A Total money to be paid for energy consumption abc−dq0 Three phase to two phase transformation amk,n nth coefficient of the kth solution set
APcp Net cost price of the energy for EV owners
APcg Total amount paid by the consumers to the grid operators during a complete day APevg Total amount paid by EV owner to grid operators during a complete day
APgev Total amount paid by the grid operators to EV owner during a complete day APloss Total financial loss to the EV owners during V2G interaction
a1−a31 Polynomial coefficients
c Total quantity of energy supplied by the grid to the EV during the peak hours
c′ Total quantity of energy supplied by the grid to the battery during the off-peak hours C Battery capacitance
Cb1Cb2 Filter capacitance of the single ac to dc converter and buck-boost converter Cdc Filter capacitance
Cm Compensation money for energy loss Me Money equivalent of the capacity lost Cr Charge rate
Crcrt Current charge rate
CrBCCS Charge/discharge rate of the individual BCCS unit Crlmt Charge rate limit
Crmin Minimum charge/discharge rate
Cruser User defined charge/discharge rate of the EVs C1,C2 Compensation capacitance
D Duration
Dn Number of days the battery takes to depreciate its value to zero Dr Discharge rate
Dcrtr Current discharge rate Dlmtr Discharge rate limit
DODcr Current depth-of-discharge DODmax Maximum depth-of-discharge D1−D14 Diodes
δ Power or load angle
δtc Difference in charging time δtd Difference in discharging time Ea activation Energy
Eavail Amount of available energy for discharging scenario
Ebn nth EV battery available or required energy to charge or discharge Eco Expected count
EGib input energy provided to the battery by the grid Eo f f−peak Total energy consumed during off-peak hour El Energy lost due to other reasons
Epeak Total energy consumed during the peak hour
Epos Possible quantity of energy available in the battery that can be sold to the grid Eq Energy lost due to the capacity loss
Erem Energy remained in the battery after vehicle transportation Er, E′r Error rate
Esup Actual quantity of energy supplied by the EV battery to the grid Estor Amount of stored energy for charging scenario
Etranspor Energy used by EV for the transportation purpose
Etrans Actual quantity of energy obtained by the grid from the EV
ET/Etotal Total energy of the EVs batteries or CS/Total processed energy of the battery
f (x) Difference between measured and calculated values of the Crand Drcharacteristics f′(x) Difference between measured and calculated values of the CL characteristics F(x) Fitness function of the charge and discharge rate characteristics
F′(x) Fitness function of the capacity loss characteristics Freq Frequency
Favg Average fitness function value fs System operating frequency gen Generation
genmax Maximum generation Iabc Three phase current Ic Charging current Id Discharging current
Ipc Primary current of the contactless coil Ire f Reference current
Isc Secondary current of the contactless coil I∗ Reference signal for battery switch I∗pre Previous reference current
k Percentage of energy loss due to capacity loss k′ Percentage of energy loss due to other reasons Lb Buck-Boost converter inductance
Lp Self inductance of the primary side coil Lr Resonant inductance
Ls Self inductance of the secondary side coil M Initial cost of purchasing the EV battery
Mdep Depreciated monetary value of the battery after a particular number of cycles n Number of cycles that the battery has interacted with the grid
n′ Maximum number of cycles that the battery can charge/discharge in its life span n′′ Daily average number of cycles of battery-grid interaction
n×m Population matrix size O1, O2 Off-string one and two
PEc Processed energy for charging scenario PEd Processed energy for discharging scenario Pc Battery power for charging scenario Pd Battery power for discharging scenario Pco Crossover probability
Pbn Distributed power to nth EV battery Pes Probability of each selected string
Pgrid Total power transfer between EVs and grid during V2G or G2V operation Pm Mutation probability
Pmea Measured power of the BCCS unit P1, P2 Parents one and two
q Total capacity loss of the battery Q Nominal battery capacity
Ql Capacity loss/fading Qr Remaining battery capacity QCl
k kth calculated value of the capacity loss characteristics QMl
k kth measured value of the capacity loss characteristics
R Gas constant
Rpeak Tariff of energy during the peak hour R′o f f−peak Tariff of energy during the off-peak hour
Rs. Monetary value is defined as per the Indian Currency RT Total resistance
R1R2 Battery internal resistance
R′, R′′ Reference output of the fuzzy logic controller
s Total quantity of energy obtained by the grid during the peak hours s′ Total quantity of energy obtained by the grid during the off-peak hours
sin cos Unit vectors
S OCcr Current state-of-charge S OCini Initial state-of-charge S OCmax Maximum state-of-charge Sn Population size
S OClt User define SOC/DOD limits S1−S14 Switches
tc Charging time td Discharging time
T Temperature
Ts Simulation Time Vabc Three phase voltage
VcCi ith calculated value of the battery terminal voltage for charging scenario VcMi ith measured value of the battery terminal voltage for charging scenario VdC
j jth calculated value of the battery terminal voltage for discharging scenario VdM
j jth measured value of the battery terminal voltage for discharging scenario Vdcmea dc measured voltage at primary side of three phase ac to dc converter Vdcre f dc reference voltage of the DC link voltage controller
Vdq0 Direct and quadrature axis voltage Vnode Node voltage
Vmax Maximum voltage Vmin Minimum voltage
Vpc Primary side contactless coil voltage Vprim Primary side voltage of the BCCS unit Vsc Secondary side contactless coil voltage V0 Open-circuit voltage
ωt Angular frequency
x Tariff paid by EV owner to grid per kWh during peak hour x′ Tariff paid by EV owner to grid per kWh during off-peak hour XT Total reactance of the system
xL1 Lower bit element of the sub-string xU1 Upper bit element of the sub-string
x1 Tariff paid by consumers to grid operators per kWh peak hour energy x′1 Tariff paid by consumers to grid operators per kWh off-peak hour energy x2 Tariff paid by grid operators to EV owner per kWh peak hour energy x′2 Tariff paid by grid operators to EV owner per kWh off-peak hour energy z Money charged by the EV owners to compensate for capacity loss.
• ac to dc converter: Converts alternating current into direct current.
• Ancillary services: The ancillary services are necessary to support the distribution system and control the flow of active power in order to maintain power quality, reliability and stability of the distribution system.
• Charge/discharge rate (Cr/Dr): A common method for indicating the discharge, as well as the charge current of a battery.
• Current depth-of-discharge (DODcr): Depth-of-discharge is another method to indicate a bat- teries state-of-charge. The depth-of-discharge is the inverse of state of charge: as one increases, the other decreases. In other words, the Depth-of-discharge is usually defined as the amount of energy removed from a battery.
• Current state-of-charge (S OCcr): The state-of-charge is related to the electric charge stored by the battery at a given time. It is defined as the ratio between the available charge at a given time and the maximum capacity.
• Cycle life: The number of charge/discharge cycles the battery can experience before it fails to meet performance criteria. Cycle life is estimated for charge and discharge conditions. The actual operating life of the battery is affected by the rate, depth of cycles and by other conditions such as temperature.
• dc to ac converter: It receives dc voltage at input side and converts ac voltage at output side.
The output voltage can controlled by varying the on and off time of the converter switch.
• dc to dc converter: Converts dc voltage to regulated dc voltage. Regulation can be achieved by controlling the duty ratio.
• Frequency regulation: The frequency regulation is required for reliable operation of the elec- tric grid. To maintain grid frequency within permissible limits, electric vehicles (EVs) batteries are used to inject/support the power from/to grid. If load exceeds the generation, the frequency of the system decrease which indicates the grid required “regulation up” and vice versa. The EVs batteries can support/inject the power to/from grid for regulation up/down for matching the generation and load demand.
• Fuzzy logic: It is derived from fuzzy set theory which can deal with uncertainties in systems.
Fuzzy logic incorporates a simple, IF-THEN rule based approach to solve a control problem rather than attempting to mathematically model a system.
• Grid-to-vehicle (G2V): The EVs’ batteries are charged from the grid during the off-peak hours.
During this operation the power flow from grid to EVs’ batteries based on node voltage and available energy of the EVs’ batteries.
• Internal resistance (R1R2): The internal resistance of battery is varying with respect to change in S OCcr/DODcrand Cr/Dr.
• Open-circuit voltage (V0): The open-circuit voltage is the voltage under a no-load condition, which is usually a close approximation to the battery terminal voltage.
• Smart grid: A smart grid is an electric network which is supply the electricity to consumers based on the digital technology. These digital systems control the electricity and improve the efficiency, reduce the energy consumption and cost.
• Terminal voltage (VcC
i or VdC
i): It is defined as the voltage measured between the battery termi- nals under load condition. The terminal voltage varies with state of charge and the charge or discharge current.
• Vehicle-to-grid (V2G): EVs’ batteries are used as a distributed energy storage system which can support the grid during peak hours or parking hours.
• Voltage regulation: To maintain system voltage within permissible limits at various points of the distribution system, reactive power compensation plays vital role. By inject/support the reactive power from/to the grid which impacts the distribution node voltage maintain within limits and also maintain system stability.