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Electric vehicle state of charge management considering voltage profile and owners’ profit improvement using linear programing approach

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Abstract

Due to the high penetration of electric vehicles (EVs) to the power grid in recent years, the electricity operators have been encouraged to use the advantages of this new equipment in the peak flattening, voltage profile improvement, reactive power control and fast frequency regulation. Electric vehicles are introduced as an appropriate alternative to small-scale power plants through distributed profits for owners. Since the electric vehicles which are connected to the grids at large-scale, they confer a number of challenges and benefits, while the operation scheduling of traditional distribution networks in their presence will be more complicated. Truthfully, the electric vehicles could be recognized as a demand supplier for a part of the network, however, the intelligent battery charging control should be carefully achieved to keep the network appropriately balanced in power procurement. In this paper, an applicable framework for charging/discharging control of EVs is provided that not only maintains the large scale of vehicles connecting to the grid, but also can improve the voltage profile of buses in each section of the power system. The proposed formulations describe the principles of electric vehicles operation and the state of charge (SOC) control regarding to the owners’ profit optimization.

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Abbreviations

\(D_{l,i}\) :

Power transfer factor transmission line \(l\) located at node \(i\)

\(E_{i,t}\) :

Charging energy of EVs’ limitation within time horizon \(t\) at node \(i\)

\(K_{i}\) :

Total capacity of transmission line \(l\)

\(N\) :

Number of total nodes

\(N_{c}\) :

Numbers of total load nodes

\(N_{n}\) :

Numbers of total non-loading nodes

\(P_{{{\text{DLMP}},i,t}}\) :

Marginal price within time horizon \(t\) at node \(i\) of the power network

\(P_{i,t} \left( {\tau_{i} ,t} \right)\) :

Earnings from demand \(\tau_{i}\) utilization within time period \(t\) at node \(i\)

\(P_{{{\text{LMP}},t}}\) :

Marginal price within time horizon \(t\)

\(S_{i,o}\) :

Initial state of charge of PEV battery at node \(i\)

\(S_{i,o}^{ - }\) :

Minimum state of charge at node \(i\) of PEV battery

\(S_{i,o}^{ + }\) :

Maximum state of charge at node \(i\) of PEV battery

\(T\) :

Entire time horizon

\(c_{i,t}\) :

Existing residential demand within time horizon \(t\) at node \(i\)

\(g\) :

Numbers of total generation nodes

\(p_{t}\) :

Auxiliary variable for active power optimization

\(q_{g,t}\) :

Power generated in electricity network within time horizon \(t\) at node \(g\)

\(r_{g,t}\) :

Total generated active power exchanged

\(r_{i,t}\) :

Total demand power exchanged

\(x_{i,t}\) :

Energy stored in PEV battery

\(d_{{i,t^{^{\prime}} }}\) :

EV internal demand

\(k_{i,t}^{ - }\) :

Auxiliary variable for minimum SOC optimization

\(k_{i,t}^{ + }\) :

Auxiliary variable for maximum SOC optimization

\(\lambda_{l,t}^{ - }\) :

Auxiliary variable for minimum line flow

\(\lambda_{l,t}^{ + }\) :

Auxiliary variable for maximum line flow

\(\mu_{i,t}^{ - }\) :

Auxiliary variable for minimum rate of charging

\(\mu_{i,t}^{ + }\) :

Auxiliary variable for maximum rate of charging

\(\xi_{i,t}\) :

Auxiliary variable for residential demand power flow

\(\rho_{i,t}\) :

Auxiliary variable for power flow balancing

\(\tau_{i,t}\) :

Instantaneous residential demand

\(\omega_{g,t}\) :

Auxiliary variable for generated active power balancing

\(\omega_{i,t}\) :

Auxiliary variable for demand power balancing

ECm :

Charging injected to battery in time slot m

\({\text{SOC}}_{m}^{f}\) :

Final SOC in time slot m while charging/discharging

\({\text{SOC}}_{m}^{f}\) :

Initial SOC in time slot m while charging/discharging

\(\underline{{V_{{{\text{bat}},m}} }}\) :

Minimum limitation of battery voltage

\(\overline{{V_{{{\text{bat}},m}} }}\) :

Maximum limitation of battery voltage

\(w_{m,t}\) :

The active power produced by the battery through power electronics inverter in time slot m

\(y_{m,t}\) :

The reactive power produced by the battery through power electronics inverter in time slot m

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Authors and Affiliations

  1. Department of Electrical Engineering, Yazd Branch, Islamic Azad University, Yazd, Iran

    Ali Masoudi, Hamidreza Akbari, Seyed Amin Saeed & Tahereh Daemi

  2. Department of Electrical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran

    Mohsen Simab

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  1. Ali Masoudi
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  2. Mohsen Simab
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  3. Hamidreza Akbari
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  4. Seyed Amin Saeed
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  5. Tahereh Daemi
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Correspondence to Mohsen Simab or Hamidreza Akbari.

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Masoudi, A., Simab, M., Akbari, H. et al. Electric vehicle state of charge management considering voltage profile and owners’ profit improvement using linear programing approach. Electr Eng 104, 1179–1191 (2022). https://doi.org/10.1007/s00202-021-01381-8

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