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Charging Coordination of Plug-In Electric Vehicle for Congestion Management in Distribution System

  • Subhasish Deb , Pratik Harsh , Jajna Prasad Sahoo und Arup Kumar Goswami EMAIL logo
Veröffentlicht/Copyright: 21. August 2018

Abstract

In modern electricity market, high penetration of Plug-In Electric Vehicle (PEV) creates a huge burden on distribution system operator (DSO). This high penetration creates a gap between demand-supply which further leads to the congestion in distribution lines. Power flow in a grid connected PEV is bidirectional i. e. it can work either in Grid to Vehicle (G2V) or Vehicle to grid (V2G) mode depending upon the grid constraints and owners demand. This paper proposes a charging coordination strategy of PEVs to alleviate congestion in distribution lines. Firstly, Active Power Flow Sensitivity Factors (PFSFs) are calculated to predict the branch flows or congestion status due to the uncoordinated charging of PEVs. Secondly, a coordination strategy of PEVs charging-discharging is made using different heuristic based algorithms in order to mitigate congestion in radial distribution system. The result of proposed work also shows the reduction in total active power loss while maintaining the electricity grid constraints. The present work is simulated and analyzed on IEEE 10 bus radial distribution system integrated with residential systems. Several case studies are analyzed to demonstrate the heftiness of the proposed work.

Nomenclature

X

Total cost of charging during G2V mode of operation ($/Day)

Y

Total revenue generated during V2G mode of operation ($/Day)

T

Total time interval in a day

∆t

1 hour time interval

V

Total number of vehicles (V1+ V2) available at time interval ∆t

V1

Total number of vehicles in G2V mode of operation at time interval ∆t

V2

Total number of vehicles in V2G mode of operation at time interval ∆t

μc

Cost per kWh duringG2V mode ($/kWh)

μd

Cost per kWh during V2G Mode($/kWh)

Pi

Power exchanged between ith vehicle and grid at time interval ∆t (kW)

Ptbattery

maximum acceptable power exchange between grid and PEV at time interval ∆t (kW)

SOC

Vehicle State of Charge (in % of battery capacity)

SOCmin and SOCmax

Minimum and maximum value of vehicle state of charge

SOCcurrent

Current status of vehicle state of charge

SOCmean

The mean value of state of charge derived from SOC curve

Bcapacity

Capacity of PEVs battery (in kWh)

Rcharging and Rdischarging

Resistance of battery during charging and discharging (in Ω)

Powner

Maximum power set by PEV owner (in kW)

λ

Degree by which burden on DSO and vehicle owners are reduced.

Pline

Active power flow through a line (kW)

Plinemax

Maximum active power flow through a line (kW)

Appendix A

A. Derivation of PFSF [30]

Where,

PT(i)Fand QT(i)F:Sum of active and reactive power flows through all the downstream branches connected to the receiving end of branch i respectively.
PF(i)Land QF(i)L:Total active and reactive load at sending end of branch i respectively.
PT(i)Land QT(i)L:Total active and reactive load at receiving end of branch i respectively.
PT(i)I and QT(i)I:Active and reactive power injection at the receiving end of branch i respectively.
PF(i)Iand QF(i)I:Active and reactive power injections at the sending end of branch i respectively.
VF(i) and VT(i):Magnitude of sending and receiving end voltages of branch i respectively.
NBr:Total number of branches in the distribution system
Pi and Qi:Active and Reactive power flow in branch i respectively.
Riand Xi:Resistance and reactance of branch i respectively
Gi and Bi:Conductance and susceptance of branch i respectively.

Power flow relation for the sending end of branch i, can be given as:

(26)Pi= PT(i)F+PT(i)LPT(i)I+VF(i)2Gi2+VT(i)2Gi2+(PiVF(i)2Gi2)2+(Qi+VF(i)2Bi2)2VF(i)2Ri
(27)Qi= QT(i)F+QT(i)LQT(i)IVF(i)2Bi2VT(i)2Bi2+(PiVF(i)2Gi2)2+(Qi+VF(i)2Bi2)2VF(i)2Xi

Voltage balance equation of receiving end bus is written below:

(28)VT(i)2= VF(i)22{ (}PiVF(i)2Gi2)Ri+(Qi+VF(i)2Bi2)Xi+(Ri2+Xi2)×(PiVF(i)2Gi2)2+(Qi+VF(i)2Bi2)2VF(i)2

Where,

PT(i)F=jPj and QT(i)F=jQj

j such that F(j)=T(i)

Differentiating eqs (26)–(28) with respect to PT(k)I and rearranging, we get

(29)Ri(2PiVF(i)2Gi1Ri)PiPT(k)I+Ri(2QiVF(i)2+Bi)QiPT(k)I+PT(i)FPT(k)I+VF(i)(Gi+Gi2+Bi22Ri2RiPi2+Qi2VF(i)4)VF(i)PT(k)I+VT(i)GiVT(i)PT(k)I=0,ifik
(30)Ri(2PiVF(i)2Gi1Ri)PiPT(k)I+Ri(2QiVF(i)2+Bi)QiPT(k)I+PT(i)FPT(k)I+VF(i)(Gi+Gi2+Bi22Ri2RiPi2+Qi2VF(i)4)VF(i)PT(k)I+VT(i)GiVT(i)PT(k)I=1,ifi=k
(31)Xi(2PiVF(i)2Gi)PiPT(k)I+Xi(2QiVF(i)2+Bi1Xi)QiPT(k)I+QT(i)FPT(k)I+VF(i)(Bi+Gi2+Bi22Xi2XiPi2+Qi2VF(i)4)VF(i)PT(k)IVT(i)BiVT(i)PT(k)I=0,
(32)VF(i)[1+RiGiXiBi+(Ri2+Xi2)×(Gi2+Bi24Pi2+Qi2VF(i)4)]VF(i)PT(k)I+[(Ri2+Xi2)(PiVF(i)2Gi2)Ri]PiPT(k)I+[(Ri2+Xi2)(QiVF(i)2+Bi2)Xi]QiPT(k)I_VT(i)VT(i)PT(k)I=0

Where,

PT(i)FPT(k)I=jPjPT(k)I

andQT(i)FPT(k)I=jQjPT(k)I

j such that F(j)=T(i)

Equations (30)–(32) are for branch i. If total system contains NBr branches, there will be 3NBr equations which can be represented in matrix form as:

(33)[C][Xk]=[ACk]

Where [C] is a [3NBr×3NBr] matrix representing coefficients of L.H.S. of eqs (30)–(32) which is further factorized using LU factorization method, [ACk] is a [3NBr×1] matrix representing R.H.S. of equations eqs (30)–(32) and [Xk] can be calculated from eq. (33) using back substitution method.

(34)[Xk]=[P1PT(k)I..............PNBrPT(k)IPFSFQ1PT(k)I..............QNBrPT(k)IV2PT(k)I..............VNBr+1PT(k)I]T

First NBr elements of Xk represents values of PFSF i. e. sensitivity of line flows in all branches with respect to injected power in bus T(i).

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Received: 2018-01-30
Revised: 2018-05-27
Accepted: 2018-07-15
Published Online: 2018-08-21

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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