Source-linked AI summary
Capacity Estimation for Vehicle-to-Grid Frequency Regulation Services with Smart Charging Mechanism
Albert Y. S. Lam, Ka-Cheong Leung, Victor O. K. Li
TL;DR
Renewable intermittency creates power-balance challenges, and dynamically arriving and departing EVs make V2G regulation capacity difficult to estimate. The paper combines a three-queue analytical model with smart charging that adapts to EV characteristics, then uses simulations to examine capacity behavior and model accuracy.
Problem
Renewable intermittency can imbalance power systems, while independently arriving and departing EVs make V2G regulation capacities difficult to estimate.
Method
The paper models an EV aggregator with queues for RD, combined RU/RD, and RU, and designs smart charging to produce analytically tractable service-time behavior.
Results
The paper reports simulated capacity behavior, including capacities that are generally below steady-state analytical values and discrepancies that grow as service rates decrease.
Takeaways & Limitations
Estimated RU and RD capacities can support regulation contracts between aggregators and grid operators.
Abstract
from arXiv · showhide
Due to various green initiatives, renewable energy will be massively incorporated into the future smart grid. However, the intermittency of the renewables may result in power imbalance, thus adversely affecting the stability of a power system. Frequency regulation may be used to maintain the power balance at all times. As electric vehicles (EVs) become popular, they may be connected to the grid to form a vehicle-to-grid (V2G) system. An aggregation of EVs can be coordinated to provide frequency regulation services. However, V2G is a dynamic system where the participating EVs come and go independently. Thus it is not easy to estimate the regulation capacities for V2G. In a preliminary study, we modeled an aggregation of EVs with a queueing network, whose structure allows us to estimate the capacities for regulation-up and regulation-down, separately. The estimated capacities from the V2G system can be used for establishing a regulation contract between an aggregator and the grid operator, and facilitating a new business model for V2G. In this paper, we extend our previous development by designing a smart charging mechanism which can adapt to given characteristics of the EVs and make the performance of the actual system follow the analytical model.
I. INTRODUCTION
Renewable intermittency complicates power balancing, while aggregated EVs can provide frequency regulation through V2G. The paper addresses capacity estimation for RU and RD services and introduces smart charging to align actual system behavior with the analytical model.
- Renewable intermittency makes accurately predicting generation difficult and can create residual gaps between generation and demand.
- Frequency regulation adjusts system frequency toward its nominal value through small positive or negative power injections.
- Because frequency regulation requires MW-scale power while each EV supplies about 10-20 kW, aggregators must coordinate groups of EVs.
- V2G supports regulation-up by supplying deficient power and regulation-down by absorbing excess power.
- Capacity payments compensate a V2G system for guaranteeing RU or RD support according to its expected supplied and absorbed power.
- The paper uses a queueing-theoretic approach to estimate RU and RD capacities and designs smart charging to adapt to EV characteristics.
II. RELATED WORK
Prior work studied V2G markets, charging coordination, queueing models, and regulation capacity, but often relied on static vehicles or exponential service times. This paper instead develops smart charging for capacity management in dynamic V2G regulation.
- Earlier V2G studies described business models and markets, noting quick response and low capital costs alongside shorter lifespans and higher operating costs per kWh.
- Existing queueing models analyzed aggregate EV charging and V2G capacity, but exponential service assumptions may require special arrangements and may be impractical.
- Prior regulation-capacity work included optimal charging, quadratic programming, probabilistic user-pattern models, and single-vehicle capacity estimates.
- The paper differs by constructing a smart charging mechanism specifically for capacity management in V2G regulation services.
- EVs are autonomous and may join or leave according to owner schedules while charging or supporting regulation during connection.
- Target SOC thresholds reflect mobility needs and reserve room for regulation, with lower and upper thresholds governing charging and RD availability.
- The three-state policy determines whether an EV supports RD only, both RU and RD, or RU only based on its SOC.
- Allowing both RU and RD uses an intermediate target threshold to balance the two services, whose aggregator capacities can be summed across aggregators.
IV. ANALYTICAL MODEL
The analytical model represents an aggregator as a three-queue network whose queue membership depends on each EV's SOC state. The network is used to estimate separate RU and RD capacities.
- The queueing network is constructed from the system settings and assumptions to estimate the aggregator's RU and RD capacities.
- The model is a queueing network with regulation-down, regulation-up-and-down, and regulation-up queues.
- An EV joins RDQ, RUDQ, or RUQ when its SOC places it in State 1, State 2, or State 3, respectively.
1) RDQ:
In RDQ, an EV is actively charged toward its upper SOC threshold, but it may leave before reaching that threshold. Reaching the threshold moves the EV onward to RUDQ.
- 1) RDQ:: An EV in RDQ is actively charged at its normalized rate until its SOC reaches the upper target threshold.
- 1) RDQ:: The RDQ service duration is determined by the charging time required to move the EV from its current SOC to the threshold.
- 1) RDQ:: An EV may depart from RDQ before reaching the threshold, representing that it quits the system.
- 1) RDQ:: After reaching the threshold, an EV leaves RDQ and joins RUDQ.
3) RUQ:
RUQ models EVs that provide regulation-up capacity while standing by without active charging. The queueing network derives steady-state EV populations and uses them to estimate RU capacity.
- RUQ contains EVs that do not actively charge and remain there until departing from the system.
- The model splits EV arrivals into three state-specific subprocesses, with RUQ receiving arrivals at rate λ3.
- RUQ is modeled as an M/M/∞ queue with combined arrival rate (λ3 + λ23) and service rate µ3.
- The expected number L3 of EVs standing by in RUQ is used in the capacity derivation.
- The steady-state RU capacity CRU is derived from the modeled queue populations and EV regulation power.
V. SMART CHARGING MECHANISM
The smart charging mechanism assigns EV service durations using arrival, departure, and state-of-charge information. It is designed to make service times approximately exponential while respecting EV availability and charging-rate constraints.
- The mechanism assigns each EV a service duration using its arrival time, expected departure time, SOC targets, and initial SOC.
- Assigned service times should statistically follow an exponential distribution, not exceed the expected stay, and produce feasible charging rates.
- These constraints allow the analytical queueing model to characterize capacity while preventing EVs from remaining longer than expected.
- A permutation lemma and corollary support reordering i.i.d. service-time samples without changing their realization properties.
- The mechanism uses variants for RDQ, RUDQ, and RUQ because the queues have different expected service times and SOC charging ranges.
1) RDQ:
For RDQ, the mechanism assigns queued exponential service-time samples to arriving EVs when they satisfy stay-duration and charging-rate requirements. Unqualified samples are retained for later assignment.
- Potential RDQ service times are generated from an exponential distribution with mean µ1.
- The earliest generated sample that fits an EV’s specifications is assigned as its service time and then removed from the sequence.
- A candidate service time must not exceed the EV’s expected stay duration.
- For an EV charged to its target SOC, the required charging rate is computed from the required energy divided by the assigned service time.
- If no queued sample qualifies, the mechanism generates additional exponential samples and stores unqualified ones in Ψ1.
2) RUDQ:
RUDQ uses the same basic smart-charging design as RDQ but adapts the service-time distribution and energy calculation to EV state transitions.
- RUDQ assigns service durations that follow an exponential distribution with mean µ2 as much as possible.
- EVs in RUDQ are charged to their upper SOC targets.
- The required charging energy depends on whether an EV entered RUDQ from RDQ or arrived directly.
- Unqualified random service-time values are stored in a separate queue Ψ2.
3) RUQ:
The RUQ smart-charging mechanism manipulates EV service times so they follow the exponential distribution required by the analytical model. A finite auxiliary queue guarantees this behavior asymptotically, while unknown EV input characteristics can remain unspecified.
- RUQ:: RUQ modifies EV service times rather than charging rates to generate exponentially distributed service times with mean µ3.EVs in RUQ need not be actively charged, so no charging-rate constraint is required.
- RUQ:: The mechanism stores unqualified random numbers in Ψ3 and assigns qualified service times to RUQ EVs.This queue-based procedure adapts the generated service times to the required distribution.
- RUQ:: If the Ψ1 queue remains finite, the adopted service-time sequence is exponentially distributed with mean µ1 almost surely.The theorem follows because only finitely many generated values are excluded, while permutations preserve exponentiality.
- RUQ:: The same mechanism applies to RUDQ and RUQ without requiring known distributions for initial SOCs, parking durations, or SOC thresholds.It generates exponential service times with the specified queue means despite unknown input distributions.
VI. PERFORMANCE EVALUATION
The performance study models a parking structure in which EVs arrive and depart independently under specified arrival, charging, SOC, and parking-duration assumptions. These settings determine the state probabilities and charging parameters used in simulation.
- Simulation settings: The simulated parking structure receives five EVs per minute on average according to a Poisson arrival process.Ninety percent of arriving EVs require charging, while one tenth require parking only.
- Simulation settings: Charging EVs have initial SOCs drawn from a truncated Normal distribution on [0, 1] with mean 0.5 and standard deviation 0.2.Their upper target thresholds are also sampled from truncated Normal distributions bounded by the initial SOC and 1.
- Simulation settings: Parking durations follow a truncated Normal distribution on [60, 780] minutes with mean 420 minutes and standard deviation 60 minutes.The lower SOC target is set to a uniformly sampled 0.6–0.8 fraction of the upper target.
- Simulation settings: The charging-rate range is set to [0, 0.05], with the upper value representing fast charging, and q1 = q2 = 0.1.The resulting state probabilities are approximately p1 = 0.5, p2 = 0.4, and p3 = 0.1.
B. Results for a Reference Set of µ1, µ2, and µ3
For the reference service-time means, the analytical model predicts nearly balanced regulation-up and regulation-down capacities. Simulation reaches steady state after about 200 minutes and the smart-charging queues remain bounded, supporting the analytical behavior.
- Reference results: CRD = 2543.22 kW and CRU = 2557.19 kW for PEV = 6 kW and ∆treg = 1 min.Each EV absorbs or delivers 0.1 kWh per regulation service under these settings.
- Simulation validation: After about 200 minutes, queue populations oscillate around their computed expected steady-state values.The simulation begins empty and then approaches the analytical population levels.
- Simulation validation: The smart-charging auxiliary queues do not grow continuously; Ψ1 and Ψ3 periodically empty, while Ψ2 stabilizes around 15.This bounded behavior supports the theorem-based claim that the actual system follows the analytical results in the long run.
C. Effects of Different Values of µ1, µ2, and µ3
Changing the service-time means changes regulation capacities according to which queue contributes to each capacity. Larger capacities come with larger analytical–simulation discrepancies, creating a capacity–accuracy tradeoff for parameter selection.
- Parameter effects: Increasing 1/µ1 raises RD capacity but leaves RU capacity unchanged because µ1 affects only RDQ.The corresponding error trend follows the same direction.
- Parameter effects: Increasing 1/µ2 raises both RU and RD capacities because both capacities involve RUDQ.The associated discrepancy also increases with 1/µ2.
- Parameter effects: Increasing 1/µ3 raises RU capacity while RD capacity remains insensitive because only RU capacity depends on RUQ.The error trend follows the same pattern.
- Capacity–accuracy tradeoff: Simulated capacities are always smaller than analytical capacities on average, and discrepancies grow with 1/µ1, 1/µ2, and 1/µ3.Errors arise from transient behavior and growth of the smart-charging auxiliary queues.
- Capacity–accuracy tradeoff: Larger capacities require tolerating larger errors, so µ1, µ2, and µ3 should be selected according to desired capacity and accuracy.For changing EV characteristics, different parameter combinations can be assigned to time periods identified from historical data.