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Get Information clear JSmol Viewer clear first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessArticle Configuration Planning of Expressway Self-Consistent Energy System Based on Multi-Objective Chance-Constrained Programming by

Xian Huang,

Wentong Ji *,

Xiaorong Ye and

Zhangjie Feng School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China * Author to whom correspondence should be addressed. Sustainability 2023, 15(6), 5605; https://doi.org/10.3390/su15065605 Received: 9 March 2023 / Revised: 19 March 2023 / Accepted: 21 March 2023 / Published: 22 March 2023 (This article belongs to the Special Issue Sustainable Transition in Transport Energy Consumption: The Charging/Discharging Infrastructure and Self-Containing Transport Energy System of New Energy Vehicles) Download Download PDF Download PDF with Cover Download XML Download Epub Browse Figures Review Reports Versions Notes

Abstract: Regarding the problem of the optimal configuration of self-consistent energy systems based on a 100% renewable energy supply for expressway electricity demand in no-grid areas, this paper proposes a multi-objective planning model based on chance-constrained programming (CCP) to achieve the optimization objectives of low cost and high reliability. Firstly, the number of units of different types of wind turbines (WT), the capacity of photovoltaic (PV) cells, and the number of sets of energy storage systems (ESS) are selected for the design variables in our configuration plan. After defining the load grading shedding and ESS scheduling strategy, the Monte Carlo Simulation (MCS) method and the backward reduction method are applied to model the uncertainties of electric load and renewable energy sources. Finally, the set of Pareto solutions are optimized by the non-dominated sorted genetic algorithm-II (NSGA-II) and its unique best solution is determined by the Criteria Importance Though Intercriteria Correlation (CRITIC) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach. Making use of the wind speed and solar radiation intensity historical data of an area in northwest China in the last five years, eight case studies of two typical scenarios are designed and carried out to explore in-depth the impact of different confidence levels and load fluctuation ranges on the planning results. The results verify that the proposed method can effectively improve the robustness of the system and satisfy the power demand in confidence scenarios. Keywords: expressway self-consistent energy system; chance-constrained programming; configuration optimization; NSGA-II; CRITIC; TOPSIS 1. Introduction 1.1. BackgroundIn the context of the global energy crisis and climate deterioration [1], transportation systems are an important sector of fossil energy consumption. The electrification of transportation has become an important channel to achieve sustainable development, and dependence on the electric power system is gradually increasing [2]. With the progress of high-density battery technology and the increase in charging facilities, the number of electric vehicles has increased rapidly. By March 2022, the number of pure electric vehicles in China reached 7.245 million, a year-on-year increase of 138.20% [3]. However, in some remote or isolated areas without grid access, the spatial layout mismatch between the expressway road network and the grid makes its electrification development difficult.At the same time, the Chinese transportation system itself contains rich natural endowments [4]. For example, the natural resource endowment of solar energy along China’s expressway is 1.023 × 1012 kW·h. If these natural resources can be fully utilized, the self-consistency level of the expressway system will be significantly improved. Therefore, the development and popularization of expressway self-consistent energy systems that rely on 100% renewable energy for power generation have become an inevitable trend.Expressway self-consistent energy is mainly composed of distributed power supplies and energy storage equipment; however, the distributed power sources, mainly WT and PV, are vulnerable to weather factors such as solar radiation, wind speed, etc., which have randomness. Moreover, unlike traditional residential and industrial electrical loads, expressway electrical loads are characterized by shock, volatility, significant temporal characteristics, and high safety requirements. The uncertainty of renewable energy and load makes renewable power abandonment and power shortage frequent [5,6,7]. Since the flexibility alternatives in the operation stage can be limited, it is necessary to fully consider the above uncertainties in the planning stage and to strive to improve the economy and robustness of the planning scheme under the premise of meeting the demand of the traffic side and the safe and reliable operation of the system, so as to make it suitable for more complex actual operation conditions. 1.2. Literature ReviewAt present, although there are few studies on uncertain optimization methods for expressway self-consistent energy systems, scholars have investigated how to optimize the design of systems by considering uncertainties. The main solutions include stochastic planning and robust optimization.The basic idea of robust optimization is to use the bounded set model to describe the fluctuation range of uncertain parameters and formulate the optimal decision scheme under the worst scenario according to the set boundary information [8]. Robust optimization is usually used to solve electric vehicle charging station planning (EVCS) problems [9], microgrid optimization dispatch problems [10,11], generation and transmission expansion planning problems [12,13], and power trading with electricity markets problems [14,15]. One of the key factors which affects the difficulty and accuracy of robust optimization solutions is the establishment of uncertainty sets. The existing uncertainty sets are represented by the Box Uncertainty Set [16,17,18], Polyhedral Uncertainty Set [19], and Ellipsoidal Uncertainty Set [20]. References [21,22] adopt KL divergence and the Wasserstein measure to construct the fuzzy set of uncertain variables. On this basis, the uncertain parameters are taken as optimization variables and solved based on the min-max-min multilayer optimization theory of deterministic optimization. However, in order to avoid the interference of uncertain parameters on the model, the solution of robust optimization is often obtained under the most conservative scenario.Compared with robust optimization, stochastic planning uses the probability distribution of uncertain variables to model uncertain variables [23] and reduces the conservatism of decision-making. References [24,25] adopt different scenario generation methods to generate typical scenery and establish a two-stage stochastic optimization model for the operation and scheduling of the energy storage system of the hybrid renewable energy system. Reference [26] considers the increasing uncertainty caused by the widespread use of electric vehicles and uses the Monte Carlo simulation and Kantorovich method to deal with the related uncertainties.However, general stochastic programming is mainly used to deal with optimization problems where random variables only exist in the objective function, and CCP can change the hard constraints into probabilistic formal constraints to realize the consideration of large probability events of random variables. Hence, it can reduce the impact of low-probability extreme events on the optimal solution and improve the rationality of the optimal solution to a certain extent. CCP is widely used in the optimal scheduling of power systems containing renewable energy. Reference [27] applies chance-constrained programming to the day-ahead scheduling of a multi-microgrid system in an uncertain environment. Reference [28] establishes a novel bi-level optimal dispatching model for the CIES with an EVCS in multi-stakeholder scenarios, which optimizes electric vehicles’ charging and discharging behavior. In [29], a multi-objective stochastic planning model based on chance constraints of the energy network is developed to minimize the investment cost and the energy pipeline risk. In [30], a unified opportunity-constrained optimization framework for island microgrid capacity is proposed and a leader-follower structure is proposed to solve the optimal capacity problem. Although there are many pieces of research on the operation scheduling and demand-side response of microgrids under uncertain conditions, there are few pieces of research that have been conducted on planning issues considering supply reliability and the hierarchical control of different levels of loads. Meanwhile, in the above-mentioned literature, the simulation of uncertain scenes is relatively crude, generating only a set of probability distribution functions [26] or using Markov Chain Monte Carlo (MCMC) simulation [31] to generate data for one year, failing to consider the influence of climate seasonal distribution on uncertain variables. Since the result of multi-objective optimization is a series of Pareto solutions, decision-makers are still required to choose the best solution from the Pareto set. Therefore, some studies adopt multi-attribute decision-making (MADM) technologies to sort these Pareto solutions and select the best compromise solution. To determine the optimal capacity of the hybrid energy storage system, Reference [32] uses NSGA-II to obtain the Pareto set and apply the improved TOPSIS to select the optimal solution from the Pareto set. In [33], an integrated fuzzy-AHP/TOPSIS/EDAS/MOORA decision-making model for a 100% renewable energy system is proposed, which considers five indicators: cost, reliability, emissions, and social and terrain standards. Reference [34] proposes an optimal two-stage decision-making procedure for the site selection of wind-photovoltaic-shared energy storage projects using veto identification coupled with the fuzzy MCDM method. Reference [35] investigates hybrid renewable energy systems to find the techno-economic and environmental trade-off solutions with the usage of HOMER software, and then uses the TOPSIS method combined with weighting methods to choose the final design among the Pareto solutions set. 1.3. Contributions and Paper OrganizationIn this paper, in order to maintain the feasibility of decision-making at a certain confidence level while minimizing costs and maximizing power supply reliability, CCP, which can ensure the economy and feasibility of planning results, is used to design the self-consistent energy system. The main contributions of this article are as follows: (1) To be as close as possible to the actual scenario, the scenarios in a year are divided into 12 groups by month for simulation, respectively, and the wind speed and solar radiation are assumed to obey the Weibull distribution and Beta distribution, respectively [36]. (2) Typical scenarios of 8760 h of a year are generated by using MCS and the backward reduction method. (3) Based on the characteristics of expressway load classification, with the operation control strategy combining load grading shedding and the ESS schedule, a multi-objective optimization model is established with the annual cost of the whole life cycle as the economic index and the power supply reliability as the reliability index. (4) The uncertainty model is converted to a scenario-based deterministic model by using CCP theory, and is solved through NSGA-II and CRITIC-TOPSIS. The rest of the paper is organized as follows. The mathematical models of expressway self-consistent energy system components are presented in Section 2. The method for calculating the probability density of wind speed and solar radiation intensity distribution and generating random scenes is presented in Section 3. Section 4 presents the proposed planning methodology and the algorithm of the methodology. The simulation results are presented and discussed in Section 5. Conclusions and future works are drawn in Section 6. 2. System Architecture and Mathematical ModelThe components of the renewable energy-based self-consistent system include WT, PV, and ESS, which are shown in Figure 1. According to the requirements for power supply reliability, the electric load of the expressway is divided into three levels [37], of which the Level I load has the highest requirements for power supply reliability. The electrical load levels of highway power equipment are shown in Table 1. 2.1. Mathematical Models for the System Components 2.1.1. Wind TurbineThe wind power generated by a wind turbine at time t can be represented by Equation (1) [38]: P W T t = 0 , v t v o u t P r v t − v i n v r − v i n , v i n ≤ v t ≤ v r P r , v r ≤ v t ≤ v o u t where Pr is the rated power; v(t) is the actual wind speed at time t at the turbine hub; vin, vr, and vout are the cut-in, rated, and cut-out wind speed, respectively.In general, the known wind speed data are at the height of the wind measurement tower; therefore, the data must be converted to the actual wind speed at the turbine hub using the following equation, Equation (2): v t = v s t d t × H h u b H s t d θ where vstd(t) is the wind speed at time t at the wind measurement tower; Hhub and Hstd are the height of the turbine hub and wind measurement tower; θ is the friction coefficient, which is taken as 0.2 in this paper. 2.1.2. Photovoltaic SystemThe output power of photovoltaic panels can be calculated by Equation (3) [38]: P PV t = f P V × C P V × I t I S T C 1 + γ T P V t − T P V − R where CPV is the rated power of the PV panel under standard test condition (STC); I(t) is the actual solar radiation intensity on the PV panel at time t and ISTC is the solar radiation intensity at the STC; f PV is the PV derating factor due to the changing effect of the temperature and dust on the panels; γ is the temperature coefficient of power; TPV (t) and TPV-R are the real-time and STC of the PV panel temperatures, respectively. 2.1.3. Energy Storage BatteryThe selection of an appropriate size of battery bank requires a complete analysis of the charge/discharge process of the battery. The main parameter of the battery to be considered is the EC (equals energy capacity), which is simulated during the charging process as [25]: E t + 1 = E t + ϕ c h P c h t Δ t − 1 ϕ d i s P d i s t Δ t where Pch(t) and Pdis(t) represent charging power and discharging power; ϕch and ϕdis are charging and discharging efficiency, respectively; Δt is the simulation step, at 1h. 2.2. Power-Flow StrategyWhen the energy storage battery is not put into operation, the value of the power imbalance is ΔP(t) of the system, as shown in Equation (5): Δ P t = P WT t + P P V t − L 1 t + L 2 t + L 3 t where L1(t), L2(t), and L3(t) are the power of level I, level II, and level III of the electrical load at moment t, respectively.The generation power of the energy self-supply system can be simulated with Equation (6): P s y s t = P W T t + P P V t , a P W T t + P P V t + P d i s t , b (a)If Δ P t ≥ 0 , the total power generated by wind turbine and PV is sufficient to cover the load demand.(b)Otherwise, when PWT(t) and PPV(t) are not sufficient to meet the demand, the battery supplies the difference. If the energy storage battery cannot meet the load demand, the load will cut off according to the order of Level III, Level II, and Level I. In this paper, Ls1(t), Ls2(t), and Ls3(t) are the load shedding of 3 levels of electrical load, respectively. The situation is classified as follows:Case 1: P s y s t ≥ L 1 t + L 2 t + L 3 t , there is no power shortage.Case 2: P s y s t

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