Research on economic dispatching strategy of electric vehicles participating in frequency regulation ancillary service

Electric vehicles (EVs) are demand-side resources capable of rapid power adjustments. When clustered as aggregators in frequency regulation (FR) services, EVs have the advantages of low deployment cost and fast response speed. This passage studies description of uncertain scenarios when aggregators participate in FR services. With a focus on the optimization of charging and frequency reserve capacity for aggregators participating in FR, a conversion method from FR signal sequence to FR demand is proposed based on historical data of FR signals. The intent is to address the uncertainty of both system FR and load electricity consumption. This passage provides an uncertain characterization of FR demand, which performs as a key indicator of proposed economic dispatching strategy. The result shows how different levels of risk appetite affects the real-time responsiveness, thus mentoring the strategic decision of how much reserve capacity should be provided for FR.


1.
Introduction The core challenge of reserve capacity optimization is to balance risks and benefits: the more reserve capacity provided by aggregators, the higher the capacity benefits, yet this might lead to an inability to meet the assessment of real-time FR response of the system, thus reducing the overall benefits and even incurring penalties.The indexes of the system to assess the FR response performance of the aggregator can be roughly classified into two aspects [1]: physical performance and FR trajectory: physical performance indexes such as adjustment rate and response time can be obtained by the system after testing the aggregator, independent of reserve capacity [2]; The FR trajectory is to examine whether the aggregator can correctly respond to the real-time FR power [3].If the reserve capacity is high, the aggregator may temporarily lose its response ability, thus reducing this part of the assessment index.Considering that EVs are energy users and generally do not have a large amount of energy reserve [3], they may not meet the FR demand or the energy storage demand of users [4]if the FR signal of the system forces the aggregator to continuously regulate the power up or down in a standby period.Such regulation could lead to a large change in the power consumption in this period (the battery is overcharged or not charged with enough power), and gets close to the feasible region boundary composed of energy storage demand and physical characteristics.As a consequence, the uncertainty of FR signal in continuous time section (that is, the characteristics of a whole time series) also needs to be studied, and then combined with the power reserve of EVs aggregators, the FR response ability of aggregator is analyzed.For example, a prior work [5] has initially addressed the issue of electricity offset after participating in FR, incorporating risk into charging/standby joint optimization based on historical data.Reference [6] introduces the consideration of power offset into the user demand, so as to maximize the interests of all Parties in considering the interplay between aggregators and users.
So, this passage will focus on the energy storage demand of real-time FR, offer a characterization method of real-time FR demand from the day-ahead perspective, verify effectiveness of the proposed characterization method in capacity optimization by real-time simulation examples, and compare the performance indexes of response results under different capacities.This thus establishes a theoretical foundation for the economic viability of electric vehicle participation in FR.

FR participation mechanism in ancillary services market
The ancillary services market generally operates as a part of the spot market [7].Flexible resources providing FR ancillary services offer their own adjustable reserve capacity to the system as a commodity.The physical meaning of the reserve capacity is that the flexible resources will adjust their own power in response to the needs of the system in a specific period of time, and the amplitude of power adjustment will not exceed the capacity.In the real-time stage, the dispatching mechanism will send the FR instruction to each flexible resource according to the real-time power deviation of the power system, and the flexible resource will adjust the active power output or input in response to the instruction, so as to restore the system frequency.To effectively schedule flexible resources, the system needs to know in advance the power consumed or emitted by each resource in this period as the baseline of power adjustment [8].The baseline is reported to the dispatching organization by each resource before the capacity is cleared, and then released by the dispatching organization after comprehensively considering the load and power generation forecast; Alternatively, the energy market and ancillary service market are jointly cleared, and the cleared energy is used as the power baseline of flexible resources.
As a consequence, the scheduling of FR service in the system is divided into two stages: first, in the market clearing stage, the power baseline and reserve capacity of each participant should be determined as the benchmark and constraint of FR instruction allocation in real-time scheduling; Then, in the realtime phase, the system sends a real-time FR instruction to each participant, and the participant tracks the instruction to increase or decrease its own power.

3.
Real-time FR scene description for reserve capacity optimization First of all, equation (1) shows the FR power that an FR resource needs to respond to at time t in realtime operation.Since Rup and Rdown have been cleared in advance, the FR signal δt (δt∈[-1,1]) can be used as the coefficient of reserve capacity to obtain the corresponding FR power PIR,t: Where, i represents the ith period of the day, Ti represents the set of time t at which the FR signal δt is received, Rup,i and Rdown,i represent the reserve capacity invoked for that period.
Subject to physical constraints, the power is an important factor that restricts the performance of FR of aggregators.When the FR instruction requires continuously adjustment of the charging power to reach the power boundary, aggregators may be unable to further adjust the power, thus greatly reducing the response performance.In the reserve capacity optimization stage, the aggregator obviously can't accurately predict the future FR instructions, and can't simulate the real-time scheduling of each reserve capacity reporting scheme to obtain its FR performance.However, it can analyze the energy storage demand of the FR aggregators when reporting different reserve capacities by leveraging the historical data of FR signal δt, so as to assess the probability of the risk of insufficient FR power.
The FR signal δt is a dimensionless quantity with a value of [-1, 1].It represents proportion of each FR instruction to the reserve capacity in this period, so as to provide a reference for the capacity optimization of FR resources and enable an estimate for FR response when reporting to a specific reserve.Assuming that the reserve capacity reported by the aggregator is Rup,i and Rdown,i, a historical FR signal is taken to form an FR instruction PIR,t, and the maximum energy storage demand in this period can be estimated by the following formula: Where, Sd_up,i and Sd_down,i respectively represent the maximum power quantity that aggregators increase or decrease according to FR instruction in this period, and n represents the number of FR signals contained in a period.By studying the probability distribution of Sd_up,i and Sd_down,i, the probability of power shortage in this period is shown when the reserve capacity of aggregators is Rup, i and Sd_down,i.
It is obvious that the essence of FR energy storage demand is the accumulation of FR instruction time series, and the energy storage demand in a period is the maximum value of FR instruction accumulation in this period.Based on the historical data of FR signals, we can analyze the energy storage demand of FR instructions in a period of time under different standby capacities.The specific method is that with given Rup,i and Rdown,i, the corresponding FR instruction data is provided based on the historical data and the FR signal δt, the FR instruction scene set is obtained by taking the FR instruction sequence of a single period as a scene, and the Sd_up,i and Sd_down,i of each scene are calculated based equation ( 2) to show the probability distribution.The FR signals are sampled from the signals for the whole year of 2020 by PJM website [9], and the time interval is 2 seconds.For generality, the above/lower reserve capacity is reported as examples, with reserve periods of 15 minutes and 60 minutes, respectively.Figure . 1 shows the energy storage demand for different standby duration.

Example verification
In this section, we will present an example based on the FR requirement characterization method given in Section 3.Under the specific power/electricity constraints of EVs aggregators, considering the risk that FR demand exceeds the flexibility of aggregators themselves, real-time FR response simulation is carried out based on capacity reporting under different risk constraints.By comparing the resulting FR response outcomes, we aim to verify the effectiveness of FR requirement characterization, which serves as the basis of subsequent research.Notably, this example does not involve uncertainties such as market price and winning capacity, but only compares the response performance when responding to FR instructions with different capacities under limited power consumption.
According to the market mechanism described above, the aggregators will first report the upward and downward reserve capacities Rup,i and Rdown,i in the next period, and respond to the FR instructionS in this period according to this reserve capacity.At time t, when the charging and discharging power of aggregators is PEV,t and the electric quantity is St, the physical constraints of aggregator include power constraint and electric quantity constraint in the charging process.
Theoretically, the reserve capacity that aggregators can report is also physically limited: up, max down, max 0 Considering the charge and discharge efficiency ε of EV battery (power exchange between battery and power grid will lose (1-ε) times of power), the FR powerPRR,t actually responded by aggregator at time t is: Based on the probability distribution of FR energy storage demand described in Section 3, the aggregator can make the upward and downward reserve capacity as large as possible with the chance constraint condition of "the probability of making the FR energy storage demand is not higher than the available energy is β".The aggregator requires solving two optimization problems: Where, P (.) refers to the probability of events in brackets, Sa_up,i and S a_down,i is the amount of energy storage that the aggregator can increase or decrease at this time, respectively.Since Sd_up,i and Sd_down,i are all calculated by Rup,i and Rdown,i, the chance constraint is coupled with both optimization problems at the same time, but the FR energy storage demand in either direction increases accordingly with the increase of reserve capacity reported so the optimization process of reserve capacity can be simplified as follows: 1) Acquiring adjustable energy storage Sa_up,i and S a_down,i; 2) Alternately increasing Rup,i and Rdown,i; 3) Calculating the probability distributions of Sd_up,i and Sd_down,i according to equation ( 16) for each set of values obtained; 4) Comparing the probability distribution with Sa_up,i and Sa_down,i, judging whether "the probability of making the FR energy storage demand not higher than the available energy is β" is met, if it is met, returning to step 2), and if not, the optimization is finished, and the values of Rup,i and Rdown,i are the maximum values that make the condition meet.
For the EVs aggregators in this example, in a certain period of time, the initial energy level is 100 kWh, the total maximum energy capacity is 800 kWh, the maximum charging power is Pmax,i=1,000 kW, the minimum charging energy is 200 kWh, the planned charging power Pch,i is 450 kW, and the charging demand is Pmin,i=200 kW, then the aggregator can increase the power by 550 kW and decrease the power by 250 kW.The regulable energy storage Sa_up,i=Sa_down,i=250 kWh.The aggregator will adopt the chance constraint optimization model of formula (6) to obtain the reserve capacity in this period and respond to FR.In this section, various probability β of power limits will be selected as risk constraints, and the FR signal is sourced from the annual historical data of PJM for 8,760 hours, with one hour in each period and 8,760 runs.
First, the charging situation in this period is investigated.In this scenario, compared with the charging requirement of 200 kWh, the aggregator can charge 500 kWh more electricity, and 250 kWh more electricity if it does not participate in FR. Figure .2 compares the storage relative to the charging demand at the end of this period under different probability constraints.a) and b) show the frequency histograms of storage at the end of each period in the simulation results when β is 0.6 and 0.95, respectively.The distribution trend is consistent: there are more scenes with storage of 250 kWh, which gradually decrease when shifting to both sides with 250 kWh as the center, but the scenes without storage or fully charged will suddenly increase, which is obviously due to the fact that the aggregator has no storage to respond to the FR demand for a period of time before the end of many periods, leading to a sustained state until the end of the period.In addition, when β is 0.6, the distribution is relatively "flat", which shows that the energy is more prone to shift under the loose probability constraint of energy exceeding the limit.The results also confirm the effect of probability constraint: the greater the probability of exceeding the limit of energy, the lower the accuracy achieved, but the more capacity that can be reported.Therefore, economically speaking, the more positive the reported capacity, the higher the capacity benefit, but it will also reduce the FR performance index, thus reducing the compensation coefficient corresponding to the performance.As a consequence, when aggregators participate in the optimization of FR ancillary services, they need to evaluate the overall compensation under the market environment, so as to weigh the benefits and risks and achieve the maximization of benefits.

Conclusion
This passage establishes a characterization method of real-time FR demand from the flexibility perspective for aggregator, based on the settlement mechanism of the FR ancillary services market.A real-time response example is provided to verify the effectiveness of the FR requirement characterization method, and the real-time response results of several key performance indicators investigated by the FR compensation mechanism under different risk preferences are quantitatively analyzed.Simulation results show that FR participation will cause the shift of total power consumption of FR resources over a period of time, so EVs aggregators with limited energy reserves need to focus on this risk in capacity optimization.

Figure. 1
Figure. 1 Energy Storage Demand for Upward and Downward Regulation.

Figure. 2
Figure. 2 Frequency Histogram of Storage of Each Interval.

Figure. 3
Figure. 3 illustrate the sensitivity analysis of β.The left figuration shows the influence of different values of β on accuracy, and the right figuration shows the influence of different values of β on reported capacity.The results also confirm the effect of probability constraint: the greater the probability of exceeding the limit of energy, the lower the accuracy achieved, but the more capacity that can be reported.Therefore, economically speaking, the more positive the reported capacity, the higher the capacity benefit, but it will also reduce the FR performance index, thus reducing the compensation coefficient corresponding to the performance.As a consequence, when aggregators participate in the optimization of FR ancillary services, they need to evaluate the overall compensation under the market environment, so as to weigh the benefits and risks and achieve the maximization of benefits.

Figure. 3
Figure. 3 Influence of β (Probability That Storage within Limit) for Accuracy and Reserve Capacity.