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Using Battery Storage for Peak Shaving and Frequency Regulation: Joint Optimization for Superlinear Gains

Yuanyuan Shi, Bolun Xu, Di Wang, Baosen Zhang

arXiv:1702.08065v3eess.SYcs.DCmath.OC

TL;DR

The paper addresses joint battery use for peak shaving and frequency regulation despite the applications’ vastly different characteristics. It formulates a joint optimization framework and reports superlinear savings, with an online control algorithm that achieves this gain.

  • Problem

    The paper examines how to jointly use battery storage for peak shaving and frequency regulation despite their vastly different characteristics.

  • Method

    The paper formulates a framework that jointly optimizes battery usage for both applications while accounting for battery degradation through a cycle-depth marginal cost.

  • Results

    Joint optimization savings can be larger than the sum of individual application savings, and an online control algorithm achieves this superlinear gain.

  • Takeaways & Limitations

    Exploring diversity and mutual benefits across applications can produce superlinear gains in battery storage economics.

Abstract

from arXiv · show

We consider using a battery storage system simultaneously for peak shaving and frequency regulation through a joint optimization framework which captures battery degradation, operational constraints and uncertainties in customer load and regulation signals. Under this framework, using real data we show the electricity bill of users can be reduced by up to 15\%. Furthermore, we demonstrate that the saving from joint optimization is often larger than the sum of the optimal savings when the battery is used for the two individual applications. A simple threshold real-time algorithm is proposed and achieves this super-linear gain. Compared to prior works that focused on using battery storage systems for single applications, our results suggest that batteries can achieve much larger economic benefits than previously thought if they jointly provide multiple services.

I. INTRODUCTION

This paper jointly optimizes battery use for peak shaving and frequency regulation while accounting for degradation, operational constraints, and uncertainty. Because the services operate at different timescales, their combination can produce superlinear economic gains.

  • Battery storage can support peak shaving and frequency regulation for commercial customers.Peak shaving reduces peak demand charges, while fast frequency regulation suits batteries because of their near-instantaneous response.
  • Peak demand charges use smoothed monthly consumption, whereas frequency regulation requires decisions every 2 to 4 seconds.
  • Joint optimization can produce a superlinear gain, with savings larger than the sum of separate peak-shaving and regulation savings.The paper attributes this possibility to diversity and mutual benefit across applications operating at different timescales.
  • A simple online threshold algorithm is used for joint optimization, while the individual-service comparisons use offline optimal solutions.
  • The framework deploys only part of the battery’s energy capacity for grid services and reserves a large portion for backup.

A. Literature Review

Prior work examined dual-use storage and co-optimization, but this paper develops a systematic framework for uncertain, multi-timescale battery services. Its contributions include degradation-aware optimization, real-time control, and evidence of superlinear gains using commercial-user data.

  • A. Literature Review: Earlier dual-use studies found higher profits than single applications, but mainly relied on heuristic analysis under different price and user patterns.
  • A. Literature Review: A systematic prior co-optimization framework handled different timescales but assumed all future information was known.That assumption prevents direct extension to uncertainties in energy and ancillary-service markets.
  • B. Our Contributions: The proposed framework jointly optimizes peak shaving and frequency regulation while accounting for battery degradation, operational constraints, and uncertainty in loads and regulation signals.The paper notes that omitting battery operating costs can lead to aggressive charging and discharging and severely suboptimal operations.
  • B. Our Contributions: The paper defines superlinear gain as joint-optimization revenue exceeding the sum of revenues from the individual applications.This comparison differs from prior studies that compared co-optimization with only one single application.
  • B. Our Contributions: The framework’s benefits are quantified with real-world data from a Microsoft data center and the University of Washington EE & CSE building.
  • B. Our Contributions: A simple threshold control algorithm is proposed to achieve the superlinear gain in real time.

A. Electricity Bill of Commercial Users

Commercial electricity bills combine energy charges with peak demand charges, motivating battery-based peak shaving and frequency regulation as complementary services.

  • Electricity bill structure: Commercial users’ bills include energy charges and peak demand charges based on maximum or smoothed power consumption.Peak demand charges may be calculated from running averages over 15 or 30 minutes.
  • Combined applications: The framework considers peak shaving and frequency regulation simultaneously as battery applications.Regulation service involves a per-MW option fee and a per-MWh mismatch penalty.
  • Peak shaving: Battery discharge during high demand and charging at other times can smooth consumption profiles and reduce grid power draw.The model defines positive battery power as discharging and negative power as charging; actual grid draw is s(t) − b(t).
  • Battery cost model: The battery-based bill model includes energy cost, peak demand cost, and a degradation function of battery actions.The resulting cost remains convex in the power-consumption profile.
  • Frequency regulation: Frequency regulation lets commercial users earn revenue by offering standby capacity while incurring mismatch penalties for deviations from instructed dispatch.The simplified PJM RegD signal is fast-ramping and approximately zero-mean over a certain interval, aligning with battery characteristics.

D. Battery Cell Degradation

Battery degradation is difficult to model across chemistries and operating timescales, so the paper captures general degradation features with a bounded, linearized operating-cost model.

  • Degradation characteristics: Battery operating cost depends substantially on cycle number and depth of discharge, which vary across battery chemistries.The paper focuses on lithium-ion batteries and notes that degradation behavior differs among chemistries.
  • Modeling scope: No single detailed degradation model applies to all battery chemistries, so this paper captures general degradation features instead.The framework does not attempt to propose one comprehensive degradation model.
  • LMO degradation model: Within a limited depth-of-discharge region, LMO cycle-life data indicate a constant marginal cost for increasing cycle depth.The stated condition is intended to avoid overcharge and over-discharge effects.
  • Linearized cost: Cycle depth of discharge is modeled as proportional to the amount of battery charging and discharging.The framework therefore assigns a linearized cost f(b) proportional to λ_b|b(t)|.
  • Cost calibration: The battery cost coefficient is derived by normalizing lifetime energy throughput and prorating cell cost into a per-MWh degradation cost.The calculation uses cell price, cycle count, and operation within specified SoC limits.
  • Frequency-regulation setting: A cycle-count degradation model suited to long-timescale applications is too aggressive for rapid frequency regulation.The paper states that interpreting degradation through frequent direction changes could imply battery failure within days, motivating a power-proportional cost.

B. Benchmark

The benchmark compares joint optimization against individually optimized peak shaving and frequency regulation under complete future information. The results show that joint optimization can produce superlinear savings, exceeding the sum of the two individual savings.

  • The benchmarks use complete knowledge of the future and represent the best possible performance of algorithms solving peak shaving or frequency regulation individually.
  • The offline peak shaving and frequency regulation benchmark problems are convex and can be solved with generic convex optimization software.The objectives combine convex functions and the constraints are linear.
  • An 8-hour benchmark horizon with 4-second resolution can be solved in about 10 minutes on the reported computer.
  • The joint optimization saving can exceed the sum of savings from the two individual benchmark applications, a phenomenon termed super-additivity.
  • Table I compares the original bill with bills after frequency regulation, peak shaving, and joint optimization for a 1MW data center.The reported bill savings show joint optimization saving more than the sum of the individual application savings.

IV. ONLINE BATTERY CONTROL

The online control method separates day-ahead planning from real-time battery operation to handle the different timescales of peak shaving and frequency regulation. A simple threshold policy uses predicted load and regulation scenarios, achieving near-optimal performance with low computational requirements.

  • The method divides control into day-ahead decisions for the peak threshold and regulation capacity bid, followed by real-time battery charging and discharging.
  • Day-ahead optimization uses multiple linear regression for load prediction and scenario reduction to represent uncertainty in regulation signals.
  • More sophisticated methods such as model predictive control and dynamic programming are not needed here because the online method combines near-optimal performance with high computational efficiency.
  • Under constant marginal battery charging and discharging cost, the optimal frequency-regulation response is a simple threshold policy.
  • The proposed real-time algorithm requires only real-time state-of-charge measurement and achieves near-optimal performance relative to offline optima with perfect foresight.

V. SIMULATION RESULTS

Simulations use real load data and PJM fast frequency-regulation signals to evaluate joint optimization under battery, market, and degradation assumptions. The study finds frequent superlinear benefits while reserving unused battery capacity for backup.

  • The evaluation uses half a year of Microsoft data-center consumption, one year of University of Washington building data, and PJM fast frequency-regulation signals.
  • Over 80% of the time, joint optimization provides superlinear benefits.
  • The modeled battery has 1MW power capacity and 15 minutes of total energy capacity, with 3-, 5-, and 10-minute portions considered for grid services.
  • Using 3 minutes of battery capacity for grid services can provide considerable gains without additional burdens under a preferred 3-year replacement cycle.
  • The remaining battery energy capacity is reserved for emergency backup.
  • The joint-optimization evaluation compares its savings with the summed savings from benchmark peak shaving and frequency regulation using the defined saving-ratio criterion q.

B. Results for Synthetic Load: Peak Shape and Superlinear Gain

Synthetic-load experiments show that superlinear gains depend on peak shape. Joint optimization is especially valuable for wide peaks because regulation fluctuations break a long peak into shorter peaks that peak shaving can address more effectively.

  • The synthetic-load analysis varies peak duration from 3 minutes to 15 minutes to study how peak shape affects superlinear-gain probability.
  • For a narrow 3-minute peak, the battery can shave a large portion of the peak before reaching its state-of-charge bound.
  • For a wide peak, peak shaving alone may reduce the bill little because the energy cost of shaving approaches or exceeds the reduced demand-charge savings.
  • Joint optimization uses regulation-signal randomness to break a flat peak into several short-time peaks, enabling additional peak-shaving savings.
  • The resulting additional savings explain the superlinear gain for the wide-peak case.

C. Results for Real-life Data: Microsoft Data Center and UW EE & CSE Building

Real-data simulations show that joint optimization produces substantial bill savings and frequently yields superlinear gains, with outcomes depending on peak duration and battery capacity.

  • Microsoft Data Center: $52,282 (10.72%) annual savings were achieved for a 1MW Microsoft data center, including $13,234 beyond benchmark optima.The data center’s annual electricity bill was $488,370.
  • UW EE & CSE Building: 362 out of 365 days produced superlinear gains for the UW building.The result is reported alongside its annual bill and savings.
  • UW EE & CSE Building: $44,420 (12.35%) annual savings were achieved for the UW EE & CSE building, with a $14,061 yearly superlinear gain.The building’s annual electricity bill was around $359,634.
  • Peak-Duration Effects: Greater gains occur for flat peaks because regulation-signal randomness breaks them into several shorter peaks suitable for additional peak shaving.The exact boundary between long and short peaks depends on battery size.
  • Peak-Duration Effects: For a 3-minute battery, peaks shorter than 3 minutes generally do not produce superlinear gains, whereas longer peaks make joint optimization important.Both case studies had high superlinear-gain probability: greater than 80%; the UW ratio was 99% versus 82.5% for the data center.

D. Sensitivity Analysis

Sensitivity analysis links superlinear gains to economic parameters and peak structure. Gains generally become more likely with lower battery prices and higher peak-demand charges, but can decline when regulation payments dominate.

  • Price Sensitivity: Superlinear-gain probability increases as battery cell price decreases or peak demand charge increases.The analysis varies battery cell price and peak-demand charge settings.
  • Mechanism: The positive interaction between peak shaving and frequency regulation is identified as the physical origin of superlinear gain.Regulation randomness breaks flat peaks into smaller peaks, enabling additional peak-shaving savings.
  • Price Sensitivity: As peak-demand prices rise, jointly optimizing the two applications yields greater economic benefits.The reported mechanism is the interaction between regulation and peak shaving.
  • Price Sensitivity: As battery prices decrease, the battery can be used more aggressively for both applications, increasing the benefits of joint optimization.The paper projects increasing joint-optimization benefits as battery prices continue to fall.
  • Regulation-Payment Sensitivity: Superlinear-gain probability is highest when battery cell price and regulation capacity payment are both low, then decreases when capacity payment becomes sufficiently high.High capacity payments favor frequency regulation over peak shaving.

APPENDIX A

The appendix describes forecasting and scenario construction for the stochastic joint optimization: day-ahead load is predicted with MLR, while regulation uncertainty is represented by reduced historical scenarios.

  • Load Forecasting: Accurate short-term load forecasting is required to solve the stochastic joint optimization problem.The appendix identifies forecasting as an input requirement for the optimization.
  • Load Forecasting: A multiple linear regression model predicts next-day power demand from trend, temperature, calendar, and recent-load features.The model uses features including trend, temperature forecasting, month, hour interactions, weekend, holiday, and prior-day load.
  • Regulation Scenarios: One year of historical regulation data yields 365 daily scenarios, with each daily realization treated as one scenario.The scenarios empirically model uncertainty in future regulation signals.
  • Regulation Scenarios: Forward scenario reduction selects 10 representative scenarios and assigns them new probabilities to balance computational complexity and performance.The selected subset is intended to preserve information from the full scenario set; four are visualized in Fig. 12.

APPENDIX C PROOF OF THEOREM 1

The proof analyzes the optimal battery action by battery-cost and regulation-signal cases. Under the linear battery-cost model, the optimal battery action follows the regulation signal’s sign, with some regimes selecting no battery action.

  • Case Analysis: The proof partitions the analysis into five cases based on coefficient magnitudes and the sign of the regulation signal.The cases examine charging and discharging behavior under the linear battery-cost model.
  • Case Analysis: The optimal battery action b*(t) and regulation signal r(t) always have the same sign under the linear battery-cost model.Thus, charging and discharging are aligned with the regulation signal.
  • Optimal Action: For one analyzed regime, the optimal solution satisfies b*(t) = Cr(t).This relationship is stated as the resulting optimal battery action under the relevant feasibility conditions.
  • Case Analysis: When λb < λmis and r(t) < 0, the proof identifies a separate case with its corresponding optimal-action condition.The supplied result states the parameter and signal-sign condition but does not include the full displayed case expression.
  • No-Action Regime: When λb ≥ λmis, b*(t) = 0 is optimal for all C ≥ 0.The proof derives this by showing the regulation-service objective is maximized at zero battery action in that regime.
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