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Adaptive Electricity Scheduling in Microgrids

Yingsong Huang, Shiwen Mao, R. M. Nelms

arXiv:1301.0528v1eess.SY

TL;DR

The paper addresses microgrid scheduling when renewable supply, resident demand, and market prices are random, while basic usage must remain guaranteed and quality usage must meet a QoSE target. It formulates this as constrained stochastic programming and applies Lyapunov virtual queues to create an online scheduler. Simulations report QoSE control, cost-quality trade-offs, market-participation gains, and deterministic performance guarantees.

  • Problem

    Microgrid scheduling must balance random renewable supply, resident demand, prices, storage evolution, operating cost, and residents’ quality-of-service requirements.

  • Method

    Lyapunov optimization transforms QoSE and energy-storage control into virtual-queue stability problems and derives an online scheduler using current system information.

  • Results

    The proposed algorithm achieves QoSE near target levels, exposes a cost-quality trade-off, and earns $947.27 from the utility market versus MECP’s $379.74.

  • Takeaways & Limitations

    The simulations validate an adaptive electricity scheduling approach that jointly manages renewable resources, storage, demand, and utility-market participation while maintaining QoSE.

Abstract

from arXiv · show

Microgrid (MG) is a promising component for future smart grid (SG) deployment. The balance of supply and demand of electric energy is one of the most important requirements of MG management. In this paper, we present a novel framework for smart energy management based on the concept of quality-of-service in electricity (QoSE). Specifically, the resident electricity demand is classified into basic usage and quality usage. The basic usage is always guaranteed by the MG, while the quality usage is controlled based on the MG state. The microgrid control center (MGCC) aims to minimize the MG operation cost and maintain the outage probability of quality usage, i.e., QoSE, below a target value, by scheduling electricity among renewable energy resources, energy storage systems, and macrogrid. The problem is formulated as a constrained stochastic programming problem. The Lyapunov optimization technique is then applied to derive an adaptive electricity scheduling algorithm by introducing the QoSE virtual queues and energy storage virtual queues. The proposed algorithm is an online algorithm since it does not require any statistics and future knowledge of the electricity supply, demand and price processes. We derive several "hard" performance bounds for the proposed algorithm, and evaluate its performance with trace-driven simulations. The simulation results demonstrate the efficacy of the proposed electricity scheduling algorithm.

I. INTRODUCTION

The paper proposes adaptive microgrid energy management that guarantees basic electricity usage while controlling quality usage according to grid conditions. A Lyapunov-based online scheduler jointly manages renewable generation, storage, residential demand, and macrogrid transactions to reduce operating cost while maintaining QoSE.

  • Microgrids combine distributed renewable generation, storage, distribution, local demand, communications, and centralized MGCC control.
  • The framework separates resident demand into hard-guaranteed basic usage and controllable quality usage that may be blocked according to grid status.Grid status includes renewable generation, storage levels, and utility prices.
  • QoSE is defined as the outage percentage of quality usage, and the MGCC schedules electricity to keep it below a contractually specified target.
  • The scheduling problem jointly considers renewable allocation, ESS management, residential demand, and utility-market participation under random supply, demand, and prices.The MGCC can purchase or sell electricity through the macrogrid while serving quality usage from renewable resources, storage, or the grid.
  • Lyapunov optimization uses QoSE and battery virtual queues to derive an online policy requiring only current system status, with deterministic performance bounds.The paper evaluates the policy through trace-driven simulations and reports exponential convergence and improved operating efficiency while guaranteeing QoSE.
  • The system assumes basic living demand can be covered by minimum microgrid capacity, while energy storage compensates for random supply and demand.The model uses time slots whose duration follows the timescale of demand and supply processes, and battery charging and discharging are separately bounded.

3) Energy Supply and Demand Model:

The model represents stochastic quality-use requests, renewable supply, storage, and macrogrid transactions in a time-slotted microgrid. The MGCC allocates energy to quality usage, purchases or sells market energy, and enforces operational constraints while balancing supply and demand.

  • Each resident’s quality-use request αn(t) is an i.i.d. random variable with bounded magnitude and mean arrival rate λn.The long-run average rate is defined using the time average of quality-use requests.
  • Renewable generation first satisfies pre-agreed basic usage, and remaining energy can serve resident quality usage.The basic-use requirement is assumed to be fully satisfiable by renewable generation U(t).
  • The energy allocated to resident n’s quality usage is pn(t), while outage In(t) equals the requested quality usage minus the allocated energy.The average outage rate ρn is evaluated from the time average of In(t).
  • The MGCC may purchase energy Q(t) from or sell excess energy S(t) to the macrogrid, but purchasing and selling cannot occur simultaneously.Both transaction quantities are bounded by transformer and transmission-line capacities.
  • Supply-demand balance is imposed while renewable generation, resident consumption, and utility prices remain stochastic.
  • The purchasing price C(t) is bounded, announced at each slot’s start, and modeled without requiring statistics about its process.The price remains constant during the time slot and is independent of the amount purchased.

4) Utility Market Pricing Model:

The paper models microgrid electricity scheduling as a stochastic cost-minimization problem with battery constraints and QoSE guarantees. It reformulates QoSE and battery requirements as virtual-queue stability conditions, yielding a control-theoretic scheduling problem.

  • Problem Formulation: The control policy minimizes long-term microgrid operation cost while satisfying electricity, QoSE, and battery queue-stability constraints.The policy includes grid purchases and sales, battery charging and discharging, and quality-usage provisioning.
  • Problem Formulation: Utility prices, renewable generation, and resident consumption are random, while battery-state evolution also affects scheduling decisions.These general stochastic processes make the original electricity scheduling problem challenging.
  • Virtual Queues: A battery virtual queue tracks each battery’s charge level and is designed with a shift that supports satisfaction of physical battery constraints.The parameter Vmax is selected to ensure battery levels remain within their prescribed limits.
  • Virtual Queues: The QoSE virtual queue evolves from tolerated outage δn·αn(t) and actual outage In(t), with [x]+ defined as max{0,x}.This queue is maintained conceptually by the MGCC rather than representing an actual physical queue.
  • Problem Reformulation: Stabilizing the QoSE virtual queue guarantees resident n’s average quality-usage outage rate satisfies ρn ≤ δn·λn.The result connects queue stability to the paper’s QoSE constraint.

2) Problem Reformulation:

The reformulation applies Lyapunov optimization to convert the stochastic scheduling problem into a per-slot drift-plus-penalty minimization. The resulting decision uses current system observations and a tunable cost–stability trade-off.

  • Problem Reformulation: The Lyapunov function is defined over battery virtual queues Xk(t) and QoSE virtual queues Zn(t).The combined system state has dimension (N+K)×1.
  • Problem Reformulation: The drift-plus-penalty method selects the control policy to minimize an upper bound combining Lyapunov drift and expected operation cost.The policy controls grid transactions, battery actions, and resident quality-usage provisioning.
  • Problem Reformulation: The parameter V controls the trade-off between stability performance and operation-cost minimization.The admissible range is 0 < V ≤ Vmax.
  • Problem Reformulation: The per-slot optimization is conditioned on current virtual queues, market prices, available renewable energy, and quality-usage requests.The relevant observations include Xk(t), Zn(t), C(t), W(t), P(t), and αn(t).
  • Problem Reformulation: The control policy is applied to the decision-dependent terms of the drift-plus-penalty bound, allowing the optimization problem to be simplified.The constraints remain those specified by the scheduling model.

III. OPTIMAL ELECTRICITY SCHEDULING

The optimal scheduling policy has threshold properties for market transactions, battery operation, and QoSE provisioning. These properties determine when the MG charges, discharges, serves quality demand, or blocks it.

  • Optimal Scheduling: If Q(t) > 0, the optimal policy sets S(t) = 0, so the microgrid does not sell electricity while purchasing energy.This is one of the threshold properties of the optimal solution.
  • Optimal Scheduling: Battery charging and discharging are selected according to virtual-queue thresholds involving V and the purchase or selling price.For example, charging is suppressed when Xk(t) is above a price-dependent threshold, while discharging is suppressed below it.
  • Optimal Scheduling: QoSE provisioning increases when Zn(t) exceeds a price-dependent threshold and is disabled when Zn(t) falls below that threshold.The policy serves at least (1−δn)αn(t) in the high-queue case and selects pn(t)=0 in the low-queue case.
  • Optimal Scheduling: If Xk(t) > −V Wmin, the optimal solution selects Rk(t) = 0; if Xk(t) < −V Cmax, it selects Dk(t) = 0.These bounds provide price-independent sufficient conditions for disabling charging or discharging.
  • Optimal Scheduling: The optimal QoSE provisioning solution has explicit threshold properties based on Zn(t), Cmax, Wmin, and αmax.These conditions characterize when quality usage is substantially served or not served.
  • Optimal Scheduling: Price conditions guide ESS management: low purchasing or selling prices favor charging, whereas high prices favor discharging or selling stored energy.This intuition explains the threshold behavior of the battery-management solution.

B. MG Optimal Scheduling Algorithm

The MGCC solves each-slot scheduling through Lyapunov optimization, using virtual queues to jointly control QoSE, battery feasibility, and operating cost. The resulting policy is online and provides deterministic performance guarantees.

  • Adaptive control policy: The MGCC solves two linear programs for each slot and selects the more competitive solution as the control policy.The subproblems use current virtual-queue states, market prices, quality usage, and available renewable energy.
  • Adaptive control policy: The algorithm initializes QoSE targets and virtual queues, receives resident requests, solves the LPs, selects a policy, and updates the queues.The procedure operates through communication between residents and the MGCC.
  • Online operation: The scheduling solution depends only on current system state and requires neither process statistics nor future supply, demand, or price information.The policy is therefore online and robust to non-i.i.d. and non-ergodic processes.
  • Virtual-queue guarantees: Stabilizing the QoSE virtual queues provisions QoSE, while stabilizing battery virtual queues ensures ESS battery constraints.The Lyapunov policy greedily minimizes drift each slot to push the system toward queue stability.
  • Performance guarantees: The QoSE virtual-queue backlog and average quality-usage outage are bounded, while average operating cost satisfies y* ≤ ŷ ≤ y* + B*/V.These are deterministic performance bounds for the adaptive policy.
  • Performance guarantees: A larger V tightens the optimality gap but is limited by Vmax for battery feasibility; larger ESS capacity can improve the resulting cost performance.This creates a performance-congestion trade-off between operating cost and virtual-queue backlog.

IV. SIMULATION STUDY

The simulations model a grid-connected microgrid with renewable generation, battery storage, residential demand, and time-varying macrogrid prices. The study uses a 500-resident system and trace-driven renewable supply.

  • Simulation setup: The simulated microgrid contains 500 residents and receives renewable electricity from a wind turbine plant using the Western Wind Resources Dataset.The ESS comprises 100 plug-in hybrid electric vehicle Li-ion battery packs, each with 16 kWh maximum capacity.
  • Simulation setup: Basic demand is uniformly distributed from 2 kW to 25 kW, quality demand from 0 kW to 10 kW, and each slot lasts 15 minutes.The grid-connected microgrid can purchase from and sell electricity to the macrogrid under time-varying utility prices.

A. Algorithm Performance

Under default settings, QoSE converges near its target while the controller manages renewable surplus and keeps battery levels within capacity. V materially changes the cost–QoSE trade-off.

  • Default performance: Average QoSEs converge near 0.08 within 200 slots, close to the requested criterion δn = 0.07.The proposed scheme is reported to converge exponentially under the simulated setting.
  • Default performance: Excess renewable generation between slots 150 and 200 is sold to the macrogrid, providing cost compensation.The operation-cost trace records net spending of $418.10 by the end of the period.
  • Battery feasibility: Battery energy remains within 0 to 16 kWh, satisfying the capacity limit under the proposed control policy.Theorem 2 guarantees feasibility when 0 < V ≤ Vmax.
  • Control-parameter trade-off: QoSEs of 0.081, 0.061, and 0.055 correspond to total operation costs of $418.10, $625.69, and $717.75 for V = {Vmax, Vmax/2, Vmax/4}.Smaller V favors quality usage but increases total operating cost.
  • Heterogeneous QoSE targets: With δ1 = 0.02 and δ2 = δ3 = 0.07, the observed QoSEs converge to 0.015 for resident 1 and about 0.063 for residents 2 and 3.The simulation uses V = Vmax/2.

B. Comparison with a Benchmark

Against the heuristic MECP benchmark, the proposed policy earns substantially more from the utility market while maintaining QoSE below the specified criterion in the reported stress scenario.

  • Benchmark design: The benchmark MECP blocks quality-usage requests by tossing a coin with the target probability and uses heuristic charging and market actions.The comparison uses δn = 0.03 and seven-day simulations with changing resident demand.
  • Comparison results: The proposed policy maintains QoSE around 0.025, below δn = 0.03, while the comparison attributes this outcome partly to a sharp price increase.The price rises from $27/MWh to $356/MWh on the last afternoon, increasing Cmax eightfold and decreasing Vmax.

V. RELATED WORK

The paper builds on smart-grid and microgrid energy-management research, positioning its contribution as an online adaptive scheduling algorithm that jointly addresses renewable generation, storage, demand, and market participation.

  • V. RELATED WORK: Prior work studies smart-grid technologies, communications, security, and microgrid energy management, including renewable integration and online resource discovery.The cited literature spans grid infrastructure, communications, and distributed renewable-energy resources.
  • V. RELATED WORK: Lyapunov optimization provides a stochastic scheduling framework previously applied to power procurement, dynamic pricing, and energy storage management.Earlier applications considered delay-tolerant consumers and data-center workload requirements.
  • V. RELATED WORK: This paper jointly considers renewable-energy penetration, energy-storage management, residential demand management, and utility-market participation in microgrid scheduling.The contribution combines these components in an online adaptive electricity-scheduling algorithm.
  • V. RELATED WORK: The proposed approach models QoSE and transforms QoSE control and energy-storage management into queue-stability problems using virtual queues.The paper reports deterministic performance bounds and validates the approach through simulations.

APPENDIX A DERIVATION OF EQUATION (18)

The appendix derives equation (18) through case-based comparisons of feasible electricity allocations, using queue and price conditions to establish when charging, discharging, or quality-service allocation choices are optimal.

  • APPENDIX A DERIVATION OF EQUATION (18): If Z_n(t) > V C(t)−α_n(t), the proof establishes p_n(t) ≥ (1−δ_n)α_n(t).A smaller allocation would be replaceable by one meeting the threshold with a lower objective value.
  • APPENDIX A DERIVATION OF EQUATION (18): When X_k(t) > −V C(t), the proof shows that purchasing from the macrogrid is unnecessary under the stated operating condition.Assuming R_k(t) > 0 leads to a lower-objective feasible allocation with R_k(t)=0.
  • APPENDIX A DERIVATION OF EQUATION (18): When X_k(t) < −V C(t), the proof shows that selling electricity is unnecessary under the corresponding operating condition.Assuming D_k(t) > 0 permits a lower-objective feasible allocation with D_k(t)=0.
  • APPENDIX A DERIVATION OF EQUATION (18): If 0 ≤ Z_n(t) < V C(t)−α_n(t), the proof establishes p_n(t)=0 when the assumed allocation is positive.The contradiction argument replaces positive quality usage with zero allocation while reducing the objective.
  • APPENDIX A DERIVATION OF EQUATION (18): When S(t)>0, the appendix notes that Q(t)=0 and states that the second proof part follows by a similar argument.The detailed proof for this case is omitted for brevity.

APPENDIX C PROOF OF LEMMA 2

The appendix proves threshold rules for macrogrid trading by combining bounded purchase and selling prices with the battery virtual-queue state.

  • APPENDIX C PROOF OF LEMMA 2: The proof uses price bounds to show R_k(t)=0 when X_k(t)<−V C_max and D_k(t)=0 when X_k(t)>−V C_min.Analogous bounds are obtained using W_max and W_min for selling-price conditions.
  • APPENDIX C PROOF OF LEMMA 2: Because C_max>W_max and C_min>W_min, the optimal solution selects R_k(t)=0 when X_k(t)>−V W_min.This identifies a high virtual-queue region where purchasing is excluded.
  • APPENDIX C PROOF OF LEMMA 2: Because C_max>W_max and C_min>W_min, the optimal solution selects D_k(t)=0 when X_k(t)<−V C_max.This identifies a low virtual-queue region where discharging is excluded.
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