Optimal decentralized valley-filling charging strategy for electric vehicles
Introduction
As alternatives to conventional vehicles, plug-in hybrid electric vehicles (PHEVs) and battery electric vehicles (BEVs) are expected to reduce petroleum-based energy consumption and greenhouse gas emissions. Consequently, their use is likely to expand drastically in the near future [1]. According to China’s “Twelfth Five Year Plan”, the number of EVs (PHEVs and BEVs) in Beijing will likely exceed 100,000 by 2017 [2].
As EVs comprise an increasing percentage of the vehicle population, unregulated charging behaviors (especially immediate charging after arriving home in the evening) will impact the power grid in two ways: (1) by increasing the peak load and local marginal prices (LMPs) and (2) by decreasing system reliability [5]. The control of EVs’ charging loads, which is also essential to smart grids, becomes a feasible option for this issue [3]. The three potential ways of participating in a smart grid are load shifting, regulation, and spinning reserve [4].
Load shifting or valley-filling charging strategies have been widely reported. These studies focus on shifting the controllable EV load to less congested hours compared with that in an unregulated charging strategy. Valley-filling charging algorithms can be categorized into two broad classes on the basis of their EV charge patterns: centralized approaches [6], [7], [8], [9], [10] and decentralized approaches [11], [12], [13].
In a centralized approach, an imaginary centralized controller communicates with each EV, collects necessary information, solves specific optimization problems, and directly controls individual charging patterns. To reduce the dimensionality in the corresponding optimization problem, engineers frequently introduce aggregators between the power grid and EV owners, forming a decentralized hierarchical scheme [2], [7], [9], [10]. Developing the computer/communication/control network and incentive program to implement this conceptual framework presents a major challenge [8]. Thus, centralized approaches are usually considered as long-term solutions to valley filling.
A decentralized approach offers more realistic alternative. In these approaches, EV owners determine individual charge patterns on the basis of an electricity pricing scheme or non-price instructions. The grid power demand can be altered by adjusting the electricity price, typically by a dual-tariff scheme [14]. While this time-varying pricing scheme encourages EV owners to charge their vehicles during valley hours, it introduces an undesirable second peak in the electricity load [3]. Zhongjing et al. [12] constructed a non-cooperative game strategy, in which each EV pursues a cost-minimizing charge pattern based on dynamic pricing schemes iteratively. This strategy drives a unique Nash equilibrium that results in the valley-filling charging effect. Although the algorithm allows autonomous charging behaviors, the iteration process requires a high-reliability bi-directional communication network between the power gird and EVs. Thus, similar to the abovementioned centralized strategies, this strategy is unsuitable for short-term applications. Ahn et al. [11] proposed an optimal decentralized charging strategy, in which the distributed EV chargers receive a simple command from the centralized grid controller, and thereby determine their individual charge patterns. This strategy behaves as the global optimal solution of a linear optimization problem, achieving near-optimal valley-filling effect. Such a command-based strategy requires no complex bi-directional network, but its valley-filling effect depends on the willingness of EV owners to relinquish charging autonomy for device-level objectives. The main challenge in such a decentralized algorithm is how to balance system-level with device-level objectives, which often constitutes a trade-off problem [3].
The system-level objective of the overnight charging scenario is to realize a valley-filling charging effect that reduces peak load and overall generation cost. At the device level, this charging strategy are usually to optimize the individual charging patterns to minimize electricity cost and battery degradation [16]. Sikha et al. developed a varying current decay (VCD) charge pattern for a lithium ion cell. VCD enables faster charging and lower capacity fade than conventional constant current/constant voltage (CC–CV) charge patterns [17]. To maximize the useful lifetime of lithium ion cells, Rahimian et al. optimized charging currents as a function of cycle number [22], [23]. Liu et al. adopted the Taguchi method in an optimization technique for designing rapid charge patterns [24]. Applying the power loss model to the battery and charger, Wang proposed that electricity cost could be minimized by efficiency-optimized charge patterns [18]. Benedikt et al. investigated the trade-off between two competitive optimizations: cost and battery lifespan [19]. Adopting a first-principles electrochemistry based battery model [25], Bashash et al. optimized the PHEV charge pattern in terms of battery longevity and energy cost [16]. They used a multi-objective genetic optimization algorithm to balance the two conflicting device-level objectives. The resulting Pareto fronts of this algorithm described the trade-off between energy cost and battery health. Although these abovementioned device-level charging algorithms generate different “optimal” charge patterns, they possess one common feature: they require charging autonomy at the device level.
An ideal valley-filling charging algorithm satisfies the following three criteria.
- 1.
Coordination: An optimal valley-filling effect is achieved by the aggregated charging load of all EVs connected in the grid.
- 2.
Practicality: No reliance on a bidirectional communication/control network.
- 3.
Autonomy: Allowing device-level charging autonomy and appropriate balance between competing objectives at two levels.
To the best of our knowledge, none of the existing valley-filling charging strategies [7], [8], [9], [10], [11], [12], [13] possess all three characteristics. This study proposes a novel decentralized optimal valley-filling charging strategy that fulfills these three criteria. The fundamental design is an optimized day-ahead two-dimensional time-power-varying pricing scheme for dynamic electricity use.
The pricing scheme is transmitted from the centralized grid broadcaster via a unidirectional communication network and is received by the intelligent chargers installed in the EV. Thereafter, the chargers determine their individual charge patterns. When EV owners optimize the varying device-level objectives, the grid automatically achieved optimized or near-optimized valley-filling charging effect. Therefore, the proposed strategy realizes multi-level optimization.
The paper is organized as follows. Section 2 describes the system and defines the optimization problem for the proposed valley-filling charging strategy. Section 3 introduces the fundamentals of the proposed strategy; namely, the pricing scheme and its design. Section 4 verifies the robustness of the proposed strategy in a series of simulations. The conclusions are presented in Section 5.
Section snippets
System description and problem definition
Fig. 1 shows the schematic of the grid–EVs system for the proposed valley-filling charging strategy. In this system, the charging behaviors of an EV fleet are indirectly coordinated by a pricing scheme. The EV owners are expected to optimize their individual charge patterns in response to the pricing scheme, enabling the aggregated charging load PEV,agg(t) to achieve a valley-filling effect.
The parameters of the grid–EV system are discussed in Sections 2.1 Grid demand and generation cost, 2.2
Design of pricing scheme to achieve valley filling
The overall aim of the proposed charging strategy is to optimize by indirectly controlling the charging behaviors of EV owners PEV(t, n) in accordance with a pricing scheme. The design process of the pricing scheme is summarized in Fig. 6. To analyze how EV owners adapt their charging behaviors to a general pricing scheme, we solve an optimization problem in Section 3.1. In Section 3.2, a specific pricing scheme with undetermined coefficients K(t) is established and the corresponding
Simulation and analysis
The proposed charging strategy aims to coordinate the autonomous charging behaviors of EV owners. To this end, it involves designing a two-dimensional pricing scheme, assuming that all EV owners minimize their electricity cost by optimizing their individual charge patterns. The main factors that likely influence the effectiveness of the proposed strategy are listed below.
- 1.
At the system level, the day-ahead non-EV load profile PnonEV(t) and number of connected EVs N may be incorrectly estimated.
- 2.
Conclusions
This study presents a decentralized valley-filling strategy that optimizes vehicle charging in a grid–EV system. In this proposed strategy, the power grid indirectly coordinates the charging behaviors of all EVs by implementing a time-power-varying pricing scheme. When the EV owners individually optimize their charge patterns in response to the pricing scheme (device-level optimization), the grid automatically achieves a valley-filling charging effect (system-level optimization).
This pricing
Acknowledgments
This research is funded by the National Natural Science of China (NSFC), contract No. 51275264, Ministry of Science and Technology (MOST) of China, Contract No. 2010DFA72760, and the Tsinghua University Initiative Scientific Research Program (Grant No. 2010THZ08116).
The authors would like to thank Enago (www.enago.cn) for the English language review.
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