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Real-Time Power Balancing via Decentralized Coordinated Home Energy Scheduling

Tsung-Hui Chang, Mahnoosh Alizadeh, Anna Scaglione

arXiv:1302.3932v1eess.SYcs.IT

TL;DR

Uncoordinated HEM scheduling can create rebound peaks and real-time power imbalance. The paper proposes a decentralized, stochastic CoHEM architecture for coordinating deferrable-appliance schedules, and simulations show reduced real-time balancing costs.

  • Problem

    Uncoordinated household HEM systems can synchronize demand into rebound peaks, motivating coordinated neighborhood scheduling for real-time power balancing.

  • Method

    The paper models random deferrable-appliance requests as a multi-stage stochastic optimization problem and solves it with approximation, decomposition, and neighbor message exchange.

  • Results

    The proposed CoHEM design and decentralized algorithm effectively decrease the retailer’s real-time power balancing cost.

  • Takeaways & Limitations

    Customers can compute coordinated scheduling solutions locally using domestic information and messages exchanged only with neighboring residences.

Abstract

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It is anticipated that an uncoordinated operation of individual home energy management (HEM) systems in a neighborhood would have a rebound effect on the aggregate demand profile. To address this issue, this paper proposes a coordinated home energy management (CoHEM) architecture in which distributed HEM units collaborate with each other in order to keep the demand and supply balanced in their neighborhood. Assuming the energy requests by customers are random in time, we formulate the proposed CoHEM design as a multi-stage stochastic optimization problem. We propose novel models to describe the deferrable appliance load (e.g., Plug-in (Hybrid) Electric Vehicles (PHEV)), and apply approximation and decomposition techniques to handle the considered design problem in a decentralized fashion. The developed decentralized CoHEM algorithm allow the customers to locally compute their scheduling solutions using domestic user information and with message exchange between their neighbors only. Extensive simulation results demonstrate that the proposed CoHEM architecture can effectively improve real-time power balancing. Extensions to joint power procurement and real-time CoHEM scheduling are also presented.

I. INTRODUCTION

The paper addresses rebound peaks and volatility caused by independently scheduled household loads by coordinating neighborhood HEM systems. It models deferrable-appliance scheduling under random customer requests as a stochastic problem to support decentralized, deadline-respecting control.

  • I. INTRODUCTION: Identical dynamic prices can synchronize household loads into a new rebound peak and make demand more volatile and less predictable.These effects create demand-supply balancing and grid stability concerns.
  • I. INTRODUCTION: CoHEM coordinates neighborhood HEM units to reduce retailer real-time balancing costs while preserving customers’ individual costs and service quality.The architecture targets deviations from bulk power purchases and maintains customers’ scheduling deadline constraints.
  • I. INTRODUCTION: The paper focuses on non-interruptible appliances whose operating times can be deferred, including PHEVs, washing machines, dishwashers, and tumble dryers.Customers specify maximum tolerable delays for appliance operation.
  • A. Multi-Mode Deferrable Appliance Load Model: Customer appliance requests arrive randomly, and requested operating modes are represented with probabilistic usage information.The model uses request probabilities and mode-selection probabilities over a finite look-ahead horizon.
  • B. HEM Design Problem: The HEM problem minimizes expected electricity cost subject to maximum-delay and task-completion constraints.Its formulation is a multi-stage stochastic optimization problem whose expectation covers random arrivals, modes, and scheduling decisions.

C. Proposed CoHEM Design

The proposed CoHEM design minimizes expected real-time market costs arising from deviations between aggregate residential demand and pre-purchased power. It coordinates residence-level schedules while preserving each customer’s deadline constraints and motivating participation through cost and comfort guarantees.

  • C. Proposed CoHEM Design: CoHEM minimizes the retailer’s expected real-time balancing cost while scheduling all residences under the customers’ existing real-time constraints.The coordinated policy operates across residences rather than solving each household independently.
  • C. Proposed CoHEM Design: The retailer’s real-time cost reflects buying insufficient energy or absorbing excess energy relative to day-ahead and hour-ahead purchases.The formulation uses real-time buying and selling prices together with the bulk power already purchased.
  • C. Proposed CoHEM Design: A control policy maps each residence’s scheduling state to appliance activation decisions while satisfying the stochastic problem’s real-time constraints.The policy is applied using state information such as operation mode, remaining job length, and remaining maximum delay.
  • C. Proposed CoHEM Design: CoHEM customers are charged no more than their selfishly optimized cost and retain their specified scheduling deadlines.These participation conditions preserve both financial outcomes and appliance-service comfort relative to individual HEM operation.

III. PROPOSED SOLUTIONS FOR HEM AND COHEM

The paper solves individual HEM scheduling with an MDP and uses that formulation as the basis for decentralized CoHEM optimization. The appliance model tracks operating mode, remaining job length, and remaining delay while accommodating random requests and deferral deadlines.

  • A. Solving HEM Problem (6) by MDP: Each appliance state records its operating mode, remaining job length, and remaining maximum delay, while the binary control decides whether to switch it on.Queued requests may be activated immediately or deferred until later, subject to scheduling constraints.
  • A. Solving HEM Problem (6) by MDP: The HEM problem is reformulated as an MDP whose control policy maps each appliance state to a real-time on/off decision.The policy is computed over the state space and then applied using the appliance’s observed real-time state.
  • A. Solving HEM Problem (6) by MDP: Random customer requests determine state transitions, including the requested operating mode, task duration, and allowable waiting time.When idle, the appliance can receive a mode-specific request; the controller then chooses activation or queuing.
  • A. Solving HEM Problem (6) by MDP: Dynamic programming computes cost-to-go values backward and requires policy optimization only for states in which a queued task may be activated or delayed.The resulting computation is efficient because the numbers of modes and possible delay values are usually small.
  • A. Solving HEM Problem (6) by MDP: The appliance model also extends to multiple alternate power profiles per mode, giving the controller an additional choice when minimizing customer cost.Figure 2 illustrates the corresponding single-mode model with alternate profiles and an expanded state representation.

B. Decentralized Stochastic Optimization for CoHEM

The proposed CoHEM solver approximates the large stochastic problem and decomposes it into residence-level subproblems coordinated through dual variables. Each residence uses the MDP policy locally, while neighboring message exchanges drive consensus on coordination prices.

  • B. Decentralized Stochastic Optimization for CoHEM: The full CoHEM MDP becomes computationally unaffordable because its state space grows exponentially with the number of residences and appliances.This motivates an approximate decentralized stochastic optimization method rather than direct centralized dynamic programming.
  • B. Decentralized Stochastic Optimization for CoHEM: The method preserves stochastic requests, approximates the objective using expected aggregate load, and solves the resulting problem through Lagrange dual decomposition.The approximation provides a lower-bound objective based on deviation between expected aggregate load and power supply.
  • B. Decentralized Stochastic Optimization for CoHEM: Residence-level inner problems are separable and have the same form as selfish HEM with a pseudo price, so each residence can solve them independently using the MDP method.This decomposition avoids requiring a central processor to solve every residence’s scheduling problem jointly.
  • B. Decentralized Stochastic Optimization for CoHEM: Consensus-subgradient updates let residences maintain local dual-variable copies and exchange messages only with connecting neighbors to reach approximate agreement.The local update uses residence information and retailer-broadcast bulk power, while neighbor averaging produces the next dual iterate.
  • B. Decentralized Stochastic Optimization for CoHEM: Within 150 iterations, the reported dual updates and normalized duality gap converge asymptotically, with consensus accuracy improving as the number of consensus steps increases.The dual iterates approach one another within a small discrepancy, and the dual objective approaches its optimum within a deviation that decreases with consensus steps.
  • B. Decentralized Stochastic Optimization for CoHEM: Unlike model predictive CEC, Algorithm 1 performs decentralized optimization once per look-ahead horizon, reducing computation and communication overhead.The method still assumes reasonably accurate estimates of real-time balancing prices.

C. Extensions

The paper extends CoHEM to jointly optimize day-ahead power procurement and real-time scheduling, and to accommodate general convex real-time cost functions. Both extensions retain separable subproblems that support decentralized solution methods.

  • 1) Joint power procurement and CoHEM optimization: Joint power procurement and CoHEM scheduling can determine day-ahead power bids together with real-time appliance schedules.The procurement problem operates hourly, while real-time scheduling uses shorter intervals such as 15-minute periods.
  • 1) Joint power procurement and CoHEM optimization: The joint procurement-scheduling problem requires accurate forecasts of day-ahead locational marginal prices and real-time prices.The paper notes that the two decisions operate on different market timescales.
  • 1) Joint power procurement and CoHEM optimization: The joint extension preserves separability: residence-level terms and the additional procurement term can be minimized in parallel, with the former solved by MDP and the latter by convex optimization.The resulting problem can be handled in a decentralized fashion similar to Algorithm 1.
  • 2) Extension to general convex cost functions: The CoHEM formulation and Algorithm 1 extend to general convex, increasing costs for buying additional power and absorbing extra power.Slack variables and consensus projected subgradient updates handle the additional cost components.

IV. SIMULATION RESULTS

The paper reports extensive simulations to evaluate the proposed CoHEM architecture and Algorithm 1.

  • IV. SIMULATION RESULTS: Extensive simulation results evaluate the performance of the proposed CoHEM architecture and Algorithm 1.

A. Simulation Setting

The simulations model four deferrable appliances over a 96-slot day, generate stochastic customer requests, and evaluate decentralized scheduling under fixed algorithmic settings.

  • System and workload model: The study models washing machines, dish washers, tumble dryers, and PHEVs over T = 96 fifteen-minute intervals.Each residence has four deferrable appliances with single operation modes.
  • System and workload model: PHEV requests use probability 0.8 across three time windows, while appliance deadlines range from 15 minutes to 2 or 3 hours.The shorter deadline range applies to washing machines and dish washers; the longer range applies to tumble dryers and PHEVs.
  • Algorithm settings: Algorithm 1 uses 100 Monte Carlo realizations, 15 consensus steps, a decreasing step size c_n = 5/(n + 5), and 200 iterations.The model-predictive CEC baseline uses 150 iterations and is executed 95 times across the day.
  • Evaluation metric: Both prices are set to one, so the real-time cost reduces to total deviation between aggregate load and the day-ahead purchase.The simulations therefore assess deviation-based balancing performance.
  • Simulation procedure: The simulations generate aggregate unscheduled loads with Monte Carlo realizations and estimate the day-ahead load using sample averages.The day-ahead bid is constructed over the 96 time slots.
  • Simulation procedure: Piece-wise averaging over every 16-sample interval emulates generation ramping constraints and imperfect customer and renewable-resource information.This averaging is applied to the first term of the bid-related expression.

B. Selfish HEM v.s. CoHEM

Uncoordinated selfish scheduling creates rebound peaks and increases aggregate deviation, whereas decentralized CoHEM scheduling substantially reduces deviation with far lower communication overhead than the model-predictive CEC method.

  • Selfish scheduling: Selfish HEM moves load toward high-supply periods but creates rebound peaks, increasing deviation from 2823.3 kW to 4350.4 kW.The result links uncoordinated neighborhood scheduling with greater real-time cost for the retailer.
  • CoHEM performance: Algorithm 1 achieves 2002.7 kW average deviation, reducing unscheduled and selfish-HEM deviations by about 29% and 53%, respectively.The corresponding unscheduled and selfish-HEM deviations are 2823.3 kW and 4350.4 kW.
  • CoHEM performance: The model-predictive CEC method reduces deviation to 1549.8 kW, while Algorithm 1 performs comparably at 2002.7 kW.Both scheduled profiles can follow the power supply more closely than the unscheduled and selfish profiles.
  • Communication overhead: Algorithm 1 requires 3000 message exchanges, compared with at most 213750 for the model-predictive CEC method.The comparison uses the simulation settings described for the two algorithms.
  • Neighborhood size: Normalized deviation cost falls from 54.5 kW to 22.4 kW as neighborhood size increases from 5 to 50 residences, then remains relatively constant.This indicates robustness of Algorithm 1 against neighborhood size for H ≥ 50.

C. Robustness of CoHEM

CoHEM remains effective when participation is incomplete: deviation cost rises with more non-cooperative residences, but scheduling still improves the profile when more than half participate.

  • Neighborhood-size robustness: Table I reports normalized average deviation cost in kW for different numbers of residences, using 100 simulation realizations.The associated scheduling policy is produced by Algorithm 1.
  • Non-cooperative participation: The aggregator can still improve on unscheduled operation when more than 50% of residences follow the CoHEM scheduling policy.This result is obtained by varying the number of non-cooperative residences under the Fig. 4(b) simulation setting.
  • Non-cooperative participation: Deviation cost increases as the number of non-cooperative residences grows.The comparison is made against the unscheduled-load reference.

D. Convergence and Complexity

Algorithm 1 converges toward the optimal CoHEM objective in a small exact-search case and is designed to scale with neighborhood size under parallel computation.

  • Convergence: Within 150 iterations, the dual updates and normalized duality gap converge asymptotically across tested neighborhood sizes.Figure 6 tracks the empirical dual objective and normalized duality gap against iteration number.
  • Scope: The exact optimality comparison is demonstrated only for a small case, while large-scale simulations support practical effectiveness for real-time power balancing.The paper cautions that the small-case result may not always hold when both residences and appliances are numerous.
  • Complexity: Algorithm 1’s per-residence computation time remains relatively constant as the number of residences increases, supporting scalability with parallel computation.The implementation used sequential execution on one computer, although the decentralized computations can be parallelized.

E. Joint power procurement and CoHEM scheduling

The paper compares separate power procurement followed by CoHEM scheduling with joint optimization of procurement and scheduling. Joint optimization reduces the reported total cost but depends on accurate future price estimates.

  • Experimental setup: The comparison evaluates a separately determined power bid followed by CoHEM scheduling against jointly optimized power bidding and load scheduling.The separate design uses an estimated aggregate unscheduled load to determine the bid before scheduling.
  • Joint optimization: Joint optimization reduces total cost from 3559.4 to 2538.8, a 28.6% reduction, while lowering both procurement and real-time deviation costs.The jointly optimized design reports component costs of 1111.0 and 1427.4, compared with 1685.0 and 1874.4 for separate optimization.
  • Limitation: The joint design requires accurate day-ahead LMP and next-day real-time price estimates, leaving price-estimation errors for future investigation.The stated scope boundary concerns estimates for the entire following day.

V. CONCLUSIONS AND FUTURE DIRECTIONS

The paper presents CoHEM coordination, an MDP model for deferrable appliances, and a decentralized algorithm for reducing retailers’ real-time balancing costs. Future work extends the framework to thermostatically controlled appliances and related uncertainty.

  • Conclusions: The CoHEM architecture coordinates scheduling across residences to reduce real-time power balancing costs.The architecture targets multiple residences rather than isolated household scheduling.
  • Conclusions: A simple MDP models deferrable appliances and solves the individual HEM problem, while Algorithm 1 handles the coordinated design decentrally.The two components form the paper’s modeling and coordination approach.
  • Results: Simulations show that the CoHEM design and its decentralized algorithm can effectively decrease the retailer’s real-time power balancing cost.This is the paper’s reported overall simulation conclusion.
  • Future directions: Future work will extend the load model and decentralized algorithms to thermostatically controlled appliances such as HVAC.The paper also discusses integrating CoHEM with additional system considerations.
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