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Integrated Energy Exchange Scheduling for Multi-microgrid System with Electric Vehicles

Dai Wang, Xiaohong Guan, Jiang Wu, Pan Li, Peng Zan, Hui Xu

arXiv:1602.07425v1math.OC

TL;DR

Independent microgrid scheduling under a shared TOU price can create exchange peaks that exceed allowable limits. The paper combines two-stage EV scheduling with a dual-variable updated price for decentralized MGCC decisions. The reported results include lower electricity cost, reduced battery-state transitions, and power exchange within a safe range.

  • Problem

    Independent microgrids optimizing under the same TOU price may synchronize storage use and push total exchange beyond allowable limits.

    Source: §II · p. 2

  • Method

    A two-stage schedule optimizes aggregate battery power and allocates it to EVs, while dual variables form an updated price for decentralized MGCC scheduling.

    Source: §II · p. 2, §V · p. 6, §VII · p. 11

  • Results

    12.97% electricity-cost reduction versus scheduling without EV coordination; the coordinated method also restrains exchange within the safe range and reduces battery wear from frequent state transitions.

    Source: §VII · p. 12

  • Takeaways & Limitations

    Each microgrid can solve its local problem using the updated price while total power exchange stays within the safe range.

    Source: §V · p. 6

Abstract

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Electric vehicles (EVs) can be considered as flexible mobile battery storages in microgrids. For multiple microgrids in an area, coordinated scheduling on charging and discharging are required to avoid power exchange spikes between the multimicrogrid system and the main grid. In this paper, a two-stage integrated energy exchange scheduling strategy for multimicrogrid system is presented, which considers EVs as storage devices. Then several dual variables, which are representative of the marginal cost of proper constraints, are utilized to form an updated price, thereby being a modification on the original electricity price. With this updated price signal, a price-based decentralized scheduling strategy is presented for the Microgrid Central Controller (MGCC). Simulation results show that the two-stage scheduling strategy reduces the electricity cost and avoids frequent transitions between battery charging/discharging states. With the proposed decentralized scheduling strategy, each microgrid only needs to solve its local problem and limits the total power exchange within the safe range.

I. NOMENCLATURE

The nomenclature defines indices and operating quantities for microgrids, EVs, scenarios, battery storage, and electricity prices.

Indices and scenarios

  • i, j, m, t, and s index microgrids, EVs, trips, hours, and scenarios, respectively.The listed parameters include scenario probabilities and EV arrival and departure times.Source: §I · p. 1

Storage and prices

  • Aggregate battery energy has lower and upper bounds, while the original and updated prices are distinguished as C(t) and C*(t).The updated price is in CNY/kWh; battery energy is measured in kWh.Source: §I · pp. 1–2

Operating parameters

  • EV and battery parameters include capacity, SOC limits, cycle life, power limits, and trip distance and efficiency.The nomenclature also defines base load, wind power, and power exchange with the distribution grid.Source: §I · p. 1

II. INTRODUCTION

The introduction frames EVs as potential mobile storage and identifies coordinated multi-microgrid scheduling as a way to manage cost and grid-exchange peaks.

II. INTRODUCTION

  • EVs can serve as idle storage because household vehicles are parked at home or work 22 hours per day on average.The introduction also cites prior V2G studies on spinning reserve and frequency regulation.Source: §II · p. 2
  • Independent microgrid decisions under the same TOU price can synchronize charging and discharging, potentially pushing total exchange beyond allowable limits.The stated concern is that each microgrid optimizes its own interests without accounting for the main-grid impact.Source: §II · p. 2
  • The proposed approach combines two-stage EV scheduling with a dual-variable updated price for decentralized MGCC decisions.It models EV driving patterns and wind volatility using scenarios, and evaluates performance through numerical simulations.Source: §II · p. 2

III. RELATED WORK

The related-work discussion identifies gaps in EV-aware aggregate storage and multi-microgrid coordination; the formulation proposes a two-stage schedule for those settings.

III. RELATED WORK

  • Prior MGCC methods mainly optimize within individual microgrids, leaving the impact of neighboring microgrids on the main grid outside their focus.The paper frames restraining that multi-microgrid impact as an additional gap.Source: §III · p. 3
  • Prior EV charging and V2G studies address allocation and storage uses, but related work leaves EV-driven storage variability and cycle-life reduction insufficiently considered.The paper also identifies limited integration of coordinated EV allocation into microgrid management.Source: §III · pp. 2–3

IV. PROBLEM FORMULATION

  • The system places one MGCC above geographically close microgrids connected to a common distribution bus through a transformer.The structure is identified in Fig. 1.Source: §IV · p. 3, Figure 1 · p. 3
  • The MGCC schedules aggregate battery power in stage one; the EV aggregator allocates it among vehicles and minimizes charging/discharging transitions in stage two.The stated dispatch resolution is 15 minutes to 1 hour; finer fluctuations are assigned to primary and secondary frequency controls.Source: §IV · p. 3

A. Stochastic Characteristics of EVs and Wind Power

The section models uncertain EV travel behavior and wind generation to construct scenarios for the scheduling problem.

A. Stochastic Characteristics of EVs and Wind Power

  • EV availability is bounded by arrival and departure times, and the paper models driving patterns using real-world NHTS2009 data.Departure time is fitted with a chi-square distribution; arrival time is modeled conditionally on departure time.Source: A. Stochastic Characteristics of EVs… · pp. 3–4
  • Arrival time conditional on a departure window is modeled with a distribution whose mean and standard deviation vary by departure window.The text defines those parameters as the arrival-time mean and standard deviation for the given departure window.Source: A. Stochastic Characteristics of EVs… · p. 4
  • Trip distance follows a truncated power law with exponent 1.25, d0 = 1.8, and α = 20.The trip-count distribution is obtained from the dataset, while EV information is assumed collectable or forecastable by the aggregator.Source: A. Stochastic Characteristics of EVs… · p. 4
  • Wind generation is modeled as normally distributed around forecast power, with volatility set as a percentage of its expected value [32].The paper generates scenarios from the statistical models and applies fast forward scenario reduction [33].Source: A. Stochastic Characteristics of EVs… · p. 4

B. MGCC Scheduling Problem

The MGCC schedules multi-microgrid energy exchange by treating connected EVs as aggregate storage and minimizing operating cost while choosing exchange capacity. Its constraints account for changing EV availability and limit total exchange, with the formulation focused on energy scheduling under a DC model.

B. MGCC Scheduling Problem

  • The MGCC minimizes average multi-microgrid operating cost while choosing the optimal electricity exchange capacity.The formulation uses a scenario tree and assumes wind power is used in priority, with remaining demand supplied by the distribution grid.Source: B. MGCC Scheduling Problem · p. 4
  • A larger ρ may lower the chosen exchange capacity while increasing electricity cost, and a smaller ρ may have the opposite trade-off.ρ converts fixed infrastructure investment into daily cost and adjusts the weight of exchange capacity against electricity cost.Source: B. MGCC Scheduling Problem · p. 4
  • The model constrains each microgrid’s exchange with the common bus and caps total system exchange within the limit for every scenario.The system-wide cap applies even in the worst case; EV aggregate storage parameters are used instead of detailed information on each EV.Source: B. MGCC Scheduling Problem · pp. 4–5
  • Aggregate battery energy and charging/discharging bounds vary with the number of connected EVs and account for arrivals, departures, and driving demand.The lower energy bound covers departing EVs’ required energy and keeps connected EVs above the safe SOC limit; the upper bound depends on the connected-EV count.Source: B. MGCC Scheduling Problem · p. 5
  • The paper focuses on energy scheduling and uses a DC model, while noting that the formulation can be extended to represent AC power-flow constraints.The authors describe the work as laying a theoretical foundation and present the DC model to avoid distracting from the energy focus.Source: B. MGCC Scheduling Problem · p. 5

C. EV Aggregator Scheduling Problem

After the MGCC determines aggregate charging and discharging power, the EV aggregator allocates it among individual vehicles. The aggregator accounts for driving feasibility and battery cycling, using a cycle-count-based degradation cost assumption.

C. EV Aggregator Scheduling Problem

  • The aggregator allocates the MGCC’s optimal aggregate charging/discharging power among individual EVs using their driving patterns.Departure and arrival times determine feasible charging periods, while trip counts and distances determine energy demand.Source: C. EV Aggregator Scheduling Problem · p. 5
  • Individual-EV constraints cover SOC, charging and discharging power, driving demand, aggregate-power matching, cycle limits, and the ban on simultaneous charging and discharging.The DOD limit is tied to the safe SOC threshold, and the sum of individual powers must equal the MGCC’s aggregate schedule.Source: C. EV Aggregator Scheduling Problem · pp. 5–6
  • The aggregator’s objective combines energy cost and battery degradation cost.Energy cost is determined by the optimal aggregate charging/discharging power; the paper notes that detailed degradation modeling is difficult and could increase computation time and complexity.Source: C. EV Aggregator Scheduling Problem · pp. 5–6
  • Battery degradation cost is represented by charging/discharging cycle count, with one charging-plus-discharging pair treated as a cycle.The paper assumes battery life depends on cycle count and that scheduling within the cycle required by daily driving adds no extra degradation.Source: C. EV Aggregator Scheduling Problem · p. 6

V. PRICE-BASED DECENTRALIZED SCHEDULING STRATEGY

The paper replaces direct centralized device control with a day-ahead updated price based on dual variables for exchange constraints. Each microgrid can then schedule independently, while the proposed strategy keeps total exchange within a safe range under the stated scenario assumption.

V. PRICE-BASED DECENTRALIZED SCHEDULING STRATEGY

  • Dual variables for power and exchange bounds represent marginal costs and are used to modify the original TOU price into an updated price signal.The updated signal is broadcast day-ahead as an internal price for individual microgrids.Source: §V · p. 6
  • In the single-scenario formulation, the updated-price problem is shown to have the same solution as the original centralized problem and can be decomposed by microgrid.The coupling constraint between microgrids is relaxed in the updated-price formulation.Source: §V · p. 7
  • For the stochastic formulation, scenario-specific dual variables incorporate scenario probabilities and inform the updated price.A nonzero difference between the upper- and lower-bound dual variables indicates that the exchange bound is reached with that scenario’s probability.Source: §V · p. 7
  • The authors state that safe-range exchange is guaranteed under the assumption that wind power does not drastically change exchange profiles, leaving only one or a few scenarios that reach the limits.The four-scenario illustration discusses scenarios in which exchange reaches the upper bound.Source: §V · p. 7
  • Each microgrid adjusts its own charging/discharging profile from the broadcast price without the MGCC directly scheduling its individual operation.The MGCC still obtains global information, while each microgrid solves its local problem without considering other microgrids’ interaction.Source: §V · p. 8, Figure 3 · p. 8

VI. NUMERICAL TESTING RESULTS

The numerical tests use a five-microgrid system with wind generation and a 24-hour scheduling period. Wind and EV uncertainties are represented by scenarios that are reduced for computation.

VI. NUMERICAL TESTING RESULTS

  • The test system has five microgrids connected to a 400 V bus, with a schedule from 12:00 to 12:00 the next day.Each microgrid's baseline load profile covers 24 hours.Source: §VI · p. 8
  • Each microgrid has a 500 kW wind turbine, and the forecast wind-speed data come from Tianjin Eco-city.The turbines are assumed to produce active power at unity power factor.Source: §VI · p. 8
  • Each microgrid has 100 EVs with 33 kWh batteries; initial energy is 10%–50% of capacity and SOC must stay above 10%.Source: §VI · pp. 8–9
  • Monte Carlo sampling generates 2,000 wind and EV scenarios, reduced to 100 with the fast forward algorithm.Source: §VI · p. 9

A. Parameters of the Aggregate Battery Storage

The aggregate EV battery's usable power and energy vary over time with driving patterns and vehicle availability. It is most useful overnight and contributes little during midday.

A. Parameters of the Aggregate Battery Storage

B. Performance of the Proposed Coordination Strategy

Coordination lowers power-exchange peaks and electricity costs while shifting exchange toward lower-price hours. The minimum-state-transition allocation also reduces unnecessary charging/discharging changes.

B. Performance of the Proposed Coordination Strategy

  • 10.18% lower power-exchange peak with coordinated versus uncoordinated scheduling.Source: Figure 5 · p. 9, B. Performance of the Proposed… · p. 9
  • With coordination, total exchanged energy is unchanged, but exchange is lower during peak-price hours and higher during valley-price hours.The aggregate storage discharges during high-price periods and charges during low-price periods.Source: B. Performance of the Proposed… · p. 9
  • Pcap fell from 7512 to 6747 kW, average cost from 15215 to 13242 CNY, and SD from 1850 to 1545 with coordination.The reported average cost reduction is 12.97% and the SD reduction is 16.49%.Source: B. Performance of the Proposed… · p. 10
  • For 100 EVs per microgrid, the proposed allocation saves an average of 67 cycles, equivalent to 1,742 CNY under the stated battery-wear assumption.No extra cycle cost is reported until the number of EVs falls from 100 to 89 per microgrid.Source: B. Performance of the Proposed… · p. 10

C. Performance of the Decentralized Scheduling Strategy

The strategy uses an updated price to decentralize microgrid scheduling while retaining a cap on total power exchange. In the worst case, it keeps the exchange peak within that cap, with a cost increase over independent TOU scheduling.

C. Performance of the Decentralized Scheduling Strategy

VII. CONCLUSIONS AND FUTURE WORK

The paper proposes two-stage EV-storage scheduling and a dual-variable-based decentralized strategy for multimicrogrid systems. Simulations report lower cost and battery wear with coordination, and reduced exchange peaks under decentralized updated pricing.

VII. CONCLUSIONS AND FUTURE WORK

  • The two-stage model first schedules aggregate battery charging/discharging under TOU price, then allocates that schedule to individual EVs to minimize state transitions.A scenario-tree method addresses uncertainty in wind power and EV charging/discharging behavior.Source: §VII · pp. 11–12
  • The coordinated two-stage method reduces electricity cost by 12.97% versus scheduling without EV coordination and decreases battery wear from frequent charging/discharging transitions.The paper also reports that the method restrains the power-exchange peak within the safe range.Source: §VII · p. 12
  • The price-based decentralized strategy decreases the exchange peak by 18.77% versus decentralized scheduling under the original TOU price.The strategy is based on interpreting dual variables as shadow prices.Source: §VII · p. 12
  • Future work will incorporate detailed AC operational constraints and system dynamics.Source: §VII · p. 12
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