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Multiple Timescale Dispatch and Scheduling for Stochastic Reliability in Smart Grids with Wind Generation Integration

Miao He, Sugumar Murugesan, Junshan Zhang

arXiv:1008.3932v2eess.SYcs.PFcs.SY

TL;DR

Volatile wind and uncertain demand make it challenging to keep generation and load balanced in smart grids. The paper combines day-ahead scheduling with real-time pricing and develops different solution approaches for non-persistent and persistent opportunistic users. Its numerical results indicate that two-timescale scheduling addresses generation volatility and opportunistic-demand uncertainty, with profit margins varying with wind penetration, opportunistic demand, and user elasticity.

  • Problem

    The paper addresses how to maintain supply-demand balance amid volatile wind generation, stochastic opportunistic demand, and decisions coupled across timescales.

    Source: A. Motivation · pp. 1–2

  • Method

    The paper combines day-ahead procurement and pricing with real-time pricing, using closed-form solutions for non-persistent users and an MMDP recast as a standard MDP for persistent users.

    Source: §VI · p. 10

  • Results

    Numerical results suggest two-timescale scheduling addresses wind-generation volatility and opportunistic-demand uncertainty, while profit margin rises with wind penetration and falls with opportunistic demand.

    Source: §V · p. 10

  • Takeaways & Limitations

    The authors conclude that multi-timescale dispatch and real-time pricing can address wind and demand uncertainty and may improve renewable-energy penetration in smart grids.

    Source: §VI · p. 10, §V · p. 10

    The authors describe the study as an initial step, noting that many questions remain open for improving renewable-energy penetration in power grids.

    Source: §VI · p. 10

Abstract

from arXiv · show

Integrating volatile renewable energy resources into the bulk power grid is challenging, due to the reliability requirement that at each instant the load and generation in the system remain balanced. In this study, we tackle this challenge for smart grid with integrated wind generation, by leveraging multi-timescale dispatch and scheduling. Specifically, we consider smart grids with two classes of energy users - traditional energy users and opportunistic energy users (e.g., smart meters or smart appliances), and investigate pricing and dispatch at two timescales, via day-ahead scheduling and realtime scheduling. In day-ahead scheduling, with the statistical information on wind generation and energy demands, we characterize the optimal procurement of the energy supply and the day-ahead retail price for the traditional energy users; in realtime scheduling, with the realization of wind generation and the load of traditional energy users, we optimize real-time prices to manage the opportunistic energy users so as to achieve systemwide reliability. More specifically, when the opportunistic users are non-persistent, i.e., a subset of them leave the power market when the real-time price is not acceptable, we obtain closedform solutions to the two-level scheduling problem. For the persistent case, we treat the scheduling problem as a multitimescale Markov decision process. We show that it can be recast, explicitly, as a classic Markov decision process with continuous state and action spaces, the solution to which can be found via standard techniques. We conclude that the proposed multi-scale dispatch and scheduling with real-time pricing can effectively address the volatility and uncertainty of wind generation and energy demand, and has the potential to improve the penetration of renewable energy into smart grids.

I. INTRODUCTION

The paper addresses the reliability challenge of balancing supply and demand under volatile wind generation and uncertain opportunistic demand. It proposes two-timescale dispatch and pricing, alongside distinct solution approaches for non-persistent and persistent users.

A. Motivation

  • Volatile, non-dispatchable wind makes instantaneous supply-demand balance difficult, while opportunistic users add bursty, fine-timescale uncertainty on the demand side.A mismatch can shift zonal frequency from nominal; severe deviations may cause outages and blackouts [1].Source: A. Motivation · p. 1

B. Summary of Main Contributions

  • Two-timescale scheduling combines day-ahead procurement and pricing for traditional users with real-time pricing for opportunistic users after wind generation and traditional demand are realized.The model also treats the persistent-user case as a multi-timescale Markov decision process recast as a standard Markov decision process.Source: B. Summary of Main Contributions · p. 2

C. Related Work

  • Prior wind-scheduling work treats demand as known or statistically known but uncontrollable, while conventional real-time pricing operates on a coarser timescale than opportunistic users require.The paper frames its challenge as supply uncertainty, stochastic opportunistic demand, and coupling across sequential timescales.Source: C. Related Work · p. 2, A. Motivation · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The scheduling horizon divides a 24-hour day into M T1-slots, each containing K shorter T2-slots, such as hours and minutes.The paper organizes dispatch around these nested timescales.Source: §II · pp. 2–3

A. Energy Sources and Generation Costs

The system schedules conventional base-load generation day-ahead and uses wind and peaking generation in real time to balance demand. Separate day-ahead and real-time prices address different user classes, while wind is modeled as non-stationary.

A. Energy Sources and Generation Costs

  • Base-load generation is scheduled day-ahead, while wind and higher-cost peaking generation balance demand in each real-time T2-slot.Base-load and peaking generation have per-unit costs c1 and c2, with c2 > c1; overscheduling incurs the start-up cost cp per unit.Source: A. Energy Sources and Generation Costs · p. 3

B. Day-Ahead Pricing and Real-Time Pricing

  • Traditional users receive day-ahead prices and opportunistic users receive real-time prices, with separate caps for each price.The paper introduces real-time pricing for opportunistic users to account for demand and supply uncertainty.Source: B. Day-Ahead Pricing and Real-Time… · p. 3

C. Supply Uncertainty of Wind Generation

  • Wind generation is modeled as a non-stationary Gaussian random process, with its statistical information available to the day-ahead scheduler.The next-day statistics are commonly supplied by EMS forecasting functions or commercial entities.Source: C. Supply Uncertainty of Wind Generation · p. 3

D. Demand Uncertainty under Real-time Pricing

Demand combines traditional users, whose modeled demand depends on the day-ahead price, and opportunistic users, whose participation responds to real-time prices. The opportunistic-user model includes random arrivals and acceptance decisions, with persistent and non-persistent behaviors.

D. Demand Uncertainty under Real-time Pricing

  • Total demand D consists of traditional demand Dt and opportunistic demand Do, with Do equal to the number of active opportunistic users times their per-user consumption Eo.The source passage specifies Do = NaEo.Source: D. Demand Uncertainty under Real-time… · pp. 3–4
  • Traditional-user demand is modeled as a random variable whose mean depends on day-ahead price u, with εt representing demand uncertainty and γt representing price elasticity.The model allows αt and γt to vary by T1-slot, reflecting differences such as noon versus evening demand.Source: D. Demand Uncertainty under Real-time… · pp. 3–4
  • Price elasticity is the ratio of the percentage change in demand to the percentage change in price, and is negative for power systems.The passage also identifies αt as a normalizing constant.Source: D. Demand Uncertainty under Real-time… · p. 4
  • Opportunistic users arrive according to a Poisson process and independently choose access times; each arriving user accepts or rejects the real-time price using a randomly assigned acceptance level.The arrival rate is constant within a T1-slot but may vary across T1-slots.Source: D. Demand Uncertainty under Real-time… · p. 4
  • Non-persistent opportunistic users leave when the real-time price is unacceptable, whereas persistent users wait for a later acceptable price.The paper links these behaviors to energy conservation without load shifting and load shifting to a later time, respectively,.Source: D. Demand Uncertainty under Real-time… · p. 4

E. General Problem Formulation

The general formulation chooses a policy across day-ahead and real-time scheduling to maximize expected profit over a horizon of T1-slots. Its real-time state includes wind and traditional demand, with carried-over opportunistic requests added for persistent users.

E. General Problem Formulation

  • The objective is to maximize overall expected profit across M T1-slots under day-ahead and real-time scheduling with non-stationary wind generation.The day-ahead policy uses statistical information about next-day wind generation to determine two-timescale decisions.Source: E. General Problem Formulation · p. 4
  • The total profit m(π) is defined per T1-slot, while k,m denotes net profit in a T2-slot and ψl_k,m denotes the observable system state there.The general formulation distinguishes slot-level profit from the state used for real-time decisions.Source: E. General Problem Formulation · p. 4
  • For persistent opportunistic users, the real-time state also includes requests carried over from the previous T2-slot.For non-persistent users, the state consists of wind energy and traditional-user demand.Source: E. General Problem Formulation · p. 4

III. DISPATCH AND SCHEDULING WITH NON-PERSISTENT OPPORTUNISTIC ENERGY USERS

Day-ahead procurement and pricing affect real-time pricing, while the real-time policy also affects day-ahead optimization. The paper therefore formulates the two schedules jointly using a bottom-up approach.

III. DISPATCH AND SCHEDULING WITH NON-PERSISTENT OPPORTUNISTIC ENERGY USERS

  • Day-ahead procurement and retail pricing affect the real-time retail price, and the real-time policy feeds back into day-ahead optimization.This coupling motivates joint optimization of the two schedules.Source: §III · p. 4
  • The formulation first solves real-time scheduling conditioned on day-ahead decisions S and u.The day-ahead problem is then introduced with the real-time scheduling policy taken into account.Source: §III · p. 4
  • The authors use this bottom-up formulation to address the tight coupling between the two scheduling timescales.Source: §III · p. 4

A. Real-time Scheduling on Timescale T2

The real-time problem sets pricing after day-ahead procurement and price are fixed, using realized wind and traditional demand. Its indicators distinguish wind sufficiency, surplus, and deficit conditions.

A. Real-time Scheduling on Timescale T2

B. Day-ahead Scheduling on Timescale T1

For non-persistent users, the day-ahead problem accounts for the real-time optimization as its inner maximization. Identically distributed wind and traditional-demand realizations across T2 slots permit a snapshot formulation.

B. Day-ahead Scheduling on Timescale T1

C. Approximate Solutions

Because uncertainty and coupling make direct joint optimization challenging, the authors approximate real-time scheduling and use that policy to derive day-ahead decisions. The resulting pricing policies differ by user elasticity and by energy surplus or deficit.

C. Approximate Solutions

  • The authors approximate real-time scheduling before deriving day-ahead solutions because direct joint optimization faces tight coupling and convolved uncertainty.Source: C. Approximate Solutions · p. 5
  • The model treats non-persistent user arrivals as Poisson and approximates active users, and thus their energy demand, as Gaussian when the arrival rate is typically large.Source: C. Approximate Solutions · p. 5
  • The real-time policy depends on statistical assumptions about wind and opportunistic demand, including variance scaling with average demand and elasticity-dependent demand variance.Source: C. Approximate Solutions · p. 6
  • For relatively inelastic users (-1 ≤ γo < 0) under condition A, the optimal real-time price is the cap vcap.The stated policy applies when wind generation cannot meet total system demand.Source: C. Approximate Solutions · pp. 5–6
  • For relatively elastic users (γo < -1), certainty equivalence approximates opportunistic demand by its mean to derive the real-time pricing policy.As elasticity increases, the price falls toward c1 − cp in surplus cases and c2 in deficit cases.Source: C. Approximate Solutions · p. 6
  • The approximate day-ahead schedule is obtained through a single-stage optimization whose expectations depend on the chosen stochastic models for wind and traditional demand.Source: C. Approximate Solutions · p. 6
  • The day-ahead decisions affect the real-time policy through adjusted procurement s′, which is formed by subtracting expected traditional demand from s.Source: C. Approximate Solutions · p. 7
  • The paper gives a closed-form complete two-timescale scheduling decision for relatively inelastic non-persistent users.Source: C. Approximate Solutions · p. 7

IV. DISPATCH AND SCHEDULING WITH PERSISTENT OPPORTUNISTIC ENERGY USERS

Persistent opportunistic users remain in the system until an acceptable real-time price arrives, making decisions across both scheduling timescales affect future system states. The paper recasts this coupled problem as a classic MDP with continuous state and action spaces.

IV. DISPATCH AND SCHEDULING WITH PERSISTENT OPPORTUNISTIC ENERGY USERS

  • Persistent users who reject a real-time price wait for a later acceptable price, and users arriving during the day leave at day’s end.Consequently, scheduling decisions across both timescales affect the system trajectory and future decisions.Source: §IV · p. 7
  • Because decisions across timescales shape future system trajectories, the persistent-user problem is formulated as a multi-timescale Markov decision process.The day-ahead decisions affect lower-level transition dynamics, while lower-level decisions affect upper-level decisions.Source: §IV · pp. 7–8
  • The day-ahead scheduler chooses energy dispatch and traditional-user retail price, while real-time decisions use realized wind, traditional demand, and carried-over users to set opportunistic-user prices.The slower-timescale state includes persistent users carried over from the previous day-ahead slot; the real-time state includes wind, traditional demand, and users carried over from the previous real-time slot.Source: §IV · p. 8
  • Treating the stationary real-time pricing rule as an additional day-ahead action recasts the problem as a classic MDP with continuous state and action spaces.After discretization, standard techniques can solve it optimally or near-optimally.Source: §IV · pp. 8–9

V. NUMERICAL RESULTS

Numerical experiments examine profit margins under two-timescale scheduling with non-persistent opportunistic users. The reported results show higher margins with real-time pricing than without it at matched wind penetration and elasticity, while margins also vary with wind penetration and opportunistic demand.

V. NUMERICAL RESULTS

  • Profit margin increases with wind penetration and decreases as opportunistic-user demand penetration increases.The authors attribute the decrease to greater demand uncertainty and losses from day-ahead overestimation or underestimation.Source: §V · p. 9, Figure 3 · p. 9
  • At fixed wind penetration and elasticity, profit margin is higher with real-time pricing than without multi-timescale pricing.The comparison assumes opportunistic users have the same elasticity as traditional users.Source: §V · p. 10, Figure 4 · p. 10
  • The numerical results suggest two-timescale scheduling addresses generation volatility and opportunistic-demand uncertainty; profit margin also varies with opportunistic-user elasticity.The paper reports margins increasing with wind penetration and decreasing with opportunistic demand.Source: §V · p. 10

VI. CONCLUSION

The conclusion presents two-timescale dispatch and pricing for integrating volatile wind into smart grids. It gives closed-form solutions for non-persistent users and recasts the persistent-user problem as a standard MDP, while noting that many questions remain open.

  • The framework uses day-ahead scheduling to procure supply and set traditional-user prices, then real-time scheduling to price opportunistic users using realized wind and traditional-user demand.Source: §VI · p. 10
  • Non-persistent opportunistic users yield closed-form scheduling solutions, whereas the persistent-user problem is recast as a classic Markov decision process.Source: §VI · p. 10
  • Many questions remain open for improving renewable-energy penetration into power grids, so the study describes its contribution as an initial step.Source: §VI · p. 10
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