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Dynamic Modeling of Load Demand in Electrified Highways Based on the EV Composition

Ashutossh Gupta, Vassilis Kekatos, Dionysios Aliprantis, Steve Pekarek

TL;DR

This work addresses the dynamic DWPT load on electrified highways, where periodic Tx coil placement and vehicle motion generate oscillatory substation currents with harmonic structure. It combines a nonlinear time-domain DWPT load model for a single EV with a Fourier-series analysis to obtain closed-form harmonic expressions, and extends to a stochastic total-load model across many EVs moving at potentially different speeds. A composition-aware framework shows that longer Rx coils reduce individual harmonic content, but EV class distribution can non-monotonically affect the total spectrum, a finding validated by SUMO traffic simulations on INDOT-like ERs. The results offer actionable insights for ER design and grid operations, including potential smoothing strategies using energy storage and careful consideration of vehicle mix and speeds to mitigate oscillatory grid effects.

Abstract

Electrified roadways (ERs) equipped with the dynamic wireless power transfer (DWPT) technology can achieve longer driving range and reduce on-board battery requirements for electric vehicles (EVs). Due to the spatial arrangement of transmitter (Tx) coils embedded into the ER pavement, the power drawn by the EV's receiver (Rx) coil is oscillatory in nature. Therefore, understanding the dynamic behavior of the total DWPT load is important for power system dynamic studies. To this end, we model the load of individual EVs in the time and frequency domains for constant EV speed. We establish that a nonlinear control scheme implemented in existing DWPT-enabled EVs exhibits milder frequency harmonics compared to its linear alternative. According to this model, the harmonics of an EV load decrease in amplitude with the Rx coil length. We further propose and analyze stochastic models for the total DWPT load served by an ER segment. Our models explain how the EV composition on the ER affects its frequency spectrum. Interestingly, we show that serving more EVs with longer Rx coils (trucks) does not necessarily entail milder harmonics. Our analytical findings are corroborated using realistic flows from a traffic simulator and offer valuable insights to grid operators and ER designers.

Dynamic Modeling of Load Demand in Electrified Highways Based on the EV Composition

TL;DR

This work addresses the dynamic DWPT load on electrified highways, where periodic Tx coil placement and vehicle motion generate oscillatory substation currents with harmonic structure. It combines a nonlinear time-domain DWPT load model for a single EV with a Fourier-series analysis to obtain closed-form harmonic expressions, and extends to a stochastic total-load model across many EVs moving at potentially different speeds. A composition-aware framework shows that longer Rx coils reduce individual harmonic content, but EV class distribution can non-monotonically affect the total spectrum, a finding validated by SUMO traffic simulations on INDOT-like ERs. The results offer actionable insights for ER design and grid operations, including potential smoothing strategies using energy storage and careful consideration of vehicle mix and speeds to mitigate oscillatory grid effects.

Abstract

Electrified roadways (ERs) equipped with the dynamic wireless power transfer (DWPT) technology can achieve longer driving range and reduce on-board battery requirements for electric vehicles (EVs). Due to the spatial arrangement of transmitter (Tx) coils embedded into the ER pavement, the power drawn by the EV's receiver (Rx) coil is oscillatory in nature. Therefore, understanding the dynamic behavior of the total DWPT load is important for power system dynamic studies. To this end, we model the load of individual EVs in the time and frequency domains for constant EV speed. We establish that a nonlinear control scheme implemented in existing DWPT-enabled EVs exhibits milder frequency harmonics compared to its linear alternative. According to this model, the harmonics of an EV load decrease in amplitude with the Rx coil length. We further propose and analyze stochastic models for the total DWPT load served by an ER segment. Our models explain how the EV composition on the ER affects its frequency spectrum. Interestingly, we show that serving more EVs with longer Rx coils (trucks) does not necessarily entail milder harmonics. Our analytical findings are corroborated using realistic flows from a traffic simulator and offer valuable insights to grid operators and ER designers.

Paper Structure

This paper contains 6 sections, 3 theorems, 31 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Time-Domain Modeling of a Single DWPT Load
  3. Frequency Spectrum of Single DWPT Load
  4. Frequency-Domain Model of Total DWPT Load
  5. Effect of EV Composition on DWPT Spectrum
  6. Numerical Tests and Conclusions

Key Result

Lemma 1

If $\ell_T > D/2$, the clipping control scheme of eq:power(x) attains a smaller harmonic ratio $c_{1,n}/c_{0,n}$ than the scaling control scheme of eq:scaling for all $(p_n^d,\ell_n)$.

Figures (3)

  • Figure 1: In a DWPT-enabled ER, transmitters Tx of length $\ell_T$ and gaps of length $d$ are arranged periodically, every $D = \ell_T + d$ meters. An EV draws power when its Rx overlaps with Tx coils. Because of their higher power requirements, trucks have longer Rx lengths than sedans ($\ell_2 > \ell_1$).
  • Figure 2: The blue curve depicts the maximum DWPT load $\bar{p}_n(x_n)$ as a function of EV position $x_n$. The orange curve depicts the clipped load $\hat{p}_n(x_n)$ for peak power demand $p_n^d \in(\alpha (\ell_n-d), \alpha \ell_n ]$. The green curve depicts $\bar{p}_n(x_n)$ scaled by a factor of $a_n\in[0,1]$; see gupta2025frequency.
  • Figure 3: Numerically computed PSD of $1$-min DWPT loads. We observe two sets of harmonics of $4.74~$Hz (red) and $6.34$ Hz (blue).

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Lemma 2
  • Corollary 1