimize both operation cost and BESS investment, which is formulated as:

minn𝒩bPn,bBESSCnpot+En,bBESSCneneTerm a+ibt𝒯Fi(Pi,b,t)xi,t+CidnSDi,t+CiupSUi,tTerm b+hbt𝒯Fh(Ph,b,t)yh,tTerm c (1)

Term a is related to energy storage installation cost; term b is related to the operation cost of thermal generation units; and term c is related to the operation cost of hydro generation units. The functions Fi() and Fh() are used to account for the operation costs of thermal and hydro generation units, respectively. A piecewise linear upper approximation of the convex cost curve is used for the 6-bus test system as in [

18], while operation costs of thermal and hydro generation units are computed by CigenPi,b,t and ChgenPh,b,t for the Colombian power system, respectively.

B. Constraints

1) System Constraint

The following constraint models the power balance in each node of the system, based on Kirchhoff’s current law.

ibPi,b,t+j𝒥bWj,b,t-(b,r)Pb,r,tpf+12Fb,r,tpf+hbPh,b,t+n𝒩bPn,b,tdc-Pn,b,tch=Db,tf    b,t𝒯 (2)

Equation (2) includes different types of generation units, power flows in each line of the system, and charging/discharging power of installed BESS units. All these variables are matched with demand forecast.

2) UC Constraints

Adequate scheduling of generation units is very important to reduce the operation cost of the power system. To carry out this scheduling, it is necessary to consider operation times, ramp rate values, and initial states of generation units. Those requirements can be modeled as:

PiminPi,b,tPimax    t𝒯,i (3)
Pi,b,t+1-Pi,b,tRiup+SUi,t+1Pimin    t𝒯,i (4)
Pi,b,t-Pi,b,t+1Ridn+SDi,t+1Pimin    t𝒯,i (5)
SUi,t-SDi,t=xi,t-xi,t-1    t𝒯,i (6)
SUi,t+SDi,t1    t𝒯,i (7)
xi,t=gion/off    t(Liup,min+Lidn,min),i (8)
tt=t-giup+1SUi,ttxi,tt    tLiup,min (9)
tt=t-gidn+1SDi,tt1-xi,tt    tLidn,min (10)

Constraint (3) maintains thermal generation units between technical limits. Constraints (4) and (5) limit ramp-up and ramp-down values of generation units. Constraint (6) relates operation statuses of generation units with binary UC variables. Constraint (7) guarantees that each generation unit is not turned on and off simultaneously. Ultimately, constraints (8)-(10) ensure the minimum up-time and down-time of generation units.

3) Hydro Power Dispatch

In power systems with high participation of hydro generation units, it is important to adequately represent their behavior. A linear approximation of the behavior of hydro generation units is given as:

PhminPh,b,tPhmaxh,t𝒯 (11)
QhminQh,d,tQhmaxh,d𝒟,t𝒯 (12)
VdminVd,tVdmaxd𝒟,t𝒯 (13)
0Sd,tSdmaxd𝒟,t𝒯 (14)
Vd,t=Vd,t-1+3600ΔtId,t-hdQh,d,t-Sd,t    d𝒟,t𝒯 (15)
Ph,t=HhQh,d,t    h,d𝒟,t𝒯 (16)

Constraint (11) maintains hydro generation units between technical limits. Constraint (12) keeps water flow through the turbine between technical limits. Constraint (13) maintains water volume in the reservoir associated with the hydro generation unit between allowed limits. Constraint (14) limits spillage in the reservoir. Constraint (15) guarantees water conservation between two consecutive time periods. Finally, the electric power generated by hydro generation units is calculated with constraint (16).

4) Transmission Line Constraints

Traditionally, the calculation of power flows implies non-linearity due to the use of trigonometric functions. DC power flow approximation is a common way to find power flows without non-linearities. The constraints that model this approximation are described as:

Pb,r,tpf=Bb,r(δb-δr)(b,r),t𝒯 (17)
-Pb,rmaxPb,r,tpf+12Fb,r,tpfPb,rmax(b,r),t𝒯 (18)

Power flow in each line is calculated by (17), while the maximum power flow for each line is limited by (18).

5) Power Loss Constraints

Fb,r,tpf=Gb,r(δb-δr)2(b,r),t𝒯 (19)
δb,r++δb,r-=k=1Kδb,r(k) (20)
αb,r(k)=(2k-1)Δδb,rk=1,2,...,K (21)
Fb,r,tpf=Gb,rk=1Kαb,r(k)δb,r(k)    (b,r),t𝒯 (22)

Calculation of power losses in (19) includes a non-linearity given by the quadratic expression in the angular difference. To solve this, [

17] proposed to divide the angular difference δb-δr into small blocks (represented by k). Therefore, two new elements are introduced to the problem formulation: the slope of linearization blocks αb,r(k) and the size of linearization blocks δb,r(k). This representation is shown in Fig. 1. The size of linearization blocks is calculated in (20). In this equation, the absolute value of the angular difference is represented by δb,r++δb,r-. The slope of linearization blocks is computed in (21). Finally, power losses are computed in (22).

Fig. 1  Piecewise linear loss function.

6) BESS Constraints

un,tch+un,tdc1n𝒩,t𝒯 (23)
en,b,t=en,b,t-1(1-ηnSoC)+ηnchPn,b,tch-Pn,b,tdcηndcΔtb,n𝒩,t𝒯 (24)
en,b,tEn,bBESSn𝒩,b,t𝒯 (25)
Pn,b,tchMun,tchn𝒩,b,t𝒯 (26)
Pn,b,tchPn,bBESSn𝒩,b,t𝒯 (27)
Pn,b,tdcMun,tdcn𝒩,b,t𝒯 (28)
Pn,b,tdcPn,bBESSn𝒩,b,t𝒯 (29)

Constraint (23) guarantees that BESS units are not charging and discharging at the same time. The relation of energy stored at two consecutive time steps is expressed in (24). In constraint (25), the energy stored in a BESS unit at time t is limited by the size found for that BESS unit. Finally, constraints (26)-(29) restrict the power size of BESS units. Since BESS units are characterized by a high ramp rate [

19]-[22] allowing nominal power changes in less than one hour, ramping constraints are not included in this paper.

III. Case Studies

The model described in Section II is tested in a 6-bus test system and in a simplified 15-bus Colombian power system. A comparison of the results with and without consideration of power losses, deactivating the term of power losses in constraints (2) and (18) and constraints (19)-(22), is also presented for the 15-bus Colombian power system. A time horizon of 720 hours (a month) with 1-hour intervals is used for all the simulations. A BESS charging/discharging efficiency of 95%, and a self-discharging efficiency of 0.0000625% are considered. To study the effect of capital recovery times and eventual technical cost drops in investment decisions, 6 cases with different equivalent costs per month are considered, as shown in Table I.

Table I  Power and Energy Equivalent Costs of BESS Units per Month for Each Case
CaseCnpot ($/MW)Cnene ($/MWh)r (year)cr (%)
A 575.3 1717.8 10 0
B 402.7 1202.5 10 30
C 383.6 1145.2 15 0
D 287.7 858.9 20 0
E 268.5 801.6 15 30
F 201.4 601.2 20 30

In these cases, the one closest to BESS costs in 2021 is case F, according to the information from Lazard in [

23]. These cases are built assuming a base total cost of 70000 $/MW (CTPBESS) and 209000 $/MW (CTEBESS) for power electronic equipment and batteries, respectively [24]. The values of Cnpot and Cnene in Table I are obtained using (30).

Cnpot=CTPBESS(1-cr)r36524thCnene=CTEBESS(1-cr)r36524th (30)

The MILP problem is implemented in Pyomo (Python) and solved with the CPLEX solver by means of NEOS server [

25]-[27]. It is worth mentioning that NEOS server offers a maximum of 3 GB of RAM, 4 threads, and 8 hours per job. That is the reason why the simulation horizon was limited to a month, as previously mentioned.

A. 6-bus Test System

The 6-bus test system proposed in [

28] and shown in Fig. 2 is used here. This system consists of seven transmission lines, three thermal generators, and a wind farm at bus 3. Tables II and III present the techno-economic characteristics of generation units and technical characteristics of transmission lines used in the simulations, respectively. The load profile is defined in [29]. The wind farm has a maximum power capacity of 40 MW and follows the wind generation profile curve shown in Fig. 3.

Fig. 2  6-bus test system.

Table II  Techno-economic Characteristics of Generation Units
BusGeneration unitβi($/MWh2)γi($/MWh)ζi ($)Pimin (MW)Pimax (MW)giup (hour)gidn (hour)Riup (MW)Ridn (MW)

Off time

(hour)

Ciup ($)Cidn ($)
N1 G1 0.00056 16.85 703.64 100 200 4 4 55 55 4 124.69 124.69
N2 G2 0.00124 40.66 576.96 10 150 2 2 50 50 2 373.82 373.82
N6 G3 0.00623 22.05 621.24 10 180 1 1 22 22 1 62.31 62.31
Table III  Technical Characteristics of Transmission Lines
LineFromToGb,r (p.u)Bb,r (p.u)Flow limit (MW)
L1 N1 N2 0.59 2.50 100
L2 N2 N3 1.18 5.00 100
L3 N1 N4 0.39 1.67 80
L4 N2 N4 0.59 2.50 100
L5 N4 N5 0.38 1.59 75
L6 N5 N6 0.38 1.64 78
L7 N3 N6 0.49 2.08 100

Fig. 3  Wind generation profile curve.

The sizing and siting results of BESS units for the 6-bus test system are shown in Table IV. For cases A, B, and C, the algorithm does not install BESS units in any bus of the system, indicating that, for these technology prices, benefits do not compensate BESS investments. For cases D, E, and F, the capacity of BESS units increases according to technical cost reductions. For the last three cases, a BESS unit is installed at bus N5, which is the bus with the minimum power transfer capability in the system, i.e., the lines connected to this bus, L5 and L6, are the ones with the lowest capacity. Note also that there is a load at bus N5, so the BESS unit might be used to partially supply the local power requirements in peak hours, as shown in Fig. 4.

Table IV  Sizing and Siting Results of BESS Units for 6-bus Test System
CaseBusInstalled power (MW)Installed energy (MWh)
A, B, C
D N5 1.58 2.44
E N5 5.41 22.19
F N5 9.92 38.43

Fig. 4  Operation characteristics of load and BESS unit at bus N5.

In case A (without BESS unit), the most expensive generator G2 produces the capacity of 12.502 GWh throughout the simulation horizon (720 hours); while for case F (with BESS unit), this generator only produces the capacity of 10.924 GWh. These results show that, due to the installation of BESS units, the generators with lower operation costs (G1 and G3) are dispatched more efficiently, thus reducing the power dispatched by G2, which has the highest operation costs, as shown in Fig. 5. For instance, in the first two days (between 0 and 48 hours) and day 4 (between 72 and 96 hours) shown in Fig. 5(a) and (b), the energy generated by G2 in case A is completely supplied by G1 and G3 in case F (with the maximum size of BESS units).

Fig. 5  Comparison of dispatch solutions in cases A and F for 6-bus test system. (a) G1. (b) G2. (c) G3.

Finally, Table V shows the reduction in operation costs as more capacity of BESS units is installed. The table also shows that, for this case study, power losses increase as the size of installed BESS units increases, but not in a proportional way. It is important to keep in mind that, even if power losses are considered in the formulation through (2), the main objective of this formulation is to minimize both the overall operation cost and BESS investment, not only the power loss cost. Therefore, a solution with higher power losses might be cheaper than that with lower power losses.

Table V  Evaluation Results of Operation Costs, BESS Investments, and Total Costs for Different Cases in 6-bus Test System
CasePower loss (GWh)BESS investment ($)Operation cost ($)Total cost ($)
Base 22.631 0 3531600 3531600
A, B, C 22.631 0 3531600 3531600
D 22.643 2550 3528600 3531100
E 22.702 19240 3511600 3530800
F 22.739 25110 3498800 3523900

B. 15-bus Colombian Power System

The power system shown in Fig. 6 was proposed by UPME, the Colombian Mining/Energy Planning Unit, to make transmission and generation planning decisions in the Colombian power system [

30]. In this system, 15 electric areas (the buses of the equivalent system) are defined, each of which represents large consumption and generation centers in Colombia. These buses are connected through equivalent power lines that represent the actual power lines of the system, with voltage levels over 220 kV. This power system is studied here for two scenarios: 2020 and 2030. The 2030 scenario considers the growth projections of renewable generation (wind and solar) for 2030 in the Colombian power system. Figure 7 shows the load profile curves for a week in both 2020 and 2030 scenarios, based on the data from [30], [31]. The rest of the information for each of the considered scenarios is available in [32].

Fig. 6  Simplified Colombian power system.

Fig. 7  Load profile curves in both 2020 and 2030 scenarios.

1) 2020 Scenario

Current installed capacity of energy mix in Colombia is strongly dominated by hydro generation, with 68.3% of participation, followed by thermal generation, with 30.6% of participation. The remaining 1.1% is composed of wind generation, solar generation, and co-generation [

33]. To model the energy mix and the transmission system in 2020 scenario, 19 thermal generation units, 22 hydro generation units, 1 wind farm (with a total of 18.42 MW of installed power), 3 solar farms (with a total of 104 MW of installed power), and 25 transmission lines are considered. The current transmission system has some weaknesses in the north of Colombia due to the delays in new transmission projects, affecting the system performance. That is why BESS units are considered as a short-term solution to reducing operation costs. Wind and solar farms are assumed to follow the power generation profile curves shown Fig. 3 and Fig. 8, respectively.

Fig. 8  Solar generation profile curve.

The sizing and siting results of BESS units for cases A-F in 2020 scenario obtained by the formulation presented in Section II, with and without consideration of power losses, are shown in Table VI. Considering power losses for case A, the results show that the installation of BESS units is not economically viable to reduce operation costs. For cases B to F, the siting results of BESS units are the same (bus BOL). In these cases, the capacity of BESS units increases as the cost of BESS units decreases, evidencing the need to improve that area of the grid. The BESS unit located at bus BOL is charged in off-peak hours and discharged in peak hours, as shown in Fig. 9. This operation characteristic of the BESS unit reduces power transfer between electric areas in critical hours and, therefore, the saturation of the lines, thus allowing an investment deferral in new transmission lines. Also note that, when power losses are not considered, the siting result of BESS units does not change; however, the sizing result of BESS units increases in cases B to F. This might be due to the fact that a higher transmission line capacity is observed in the network because power losses are zero, thus allowing sizing a bigger BESS unit and obtaining more benefits.

Table VI  Sizing and Siting Results of BESS Units with and Without Consideration of Power Losses for Different Cases in 2020 Scenario
CaseWith consideration of power lossesBusInstalled power (MW)Installed energy (MWh)
A Yes 0 0
No 0 0
B Yes BOL 5.84 6.93
No 9.81 11.65
C Yes BOL 7.66 9.10
No 11.70 13.90
D Yes BOL 20.33 27.74
No 25.53 39.67
E Yes BOL 21.80 34.12
No 28.38 44.92
F Yes BOL 35.93 61.44
No 43.90 74.08

Fig. 9  Operation characteristics of load and BESS units at bus BOL in 2020 scenario.

Table VII shows the operation costs and BESS investments for different cases. It also shows that, when power losses are considered, the bigger the size of BESS units is, the bigger the system power losses are. As mentioned above, the reason is that the objective function is to reduce both the overall operation cost and BESS investment, therefore, a more economic commitment of generators, due to the installation of BESS units, might result in bigger power losses in power lines. On the other hand, without consideration of power losses, BESS investment increases due to the increase in the size of BESS units. However, overall operation cost decreases according to the increase in BESS capacity.

Table VII  Evaluation Results of Operation Costs, BESS Investments, and Total Costs with and Without Consideration of Power Losses for Different Cases in 2020 Scenario
CasePower loss (GWh)BESS investment ($)Operation cost ($)Total cost ($)
Base 50.755 0 317798000 317798000
0 314015000 314015000
A 50.755 0 317798000 317798000
0 314015000 314015000
B 50.812 10690 317786000 317797000
17960 313994000 314012000
C 50.825 13360 317783000 317796000
20410 313991000 314011000
D 50.888 29670 317760000 317790000
41420 313960000 314002000
E 50.898 33200 317755000 317788000
43630 313955000 313999000
F 51.017 44170 317733000 317777000
53380 313932000 313985000

2) 2030 Scenario

In this scenario, 19 thermal generation units, 23 hydro generation units, 4 wind farms (with a total of 2154 MW of installed power), 9 solar farms (with a total of 2917 MW of installed power), and 25 transmission lines are considered, based on the information presented in [

34]. Reinforcement of transmission networks is disregarded. As in the 2020 scenario, renewable generators are assumed to follow the generation profile curves shown in Fig. 3 and Fig. 8.

Table VIII shows sizing and siting results of BESS units obtained for cases A-F in 2030 scenario with and without consideration of power losses. Note that the sizes of BESS units are bigger in this scenario than those in the 2020 scenario, mainly due to an increase in total demand, a significant capacity of renewable sources incorporated at buses GCM and CSU, and the network is not reinforced with respect to 2020 scenario. The siting result of BESS unit also changes with respect to the 2020 scenario (from bus BOL to buses BOL, GCM and CAU). The reason is that BESS units use the available renewable energy (low-cost energy) at bus GCM to perform energy arbitrage, thus, minimizing operation costs. As in the 2020 scenario, the sizes of BESS units increase when power losses are not considered. Moreover, the siting result of BESS units does not change except in case F, because there is a better transmission capacity in the case without power losses, and the BESS units are located in fewer buses. The results also suggest that BESS units could be used to defer the investments in transmission networks.

Table VIII  Sizing and Siting Results of BESS Units with and Without Consideration of Power Losses for Different Cases in 2030 Scenario
CaseWith consideration of power lossesBusInstalled power (MW)Installed energy (MWh)
A Yes BOL, GCM 201.94 1179.8
No 202.49 1200.3
B Yes BOL, GCM 476.98 2791.6
No 492.71 2877.3
C Yes BOL, GCM 496.99 2893.5
No 509.47 2983.9
D Yes BOL, GCM 551.90 3339.6
No 566.08 3452.8
E Yes BOL, GCM 562.50 3442.9
No 577.16 3559.7
F Yes CAU, BOL, GCM 610.67 3748.7
No BOL, GCM 623.07 3858.2

The evaluation results of operation costs, BESS investments, and total costs with and without consideration of power losses for different cases in 2030 scenario is shown in Table IX.

Table IX  Evaluation Results of Operation Costs, BESS Investments, and Total Costs with and Without Consideration of Power Losses for Different Cases in 2030 Scenario
CasePower loss (GWh)BESS investment ($)Operation cost ($)Total cost ($)
Base 57.327 0 259353000 259353000
0 254896000 254896000
A 56.664 2143000 256819000 258962000
2178000 252345000 254524000
B 56.416 3549000 254310000 257859000
3658000 249715000 253373000
C 56.501 3504000 254180000 257684000
3613000 249579000 253191000
D 56.910 3027000 253707000 256734000
3128000 249083000 252211000
E 57.035 2911000 253615000 256526000
3008000 248988000 251997000
F 57.385 2377000 253419000 255796000
2445000 248797000 251242000

It can be observed that a more efficient dispatch of generators, resulting in a lower operation cost, compensates the cost associated with the higher power losses presented in cases where a bigger capacity of BESS units is installed, e.g., case F. As in the 2020 scenario, BESS investment increases when power losses are not considered.

Figure 10 shows a comparison of the number of hourly dispatched generators in base case and cases C and F with consideration of power losses. Note that, in most of the hours, the number of dispatched generators decreases in the cases where BESS units are installed, especially in peak hours. Consequently, the operation costs are reduced.

Fig. 10  Comparison of number of hourly dispatched generators for different cases in 2030 scenario.

Finally, Table X presents the renewable energy curtailment results with and without consideration of power losses in 2030 scenario. Note that as the capacity of BESS units increases, wind and solar generations are more efficiently used (less curtailment). In fact, this curtailment can be avoided by charging BESS units when there is a renewable energy excess and discharging the excess energy in peak-demand hours. The use of BESS units to avoid power curtailment is also shown in Fig. 11.

Table X  Renewable Energy Curtailment Results with and Without Consideration of Power Losses in 2030 Scenario
CaseWith consideration of power lossesEnergy dispatched (GWh)Curtailment (GWh)
Base Yes 6776.75 90.27
No 6719.39 89.39
A Yes 6779.30 58.97
No 6722.63 57.66
B Yes 6783.10 18.72
No 6726.74 17.13
C Yes 6783.37 17.07
No 6727.01 15.46
D Yes 6784.88 11.19
No 6728.18 10.00
E Yes 6785.28 10.13
No 6728.43 9.20
F Yes 6785.72 8.90
No 6729.14 7.41

Fig. 11  Operation characteristics of load and BESS units at bus GCM in 2030 scenario.

Note that in Fig. 11, the BESS unit located at bus GCM is charged when the solar farms located at the same bus dispatch their power. Then, the BESS unit discharges this power in peak hours.

IV. Conclusion

This paper describes a formulation to determine the sizing and siting of BESSs to reduce operation costs in a power system. Simulation results for different studied systems demonstrate the adequacy of the proposed formulation to reduce operation costs by optimally determining the sizing and siting results of BESSs. Moreover, it is also shown that the sizing and siting results of BESSs obtained with the proposed formulation improve the use of renewable sources by reducing power curtailment, especially in systems with high penetration of renewable sources. Furthermore, the simulations show that a deferral in new transmission line investment is possible with BESS inclusion. Additionally, the comparison with and without consideration of power losses shows the impact of transmission capacity of the systems on the sizing and siting results of BESSs to minimize the operation cost. Finally, the results shows that possible projected reductions in BESS costs will allow a further use of this technology in power systems, due to its benefits to the system.

Nomenclature

Symbol —— Definition
A. —— Indices
b,r —— Buses
d —— Reservoir
h —— Hydro generation unit
i —— Thermal generation unit
j —— Renewable generation unit
n —— Battery energy storage system (BESS) unit
t —— Time period
B. —— Sets
—— Set of all buses
𝒟 —— Set of all reservoirs
—— Set of all hydro generation units
b —— Subset of hydro generation units at bus b
d —— Subset of hydro generation units in reservoir d
—— Set of all thermal generation units
b —— Subset of thermal generation units at bus b
𝒥 —— Set of all renewable generation units
𝒥b —— Subset of renewable generation units at bus b
—— Set of all lines
𝒩 —— Set of all BESS units
𝒩b —— Subset of BESS units at bus b
𝒯 —— Set of all time periods
K —— Set of blocks
C. —— Parameters
αb,r(k) —— Slope of block voltage angle linearization
βi, γi, ζi —— Coefficients of thermal generation units of quadratic cost curves
ηnch, ηndc —— Charging and discharging efficiencies of BESS units
ηnSoC —— Self-discharging efficiency of BESS units
Δδb,r —— The maximum angular difference
Bb,r —— Susceptance of line
cr —— Cost reduction in power and energy elements
CTP,EBESS —— Power/energy cost of BESS units
Cnpot, Cnene —— Power and energy equivalent costs of BESS units
Ciup, Cidn —— Start-up and shut-down costs of thermal generation units
Cigen, Chgen —— Thermal and hydro generation costs
Db,tf —— Demand forecast
gion/off —— Initial status of thermal generation units
giup, gidn —— The minimum up-time and down-time
Gb,r —— Line conductance
Hh —— Conversion factor
Id,t —— Forecasted water rate in reservoir d
Liup,min, Lidn,min —— Number of time steps that thermal generation unit is required to stay on and off at the beginning of the optimization horizon
M —— Large enough positive constant
Pb,rmax —— The maximum limit of line capacity
Pimin, Pimax —— The minimum and maximum thermal generation capacities
Phmin, Phmax —— The minimum and maximum hydro generation capacities
Qhmin, Qhmax —— The minimum and maximum water flows in turbine
r —— Capital recovery time
Riup, Ridn —— Ramp-up and ramp-down rate limits
Sdmax —— The maximum spillage in reservoir d
th —— Time horizon of the optimization problem
Vdmin, Vdmax —— The minimum and maximum water volumes in reservoir d
D. —— Variables
δb,δr —— Voltage angles of buses d and r
δb,r(k) —— Size of block voltage angle linearization
δb,r+,δb,r- —— Auxiliary variables to calculate the absolute value of δb,r
en,b,t —— Energy stored in BESS units
En,bBESS —— Energy capacity of BESS units
Fb,r,tpf —— Power losses in the line connecting buses b and r
Pi,b,t, Ph,b,t —— Active power generated by thermal and hydro generation units
Pb,r,tpf —— Power flow in the line connecting buses b and r
Pn,b,tch, Pn,b,tdc —— Charging and discharging power of BESS units
Pn,bBESS —— Power capacity of BESS units
Qh,d,t —— Water flow rate in the turbine
SUi,t, SDi,t —— Start-up and shut-down decision variables
Sd,t —— Spillage in reservoir d
un,tch, un,tdc —— Binary variables to model the status of BESS units
Vd,t —— Water volume in reservoir d
Wj,b,t —— Power output of renewable generation units
xi,t, yh,t —— Generation states of thermal and hydro generation units

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