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Robust Energy-Constrained Frequency Reserves from Aggregations of Commercial Buildings

Evangelos Vrettos, Frauke Oldewurtel, Göran Andersson

arXiv:1506.05399v1eess.SYcs.SYmath.OC

TL;DR

Energy-constrained and potentially biased frequency signals make reliable reserve scheduling important for commercial-building aggregations. The paper proposes a robust, three-level framework for allocating reserves, controlling HVAC consumption, and providing reserves in real time. In simulations, the authors report that aggregations of approximately 100 commercial buildings can reliably offer significant SFC reserves without loss of occupant comfort.

  • Problem

    Because buildings are energy-constrained, biased frequency signals can limit reserve availability, making a priori scheduling important for reliable participation without compromising comfort.

    Source: §1 · p. 3

  • Method

    A robust framework schedules and allocates reserves among buildings, uses robust MPC for HVAC control, and applies feedback control for real-time reserve provision.

    Source: §1 · p. 3, §4.1 · pp. 9–10

  • Results

    Approximately 100 commercial buildings can reliably offer significant SFC reserves without loss of occupant comfort; energy-constrained signals increase reserves by up to approximately 10% compared with traditional signals.

    Source: §7 · p. 25

  • Takeaways & Limitations

    The simulations indicate that commercial-building aggregations can provide substantial SFC reserves while maintaining occupant comfort.

    Source: §7 · p. 25

    The reported results assume no plant-model mismatch, perfect weather and occupancy predictions, measured building states, and fast devices without wear, and therefore provide an upper bound on building reserves.

    Source: §7 · p. 25

Abstract

from arXiv · show

It has been shown that the heating, ventilation, and air conditioning (HVAC) systems of commercial buildings can offer ancillary services to power systems without loss of comfort. In this paper, we propose a new control framework for reliable scheduling and provision of frequency reserves by aggregations of commercial buildings. The framework incorporates energy-constrained frequency signals, which are adopted by several transmission system operators for loads and storage devices. We use a hierarchical approach with three levels: (i) reserve capacities are allocated among buildings (e.g., on a daily basis) using techniques from robust optimization, (ii) a robust model predictive controller optimizes the HVAC system consumption typically every 30 minutes, and (iii) a feedback controller adjusts the consumption to provide reserves in real time. We demonstrate how the framework can be used to estimate the reserve capacities in simulations with typical Swiss office buildings and different reserve product characteristics. Our results show that an aggregation of approximately 100 buildings suffices to meet the 5 MW minimum bid size of the Swiss reserve market.

1 Introduction

The paper addresses reliable frequency-reserve scheduling by commercial-building aggregations, where energy-constrained signals and biased activation complicate reserve availability. It proposes a robust, hierarchical framework to allocate reserves and estimate capacity across buildings and signal conditions.

1 Introduction

  • Commercial HVAC systems are promising demand-response resources because they are large loads with thermal inertia and building automation, while prior commercial-building work mainly addressed slower services.Earlier SFC studies examined fan-power control, campus buildings, and heat-pump control, including simulation and experimental demonstrations.Source: §1 · p. 2
  • Energy-constrained signals can remain biased over several hours, making reserve scheduling important for buildings whose available flexibility is limited by energy.Biased renewable-energy forecast errors may contribute to biased signals; the authors argue that scheduling capacity according to signal bias will matter increasingly.Source: §1 · pp. 3–4
  • The framework combines reserve scheduling and allocation, HVAC control, and real-time reserve provision using robust optimization and model predictive control.It accounts for weather, occupancy, electricity prices, reserve payments, and comfort, and allocates reserves according to individual building characteristics.Source: §1 · p. 3
  • The framework estimates capacity for energy-constrained signals and allocates reserves among buildings, rather than scaling a single-building estimate to an aggregation.It also derives upper bounds on untapped potential across building types and reserve products varying in duration, symmetry, and energy content.Source: §1 · p. 3
  • The paper proposes methods to schedule aggregation reserve capacity according to the bias of an energy-constrained frequency signal.The authors describe this as the first systematic approach of this kind for building aggregations.Source: §1 · p. 4

2 Frequency Control in Power Systems

Frequency control balances electricity supply and demand to keep system frequency and voltage near nominal values. This section outlines the roles of primary, secondary, and tertiary control and describes how reserve markets procure and activate secondary frequency-control reserves.

2 Frequency Control in Power Systems

  • Primary control stabilizes frequency after a disturbance, secondary control restores nominal frequency and desired inter-area exchanges, and tertiary control releases secondary control during large disturbances.Primary control is distributed and proportional; secondary control is centralized and proportional-integral; tertiary control is typically activated manually.Source: §2 · pp. 4–5
  • Reserve products and auctions vary by country; bid requirements commonly range from 1 to 10 MW, and Switzerland's minimum bid size is 5 MW.Markets may require symmetric or allow asymmetric reserves, and activation may be pro-rata or merit-order.Source: §2 · p. 5
  • TSOs typically send reserve-energy requests every 2–4 seconds, while reserve-energy remuneration is country-dependent and may be separate from capacity payments.In Switzerland, reserve-energy remuneration is coupled with the spot-market energy price.Source: §2 · p. 5
  • The paper treats the SFC signal as uncertain because it is unknown when reserve capacities are determined.Source: §2 · p. 5

3 Modeling

The modeling section represents commercial buildings, their reserve response, and the frequency signals that constrain reserve activation. It formulates building and aggregation constraints and identifies uncertainty assumptions used by the framework.

3.1 Building Aggregation

  • Integrated room automation buildings are represented with validated 12th-order bilinear thermal models, capturing HVAC and other controls while remaining suitable for MPC.The model covers heating, cooling, ventilation, blinds, and lighting, and can be customized for representative building types.Source: §3.1 · p. 5
  • The aggregation model combines building states, inputs, disturbances, and actuator reserve capacities; reserve-induced heat-flux changes depend on the SFC signal.The reserve-capacity matrix is block diagonal in the formulation, so each time-step reserve depends on the current signal; the paper notes that its more general lower-triangular form can represent past-signal effects.Source: §3.1 · pp. 6, 8
  • The building model constrains HVAC inputs and comfort outputs, while aggregation enables market participation when individual buildings cannot meet bid-size or product requirements.The paper also notes that aggregating buildings with different characteristics can yield more total reserve capacity than individual market participation.Source: §3.1 · p. 7

3.2.1 Power Constraints (PC)

  • For power-constrained activation, the normalized SFC signal is bounded between −1 and 1, representing activation from full up-reserve to full down-reserve.Source: §3.2.1 · p. 8

3.2.2 Power and Energy Constraints (PEC)

  • For power-and-energy-constrained signals, the TSO fixes bias coefficient ε and averaging period T, bounding the signal's mean over T while retaining power constraints.Stacking these conditions produces a polyhedral uncertainty set for the SFC signal.Source: §3.2.2 · pp. 8–9

3.3 Other Sources of Uncertainty

  • The formulation assumes perfect weather and occupancy predictions and constant retail electricity tariffs; it excludes uncertainty in reserve-market clearing prices.Weather and occupancy uncertainty could be incorporated using approaches such as stochastic MPC, scenario-based MPC, or constraint tightening.Source: §3.3 · p. 9

4.1 Hierarchical Scheme

The hierarchical scheme coordinates reserve scheduling, local HVAC control, and real-time tracking. It trades energy-efficient operation against the slack needed to deliver reserves while maintaining occupant comfort.

4.1 Hierarchical Scheme

  • The aggregator centrally schedules reserve capacity and its allocation among buildings each day, balancing energy consumption against the slack needed for reserve provision.The tradeoff depends on reserve-capacity payments and electricity costs.Source: §4.1 · p. 9
  • Scheduling uses building-state measurements and electricity and reserve prices, together with weather and occupancy predictions, to respect comfort when reserves are requested.Robust optimization is used because TSOs typically require 100% reserve-capacity availability and HVAC input limits are hard constraints.Source: §4.1 · p. 10
  • Local robust MPC determines energy-optimal HVAC inputs every 30 minutes and leaves slack for reserves; a feedback controller tracks the SFC signal in real time, for example every 10 seconds.Source: §4.1 · p. 10

4.2 Lv1: Aggregator Scheduling

Lv1 schedules and allocates reserve capacity by minimizing costs while accounting for reserve payments and worst-case uncertainty. Its robust counterparts differ for power-only and power-and-energy constraints, with a limitation for asymmetric reserves under energy constraints.

4.2 Lv1: Aggregator Scheduling

  • Lv1 chooses the reserve capacities to offer by balancing electricity costs against reserve payments, with actuator efficiency and building losses included in those vectors.The robust constraints require input and output limits to hold under the worst-case uncertainty realization.Source: §4.2 · pp. 10–11

4.2.1 Robust Counterpart for Power Constraints

  • For power constraints, analytic maximization yields an L1-norm robust counterpart; its linear program grows quadratically with the prediction horizon.When each building uses only heating or only cooling actuators, the formulation can be simplified to a linear program the same size as the original scheduling problem.Source: §4.2.1 · pp. 11–12

4.2.2 Robust Counterpart for Power and Energy Constraints

  • For power-and-energy constraints, dualization yields a linear-program counterpart that grows quadratically with the prediction horizon; asymmetric reserves cannot use this approach when simultaneous up- and down-requests are excluded.That exclusion makes the uncertainty set non-polyhedral.Source: §4.2.2 · pp. 12–13

4.3 Lv2: Building HVAC Control

Lv2 sets each building’s HVAC consumption using robust MPC based on the Lv1 reserve allocation. Its schedule provides a baseline while accounting for uncertainty and rebound effects.

4.3 Lv2: Building HVAC Control

  • Every 30 minutes, robust MPC determines building HVAC inputs using the reserve allocation from Lv1, and the first optimized input sets consumption for the next interval.The controller uses open-loop predictions because closed-loop predictions showed minor or zero performance improvement in this case.Source: §4.3 · p. 13

4.3.1 Robust Counterpart for Power Constraints

  • The Lv2 schedule is the building’s baseline consumption, communicated to the aggregator, and MPC accounts for future rebound effects when setting HVAC inputs.Its closed-loop operation can reduce constraint violations under plant-model mismatch; the formulation also avoids requiring separate baseline-prediction methods.Source: §4.3.1 · p. 13

4.3.2 Robust Counterpart for Power and Energy Constraints

  • For power-and-energy constraints, the robust counterpart uses time-varying constraint matrices, and its energy coupling depends on the SFC signal’s already-realized history in the averaging interval.The allocated reserve is fixed in Lv2.Source: §4.3.2 · p. 14

4.4 Lv3: Frequency Signal Filtering and Tracking

Lv3 adjusts HVAC consumption in real time to track reserve requests, while signal filtering provides energy-constrained requests and their bias is conveyed to the slower scheduling levels. The simulations assume negligible heat-pump dynamics and perfect tracking when comfort and input constraints are met.

4.4 Lv3: Frequency Signal Filtering and Tracking

  • Lv3 controls heat-pump consumption around the Lv2 setpoint, using valve-based refrigerant-flow control and a feedback PI controller to track the desired consumption.The paper considers common European water-based HVAC systems and notes that the reserve-scheduling problem also applies to air-based systems.Source: §4.4 · p. 14
  • A causal Chebyshev filter produces energy-constrained SFC requests whose bias may remain nonzero but bounded; the slower Lv1 and Lv2 optimizations account for filtering through signal-integral constraints.The bias coefficients for different averaging periods can be empirically obtained by filtering historical SFC data.Source: §4.4 · p. 15
  • Robust design keeps comfort-zone and input constraints satisfied for admissible reserve requests only when there is no significant plant-model mismatch; simulations assume negligible heat-pump dynamics and perfect tracking under those constraints.Tracking quality otherwise depends on actuator delays, dead-times, ramping limits, and minimum run-times or down-times.Source: §4.4 · pp. 15–16

5 Performance of Control Framework

Simulations with typical Swiss office buildings show seasonal reserve capacities that extrapolate to roughly 100 similar buildings for the Swiss 5 MW minimum. The framework’s operation also involves a reserve-capacity trade-off with energy use, and its guarantees assume perfect weather and occupancy predictions.

5.1 Investigation Setup

  • The simulations use six 15,000 m2 Swiss office buildings, two HVAC system types, and 30-minute optimization steps.The study varies envelope, window area, and internal gains, and excludes ventilation from reserve provision.Source: §5.1 · p. 16

5.2 Parameters of Energy Constraints

  • For the simulations, the 2012 high-frequency signal uses an energy constraint of T = 2 h and ε = 0.3.These parameters were selected from historical Swiss SFC signals; the original signals could be significantly biased over periods of several hours.Source: §5.2 · p. 17

5.3 Operation for Typical Weeks

  • The original SFC signal is mostly negative, while its bias is absorbed by the LF component, leaving the HF component approximately zero-mean.The SFC bias exceeds 0.3, whereas the energy-constrained HF signal’s bias is below 0.15.Source: §5.3 · p. 17, Figure 2 · p. 18, Figure 3 · p. 18
  • 313 kW in winter and 323 kW in summer are the six-building aggregation’s respective average weekly reserve capacities.Winter capacity ranges from approximately 260 kW Friday to 380 kW Saturday; summer ranges from approximately 60 kW Sunday to 420 kW Saturday.Source: §5.3 · pp. 17–18
  • HVAC inputs and room temperature remain within the robust region in simulations, which supports feasibility for admissible reserve requests under the stated conditions.The guarantee assumes no significant plant-model mismatch; the paper’s formulations and simulations also assume perfect weather and occupancy predictions.Source: §5.3 · p. 18, Figure 5 · p. 19, Figure 6 · p. 19
  • 96 similar buildings in winter and 93 in summer are estimated to meet Switzerland’s 5 MW minimum reserve capacity.The estimate uses linear extrapolation and is described as rough, based on average reserve capacity values.Source: §5.3 · p. 19

5.4 Effect on Energy Consumption

  • 60% higher winter-week consumption is reported versus energy-efficient MPC without reserves, while the reserve operation minimizes total cost for the given prices and payments.Buildings operate nearer the middle of the device power range to provide reserves in both directions; the comparison is against MPC-based energy-efficient control.Source: §5.4 · pp. 19–20

5.5 Discussion on Imperfect Disturbance Predictions

  • Perfect weather and occupancy predictions are assumed; the robust formulation does not mathematically guarantee worst-case temperature deviations under imperfect predictions.The authors suggest Monte Carlo simulations or scenario-based methods for investigating imperfect predictions.Source: §5.5 · p. 20

6 Sensitivity Analysis

The sensitivity analysis relates reserve capacity to capacity payments and reserve-product design. Energy-constrained signals, shorter products, and the parameters governing energy constraints affect the capacities buildings are willing or able to offer.

6.1 Capacity Payments

  • For conventional signals, reserve provision requires k/c > 1 pointwise; with daily reserves, a higher day-average ratio can suffice even when k/c < 1 during daytime.The paper explains this through the scheduling problem’s optimal solution and electricity prices that may be lower at night.Source: §6.1 · p. 21
  • Energy-constrained signals let buildings store part of requested daytime up-regulation as thermal energy, reducing heating or cooling needs and costs the following day.The capacity threshold is k/c = 0.32 in both seasons, and capacity rises slowly from 0.32 to 0.99 before jumping as k/c approaches 1.Source: §6.1 · p. 22
  • At k/c = 1.01, unconstrained SFC signals tap most reserve potential; energy-constrained signals can lower the provision threshold to 0.32, but with much less capacity.The bid curves compare winter and summer; the 0.32 threshold depends on ε and T.Source: §6.1 · p. 22, Figure 7 · p. 23

6.2 Reserve Product Characteristics

  • For conventional signals, hourly symmetric reserves increase capacity by 2.9% in winter and 3.3% in summer versus daily reserves; asymmetric products favor down-reserves.Down-reserves can be offered on the energy-efficient trajectory, whereas up-reserves require a higher baseline that increases energy costs.Source: §6.2 · p. 23
  • Compared with conventional signals, energy-constrained signals increase reserves by up to 3.8% in winter and 5.6% in summer; hourly products add up to 2% and 9.6%, respectively.The hourly-product increases are higher for large T.Source: §6.2 · p. 23
  • The T-and-ε exploration simulated reserve scheduling only, because many combinations were not achievable by the Chebyshev filter and likely made HVAC control infeasible.It covers 60 (T, ε) combinations per season and is intended to provide intuition for filter design; Table 2 results are not directly comparable with the earlier paper’s because the COP values differ.Source: §6.2 · pp. 23–24
  • Increasing T or ε generally reduces capacity, and in 70% of equal-εT winter and summer comparisons, smaller ε is preferable to smaller T.For εT = 2, (8 h, 0.25) yields 96.72 MW, while (4 h, 0.5) yields 93.61 MW.Source: §6.2 · p. 24

7 Concluding Remarks

The conclusion presents a robust-optimization and MPC framework for scheduling and providing SFC reserves from commercial-building HVAC systems. It reports substantial reserves from about 100 buildings without loss of comfort, while noting that idealized assumptions make the estimates an upper bound.

7 Concluding Remarks

  • The framework uses robust optimization and MPC to schedule and provide SFC reserves through commercial-building HVAC systems, with decentralized provision to reduce real-time communication needs and preserve privacy.It also estimates the reserve potential of commercial buildings.Source: §7 · p. 25
  • The reported reserve results are upper bounds because the analysis assumes no plant-model mismatch, perfect weather and occupancy predictions, measurable building states, and fast, wear-free device responses.Real implementation requires addressing these assumptions, including prediction errors, state estimation, and device dynamics.Source: §7 · p. 25
  • About 100 commercial buildings can reliably offer significant SFC reserves without loss of occupant comfort; energy-constrained signals reduce necessary capacity payments and increase reserves by up to ∼10%.Reducing reserve-product duration from one day to one hour increases reserves by up to ∼9%.Source: §7 · p. 25
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