Abstract
The operation characteristics of energy storage can help the distribution network absorb more renewable energy while improving the safety and economy of the power system. Mobile energy storage systems (MESSs) have a broad application market compared with stationary energy storage systems and electric vehicles due to their flexible mobility and good dispatch ability. However, when urban traffic flows rise, the congested traffic environment will prolong the transit time of MESS, which will ultimately affect the operation state of the power networks and the economic benefits of MESS. This paper proposes a bi-level optimization model for the economic operation of MESS in coupled transportation-power networks, considering road congestion and the operation constraints of the power networks. The upper-level model depicts the daily operation scheme of MESS devised by the distribution network operator (DNO) in order to maximize the total revenue of the system. With fuzzy time windows and fuzzy road congestion indexes, the lower-level model optimizes the route for the transit problem of MESS. Therefore, road congestion that affects the transit time of MESS can be fully incorporated in the optimal operation scheme. Both the IEEE 33-bus distribution network and the 29-node transportation network are used to verify and examine the effectiveness of the proposed model. The simulation results demonstrate that the operation scheme of MESS will avoid the congestion period when considering road congestion. Besides, the transit energy consumption and the impact of the traffic environment on the economic benefits of MESS can be reduced.
WITH the rapid development of wind power and photovoltaics worldwide, a high proportion of renewable energy will become normal in future power systems. The power system with large penetration of renewable energy sources (RESs) will confront the challenges with system planning and operation as well as power supply security and power quality due to the volatility, randomness, and intermittency of RESs [
Demand-side management, energy arbitrage, load smoothing, equipment utilization enhancement, and consumption of RESs can all be accomplished by using ESS [
In view of these, a kind of dedicated large-scale mobile energy storage system (MESS) is gradually emerging. MESS can not only meet the dispatch instructions of DNO in time, but also has the flexibility of EV dispatch. The detailed structure of MESS is given in [
Nowadays, the commercial applications of MESS are becoming more abundant. MESS is currently available at 1000 kW, 5000 kW, and other power levels [
With the increasing application of MESS projects, the related theoretical research is getting more and more advanced. Currently, theoretical research on MESS mainly focuses on two aspects.
One is the application of MESS in the restoration of the distribution network after a disaster or the improvement of distribution network resiliency. Aiming at the restoration of the distribution network after natural disasters, [
The other is the economic scheduling problem of MESS in the distribution network. In [
Based on the above background, this paper establishes a bi-level programming model to develop the economic dispatch of MESS under the coupled transportation-power networks. The general situation of the coupled networks is shown in Fig. B1 of Supplementary Material B. The upper-level model is an economic dispatch model with chance constraints. According to the state of the power networks, the upper-level model formulates the operation plan of MESS and transfers it to the lower level. The lower-level model is a fuzzy route planning model considering road congestion. Based on the state of the transportation network, the route scheme of MESS is updated and returned to the upper level along with the energy consumption. Finally, the bi-level programming model is solved iteratively by the column-and-constraint generation (C&CG) algorithm to obtain the optimal operation scheme of MESS. The main contributions of this paper are as follows.
1) A new transit model of MESS is established. The model does not require whether the transportation network satisfies the consistency condition. For the transportation network that does not satisfy the consistency condition, the upper-level model can still obtain the optimal solution.
2) The uncertainty of road congestion in a time-varying traffic environment is considered. In this paper, the road saturation parameter, which reflects the degree of road congestion, is considered as a fuzzy number and is processed by the expectation value method. On this basis, a route planning scheme with stopping strategy is proposed. With the premise of avoiding road congestion and ensuring time satisfaction, the energy consumption in the transit process is minimized, thus further optimizing the operation economy of MESS.
The rest of this paper is arranged as follows. Firstly, Section II describes the bi-level optimization model for economic dispatch of MESS. Secondly, solution methods are given in Section III. Furthermore, case studies and results are given in Section IV. Finally, Section V provides the conclusion.
With the rapid growth of EVs, electrified transportation with EVs as the core is driving the coupling between the transportation network and power networks, and the deep coupling between them also provides the conditions for the wide application of MESS. In this paper, the main work of MESS is to transit and perform charging/discharging between different charging stations in the transportation network. Before building the model, it is necessary to clarify the meaning of the coupled transportation-power networks. To show the difference, “bus” is used for the power networks, while “node” is used for the transportation network. The specific model of the coupled networks is shown in Supplementary Material C.
First and foremost, this paper treats DNO as an MESS investor. Considering the intermittent power generation of RESs and the investment cost of MESS, fossil-energy distributed generations (DGs) are added to the distribution network for auxiliary adjustment such as gas turbines and diesel generations. It should be noted that MESS and fossil-energy DGs are the assets of DNO. RESs are owned by the private company, from whom DNO purchases renewable energy.
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
The objective function is to maximize the profit of DNO, as shown in (1).
This paper adopts the linear dist-flow branch power flow model [
(7) |
(8) |
(9) |
(10) |
In (7)-(10), the square of voltage on buses i or j is represented by a single variable or to ensure the linearity of the equation. Specific linear dist-flow power flow equations are given in Supplementary Material C.
The operation constraints of MESS consist of two parts: ESS operation model and transit model. The ESS operation model limits the state of charge (SOC) [
(11) |
(12) |
(13) |
(14) |
(15) |
(16) |
(17) |
(18) |
(19) |
(20) |
The transit models of [
In short, a transportation network satisfying the consistency condition means that vehicles that depart earlier would arrive at their destinations earlier than those that depart later. Since the linear transit model has high data requirements for the transit time matrix, it cannot solve the scenarios where the transportation network does not satisfy the consistency condition, e.g., when road congestion or traffic accident occurs. For this reason, a novel transit model is developed in this paper, which does not have high data requirements for the transit time matrix.
(21) |
(22) |
(23) |
(24) |
(25) |
Detailed explanations of (21)-(25) are given in Supplementary Material D.
In this paper, DGs of two energy types are considered. One is in the form of renewable energy, and the other is in the form of fossil energy. The output of fossil-energy DGs is the only factor that is constrained. To ensure that the equation is a convex one, the output power of fossil-energy DGs is constrained to be linear [
(26) |
(27) |
(28) |
(29) |
Due to the uncertainty of RESs and load forecasting, the chance constraint method is used to deal with the randomness of both. It is assumed that the actual power of RESs and load can be divided into two parts: predicted value and error value. At the same time, the power factors of RESs and load are assumed to be constant.
(30) |
(31) |
(32) |
(33) |
Affected by the randomness of RESs and load, voltage and current may exceed the limits. Therefore, the corresponding chance constraints are constructed to describe this phenomenon. The chance constraints of branch power flow are shown in Supplementary Material E.
(34) |
(35) |
After the lower-level model gets the operation scheme of MESS from the upper-level model, it needs to re-route each transit process of MESS to reduce energy consumption as much as possible. Therefore, the lower-level model is essentially a time-dependent route planning model.
To quantify the energy consumption of MESS during road congestion, the energy consumption model given in [
(36) |
Since the road congestion is often accompanied by frequent acceleration and deceleration of vehicles, the change in speed will affect the energy consumption. To visually depict this variation,

Fig. 1 Relationship between energy consumption and speed.
It is clear that either too high or too low speed leads to high energy consumption, especially at low speeds. In order to ensure that MESS can keep the driving speed with low energy consumption during the transit, a route planning scheme that includes a stopping strategy is proposed. In

Fig. 2 Time-dependent speed profile.
The transit comparison of MESS on road section between nodes m and n with and without stopping strategy is given in

Fig. 3 Transit comparison of MESS with and without stopping strategy. (a) With stopping strategy. (b) Without stopping strategy.
It can be found that the route planning, including the stopping strategy, keeps the MESS moving at a good speed. To balance the relationship between the transit time and energy consumption, the arrival time of MESS is extended into a fuzzy time window and the membership function of fuzzy numbers is used to describe the time satisfaction of arriving at the charging station. By setting three objective functions in the lower-level model, (37) denotes the time satisfaction, (38) denotes the transit time, and (39) denotes the energy consumption, and the energy consumption is minimized while ensuring time satisfaction.
(37) |
(38) |
(39) |
In order to obtain the speed parameter , it is necessary to quantitatively evaluate the road congestion condition of each road section at each time period. Since there is no unified international standard for the quantitative analysis of road congestion, this paper will adopt the Evaluation Index System of Urban Traffic Management issued by the Ministry of Public Security of China [
The route planning constraints are:
(40) |
(41) |
(42) |
(43) |
(44) |
(45) |
(46) |
(47) |
(48) |
(49) |
(50) |
The specific meanings of the above constraints are explained in the Supplementary Material G.
Through the above modeling, it can be found that the upper-level model is a stochastic programming with chance constraints, and the lower-level model is a multi-objective programming with fuzzy parameters. To facilitate the problem solving, the models will be transformed to deterministic forms.
Referring to the methods in [
(51) |
(52) |
Specific derivation process of the approximation processing can be found in Supplementary Material E.
Thus, the chance constraints in the upper-level model can be transformed to deterministic forms. It is assumed that the errors in RES output and load prediction are symmetrically distributed and independent of each other. According to (7)-(8) and (30)-(33), a linear equation between the voltage and the above error variables can be derived.
(53) |
Substitute (53) into the chance constraint (52), and then transform it into the following deterministic equations.
(54) |
(55) |
Similarly, the chance constraints of branch power flow can also be transformed deterministically. See Supplementary Material E for specific steps.
After the deterministic conversion, the error variable is no longer included, so can be replaced by . Obviously, the transformed constraints are the contraction of the original constraints, which reflect the robustness of the chance constraints.
Since the former part of (23) has a value of 1 or 0, it can be considered as a binary variable. Therefore, (23) contains the product of two variables and is a nonconvex constraint. To eliminate the nonconvexity, (23) is linearized by adding the artificial variable and using the big M method.
(56) |
(57) |
(58) |
By adding in (23), we can obtain:
(59) |
For the lower-level model, it is necessary to deal with the fuzzy number and the multi-objective function. Firstly, the expected interval and the expected value of the triangular fuzzy number are presented through the membership function [
(60) |
The expected interval is:
(61) |
The expected value is:
(62) |
The fuzzy number of road section saturation can be transformed by the expected value of , and then the speed of MESS in the corresponding road section can be obtained according to the Table BI of Supplementary Material B.
Secondly, the efficiency coefficient method is used to convert multiple objectives into a single objective, i.e., each objective function is normalized. Since is in the range of , only and are treated.
(63) |
(64) |
(65) |
In the above equations, , , and () are used to control the ratio of the three functions.
Finally, the upper-level problem is transformed into a mixed-integer second-order cone programming problem, and the lower-level problem is transformed into a mixed-integer programming problem. The bi-level programming problem can be summarized as:
(66) |
Given that the lower-level model contains binary variables, it is impossible to convert the bi-level model into a single-level model through strong duality theory or Karush-Kuhn-Tucker (KKT) optimality conditions. Hence, according to the methods in [
The coupled transportation-power networks consisting of an IEEE 33-bus distribution network and a 29-node transportation network [
The detailed information about the coupled networks is as follows. The rated capacity and rated voltage of the power networks are 10 MVA and 12.66 kV, respectively; the power networks has 33 buses and 32 branches; and the transportation network has 29 nodes and 49 roads. The mapping relationship between power networks buses and transportation network nodes is shown in Table BII of Supplementary Material B. The mapping relationship between road sections and nodes in the transportation network is shown in Table BIII of Supplementary Material B.
According to the load characteristics, the areas are divided into residential, suburban, industrial, and commercial areas. And the load curves, wind power output curves, and photovoltaic output curves for each zone are generated by the methods in [
Regarding the setting of the chance constraint parameter in the upper-level model, the probability of not satisfying the inequality constraint is set to be 0.05, i.e., . The sample values of the forecasting error of load and the output error of RESs are randomly generated from two normal distributions N(0,0.06). These two normal distributions are independent of each other and both take values in the range of . In addition, the electricity price is shown in

Fig. 4 Electricity price.
The planning results of the lower-level model include the energy consumption of a single MESS in a single transit, but the final energy consumption is generated by multiple MESSs in multiple transits. Therefore, the lower-level model needs to be cycled through the optimization several times to generate the final energy consumption. In addition, the saturation of each road section at each time period based on the predicted traffic flow is shown in Fig. B7 of Supplementary Material B.
The optimization models are implemented in MATLAB with the YALMIP toolbox [
Based on the established mathematical model and the designed solving process, the optimal scheduling scheme can be solved. The iteration and computation time are shown in
Firstly, the index parameters of the original system and the system with MESS are analyzed from the economic point of view. According to the data in

Fig. 5 Voltage comparison between original system and system with MESS.

Fig. 6 Diagram of MESS transit with stopping strategy.
The charging or discharging of MESS is not only driven by the electricity price, but also by the net load of the system. The net load of the system can be understood by observing the output of fossil-energy DGs.
For example, the output of fossil-energy DGs is generally at its peak during periods with large values of net load. And the output of fossil-energy DGs is generally at a trough during periods with small values of net load. As shown in

Fig. 7 Active power of fossil-energy DGs. (a) DG 1. (b) DG 2. (c)DG 3.

Fig. 8 Operational status of MESS with stopping strategy.

Fig. 9 MESS reactive power with stopping strategy.
To get a clear picture of the impact of the stopping strategy, specific path of each transit process, total energy consumption, and transit time are given in Tables
The process of transit No. 2 is used as an example to further observe when MESS adopts a stopping strategy to avoid road congestion. Tables
The traversal method is used to determine the weights of each objective function in the lower-level model, and the traversal step is 0.01. Taking the process of transit No. 2 as an example, 300 optimal solutions are obtained by traversing the weights of the three objective functions. These 300 optimal solutions can be categorized into three types, as shown in
Finally, the differences between the transit model in [

Fig. 10 Update process of transit time matrix.
The original transit time matrix is obtained by performing path planning with the non-stopping strategy. The original transit time matrix ensures the shortest transit time for MESS. Since the lower-level model uses the stopping strategy for route planning, its optimized transit time will be larger than the value in the original transit time matrix. Therefore, the transit time matrix after the data update will not satisfy the consistency condition, and the transit model in [
The simulation step is set to be 1 hour considering the speed of solution. The transit time matrix 1 is considered as the original transit time matrix, as shown in Table BV of Supplementary Material B. The transit time matrix 2 is obtained by changing one of the data on the basis of matrix 1, as shown in Table BVI of Supplementary Material B. Substituting matrix 1 into the upper-level model of this paper, the transit scheme of MESS is obtained, as shown in

Fig. 11 Comparison of MESS route under different transit models. (a) Transit time matrix 1. (b) Transit time matrix 2.
The increasing number of DGs in the form of RESs in the distribution network provides favorable conditions for the commercial application of MESS. As a coupling point between power networks and transportation network, the operational scheme of MESS needs to consider the status of both. This paper proposes a bi-level optimal operation model of MESS in coupled transportation-power networks. The upper-level model is an economic scheduling problem for MESS with chance constraints. The lower-level model performs multi-objective fuzzy path planning for MESS based on the optimization result of the upper-level model. Finally, the final optimal operation solution of MESS is obtained by iterative solution of the upper-level and the lower-level models. The verification and analysis of the algorithm show that the optimized operation solution of MESS in this paper avoids the most congestion-prone road sections during each time period, and reduces the energy consumption of MESS during transit while ensuring the stable operation of the distribution network.
Nomenclature
Symbol | —— | Definition |
---|---|---|
A. | —— | Set and Indices |
, | —— | Indexes of branches in power networks |
—— | Index of fossil-energy distributed generations (DGs) | |
, , | —— | Indexes of buses in power networks |
—— | Index of mobile energy storage system (MESS) charging stations | |
—— | Index of vector dimension | |
, | —— | Indexes of nodes in transportation network |
—— | Set of all branches in power networks | |
—— | Set of all fossil-energy DGs | |
—— | Set of all buses in power networks | |
—— | Set of all MESS charging stations | |
—— | Set of all nodes in transportation network | |
—— | Set of all renewable energy DGs | |
—— | Set of all road sections | |
—— | Set of time intervals | |
—— | Index of renewable energy DGs | |
, t' | —— | Indexes of time intervals in one day |
B. | —— | Variables |
—— | Vector of error variables | |
, | —— | Error variables of load on buses i and j during period t |
—— | Error variable of renewable energy sources (RESs) during period t | |
—— | Binary variable, which equals to 1 if the fossil-energy DG is in “ON” state | |
—— | Operating cost of fossil-energy DGs | |
—— | Cost (income) when distribution network operator (DNO) purchases (sells) the electricity from the upper-level power networks | |
—— | Operating cost of MESS | |
—— | Cost of RES purchased by DNO | |
d | —— | Distance in energy consumption calculation |
—— | Driving distance of MESS on road section between nodes m and n during period t | |
—— | Energy consumption from l to during period | |
—— | Departure time at node | |
, | —— | Arrival time at nodes and n |
—— | Time spent on road section between nodes and n during period t | |
—— | Income of DNO | |
—— | MESS cycles during period | |
—— | Time satisfaction of MESS | |
, | —— | Transit time before and after normalization |
, | —— | The maximum and minimum values by solving |
, | —— | Energy consumptions before and after normalization |
, | —— | Objective functions of the upper- and lower-level models |
—— | Active and reactive power on branch during period | |
—— | Active and reactive power on branch b' during period | |
—— | Active and reactive power of fossil-energy DG during period | |
—— | Charging and discharging active power for charging station during period | |
—— | Active and reactive power from upper-level grid during period | |
—— | Reactive power for charging station l during period t | |
—— | Artificial variable for charging station l during period t | |
—— | State of charge (SOC) of MESS during period | |
, | —— | SOCs of MESS at final and initial periods |
—— | Arrival time for each MESS transit | |
—— | Transit time from station to during period | |
—— | Start and end time for each transit | |
—— | Binary variable indicating if road section is between nodes m and n | |
—— | Binary variable indicating if road section is between nodes m and n during period t | |
, | —— | Second norms of voltage on buses and j |
, | —— | Voltage on buses and j without considering error |
, | —— | Start and end nodes for each transit |
—— | Condition flag for station during period | |
, | —— | Binary variables, which equal to 1 if MESS is charging and discharging for station l during period t |
—— | Preparation transit flag for station during period t | |
—— | Destination flag from station to during period t | |
C. | —— | Parameters |
—— | Economy coefficients of fossil-energy DG g | |
, , | —— | Weights of lower-level model functions |
—— | Probability of constraint failure | |
—— | Engine module constant | |
—— | Charging and discharging efficiencies of MESS | |
—— | Weight of MESS | |
—— | Speed module constant | |
—— | Weight module constant | |
—— | Linear output range of fossil-energy DG | |
—— | Column vector | |
—— | One-dimensional coefficient vector | |
—— | Number of branches in power networks | |
, | —— | Error standard coefficients of load on buses i and j during period t |
—— | Error standard coefficient of RES on bus i during period t | |
—— | Levelized cost of MESS | |
D | —— | Number of buses in power networks |
—— | Rated capacity of MESS | |
—— | Number of fossil-energy DGs | |
—— | Dimension number of a | |
—— | Road distance between nodes and | |
—— | Labor cost of staff | |
—— | Number of MESS charging stations | |
—— | A large number | |
—— | The maximum number of MESS cycles | |
—— | Probability density distribution function satisfied by error variable | |
—— | Purchase price of power for DNO during period | |
—— | Purchase price of RES for DNO | |
, | —— | Active and reactive power on bus i during period |
, | —— | Active and reactive power on bus j during period |
, | —— | Predicted active and reactive power on bus i during period |
, | —— | Predicted active and reactive power on bus j during period |
, | —— | Active and reactive power of renewable energy DG during period |
, | —— | Predicted active and reactive power of renewable energy DG during period |
—— | Purchase price of power for users during period | |
, | —— | The maximum active and reactive power of MESS |
, | —— | The maximum and minimum active power of fossil-energy DG |
, | —— | The maximum and minimum reactive power of fossil-energy DG |
—— | Road saturation between nodes and | |
—— | Triangular fuzzy number of road saturation between nodes and | |
, | —— | Upper- and lower- boundary values of triangular fuzzy number between nodes and |
—— | Number of distributed renewable energy | |
, | —— | Climbing rates of load increase and reduction |
, | —— | Resistance and reactance on branch |
—— | Rated apparent power of MESS | |
—— | Apparent power capacity of branch b | |
—— | SOC of MESS at initial period | |
, | —— | The maximum and minimum values of SOC |
s | —— | Speed in energy consumption calculation |
—— | Moving speed of MESS on road section between nodes m and n during period t | |
—— | Number of simulation periods | |
—— | Simulation step size | |
, | —— | The maximum and minimum values of second normal voltage |
D. | —— | Functions |
—— | Membership calculation of fuzzy numbers | |
—— | Probability of event occurring | |
—— | Energy consumption during transit process |
References
G. Magdy, E. A. Mohamed, G. Shabib et al., “Microgrid dynamic security considering high penetration of renewable energy,” Protection and Control of Modern Power Systems, vol. 3, no. 1, pp. 23-33, Aug. 2018. [Baidu Scholar]
K. Ahmed, M. Seyedmahmoudian, S. Mekhilef et al., “A review on primary and secondary controls of inverter-interfaced microgrid,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 5, pp. 969-985, Sept. 2021. [Baidu Scholar]
S. K. Kyung, K. J. McKenzie, Y. L. Liu et al., “A study on applications of energy storage for the wind power operation in power systems,” in Proceeding IEEE PES General Meeting, Montreal, Canada, Jun. 2006, pp. 1-5. [Baidu Scholar]
T. Chen, X. Zhang, J. Wang et al., “A review on electric vehicle charging infrastructure development in the UK,” Journal of Modern Power Systems and Clean Energy, vol. 8, no. 2, pp. 193-205, Mar. 2020. [Baidu Scholar]
H. Cai, Q. Chen, Z. Guan et al., “Day-ahead optimal charging/discharging scheduling for electric vehicles in microgrids,” Protection and Control of Modern Power Systems, vol. 3, no. 1, pp. 9-33, Apr. 2018. [Baidu Scholar]
W. Sun, J. Zhang, J. Yang et al., “Probabilistic evaluation and improvement measures of power supply capability considering massive ev integration,” Electronics, vol. 8, no. 10, pp. 1-18, Oct. 2019. [Baidu Scholar]
H. H. Abdeltawab and A. R. I. Mohamed, “Mobile energy storage scheduling and operation in active distribution systems,” IEEE Transactions on Industrial Electronics, vol. 64, no. 99, pp. 6828-6840, Sept. 2017. [Baidu Scholar]
Winston Energy Group Limited. (2021, Jan.). [Online]. Available: http://en.winston-battery.com/index.php/products/mobile-power [Baidu Scholar]
EnergyTrend. (2021, Jan.). [Online]. Available: https://www.energytrend.cn/news/20190916-75678.html [Baidu Scholar]
EnergyTrend. (2021, Jan.). [Online]. Available: https://www.energytrend.cn/news/20191101-77578.html [Baidu Scholar]
Chuneng BJX. (2021, Jan.). [Online]. Available: http://chuneng.bjx.com.cn/news/20201106/1114418.shtml [Baidu Scholar]
Chuneng BJX. (2021, Jan.). [Online]. Available: http://chuneng.bjx.com.cn/news/20210104/1126688.shtml [Baidu Scholar]
J. Kim and Y. Dvorkin, “Enhancing distribution system resilience with mobile energy storage and microgrids,” IEEE Transactions on Smart Grid, vol. 10, no. 5, pp. 4996-5006, Sept. 2018. [Baidu Scholar]
S. Lei, C. Chen, H. Zhou et al., “Routing and scheduling of mobile power sources for distribution system resilience enhancement,” IEEE Transactions on Smart Grid, vol. 10, no. 5, pp. 5650-5662, Sept. 2019. [Baidu Scholar]
S. Yao, P. Wang, and T. Zhao, “Transportable energy storage for more resilient distribution systems with multiple microgrids,” IEEE Transactions on Smart Grid, vol. 10, no. 3, pp. 3331-3341, Aug. 2019. [Baidu Scholar]
S. Yao, P. Wang, and X. Liu, “Rolling optimization of mobile energy storage fleets for resilient service restoration,” IEEE Transactions on Smart Grid, vol. 11, no. 2, pp. 1030-1043, Jul. 2019. [Baidu Scholar]
K. Ling, Z. Guan, H. Wu et al., “Active distribution network dispatch strategy with movable storage considering voltage control,” Electric Power Construction, vol. 38, no. 6, pp. 44-51, Jun. 2017. [Baidu Scholar]
S. Y. Kwon, J. Y. Park, and Y. J. Kim, “Optimal operation of mobile energy storage devices to minimize energy loss in a distribution system,” in Proceedings of IEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe, Palermo, Italy, Jun. 2018, pp. 1-6. [Baidu Scholar]
M. E. Baran and F. F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing,” IEEE Transactions on Power Delivery, vol. 4, no. 2, pp. 1401-1407, May 1989. [Baidu Scholar]
Y. Liu, W. Wu, B. Zhang et al., “A mixed integer second-order cone programming based active and reactive power coordinated multi-period optimization for active distribution network,” Proceedings of the CSEE, vol. 34, no. 16, pp. 2575-2583, Jun. 2014. [Baidu Scholar]
G. He, Q. Chen, C. Kang et al., “Optimal bidding strategy of battery storage in power markets considering performance-based regulation and battery cycle life,” IEEE Transactions on Smart Grid, vol. 7, no. 5, pp. 2359-2367, Sept. 2016. [Baidu Scholar]
B. Xu, A. Oudalov, A. Ulbig et al., “Modeling of lithium-ion battery degradation for cell life assessment,” IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 1131-1140, Mar. 2018. [Baidu Scholar]
S. Beak, H. Kim, and Y. Lim, “Multiple-vehicle origin destination matrix estimation from traffic counts using genetic algorithm,” Journal of Transportation Engineering, vol. 130, no. 3, pp. 339-347, May 2004. [Baidu Scholar]
D. E. Kaufman and L. S. Robert. “Fastest paths in time-dependent networks for intelligent vehicle highway systems application,” Journal of Intelligent Transportation Systems, vol. 1, no. 1, pp. 1-11, Jan. 1993. [Baidu Scholar]
J. Lu, Y. Chen, J. K. Chao, “The time-dependent electric vehicle routing problem: model and solution,” Expert Systems with Applications, vol. 161, pp. 1-17, Dec. 2020. [Baidu Scholar]
Y. Zhu, “Modeling technology and optimization method of urban road traffic congestion situation assessment,” Ph.D. dissertation, Department of Systems Engineering, Nanjing University of Science and Technology, Nanjing, China, 2018. [Baidu Scholar]
B. Ghosh, B. Basu, and M. O’mahony, “Bayesian time-series model for short-term traffic flow forecasting,” Journal of Transportation Engineering, vol. 133, no. 3, pp. 180-189, Mar. 2007. [Baidu Scholar]
M. Castro-neto, Y. S. Jeong, and M. K. Jeong, “Online-SVR for short-term traffic flow prediction under typical and atypical traffic conditions,” Expert Systems with Applications, vol. 36, no. 3, pp. 6164-6173, Apr. 2009. [Baidu Scholar]
K. Y. Chan, T. S. Dillon, and J. Singh, “Neural-network-based models for short-term traffic flow forecasting using a hybrid exponential smoothing and Levenberg-Marquardt algorithm,” IEEE Transactions on Intelligent Transportation Systems, vol. 13, no. 2, pp. 644-654, Jun. 2012. [Baidu Scholar]
F. Wen, G. Zhang, L. Sun et al., “A hybrid temporal association rules mining method for traffic congestion prediction,” Computers & Industrial Engineering, vol. 130, Apr. 2019. [Baidu Scholar]
W. Zhao, X. Sun, S. Si et al., “Multi-objective routing optimization of military resources distribution based on fuzzy constraints,” Systems Engineering and Electronics, vol. 40, no. 12, pp. 2699-2706, Dec. 2018. [Baidu Scholar]
Z. Li, W. Wu, J. Zhu et al., “Chance-constrained model for day-ahead heat pump scheduling in active distribution network and its tractability transformation,” Automation of Electric Power Systems, vol. 42, no. 11, pp. 24-31, Jun. 2018. [Baidu Scholar]
A. Nemirovski, “On safe tractable approximations of chance constraints,” European Journal of Operational Research, vol. 219, no. 3, pp. 707-718, Jun. 2012. [Baidu Scholar]
M. Jiménez, M. A. Parra, A. Bilbao et al., “Linear programming with fuzzy parameters: an interactive method resolution,” European Journal of Operational Research, vol. 177, no. 3, pp. 1599-1609, Feb. 2007. [Baidu Scholar]
L. Zhao and B. Zeng. (2012, Jan.). An exact algorithm for two-stage robust optimization with mixed integer recourse problems. [Online]. Available: http://www.optimizationonline.org/DB_FILE/2012/01/3310.pdf [Baidu Scholar]
D. Yury, F. Ricardo, and Y. Wang, “Co-planning of investments in transmission and merchant energy storage,” IEEE Transactions on Power Systems, vol. 33, no. 1, pp. 245-256, Jan. 2018. [Baidu Scholar]
Y. Shao, Y. Mu, X. Yu et al., “A spatial-temporal charging load forecast and impact analysis method for distribution network using EVS-traffic-distribution model,” Proceedings of the CSEE, vol. 37, no. 18, pp. 3-15, Sept. 2017. [Baidu Scholar]
M. R. Dorostkar-Ghamsari, M. Fotuhi-Firuzabad, M. Lehtonen et al., “Value of distribution network reconfiguration in presence of renewable energy resources,” IEEE Transactions on Power Systems, vol. 31, no. 3, pp. 1879-1888, May 2016. [Baidu Scholar]
M. E. Baran and F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing,” IEEE Transactions on Power Delivery, vol. 4, no. 2, pp. 1401-1407, Apr. 1989. [Baidu Scholar]
S. Lei, Y. Hou, and F. Qiu, “Identification of critical switches for integrating renewable distributed generation by dynamic network reconfiguration,” IEEE Transactions on Sustainable Energy, vol. 9, no. 1, pp. 420-432, Jan. 2018. [Baidu Scholar]
M. Nick, R. Cherkaoui, and M. Paolone, “Optimal siting and sizing of distributed energy storage systems via alternating direction method of multipliers,” International Journal of Electrical Power & Energy Systems, vol. 72, pp. 33-39, Mar. 2015. [Baidu Scholar]
J. Lofberg: “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, China, Jun. 2004, pp. 284-289. [Baidu Scholar]
Z. Gu, E. Rothberg, and R. Bixby. (2019, Jan.). Gurobi Optimizer Reference Manual. [Online]. Available: http://www.gurobi.com [Baidu Scholar]