- About me
- Publications
- Ren. in El. Markets
- Module 1 – Fundamentals of electricity markets
- Module 2 – Electricity spot markets (e.g., day-ahead)
- Module 3 – Intra-day and balancing markets
- Module 4 – Ancillary services
- Module 5 – Impact of renewables on electricity markets
- Module 6 – Participation of renewables in electricity markets
- Module 7 – Introduction to renewable energy analytics
- Module 8 – Verification of renewable energy forecasts
- Module 9 – Renewable energy forecasting – First steps
- Module 10 – Renewable energy forecasting – Advanced topics
- Additional industry interviews
- Interviews with former students
- Exercises
- Int. J. Forecasting
- Contact
- Download CV
Pierre Pinson
Chair of Data-centric Design Engineering - Imperial College London
Preprint
Publication Types:
How long is long enough? Finite-horizon approximation of energy storage scheduling problems
Energy storage scheduling problems, where a storage is operated to maximize its profit in response to a price signal, are essentially infinite-horizon optimization problems as storage systems operate continuously, without a foreseen end to their operation. Such problems can be solved to optimality with a rolling-horizon approach, provided that the planning horizon over which the problem is solved is long enough. Such a horizon is termed a forecast horizon. However, the length of the planning horizon is usually chosen arbitrarily for such applications. We introduce an easy-to-check condition that confirms whether a planning horizon is a forecast horizon, and which can be used to derive a bound on suboptimality when it is not the case. By way of an example, we demonstrate that the existence of forecast horizons is not guaranteed for this problem. We also derive a lower bound on the length of the minimum forecast horizon. We show how the condition introduced can be used as part of an algorithm to determine the minimum forecast horizon of the problem, which ensures the determination of optimal solutions at the lowest computational and forecasting costs. Finally, we provide insights into the implications of different planning horizons for a range of storage system characteristics.
Do we actually understand the impact of renewables on electricity prices? A causal inference approach
The energy transition is profoundly reshaping electricity market dynamics. It makes it essential to understand how renewable energy generation actually impact electricity prices, among all other market drivers. These insights are critical to design policies and market interventions that ensure affordable, reliable, and sustainable energy systems. However, identifying causal effects from observational data is a major challenge, requiring innovative causal inference approaches that go beyond conventional regression analysis only. We build upon the state of the art by developing and applying a local partially linear double machine learning approach. Its application yields the first robust causal evidence on the distinct and non-linear effects of wind and solar power generation on UK wholesale electricity prices, revealing key insights that have eluded previous analyses. We find that, over 2018-2024, wind power generation has a U-shaped effect on prices: at low penetration levels, a 1 GWh increase in energy generation reduces prices by up to 7 GBP/MWh, but this effect gets close to none at mid-penetration levels (20–30%) before intensifying again. Solar power places substantial downward pressure on prices at very low penetration levels (up to 9 GBP/MWh per 1 GWh increase in energy generation), though its impact weakens quite rapidly. We also uncover a critical trend where the price-reducing effects of both wind and solar power have become more pronounced over time (from 2018 to 2024), highlighting their growing influence on electricity markets amid rising penetration. Our study provides both novel analysis approaches and actionable insights to guide policy makers in appraising the way renewables impact electricity markets.
Many industries rely on data-driven analytics, yet useful datasets are often distributed amongst market competitors that are reluctant to collaborate and share information. Recent literature proposes analytics markets to provide monetary incentives for data sharing, however many of these market designs are vulnerable to malicious forms of replication — whereby agents replicate their data and act under multiple identities to increase revenue. We develop a replication-robust analytics market, centering on supervised learning for regression. To allocate revenue, we use a Shapley value-based attribution policy, framing the features of agents as players and their interactions as a characteristic function game. We show that there are different ways to describe such a game, each with causal nuances that affect robustness to replication. Our proposal is validated using a real world wind power forecasting case study.
Energy management costs can be reduced by increasing load forecasting accuracy. Many studies use multiple data sources to potentially yield improved forecasts. However, data owners may be hesitant to share their data due to privacy concerns and a lack of monetary incentives. Here, we establish a model trading market to encourage collaboration, in which a buyer can purchase advanced load forecasting models that have been trained by sellers’ data to facilitate his decision-making. Specifically, we first propose a cost-oriented loss function that links to the buyer’s decision-making problem, which serves as a basis for market participants to evaluate the model quality and design their utility functions. Then, an iterative model auction mechanism is proposed to orchestrate selfish market participants to reach a consensus on the social welfare-maximizing solution, where the model quality and price for trading are determined through a distributed process. Furthermore, we propose a model adaptation strategy, including model fine-tuning and ensembling, for the buyer to enhance the applicability of purchased models to his decision-making problem. Experiments for building energy management are conducted based on public datasets. Results show that our approach converges to the socially optimal point and every participant can benefit from the market: sellers are compensated for providing models; and, the buyer can greatly reduce operational costs by employing the purchased models.
This paper studies how to aggregate prosumers (or large consumers) and their collective decisions in electricity markets, with a focus on fairness. Fairness is essential for prosumers to participate in aggregation schemes. Some prosumers may not be able to access the energy market directly, even though it would be beneficial for them. Therefore, new companies offer to aggregate them and promise to treat them fairly. This leads to a fair resource allocation problem.
We propose to use acceptability constraints to guarantee that each prosumer gains from the aggregation.
Moreover, we aim to distribute the costs and benefits fairly, taking into account the multi-period and uncertain nature of the problem. Rather than using financial mechanisms to adjust for fairness issues, we focus on various objectives and constraints, within decision problems, that achieve fairness by design. We start from a simple single-period and deterministic model, and then generalize it to a dynamic and stochastic setting using, e.g., stochastic dominance constraints.
Privacy-preserving convex optimization: When differential privacy meets stochastic programming
Convex optimization finds many real-life applications, where – optimized on real data – optimization results may expose private data attributes (e.g., individual health records, commercial information, etc.), thus leading to privacy breaches. To avoid these breaches and formally guarantee privacy to optimization data owners, we develop a new privacy-preserving perturbation strategy for convex optimization programs by combining stochastic (chance-constrained) programming and differential privacy. Unlike standard noise-additive strategies, which perturb either optimization data or optimization results, we express the optimization variables as functions of the random perturbation using linear decision rules; we then optimize these rules to accommodate the perturbation within the problem’s feasible region by enforcing chance constraints. This way, the perturbation is feasible and makes different, yet adjacent in the sense of a given distance function, optimization datasets statistically similar in randomized optimization results, thereby enabling probabilistic differential privacy guarantees. The chance-constrained optimization additionally internalizes the conditional value-at-risk measure to model the tolerance towards the worst-case realizations of the optimality loss with respect to the non-private solution. We demonstrate the privacy properties of our perturbation strategy analytically and through optimization and machine learning applications.