Coordinated Charging and Discharging Strategies for Plug-in Electric Bus Fast Charging Station with Energy Storage System

Plug-in electric bus (PEB) is an environmentally friendly mode of public transportation and plug-in electric bus fast charging stations (PEBFCSs) play an essential role in the operation of PEBs. Under effective control, deploying an energy storage system (ESS) within a PEBFCS can reduce the peak charging loads and the electricity purchase costs. To deal with the (integrated) scheduling problem of (PEBs charging and) ESS charging and discharging, in this study, we propose an optimal real-time coordinated charging and discharging strategy for a PEBFCS with ESS to achieve maximum economic benefits. According to whether the PEB charging loads are controllable, the corresponding mathematical models are respectively established under two scenarios, i.e., coordinated PEB charging scenario and uncoordinated PEB charging scenario. The price and lifespan of ESS, the capacity charge of PEBFCS and the electricity price arbitrage are considered in the models. Further, under the coordinated PEB charging scenario, a heuristics-based method is developed to get the approximately optimal strategy with computation efficiency dramatically enhanced. Finally, we validate the effectiveness of the proposed strategies, interpret the effect of ESS prices on the usage of ESS, and provide the sensitivity analysis of ESS capacity through the case studies. 1. Nomenclature Indices and Sets n Index of PEB. m Index of fast charging port. k Index of time interval in the following optimising time horizon. , n n i j Index of parking of PEB n in the following optimising time horizon. c / d Subscript of charging/discharging. N Index set of PEBs. M Index set of fast charging ports. K Index set of time intervals in the following optimising time horizon. ( ) n P i Index set of time intervals during parking n i of PEB n . ( ) I n Index set of parking of PEB n in the following optimising time horizon. ( ( )) P I n Index set of time intervals in the following optimising time horizon when PEB n is expected to be parking. card( ) X The number of elements in set X . Parameters and Variables PEB n S Battery capacity of PEB n (kWh). ESS S Energy capacity of ESS (kWh). PEB c P Rated charging power of PEBs (kW). peak P Peak load of PEBFCS (kW). ESS c,max P Maximum charging power of ESS (kW). ESS d,max P Maximum discharging power of ESS (kW). PEB c  Charging efficiency of PEBs. ESS c  Charging efficiency of ESS. ESS d  Discharging efficiency of ESS. PEB min SOC Minimum state of charger (SOC) for PEB batteries. ESS min SOC Minimum SOC for ESS. PEB , n n i SOC SOC of n i th arrival of PEB n . ESS k SOC SOC of ESS at the beginning of time interval k . PEB , n n i SOC  SOC difference of PEB n between n i th departure and the next return. , n n i a Time interval of n i th expected return of PEB n ( , n n i a K  ). , n n i l Time interval of n i th expected departure of PEB n ( , n n i l K  ). k L Power of other loads excluding PEB charging loads in time interval k (kW). t  Duration of a time interval (min). TOU k  Electricity price in time interval k (RMB/kWh). ESS  Price of ESS (RMB/kWh). Cap  Capacity charge of PEBFCS (RMB/kW). ESS n The number of charge-discharge cycle of ESS.  Discount rate of the capacity charge (%).  Life cycle of PEBFCS (year). PEB C Charging state matrix of PEBs (dimensions: card( ) card( ) N K  ). FCP C Charging state matrix of fast charging ports (dimensions: card( ) card( ) M K  ). ESS c P Vector of charging power of ESS (dimensions: 1 card( ) K  ). ESS d P Vector of discharging power of ESS (dimensions: 1 card( ) K  ). PEB , n k c Element of PEB C , binary variable, 1: on