Electrification of the transportation sector can play a vital role in reshaping smart cities. With an increasing number of electric vehicles (EVs) on the road, deployment of well-planned and efficient charging infrastructure is highly desirable. Unlike level 1 and level 2 charging stations, level 3 chargers are super-fast in charging EVs. However, their installation at every possible site is not techno-economically justifiable because level 3 chargers may cause violation of critical system parameters due to their high power consumption. In this paper, we demonstrate an optimized combination of all three types of EV chargers for efficiently managing the EV load while minimizing installation cost, losses, and distribution transformer loading. Effects of photovoltaic (PV) generation are also incorporated in the analysis. Due to the uncertain nature of vehicle users, EV load is modeled as a stochastic process. Particle swarm optimization (PSO) is used to solve the constrained nonlinear stochastic problem. MATLAB and OpenDSS are used to simulate the model. The proposed idea is validated on the real distribution system of the National University of Sciences and Technology (NUST) Pakistan. Results show that an optimized combination of chargers placed at judicious locations can greatly reduce cost from $3.55 million to $1.99 million, daily losses from 787kWh to 286kWh and distribution transformer congestion from 58% to 22% when compared to scenario of optimized placement of level 3 chargers for 20% penetration level in commercial feeders. In residential feeder, these statistics are improved from $2.52 to $0.81 million, from 2167kWh to 398kWh and from 106% to 14%, respectively. It is also realized that the integration of PV improves voltage profile and reduces the negative impact of EV load. Our optimization model can work for commercial areas such as offices, university campuses, and industries as well as residential colonies. INDEX TERMS Charging stations placement, distribution system, electric vehicles (EVs), optimization. NOMENCLATURE SETS N Set of buses in the system T Set of time periods M Set of line sections O Set of types of chargers E Set of electric vehicles INDICES i Index of bus number t Index of time period j Index of line section l Index of level of charging station e Index of electric vehicle The associate editor coordinating the review of this manuscript and approving it for publication was Zhiyi Li. PARAMETERS P j,loss Power loss of jth line section C Charging power of a charger SOC init Initial state of charge of a battery c Cost of a charger c p,l Per unit electrical energy cost S j,max Maximum transfer capacity of line section j η ch Charging efficiency of EV d max Maximum range when EV is fully charged VARIABLES n Number of charging station V i,t Voltage magnitude of bus i at time interval t S j,t Power flow through line section j at time interval t dist trav,e Travelled distance by electric vehicle e
This paper presents a methodology that aims at identifying virtual inertia (VI) gain limitations from virtual synchronous generators (VSGs) while maintaining the frequency stability considering the delay associated with the frequency measurement process. The phase-locked loop (PLL) is typically used for frequency estimation that is used to calculate the rate of change of frequency (RoCoF) and it drives the VI loop. The PLL is generally accompanied by a low-pass filter that aims to suppress the impact of harmonics. This filter introduces a delay that when used with the VI control loop causes stability issues for high values of VI gain. A comparison of various PLL approaches suggests that certain variants tend to permit higher value of cut-off frequencies which can be utilized to increase the VI gain limit from VSG. This study presents a method by which the upper limit on VI gain can be quantified and related to the cut-off frequency of the PLL low pass filter that is indirectly representing the delay. It is performed using small signal frequency stability analysis on the frequency domain model of the grid with virtual inertia emulating VSG. The effective maximum VI gain from VSG is explored while satisfying the frequency measurement accuracy specification considering harmonics. The results show that the requirements of reaching a stable operation with sufficient stability margins can still be met with a faster PLL-based system and the potential increases in VI support from VSG can be quantified using the proposed method. The study has been first performed on a single machine single inverter bus (SMSIB) system and is generalized to the multi-machine and multi-inverter system.
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