Source-linked AI summary
Operational thermal load forecasting in district heating networks using machine learning and expert advice
Davy Geysen, Oscar De Somer, Christian Johansson, Jens Brage, Dirk Vanhoudt
TL;DR
Thermal-load forecasts support optimization of district-heating controllers. This paper combines forecasts from multiple data-driven experts, and its expert system tracks the best expert over the test set, the ANN with the full feature set.
Problem
District-heating controller optimization depends on predicting future thermal load and network behavior.
Source: §1 · p. 2Method
A fixed-share expert system combines forecasts from eight experts that vary by machine-learning method and input feature set.
Source: §4.1 · p. 9, §8 · p. 20Results
Over the test set, the expert system tracked the best expert, the ANN with the full feature set.
Source: §8 · p. 22Takeaways & Limitations
The forecaster's performance increased with higher thermal loads, a helpful property for a control system intended to limit high loads.
Source: §7.2 · p. 18The evaluation is a 27-month case study, and daily retraining did not improve performance when the DHS remained unchanged.
Source: §7.2 · p. 20, §8 · pp. 20, 22
Abstract
from arXiv · showhide
Forecasting thermal load is a key component for the majority of optimization solutions for controlling district heating and cooling systems. Recent studies have analysed the results of a number of data-driven methods applied to thermal load forecasting, this paper presents the results of combining a collection of these individual methods in an expert system. The expert system will combine multiple thermal load forecasts in a way that it always tracks the best expert in the system. This solution is tested and validated using a thermal load dataset of 27 months obtained from 10 residential buildings located in Rottne, Sweden together with outdoor temperature information received from a weather forecast service. The expert system is composed of the following data-driven methods: linear regression, extremely randomized trees regression, feed-forward neural network and support vector machine. The results of the proposed solution are compared with the results of the individual methods.
1. Introduction
Forecasting district-heating thermal load supports prediction of network behavior and controller optimization. The paper situates its work among data-driven approaches that learn from historical behavior.
1. Introduction
- Thermal-load forecasts help predict district-heating network behavior and support controller optimization.The work is presented as part of the Horizon 2020 STORM project to develop a generic district heating and cooling network controller.Source: §1 · p. 2
- Thermal-load forecasting approaches range from historical-load-only models to methods adding occupancy, weather, or building-physics inputs.The paper distinguishes forward methods based on physical equations from data-driven methods based on historical system behavior; data-driven methods include statistical and machine-learning models.Source: §1 · p. 2
2. Forward versus data-driven
The section contrasts physical forward models with data-driven forecasting and argues that the latter better fit operational thermal-load prediction.
2. Forward versus data-driven
- Forward methods approximate building thermal load from physical principles, using models ranging from simple material-property estimates to detailed building simulations.Developing detailed models can be costly and time-consuming because they require extensive system information and expert knowledge; tools such as EnergyPlus and TRN-SYS include such models.Source: §2 · pp. 2–3
- Data-driven methods model thermal load from historical building behavior and relate it to influential inputs such as weather and past load.They require historical behavioral data and are often used as baselines against more elaborate methods.Source: §2 · p. 3
- The paper argues data-driven methods are better suited to operational thermal-load prediction because forward models are costly, time-consuming, and poorly generalizable.Prior comparisons found forecast errors from detailed EnergyPlus models comparable to ANNs trained on 17 months of historical data.Source: §2 · p. 3
3. Machine learning
The paper applies linear regression, artificial neural networks, support vector machines, and extremely randomized trees to thermal-load forecasting, alongside varying levels of input complexity.
3. Machine learning
- The study applies LR, ANNs, SVMs, and ETRs as data-driven forecasting methods.These methods are introduced as machine-learning approaches for constructing complex models and prediction algorithms [10, 13–19].Source: §3 · p. 4
3.1. Linear regression
- LR models a scalar dependent variable from explanatory variables and serves as a baseline for evaluating machine-learning methods.The paper restricts its treatment to multiple linear regression and models thermal load P at time t with a linear equation [8],,.Source: §3.1 · p. 4
3.2. Artificial Neural Networks
- ANNs process inputs through weighted linear combinations and nonlinear transformations to produce forecast outputs.They learn patterns and relationships from available data; cited applications include electricity consumption in Iranian agriculture and gasoline consumption in Lebanon.Source: §3.2 · pp. 4–5
3.3. Support vector machines
- SVM regression maps inputs to a higher-dimensional feature space to learn a nonlinear function for continuous target values.Earlier studies report differing comparisons with ANNs: SVMs were more accurate in one cooling-load study, while another found comparable performance.Source: §3.3 · p. 5
3.4. Extremely randomized trees regressor
- ETRs average predictions from trees built with randomly generated input-space splits, which the paper associates with better generalization and reduced noise susceptibility.The approach is also described as less computationally complex than classical trees and other ensemble methods; prior work found ETRs more accurate than extreme-learning machines.Source: §3.4 · pp. 5–6
4. Expert advice
The paper combines daily forecasts from a fixed set of experts to track the best expert, using weighted aggregation rules that update experts according to their losses.
4. Expert advice
- Prediction with expert advice combines multiple thermal-load forecasting experts to track the best-performing expert rather than merely compare individual methods.The approach accommodates stochastic models with different assumptions [25–29].Source: §4 · p. 6
- Each day, experts forecast the next 24 hours; the forecaster combines their predictions and evaluates their losses against observed thermal load.The procedure repeats across daily rounds using a fixed, finite expert set and a fixed loss function.Source: §4 · pp. 6–7
- The forecaster aims for small regret, defined as its accumulated loss minus the loss of the best expert in hindsight.Regret measures the cost of not having followed a particular expert's advice.Source: §4 · p. 7
4.1. Aggregation rules
- Fixed share and ML-Poly assign weights to experts based on losses; fixed share adds a mixing parameter α, and both rules minimize regret.A positive α gives each expert a minimum weight; ML-Poly performed as well as fixed share in this study, so the paper discusses fixed-share results for simplicity.Source: §4.1 · pp. 8–9
5. Case study
The case study uses the Rottne, Sweden district heating system and its ten largest consumers, which represent nearly one-third of system heat demand. Forecasting matters because reaching about 2.7 MW normally triggers the diesel burner.
5. Case study
- The study uses a traditional third-generation district heating system in Rottne, southern Sweden, operated by Växjö Energi.Its piping is about 10,300 m long, with a total volume of about 64 m3.Source: §5 · p. 9
- The ten largest consumers in Rottne represent nearly one-third of total heat demand, including distribution losses.About 200 buildings are connected to the system, including roughly 150 single-family homes.Source: §5 · p. 10
- At about 2.7 MW thermal load, the diesel burner normally starts, making forecasts near this level operationally important.The paper says demand-side management can help minimise or avoid such peak loads.Source: §5 · p. 10
6. Available input data
The study combines real-time and historical operating data with weather forecasts spanning 27 months. It selects calendar, temperature, lagged-load, and lagged-control features, then compares feature sets using a 20-month training period and a seven-month test period.
6. Available input data
- The 27-month dataset combines quarter-hourly thermal load and control signals with hourly weather forecasts from the Rottne system platform.The control signal, called delta T, is the difference between the actual outdoor temperature and a virtual one.Source: §6 · p. 11
6.1. Dataset analysis and feature selection
- Weekday morning peaks exceed weekend peaks, and forecast outdoor temperature has a -0.92 Pearson correlation with load, especially below 15 °C.The selected features include day of week, hour of day, and forecast outdoor temperature.Source: §6.1 · pp. 11–12
- Thermal load correlates with loads at multiples of 24 hours, with correlation declining further back in time; 24-hour and 168-hour load and control-signal lags are included.Source: §6.1 · p. 12
- Three feature sets retain all features, omit lagged control signals, or omit both lagged control signals and lagged loads.The first 20 months (November 2014–July 2016) are used for training and validation, and the final seven months (August 2016–February 2017) for testing.Source: §6.1 · pp. 12, 14
7. Implementation and results
The authors implement eight forecasting experts and combine their daily predictions. The combined forecast nearly matches the best individual forecaster, and daily retraining produces almost identical MAPEs to training once.
7.1. Implementation
- The ANNs used two hidden layers with twelve units each and 200 epochs; each ETR had 100 trees and a minimum of 7 samples per leaf.GridSearchCV selected C = 1000, γ = 0.00001, and ϵ = 0.01 for the RBF ϵ-SVRs.Source: §7.1 · pp. 15–17
- The eight-expert pool comprises one full-feature LR baseline, two ANNs, two SVMs, and three ETRs with different feature sets.The ETR feature sets successively omit historical control signals, then both control signals and historical thermal load.Source: §7.1 · pp. 15–17
7.2. Results and discussion
- MAPE assessed the individual experts and global forecaster on hourly forecasts over a 24-hour horizon.The passages define predicted value, actual value, and number of predictions as the quantities used in the metric.Source: §7.2 · pp. 17–18
- Experts trained from November 2014 to July 2016, then forecast next-day hourly loads across the August 2016 to February 2017 test period.No data were available from November 17 to 29, 2016, because of an IT infrastructure failure.Source: §7.2 · p. 18
- 12.06% MAPE: the compound forecaster performs almost exactly like the best individual forecaster, which is the full-feature ANN.The comparison uses the test period; the paper also reports a high-load-period result without a value in these passages.Source: §7.2 · p. 18
- With full-feature experts, daily retraining produced almost identical MAPEs, which the authors take as evidence that the DHS and buildings did not change during testing.Table 3 compares results with no retraining and daily retraining.Source: Table 3 · p. 20, §7.2 · p. 20
8. Conclusion
The eight-expert system tracked the best expert, the ANN with the full feature set, over the test set. The authors report that combining experts adds robustness and that retraining did not improve performance in this case study.
8. Conclusion
- The fixed-share forecaster combines eight experts spanning LR, ANNs, SVMs, and ETRs with three feature sets of increasing information.The feature sets add historic thermal load and then historic control signals to timing information and an outdoor-temperature forecast.Source: §8 · p. 20
- Figure 4 presents expert weights and moving-average MAPEs.Source: Figure 4 · p. 21
- The expert system tracked the best expert, the ANN with the full feature set, over the test set.The authors also report that combining experts adds robustness and reduces susceptibility to changes in the district heating system.Source: §8 · p. 22
- Retraining did not increase performance in this case study, which the authors attribute to the extensive initial training set and an unchanged district heating system during testing.Source: §8 · p. 22
- The dataset spans November 2014 to February 2017, with 20 months for training and validation and the final 7 months for testing.Source: §8 · p. 22