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Frequency-Domain Characterization of Load Demand from Electrified Highways

Ashutossh Gupta, Vassilis Kekatos, Ruoyu Yang, Dionysios Aliprantis, Steve Pekarek

Abstract

Electrified roadways (ER) equipped with dynamic wireless power transfer (DWPT) capabilities can patently extend the driving range and reduce the battery size of electric vehicles (EVs). However, due to the spatial arrangement of the transmitter coils in the ER, the DWPT load exhibits frequency content that could excite power system frequency dynamics. In this context, this work aims to study the spectrum of DWPT loads under different traffic conditions. Under simplifying assumptions, we develop statistical models to identify the location and relative magnitude of DWPT load harmonics. Our analysis reveals that the fundamental frequency depends on ER coil spacing and average EV speed. In the worst-case yet unlikely scenario that EVs move in a synchronized fashion, the amplitude of harmonics scales with the EV count. On the contrary, when EVs move freely, harmonics scale with the square root of the EV count. Platoon formations can accentuate harmonics. The spectral content around harmonics decreases in magnitude and increases in bandwidth with the harmonic index. The load of a single EV moving at a time-varying speed can be modeled as a frequency-modulated (FM) signal. Despite the simplifying assumptions, the derived models offer valuable insights for ER planners and grid operators. Dynamic simulations of a modified WECC model with DWPT loads synthesized from realistic EV trajectories and ER specifications corroborate some of these insights.

Frequency-Domain Characterization of Load Demand from Electrified Highways

Abstract

Electrified roadways (ER) equipped with dynamic wireless power transfer (DWPT) capabilities can patently extend the driving range and reduce the battery size of electric vehicles (EVs). However, due to the spatial arrangement of the transmitter coils in the ER, the DWPT load exhibits frequency content that could excite power system frequency dynamics. In this context, this work aims to study the spectrum of DWPT loads under different traffic conditions. Under simplifying assumptions, we develop statistical models to identify the location and relative magnitude of DWPT load harmonics. Our analysis reveals that the fundamental frequency depends on ER coil spacing and average EV speed. In the worst-case yet unlikely scenario that EVs move in a synchronized fashion, the amplitude of harmonics scales with the EV count. On the contrary, when EVs move freely, harmonics scale with the square root of the EV count. Platoon formations can accentuate harmonics. The spectral content around harmonics decreases in magnitude and increases in bandwidth with the harmonic index. The load of a single EV moving at a time-varying speed can be modeled as a frequency-modulated (FM) signal. Despite the simplifying assumptions, the derived models offer valuable insights for ER planners and grid operators. Dynamic simulations of a modified WECC model with DWPT loads synthesized from realistic EV trajectories and ER specifications corroborate some of these insights.

Paper Structure

This paper contains 15 sections, 5 theorems, 58 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Time-Domain Model of DWPT Load Demand
  3. EVs Moving at Common Constant Speeds
  4. Scenario S$_1$: Perfect Time Synchronization
  5. Scenario S$_2$: Independent Uniformly Distributed Timings
  6. Scenario S$_3$: Vehicle Platoons
  7. EVs Moving at Constant but Unequal Speeds
  8. Scenario S$_4$: Constant Gaussian-Distributed Speeds
  9. Periodograms of DWPT Load Demands
  10. EVs Moving at Time-Varying Speeds
  11. Scenario S$_5$: EV Moving at Time-Varying Speed
  12. Tests Using the SUMO Simulator
  13. Effects of DWPT Loads on a Power System
  14. Conclusions
  15. Appendix

Key Result

Lemma 1

Under the assumption of a common constant EV speed, the maximum THC is realized if EVs have equal timings $\{t_n\}_{n=1}^N$, regardless of the EV densities $\{a_n\}_{n=1}^N$. Then, the maximum THC for $p(t)$ coincides with the THC of $h_T(t)$. Equal timings also maximize the harmonic ratios $|\tilde where $\delta(\omega)$ is the Dirac delta function.

Figures (13)

  • 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 of length $\ell_R$ overlaps with the Tx coils.
  • Figure 2: The INDOT ER prototype is powered by a substation that steps down grid voltage to $12.47$ kV. Each feeder is connected to a transformer-rectifier unit that converts power from AC to DC. DC power is then fed to inverters installed at the side of each Tx coil Diala19. The Tx coils are designed to operate at around $765$ V and can supply $190$ kW of power.
  • Figure 3: Top: The DWPT load $p_n(t)$ for an EV with Rx length $\ell_R = 1.8$ m moving at $v = 24.65$ m/s ($55$ mph) on the INDOT ER testbed. The blue and green load waveforms occur when the EV controller follows the multiplicative model with $a_n = \bar{a}$ and $a_n = 0.75 \bar{a}$, respectively. The red load waveform occurs when the EV controller clips the drawn power at $0.63\bar{a}$. The maximum power of the clipped DWPT load is chosen such that the DC component of the red and green waveforms is the same. Additionally, since $\ell_R >d$, the clipped DWPT load is strictly positive at all times. Bottom: The FS line spectrum of the red and green load waveform shown on the top panel ($c_0 = 0.6$ p.u.). The spectrum peaks at harmonics $mf_0$ with $f_0=5.38$ Hz. Observe that the clipped DWPT load introduces harmonics of lower amplitude compared to the load generated by the multiplicative model (see gupta2025dynamicmodelingloaddemand for more details on the comparison between different DWPT load models).
  • Figure 4: Periodograms of 1-min DWPT loads simulated under scenario S$_2$ for two values of $N$. The magnitude and location of harmonics agree with those predicted by Lemma \ref{['le:s2']}. Moreover, as asserted by Lemma \ref{['le:s2']}, the ratio of the two periodograms should be $10\log_{10}(192/64)^2 = 9.54$ dB at DC, and about $10\log_{10}\left({192}/{64}\right) = 4.77$ dB at harmonic components.
  • Figure 5: Periodograms of 1-min DWPT loads simulated under S$_2$--S$_4$ for $N=192$ EVs. Harmonics increase in power under S$_3$ due to platoons. The increase is about $10\log_{10}Q = 6.98$ dB per Lemmas \ref{['le:s2']}--\ref{['le:s3']}. The lobes under S$_4$ are centered around the harmonics of S$_2$ because $\mu_v = 55$ mph. lobes reduce in magnitude and spread in bandwidth with $m$ per Lemma \ref{['le:s4']}.
  • ...and 8 more figures

Theorems & Definitions (9)

  • Example 1
  • Remark 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Remark 2
  • Lemma 4
  • Corollary 1
  • Remark 3