Investment optimization of grid-scale energy storage for supporting different wind power utilization levels
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Abstract
With the large-scale integration of renewable generation, energy storage system (ESS) is increasingly regarded as a promising technology to provide sufficient flexibility for the safe and stable operation of power systems under uncertainty. This paper focuses on grid-scale ESS planning problems in transmission-constrained power systems considering uncertainties of wind power and load. A scenario-based chance-constrained ESS planning approach is proposed to address the joint planning of multiple technologies of ESS. Specifically, the chance constraints on wind curtailment are designed to ensure a certain level of wind power utilization for each wind farm in planning decision-making. Then, an easy-to-implement variant of Benders decomposition (BD) algorithm is developed to solve the resulting mixed integer nonlinear programming problem. Our case studies on an IEEE test system indicate that the proposed approach can co-optimize multiple types of ESSs and provide flexible planning schemes to achieve the economic utilization of wind power. In addition, the proposed BD algorithm can improve the computational efficiency in solving this kind of chance-constrained problems.
Keywords
Wind power Capacity investment Energy storage Power system planning Chance constraint1 Introduction
Nowadays, many countries are committed to promoting the development of renewable power generation to cope with global warming and fossil energy crisis. As reported in [1], China pledged to prioritize renewable generation and reach the non-fossil energy target of 20% by 2030. Nevertheless, owing to the natural intermittency and stochastic volatility of renewable energy, the utilization of renewable generation, especially centralized wind power generation, is still technically difficult. Reference [2] mentions that in China, the annual wind curtailment in 2012 has exceeded 20 GWh, which accounted for 17% of all the available wind power. It is urgent to integrate and consume wind power safely and economically.
As far as the wind curtailment issue is concerned, power systems should have sufficient flexibility to mitigate short-term fluctuations of wind power as well as the temporal mismatch between wind power and load. With the increasingly mature energy storage technology, grid-scale ESS is regarded as a potential solution to provide the required flexibility for accommodating large-scale wind power generation [3]. The related grid applications of ESSs include, but are not limited to: peak shaving, power balancing and system upgrade deferral [4]. However, considering the high capital cost of ESS, installing large-capacity ESSs for such applications may lead to poor investment economy [5]. Hence, it requires an optimization-based ESS planning method to ensure that the ESS investment is reasonable and economic for improving wind power utilization.
- 1)
Price-guidance methods. References [9, 10] propose a market-based optimal power flow framework to optimize the sizing and siting of compressed air energy storage (CAES) considering different wind penetration levels. Reference [11] incorporates the unit commitment problem into the ESS planning and designs a near-optimal solution strategy. This type of research makes use of the price advantage of wind power, that is, due to the low marginal price, the wind power can be utilized preferentially to minimize the total cost of meeting the load demand.
- 2)
Robust-oriented methods. Reference [12] proposes a scenario tree-based stochastic programming model for CAES planning considering nonanticipative operating behaviors. In [13, 14], the impacts of uncertain wind power on the voltage profiles, transmission congestion costs are respectively considered in ESS planning problems by using the AC power flow model. All these models [12, 13, 14] are formulated to cater for the full utilization of available wind power. In addition, robust optimization has also been well adopted in ESS planning studies [15, 16] to obtain robust solutions that can ensure reliable system operation without any wind curtailment under uncertainties.
- 3)
Penalty-based methods. Reference [17] provides a practical and feasible ESS planning method for realistic large-scale systems. Reference [18] introduces specific constraints to guarantee a certain level of profitability in ESS investment. In [19], a dynamic programming model is presented to address the multi-stage impacts of uncertainties on the investment of BES. What the above studies [17, 18, 19] have in common is that they penalize the wind curtailment as one of the optimization objectives to enhance wind power utilization.
All the three types of models above for minimizing wind curtailment can provide reasonable ESS planning decisions that ensure high utilization of wind power. However, few of these studies pay attention to the conflict between wind power utilization and ESS investment economy. We believe that the level of wind power utilization will have a significant impact on ESS investment costs. The problem which motivates this paper is the need for flexible ESS planning models that support the precise adjustment of wind power utilization level and help decision makers achieve a desired trade-off.
On the other hand, different technologies of energy storage have significantly different operation characteristics and cost-effectiveness performances. Reference [20] indicates that there is no single ideal storage technology that can well satisfy the needs of power systems for power and energy services. Therefore, how to determine the optimal storage portfolio for the reliable and economic operation of power systems is also a critical problem when various storage technologies are available. Reference [21] designs both analytical and optimization-based frameworks for joint sizing of multiple storage technologies based on the predetermined net load profiles. Reference [22] further considers transmission constraints and proposes a storage portfolio optimization method under a deterministic environment. So far, however, there has been little discussion about the non-deterministic storage portfolio optimization problem with full consideration of wind power uncertainties.
In light of the above issues, this paper proposes a flexible transmission-constrained ESS planning approach considering uncertain wind power and load. To precisely control the wind power utilization level, specific chance constraints are formulated on the occurrence probability and amount of curtailing wind power generation for each wind farm. Then we establish a scenario-based chance-constrained programming model that supports the non-deterministic optimization of storage portfolio. The resulting nonlinear nonconvex problem is reformulated using a proper relaxation process and is solved by a customized variant of Benders decomposition (BD) algorithm. Finally, case studies on a modified IEEE-24 system are presented to validate the proposed method.
The main contributions of this paper are threefold: ① A scenario-based chance-constrained model is proposed to achieve flexible adjustment of the risk level of wind power curtailment and the wind power utilization rate in the ESS planning under uncertainty; ② In addition to consideration of wind power uncertainties, the modeling of storage portfolio problem takes into account a number of factors that reflect differences between different storage technologies, including the lifetime, the investment costs per unit power/energy capacity, the typical energy/power ratio of energy storage and the storage loss during the charging and discharging; ③ According to the problem structure, a modified BD algorithm is developed to improve the computational efficiency of solving this kind of chance-constrained programming problem. Detailed techno-economic analysis for ESS planning is provided considering different energy storage portfolios and wind power utilization levels.
The remainder of this paper is organized as follows. Section 2 introduces the mathematical formulation of the chance-constrained ESS planning problem. Section 3 gives the BD type solution method. Case studies are given and discussed in Section 4. Then Section 5 concludes this paper.
2 Problem formulation
This paper concentrates on the static ESS planning problem driven by uncertain load and wind power generation. As with the classical stochastic ESS studies [9, 10, 11, 12], this paper employs stochastic programming to model the above uncertainties by using a finite set of scenarios. Note that both the wind power output and wind power fluctuation have peak distribution characteristics, that is, a high level of wind power output or wind power variability only occurs in small probability. Since a typical stochastic programming model generally considers every scenario in the scenario pool, ESSs should be built to cater for the peak wind power output or mitigate the high-level wind power volatility, which may result in costly and inefficient planning schemes. To avoid overinvestment in ESS, this paper extends conventional ESS planning models by adding scenario-based chance constraints on wind power utilization, where a proper amount of wind curtailment is allowed over the planning period. The detailed problem formulation is given below.
2.1 Scenario reduction
Considering that for multiple uncertainties, it is easier to obtain their scenario information than the specific probability distribution, we adopt the scenario-based method to characterize multiple uncertainties by discrete scenarios. The scenarios defined in this paper are composed of the daily time series of load and wind power. In the real-world applications, the raw scenario set can be obtained with the historical load and wind speed data. Given that it is computationally intractable to deal with large numbers of scenarios in the optimization model, a clustering-based scenario reduction method is proposed here to generate a representative scenario set from the raw scenario set.
A clustering method called density peaks clustering (DPC) [23] is then adopted to divide the raw scenario set into several clusters. Compared with traditional clustering techniques, DPC is more suitable for the actual time series dataset because it can determine the optimal cluster number. Through clustering analysis, the scenarios with similar daily net load shapes will be assigned to the same cluster, then we can intuitively produce a representative scenario set by sampling few scenarios in each cluster. In addition, to ensure the effectiveness of scenario reduction, we carry out the scenario sampling and determine the weight coefficient of each scenario by solving an optimization problem of minimizing the Kantorovich distance between the raw scenario set and the reduced scenario set, a detailed description of which can be found in [24].
2.2 Mathematic formulation
2.2.1 Constraints at planning level
Constraints (2) and (3) limit the number of energy storage units built at the local and system-wide levels. In addition, the value of parameter \(u_{i}^{q}\) can be artificially set to reflect the geographic location restrictions of some storage technologies, such as pumped hydro energy storage (PHES) and CAES.
2.2.2 Constraints at operational level
- 1)
DC power flow constraints.
- 2)
Operational constraints for conventional generators. In this study, the quadratic fuel cost function of the conventional generator is approximated by a piecewise linearization. Specifically, the generator output PG_{ik}(t) is divided into l linear segments, each of which is subject to:
- 3)
Operational constraints for ESS. Firstly, the charging/discharging power is restricted by the power rating of ESS as follows:
2.2.3 Constraints on wind curtailment
2.2.4 Objective function
Due to the existence of bilinear terms in (12), (13) and (20), the proposed ESS planning model is a complicated mixed integer nonlinear programming (MINLP) problem. In Section 3, a solution method inspired by the bilinear BD algorithm [25] is presented to solve this chance-constrained problem.
3 Solution method
3.1 Linear formulation of original MINLP problem
Obviously, by replacing (12) and (13) with (28), a total of 2|Ω||Η||Ψ||Γ| binary decision variables can also be removed to reduce the problem-solving scale.
Using the above relaxation, the original ESS planning model is reformulated into a mixed integer linear programming (MILP) model. However, it is still a challenge to directly solve this problem due to the multiple scenarios. Given that its computational complexity can be decentralized by decomposing the two-stage problems with respect to each scenario, a BD type solution method is presented in the following.
3.2 Modified BD algorithm
According to the general BD framework [27], the proposed ESS planning problem can be decomposed into an investment master problem and a series of operation subproblems over the reduced scenario set.
3.2.1 Operation subproblems
Although the bilinear terms in (35) and (37) can be linearized by the McCormick method, the unavoidable introduction of auxiliary variables and constraints will increase the computational burden of the master problem. This study therefore develops another linearized counterpart of this kind of bilinear optimality cuts.
Remark
which also indicates that the reduced cut is valid for any feasible solution (n_{i}^{q}, z_{k} = 1), thus proving the validity of the proposed cut (39). It can be further observed that, by introducing parameter \(\zeta_{k}^{1(m)}\), cut (39) is not only inherently linear without adding auxiliary variables or constraints, but also avoids excessive relaxation of (35). As the upper/lower bounds of decision variables \(n_{i}^{q}\) are naturally available, it is feasible to perform this linearization in practice.
3.2.2 Investment master problem
4 Case study
- 1)
To render the test system less reliable and aggravate the transmission congestion, all the loads are assumed to be 1.3 times of the original values, and capacities of all transmission lines are reduced by 20%. The ramp-rate limitations are also imposed on the conventional generators.
- 2)
Five wind farms, each with a capacity of 250 MW, 250 MW, 250 MW, 550 MW and 550 MW, are added to buses 1, 4, 5, 14 and 17, respectively. The penetration level of wind generation with respect to the overall load is 49.93%.
- 3)
Three different storage technologies, PHES, CAES and BES, are considered in the case studies. For each storage technology, the energy capacity per unit is set to 1000 MWh, 400 MWh and 40 MWh, respectively, and the rated discharge duration is set to 10 hours, 8 hours and 2 hours, respectively. Detailed parameter setting can be found in [28].
4.1 Experiments with different storage technologies
- 1)
Case R1 only considers PHES, and the site locations are limited to buses 3, 7, and 22 to reflect geographic restrictions.
- 2)
Case R2 only considers CAES while the site locations are the same as those in C1.
- 3)
Case R3 only considers BES, and the site locations are limited to buses 6, 8, 10, 16 and 17, which are selected based on the most congested lines.
ESS planning results with single storage technology
Case | Planning scheme | Daily cost ($ per day) | Total cost ($ per day) | |||
---|---|---|---|---|---|---|
Investment cost | O&M cost | Fuel cost | ESS loss cost | |||
R1 | PHES (300 MW/3000 MWh): n_{3}=100 MW/1000 MWh, n_{22}=200 MW/2000 MWh | 253538 | 4562 | 1050374 | 26017 | 1334491 |
R2 | CAES (300 MW/2400 MWh): n_{7}=50 MW/400 MWh, n_{22}=250 MW/2000 MWh | 239049 | 4553 | 1066982 | 29551 | 1340135 |
R3 | BES (500 MW/1000 MWh): n_{6}=120 MW/240 MWh, n_{8}=60 MW/120 MWh, n_{10}=60 MW/120 MWh, n_{16}=60 MW/120 MWh, n_{17}=200 MW/400 MWh | 231202 | 9926 | 1072301 | 8703 | 1322132 |
Obviously, in terms of energy capacity, case R3 fully utilizes the built BESs in almost all scenarios, whereas the maximum ECUL in cases R1 and R2 are no larger than 80%, which means the corresponding built energy capacity has already exceeded the system operation requirements. On the other hand, cases R1 and R2 make better use of the built power capacity than case R3 in which the PCUL is less than 60% in a probability of 93.97%. It can be observed that the power capacity built in case R3 is over-invested because the power regulation requirements are also met in cases R1 and R2 with less power capacity. Therefore, under such circumstance, the main driving factor of PHES and CAES construction is the demand for power service, while that of BES construction is the demand for energy service. The above discussion demonstrates that in the ESS planning, using only one type of ESS can hardly meet the unstructured demand for power and energy capacity of system operation without redundant capacity investments.
4.2 Experiments with different storage technology portfolios
ESS planning results with two storage technologies
Case | Planning scheme | Daily cost ($ per day) | Total cost ($ per day) | |||
---|---|---|---|---|---|---|
Investment cost | O&M cost | Fuel cost | ESS loss cost | |||
R4 | PHES+CAES (300 MW/2800 MWh): PHES: n_{22}=200 MW/2000 MWh; CAES: n_{22}=100 MW/800 MWh | 248708 | 4297 | 1055031 | 25382 | 1333418 |
R5 | PHES+BES (400 MW/1600 MWh): PHES: n_{22}=100 MW/1000 MWh; BES: n_{6}=20 MW/40 MWh, n_{8}=20 MW/40 MWh n_{10}=60 MW/120 MWh, n_{17}=200 MW/400 MWh | 223233 | 7482 | 1063501 | 14283 | 1308499 |
R6 | CAES+BES (350 MW/1600 MWh): CAES: n_{3}=100 MW/800 MWh, n_{22}=50 MW/400 MWh; BES: n_{10}=20 MW/40 MWh, n_{17}=180 MW/360 MWh | 212005 | 6313 | 1071247 | 19052 | 1308617 |
ESS planning results with all three storage technologies
Case | Planning scheme | Daily cost ($ per day) | Total cost ($ per day) | |||
---|---|---|---|---|---|---|
Investment cost | O&M cost | Fuel cost | ESS loss cost | |||
R7 | PHES+CAES+BES (350 MW/1800 MWh): PHES: n_{3}=100 MW/1000 MWh; CAES: n_{22}=50 MW/400 MWh; BES: n_{10}=20 MW/40 MWh, n_{17}=180 MW/360 MWh | 216835 | 6216 | 1064369 | 17654 | 1305074 |
As indicated in Tables 2 and 3, all planning schemes (R4-R7) involving multiple storage technologies cost less than the previous schemes (R1-R3) in terms of the total cost. In particular, case R7, which introduces all three storage technologies, has the minimum total cost among cases R1-R7, thus revealing the effectiveness and necessity of the joint planning of various types of energy storage. Furthermore, it can be seen that although the investment cost of case R7 is larger than that of case R6, the cost savings in the remaining three types of costs still render case R7 the most economic planning scheme. Actually, there is no clear positive or inverse relationship between the above four types of costs, it is therefore necessary to introduce all of them as optimization objectives in the ESS planning model.
As a conclusion, compared with cases R1-R3, case R7 takes better advantage of the low-cost energy capacity of PHES and CAES as well as the low-cost power capacity of BES, thus providing a more reasonable planning scheme.
4.3 Additional analyses
4.3.1 Impact of ESS loss cost
ESS planning results without considering ESS loss cost
Case | Planning scheme | Daily cost ($ per day) | Total cost ($ per day) | |||
---|---|---|---|---|---|---|
Investment cost | O&M cost | Fuel cost | ESS loss cost (post evaluation) | |||
R8 | PHES+CAES (300 MW/2800 MWh): PHES: n_{22}=200 MW/2000 MWh; CAES: n_{22}=100 MW/800 MWh | 239049 | 6157 | 1056082 | 46981 | 1348269 |
R9 | PHES+BES (320 MW/2240 MWh): PHES: n_{22}=200 MW/2000 MWh; BES: n_{10}=20 MW/40 MWh, n_{17}=100 MW/200 MWh | 224513 | 5619 | 1057107 | 24197 | 1311436 |
4.3.2 Sensitivity analysis
ESS planning results under different wind power utilization levels
κ (%) | ε (%) | Planning scheme | Daily cost ($ per day) | Curtailment cost ($ per day) | Total cost ($ per day) | |||
---|---|---|---|---|---|---|---|---|
Investment cost | O&M cost | Fuel cost | Loss cost | |||||
95.0 | 10.0 | R6 (350 MW/1600 MWh): CAES: n_{3}=100 MW/800 MWh, n_{22}=50 MW/400 MWh; BES: n_{10}=20 MW/40 MWh, n_{17}=180 MW/360 MWh | 212005 | 6313 | 1071247 | 19052 | 60247 | 1368864 |
95.0 | 7.5 | R10 (320 MW/2440 MWh): CAES: n_{3}=100 MW/800 MWh, n_{22}=200 MW/1600 MWh; BES: n_{17}=20 MW/40 MWh | 248297 | 4987 | 1065873 | 30213 | 52867 | 1402237 |
95.0 | 12.5 | R11 (260 MW/1120 MWh): CAES: n_{22}=100 MW/800 MWh; BES: n_{6}=20 MW/40 MWh, n_{17}=140 MW/280 MWh | 153668 | 4795 | 1096793 | 13634 | 66551 | 1335441 |
97.5 | 10.0 | R12 (440 MW/2080 MWh): CAES: n_{3}=200 MW/1600 MWh; BES: n_{10}=60 MW/120 MWh, n_{17}=180 MW/360 MWh | 270343 | 7639 | 1066263 | 22260 | 49326 | 1415831 |
92.5 | 10.0 | R13 (230 MW/1360 MWh): CAES: n_{3}=50 MW/400 MWh, n_{22}=100 MW/800 MWh; BES: n_{10}=20 MW/40 MWh, n_{17}=60 MW/120 MWh | 156517 | 4041 | 1083196 | 17934 | 71089 | 1332777 |
Table 5 indicates that owing to the restrictive requirements for wind power utilization, the storage investment costs in cases R10 and R12 are respectively increased by 17.12% and 27.5% as compared with the benchmark (case R6). However, the cost savings corresponding to wind curtailment reduction are quite limited because of the peak distribution characteristics of wind power, which leads to poor economy in cases R10 and R12. On the contrary, with an appropriate decrease in the wind power utilization level, less storage devices are required to be built in cases R11 and R13 whereas the corresponding wind curtailment costs slightly increase, thus the total cost is effectively reduced.
The above observations show that: ① the proposed chance-constrained approach can flexibly adjust the wind power utilization level in the ESS planning, thus helping decision-makers to better determine the most suitable planning scheme; ② blindly maximizing the wind power utilization does not necessarily help to improve the overall economy of power systems. Instead, the economy of system planning and operation can be improved by allowing the wind curtailment in an appropriate proportion.
4.3.3 Computational performance
Computational performance
Case | Solution time (s) | |
---|---|---|
BD | CPLEX | |
R1 | 117.32 | 426.74 |
R2 | 111.46 | 627.31 |
R3 | 164.31 | 4684.77 |
R4 | 385.79 | 2618.99 |
R5 | 1771.23 | 27219.41 |
R6 | 1171.76 | 9441.81 |
R7 | 3498.11 | 19747.82 |
R8 | 320.64 | 4971.80 |
R9 | 1643.93 | 9731.70 |
R10 | 1579.53 | 5334.36 |
R11 | 716.44 | 5112.57 |
R12 | 1039.03 | 8623.44 |
R13 | 410.04 | 6282.77 |
It can be observed that the proposed BD algorithm performs faster than the commercial solver CPLEX in all experiments. Specifically, the computational time by the BD algorithm is reduced by more than 80% in 11 of the above cases. Note that the subproblems are independent of each other, the solution efficiency of the BD algorithm can be further improved by parallel computing techniques.
5 Conclusion
This paper presents a chance-constrained ESS planning approach under uncertainty. A density-based clustering method is employed to generate a reduced scenario set to represent uncertain wind power and load. A scenario-based stochastic ESS planning model is established to achieve the joint planning of different energy storage technologies in transmission-constrained networks, and specific chance constraints are designed to ensure a certain level of wind power utilization. Numerical results in a modified IEEE 24-bus system indicate that: ① the planning schemes based on co-optimizing different storage technologies are more reasonable and economically efficient; ② more than 5.9% savings can be achieved in terms of the total cost by allowing a proper amount of wind curtailment; ③ the proposed BD algorithm performs at least 70% faster than using CPLEX to directly solve this kind of chance-constrained problems.
Although employing ESS can help defer the transmission construction, the economic relationship between the construction of ESSs and transmission lines is still ambiguous and needs to be further investigated. In the future, more efforts will be made to carry out the multi-stage co-planning of ESS and transmission network.
Notes
Acknowledgment
This work was supported by National Key Research and Development Program of China (No. 2017YFB0902200) and the Science and Technology Project of State Grid Corporation of China (No. 5228001700CW).
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