Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs for charging the vehicles should be minimized w.r.t. time-dependent electricity costs. A particular challenge investigated in this work is that the maximum power at which a vehicle can be charged is dependent on the current state of charge (SOC) of the vehicle. Such a consideration is particularly relevant in the case of fast charging. Considering this aspect for a discretized time horizon is not trivial, as the maximum charging power of an EV may also change in between time steps. To deal with this issue, we instead consider the energy by which an EV can be charged within a time step. For this purpose, we show how to derive the maximum charging energy in an exact as well as an approximate way. Moreover, we propose two methods for solving the scheduling problem. The first is a cutting plane method utilizing a convex hull of the, in general, nonconcave SOC–power curves. The second method is based on a piecewise linearization of the SOC–energy curve and is effectively solved by branch-and-cut. The proposed approaches are evaluated on benchmark instances, which are partly based on real-world data. To deal with EVs arriving at different times as well as charging costs changing over time, a model-based predictive control strategy is usually applied in such cases. Hence, we also experimentally evaluate the performance of our approaches for such a strategy. The results show that optimally solving problems with general piecewise linear maximum power functions requires high computation times. However, problems with concave, piecewise linear maximum charging power functions can efficiently be dealt with by means of linear programming. Approximating an EV’s maximum charging power with a concave function may result in practically infeasible solutions, due to vehicles potentially not reaching their specified target SOC. However, our results show that this error is negligible in practice.

Two-Stage Multi-Period Coordinated Load Restoration Strategy for Distribution Network Based on Intelligent Route Recommendation of Electric Vehicles

To cope with the frequent blackouts in recent years and improve the resilience of the distribution network, a two-stage multi-period coordinated load restoration strategy for the distribution network based on intelligent route recommendation of electric vehicles (EVs) is proposed. The first stage of the model aims at maximizing the weighted power supply time of load, minimizing the total network loss, optimizing the output of each power supply source at each time period, and determining the optimal charging station assignment scheme for schedulable EVs. The second stage is based on the optimal charging station assignment scheme for EV determined in the first stage, with the shortest total time for all EVs to reach the designated charging stations as the objective and determining the optimal travel route of each EV. The model dispatches the idle EVs during blackout as a flexible power supply resource, realizing the multi-period coordination output of multiple sources and recommending the routes for EVs to reach the designated charging stations to optimize the restoration effect of critical loads. The methods of piecewise linearization, second-order conic relaxation (SOCR) and the Dijkstra algorithm are applied to ensure the feasibility and accuracy of the model. Finally, by comparing the proposed strategy with two different single-stage strategies, the effect of these three strategies on the critical load’s restoration and the operation status of the distribution network is further analyzed, which verifies the effectiveness and superiority of the proposed strategy.

Day-Ahead and Intra-Day Collaborative Optimized Operation among Multiple Energy Stations

An integrated energy system (IES) shows great potential in reducing the terminal energy supply cost and improving energy efficiency, but the operation scheduling of an IES, especially integrated with inter-connected multiple energy stations, is rather complex since it is affected by various factors. Toward a comprehensive operation scheduling of multiple energy stations, in this paper, a day-ahead and intra-day collaborative operation model is proposed. The targeted IES consists of electricity, gas, and thermal systems. First, the energy flow and equipment composition of the IES are analyzed, and a detailed operation model of combined equipment and networks is established. Then, with the objective of minimizing the total expected operation cost, a robust optimization of day-ahead and intra-day scheduling for energy stations is constructed subject to equipment operation constraints, network constraints, and so on. The day-ahead operation provides start-up and shut-down scheduling of units, and in the operating day, the intra-day rolling operation optimizes the power output of equipment and demand response with newly evolved forecasting information. The photovoltaic (PV) uncertainty and electric load demand response are also incorporated into the optimization model. Eventually, with the piecewise linearization method, the formulated optimization model is converted to a mixed-integer linear programming model, which can be solved using off-the-shelf solvers. A case study on an IES with five energy stations verifies the effectiveness of the proposed day-ahead and intra-day collaborative robust operation strategy.

A High Efficiency Linear Power Supply with Pure Sine Wave for High Voltage Test

The input part of the high-voltage test power supply is usually composed of switching devices; however, the pulse-type periodic interference caused by the switching devices makes the monitoring of the test power supply partial discharge more difficult. Therefore, this paper proposes a high-efficiency and distortion-free linear power supply based on piecewise-linearization with all N-type transistor. Under the same DC input, multiple power transistors are connected to different taps of the same transformer. By controlling the period of linear conduction of each power transistor in turn, we ensure that the power transistor works on the linear side (biased towards saturation) to reduce its conduction voltage drop and the output realizes sinusoidal piecewise linearization, so that the converter can greatly improve the system efficiency. After that, from the perspective of the lowest sum of the transistor loss, an optimization method for the design of the multi-winding transformer ratio at each stage is proposed. Finally, a power supply prototype based on four-piece linear converter with an output voltage of 220 V was built. The experimental efficiency reaches 87.03%, and, additionally, if the linear amplification is divided into more sections, the efficiency can be further improved.

AN ITERATIVE ALGORITHM FOR NONLINEAR FRACTIONAL-ORDER OSCILLATORS WITH MODIFIED RIEMANN-LIOUVILLE DERIVATIVE

This paper presents an iterative analytic algorithm for the approximate solution of nonlinear fractional-order oscillators. He fractional transform was applied to convert the fractional-order model, defined by a modified Riemann-Liouville derivative, to a model in continuous spacetime. Then, the approximate solution of the continuous model was applied to obtain an approximate solution for the fractional-order oscillator. The solution was obtained using the continuous piecewise linearization method (CPLM), which is a simple, accurate and efficient analytic algorithm. The applicability of the CPLM was demonstrated using representative examples in science and engineering and the maximum relative error of the approximate solution was found to be less than 0.2%. This paper provides an analytical tool that can be applied in the study of fractional-order oscillations arising in various physical systems and technological processes.