Risk-Aware Unit Commitment in District Heating Networks: Chance-Constrained and CVaR Optimization Under Demand Uncertainty
Abstract
While district heating networks are a key component of the energy transition, their operational planning is challenging due to substantial uncertainty in heat demand. We study how unit-commitment schedules can account for this uncertainty and what reliability costs. By adapting chance-constrained programming (CC) and conditional value-at-risk (CVaR) optimization to the mixed-integer unit-commitment problem for district-heating networks, we can compute optimal unit-commitment schedules under demand uncertainty. We generate heat demand scenarios using a Bayesian model, which explicitly quantifies forecasting uncertainty and yields predictive distributions as input to the network optimization. To handle the inherent uncertainty in heat demand, we apply two stochastic optimization approaches that exploit this distribution: chance-constrained programming limits the probability of unmet demand, and in our scenario-based setting reduces to a deterministic MIP in which demand is replaced by an empirical quantile, while CVaR optimization penalizes severe shortfalls in the tail of the distribution. We evaluate the approaches both on real-world data from the Berlin district heating network and on a benchmark set of synthetic, realistically parameterized instances of varying sizes. The results show that the two methods are complementary: CC cheaply traces the high-reliability end of the cost--reliability trade-off and reveals the physical reliability limit of the network, whereas CVaR covers the low-cost, risk-tolerant regime at considerably higher computational effort.
Related
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BibTeX
@misc{buchholz2026riskaware,
title = {{Risk-Aware Unit Commitment in District Heating Networks: Chance-Constrained and CVaR Optimization Under Demand Uncertainty}},
author = {Annika Buchholz and Janina Zittel and Thorsten Koch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.10899},
eprint = {2608.10899},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10899},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Risk-Aware Unit Commitment in District Heating Networks: Chance-Constrained and CVaR Optimization Under Demand Uncertainty
AU - Annika Buchholz
AU - Janina Zittel
AU - Thorsten Koch
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2608.10899
UR - https://arxiv.org/abs/2608.10899
AB - While district heating networks are a key component of the energy transition, their operational planning is challenging due to substantial uncertainty in heat demand. We study how unit-commitment schedules can account for this uncertainty and what reliability costs. By adapting chance-constrained programming (CC) and conditional value-at-risk (CVaR) optimization to the mixed-integer unit-commitment problem for district-heating networks, we can compute optimal unit-commitment schedules under demand uncertainty. We generate heat demand scenarios using a Bayesian model, which explicitly quantifies forecasting uncertainty and yields predictive distributions as input to the network optimization. To handle the inherent uncertainty in heat demand, we apply two stochastic optimization approaches that exploit this distribution: chance-constrained programming limits the probability of unmet demand, and in our scenario-based setting reduces to a deterministic MIP in which demand is replaced by an empirical quantile, while CVaR optimization penalizes severe shortfalls in the tail of the distribution. We evaluate the approaches both on real-world data from the Berlin district heating network and on a benchmark set of synthetic, realistically parameterized instances of varying sizes. The results show that the two methods are complementary: CC cheaply traces the high-reliability end of the cost--reliability trade-off and reveals the physical reliability limit of the network, whereas CVaR covers the low-cost, risk-tolerant regime at considerably higher computational effort.
ER -