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Optimal Coordination of Heat Pump Demand Flexibility and Battery Energy Storage Considering the Operation of Distribution Networks

Gustavo L. Aschidamini, Guilherme S. Castiglio, Mariana Resener

arXiv:2610.07841v1eess.SYcs.SY

TL;DR

Heating setpoints and battery operation are time-coupled, while rule-based and day-ahead approaches cannot both anticipate peaks and correct for realized conditions. The paper uses rolling-horizon MILP-based MPC to coordinate thermostat setpoints, storage, and voltage-regulation devices. The coordinated control lowered feeder peaks and relieved network constraints in the evaluated distribution networks.

  • Problem

    Heating setpoints and BESS operation are time-coupled, while rule-based and day-ahead approaches cannot both anticipate peaks and correct for realized demand and weather deviations.

    Source: §1 · p. 3

  • Method

    A rolling-horizon MILP-based MPC co-optimizes household HP/ERH thermostat setpoints, grid-scale BESS, and voltage-regulation devices.

    Source: §1 · p. 4

  • Results

    Coordinated control lowered feeder peak demand, relieved branch and transformer congestion, and recovered nodal voltages while maintaining indoor comfort and reducing heating energy use.

    Source: §5 · p. 15

  • Takeaways & Limitations

    Coordinating heating flexibility with voltage-regulation assets and BESS allows MV distribution feeders to host higher HP electrification without reinforcement.

    Source: §5 · p. 15

    Future work includes unbalanced-network modeling and robust or chance-constrained voltage control to strengthen undervoltage mitigation under forecast uncertainty, at added rolling-horizon computational cost.

    Source: §5 · p. 15

Abstract

from arXiv · show

Electrifying space heating with heat pumps (HP) and backup electric-resistance heaters (ERH) is incentivized to support decarbonization but increases voltage and thermal issues in distribution networks. Direct load control (DLC) of smart thermostats (ST) provide grid support, yet, to the best of our knowledge, existing methods do not co-optimize this flexibility with grid-scale battery energy storage systems (BESS) and voltage-regulation devices, and do not use ERH for preheating, limiting peak demand reduction and undervoltage mitigation. We propose a mixed-integer linear programming (MILP)-based model predictive control (MPC) framework that coordinates ST setpoints for preheating and setback, grid-scale BESS, on-load tap changers, switched capacitor banks, and step voltage regulators. The framework is evaluated on 23-node and 733-node distribution networks, including a real-data-based feeder, across multiple realized days. On the 23-node feeder with 50% HP penetration and 50% DLC participation, the proposed framework reduces the feeder peak by 23.1%, and by 27.1% with the co-optimized BESS. Rolling-horizon setpoint optimization contributes 6.5 percentage points beyond a day-ahead ST schedule (16.6%), and dispatching the ERH for preheating adds 2.7 percentage points beyond backup-only operation (20.4%). On the 733-node feeder, where thermal congestion is the binding constraint, the framework reduces overloaded branches by 94% and overloaded transformers by 47%. These results demonstrate the potential of coordinated demand flexibility and voltage regulation to accommodate heating electrification.

1. Introduction

Heating electrification increases pressure on distribution networks, while existing approaches leave household thermal flexibility, storage, and utility voltage-regulation assets insufficiently coordinated. The paper proposes rolling-horizon control of these resources and evaluates its effects on feeder peaks, congestion, and voltage.

1. Introduction

  • Prior methods address aggregated heating loads, network-constrained flexibility, storage, or utility voltage-device coordination, but leave key resources uncoordinated.The identified gap includes ST thermal-setpoint control, ERH preheating, grid-scale BESS, and utility voltage-regulation devices.Source: §1 · p. 3
  • Rolling-horizon MPC combines forecast-based planning with feedback re-optimization, unlike rule-based control or day-ahead schedules that cannot correct realized demand and weather deviations.Heating setpoints and BESS state of charge link decisions across time intervals.Source: §1 · p. 3
  • The proposed centralized MILP-based MPC co-optimizes household HP/ERH thermostat setpoints, grid-scale BESS, and OLTC, SCB, and SVR voltage-regulation devices.It re-solves over a forecast look-ahead horizon using realized base-load and outdoor-temperature states.Source: §1 · p. 4
  • ERH preheating adds flexibility to shift heating demand away from feeder peaks when HP capacity alone cannot provide sufficient preheating.The ERH is used for additional preheating rather than only as a comfort backup.Source: §1 · p. 4
  • The co-optimized BESS supplies flexibility alongside building thermal mass and voltage-regulation devices, with an intra-day switching limit constraining battery cycling.The evaluation benchmarks the coordinated scheme against controls that add a grid-scale BESS.Source: §1 · p. 4
  • Coordinated control lowered feeder peak demand, relieved branch and transformer congestion, and recovered nodal voltages while maintaining indoor comfort and reducing heating energy use.The framework was evaluated on a 23-node test system and a real 733-node network.Source: §1 · p. 4

2. Proposed Optimization Model

The proposed MILP-based MPC coordinates building heat flexibility with batteries and voltage-regulation devices using day-ahead forecasts and rolling-horizon control. Its model represents building heating, network operation, and alternative control regimes.

2. Proposed Optimization Model

  • The MILP-based MPC coordinates ST-controlled HP and ERH, grid-scale BESS, and voltage-regulation devices, with day-ahead SVR settings and rolling-horizon control actions.It minimizes power-loss and voltage-violation costs while updating forecasts and implementing only the first action at each solve.Source: §2 · p. 4

2.1. Building Thermal Dynamics Modeling

  • A single-zone RC model links indoor temperature to HP and ERH heating, with thermostat setpoints constrained to the thermal-comfort band.HP output tracks the commanded setpoint; ERH heating is modeled in discrete stages.Source: §2.1 · p. 5

2.2. Non-DLC Household Heating Simulation

  • Non-DLC households’ HP and ERH powers are simulated as loads before each rolling solve, with ERH enabled below the HP balance-temperature threshold.If combined heating capacity cannot reach the setpoint, indoor temperature undershoots it.Source: §2.2 · p. 6

2.3. Battery Energy Storage Systems

  • BESS state of charge is bounded, updated over time, and closed cyclically so end-of-day charge returns to its initial value.Charging and discharging are mutually exclusive, and current limits use a polygonal approximation of the feasible region.Source: §2.3 · p. 6

2.4. Switched Capacitor Banks

  • The SCB selects one discrete operating level, setting reactive current injection according to the selected level and nodal voltage.The model uses a big-M formulation with a constant-impedance characteristic.Source: §2.4 · p. 7

2.5. Voltage-Regulation Devices

  • OLTC, SVR, and SCB operation is represented through tap, voltage-band, and switching constraints, with SVR saturation allowing voltage outside its dead band.The SVR uses load-drop compensation to estimate downstream voltage from local voltage and branch current.Source: §2.5 · p. 7

2.6. Control Regimes

  • The control regimes compare rolling-horizon ST flexibility against day-ahead setpoints, local voltage-device control, ERH backup-only operation, and co-optimized BESS.The comparisons isolate the effects of each design choice while retaining the remaining network, thermal, and device constraints.Source: §2.6 · p. 8

3. Case Studies Setup

The case studies use two three-phase, 13.8 kV networks and heterogeneous building-heating models, then test control configurations across realized base-load days. Weather, comfort bounds, and customer participation define the evaluation conditions.

3. Case Studies Setup

  • The framework is tested on a 23-node network and a real 733-node network, both three-phase overhead systems operating at 13.8 kV.The networks serve 1,760 and 3,215 end-users, respectively.Source: §3 · p. 8, Figure 3 · p. 9

3.1. Building Thermal Dynamics Characteristics and Weather Data

  • Across the 2014–2024 winter record, modeled per-house space-heating demand ranges from approximately 6.2 to 9.8 MWh per winter.House thermal resistance and capacitance are sampled independently to represent variation in insulation and thermal mass.Source: §3.1 · p. 9
  • Heat pumps are sized for −12°C, a deliberately cold design temperature between the winter average of −10.9°C and minimum of −14.5°C.Only 0.13% of recorded winter hours fall below −12°C.Source: §3.1 · p. 9
  • Backup ERHs engage below house-specific balance-point thresholds clustered between −9.4°C and −13.4°C; in the historical coldest scenario, they operate for 29% of the day.They remain off when outdoor temperatures stay above their thresholds.Source: §3.1 · p. 10
  • Indoor comfort is assessed with mean absolute indoor-temperature error and the percentage of time deviation exceeds 0.5°C.These are the temperature deviation index and deviation period index, respectively.Source: §3.1 · p. 10

3.2. Control Configurations

  • The MPC uses an eight-step look-ahead with 0.5-hour steps and indoor-temperature bounds of 19–21°C.Uncontrolled houses use a fixed 20°C setpoint.Source: §3.2 · p. 10
  • Scenarios vary heat-pump penetration and DLC participation, using 5 realized base-load days for the 23-node network and 15 for the 733-node network.Realized peaks span 5.35–6.04 MW and 4.17–5.77 MW, respectively, versus day-ahead predictions of 5.02 MW and 4.44 MW.Source: §3.2 · p. 10

4. Numerical Results

The results compare coordinated thermostat control and battery storage with restricted-control baselines across two distribution networks. They assess peak demand, heating use and comfort, voltage, congestion, and computational performance.

4.1.1. Value of Demand-Side Flexibility

  • At 50% HP penetration and 50% DLC, ST reduces the 23-node feeder peak by 23.1%; adding BESS raises the reduction to 27.1% while lowering voltage-violation cost from $19.0 to $1.3–1.5.ST and ST+BESS also achieve an average objective-function cost of $818.1–827.1, 17% below BASE.Source: §4.1.1 · p. 10, Figure 4 · p. 11, Table 4 · p. 11
  • At 50% HP penetration and 50% DLC, rolling-horizon ST lowers the peak to 7.7 MVA versus 8.3 MVA for ST-DA, a 23.1% versus 16.6% reduction relative to BASE.The rolling-horizon schedule also lowers objective-function cost to $827.1 versus $848.8.Source: Figure 4 · p. 11, §4.1.1 · p. 11, Table 4 · p. 11

4.1.2. Heating Energy Use, Comfort, and Efficiency

  • DLC reduces heating electricity use by about 8% at 50% HP penetration, while controlled-house temperatures remain within the admissible 19–21°C band.At 50% HP penetration, dispatching ERH for preheating lowers peak demand to 7.7 MVA versus 8.0 MVA for backup-only operation, but lowers effective COP from 2.04 to 1.94.Source: §4.1.2 · pp. 11–12, Table 5 · p. 12, Table 6 · p. 13

4.1.3. Rolling Horizon Co-Optimization of the Voltage Regulation Devices

  • At 50% HP penetration and 50% DLC, ST recovers minimum MV voltage to approximately 0.95 pu; STVR-DA leaves it at 0.91 pu.Central coordination achieves 0.947 pu versus 0.949 pu for STVR-local, while lowering peak demand to 7.7 MVA versus 8.0 MVA.Source: §4.1.3 · p. 13, Figure 8 · p. 14

4.1.4. Battery Energy Storage System Operation

  • Across realized days, ST provides 2.31 ± 0.30 MVA of daily-peak reduction, while BESS adds 0.40 ± 0.17 MVA; thermostats deliver about 85% of the total reduction.Together they reduce the peak by 2.72 ± 0.44 MVA, or 27.1%.Source: Figure 9 · p. 14, §4.1.4 · p. 14

4.2. Application Example: 733-Node Distribution Network

  • At 50% HP penetration, ST+BESS cuts 733-node peak demand by 19.4% to 10.3 MVA; at 50% DLC, ST reduces overloaded branches by 93.7% and overloaded transformers by 47%.ST+BESS reduces overloaded branches to 0.1 at 50% DLC.Source: §4.2 · pp. 14–15, Figure 10 · p. 15, Figure 11 · p. 15

4.3. Computational Performance of the Proposed MILP-based MPC Framework

  • The maximum solution time generally increases with HP penetration, DLC rate, and inclusion of BESS in the co-optimization.Table 8 reports maximum computational time across penetration levels, DLC rates, and BASE, ST, and ST+BESS regimes.Source: §4.3 · p. 15, Table 8 · p. 15

5. Conclusions

The framework coordinates household heating flexibility, voltage-regulation devices, and grid-scale BESS through rolling-horizon MILP-based MPC. Its evaluation finds feeder-specific improvements in peak demand, congestion, voltage, comfort, and heating energy use, while identifying extensions for future work.

5. Conclusions

  • Across the evaluated networks, coordinated ST control lowers feeder peaks, relieves congestion, recovers nodal voltages, keeps indoor temperatures within the comfort band, and reduces end-user heating energy use.Undervoltage binds on the long, high-impedance 23-node feeder; thermal congestion binds on the 733-node feeder.Source: §5 · p. 15
  • Coordinating ST setpoints with voltage-regulation devices and storage may turn existing ST demand-response programs into a network-operation resource.The comparisons find rolling-horizon setpoints outperform day-ahead ST scheduling; ERH preheating deepens peak reduction at a small heating-efficiency cost.Source: §5 · p. 15
  • Future work includes unbalanced-network representation and robust or chance-constrained voltage control, with additional computation for rolling-horizon operation.Source: §5 · p. 15

A. Autonomous Operation of OLTC and SCB

The OLTC uses autonomous line-drop control, mapping substation current to a voltage target that is quantized to a physical tap. The SCB switches locally to maintain a voltage threshold, with relaxation only when it is saturated.

A. Autonomous Operation of OLTC and SCB

  • The OLTC maps substation current to a continuous voltage target, quantizes it to the nearest physical tap, and allows resting at either regulation limit.Saturation slacks accommodate targets outside the regulation range.Source: A. Autonomous Operation of OLTC and SCB · p. 16
  • The SCB switches autonomously from its own node voltage, retaining level selection and constant-impedance injection while adding local switching logic.Its voltage threshold can be relaxed only when all levels are switched in and no further level can be added.Source: A. Autonomous Operation of OLTC and SCB · p. 16
  • The OLTC droop is calibrated to 0.068 pu/pu, with a 0.989 pu base point and 0.00625 pu tap deadband.The calibration spans 1.00–1.05 pu substation voltage and 54–301 A load current.Source: A. Autonomous Operation of OLTC and SCB · p. 16
  • At node 21, the SCB holds voltage at or above 0.98 pu and incurs a switching penalty of 1.0 per level per step.The penalty encourages switching in only the fewest levels needed to meet the threshold and is excluded from reported objective values.Source: A. Autonomous Operation of OLTC and SCB · p. 16

B. Control of ST with ERH as Comfort-Floor Backstop Only (STERH-bkp)

When any stage is on, the commanded setpoint is pinned to the lower comfort bound.

B. Control of ST with ERH as Comfort-Floor Backstop Only (STERH-bkp)

CRediT authorship contribution statement

The contribution statement assigns conceptualization, methodology, analysis, and writing roles across the three authors, alongside supervision, project administration, and funding acquisition.

CRediT authorship contribution statement

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process

The authors used Claude and ChatGPT to refine clarity and grammar during manuscript preparation, and state that the tools were not used for analysis, interpretation, or original findings.

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process

  • Claude and ChatGPT assisted with clarity and grammar; authors reviewed and revised the generated content and retained responsibility for the research and conclusions.The authors state that no AI tools were used in analysis, data interpretation, or generation of original findings.Source: Declaration of generative AI and… · p. 16
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