arXiv subjects

Giovanni Micheli

Publications and source records attributed to Giovanni Micheli.

5 recordsLinked to original sources

arXiv2026

Bounds for multi-horizon stochastic optimization with application to power generation and transmission expansion planning

This paper investigates computationally efficient methods for deriving bounds on the optimal value of multi-horizon stochastic optimization problems, with a particular focus on applications in power generation and transmission expansion planning. Multi-horizon stochastic programs capture sequential decision-making under uncertainty across multiple time scales---e.g., strategic (long-term) and operational (short-term)---jointly. Due to their inherent complexity, especially when uncertainties span several time horizons, solving these problems directly becomes computationally prohibitive. To address this, the paper develops and analyzes various novel bounding techniques, based on the dissection of scenario trees. We investigate systematically dissecting (i) only the operational, (ii) only the strategic, or (iii) both scenario trees simultaneously, and we devise two ways to recombine them to obtain valid bounds. Each method leads to a monotonic chain of inequalities that approximate the optimal value of the original problem from below. One of these methods results in a significantly smaller number of subgroups to recombine in the operational and simultaneous dissections, leading to substantial computational savings. Numerical results on a multi-horizon mixed-integer generation and transmission expansion planning problem show the efficiency of the proposed approach through different dissection and recombination strategies.

math.OC↗

arXiv2026

Multi-horizon optimization for domestic renewable energy system design under uncertainty

In this paper we address the challenge of designing optimal domestic renewable energy systems under multiple sources of uncertainty appearing at different time scales. Long-term uncertainties, such as investment and maintenance costs of different technologies, are combined with short-term uncertainties, including solar radiation, electricity prices, and uncontrolled load variations. We formulate the problem as a multistage multi-horizon stochastic Mixed Integer Linear Programming (MILP) model, minimizing the total cost of a domestic building complex's energy system. The model integrates long-term investment decisions, such as the capacity of photovoltaic panels and battery energy storage systems, with short-term operational decisions, including energy dispatch, grid exchanges, and load supply. To ensure robust operation under extreme scenarios, first- and second-order stochastic dominance risk-averse measures are considered preserving the time consistency of the solution. Given the computational complexity of solving the stochastic MILP for large instances, a rolling horizon-based matheuristic algorithm is developed. Additionally, various lower-bound strategies are explored, including wait-and-see schemes, expected value approximations, multistage grouping and clustering schemes. An extensive computational experiment validates the effectiveness of the proposed approach on a case study based on a building complex in South Germany. We tackle models with over 43 million constraints and 12 million binary, 700 hundred integer and 10 million continuous variables; they are solved with up to 0.32% optimality gap in reasonable computing time, where the value of the stochastic decisions as well as the benefit of the integrated risk-averse measures are quantified.

math.OC↗

arXiv2026

Equilibrium models to analyse the impact of different coordination schemes between TSO and DSOs on market power in sequentially-cleared energy and ancillary services markets under load and renewable generation uncertainty

The current massive installation of distributed resources in electricity distribution systems is transforming these systems into active dispatching subjects. At the same time, the need to compensate for the intermittent generation of an increasing amount of renewable sources creates the need to acquire more ancillary services. Flexible resources in the distribution system could provide these services not only within the perimeter of the distribution network to which they are connected but also for the benefit of the transmission system. However, this requires Transmission System Operators (TSOs) and Distribution System Operators (DSOs) to coordinate their dispatching actions effectively. One critical aspect of this coordination is establishing a market architecture that limits market power. This paper presents an innovative game-theoretic approach to compare different TSO-DSO coordination models for acquiring ancillary services from distribution resources. Several schemes are considered: some with coordinated market management by TSOs and DSOs, others with sequential or independent local markets. For each scheme, the dispatching problem is formulated as a two-stage stochastic sequential game, where the first stage is the day-ahead market and the second stage is the balancing market. Nash equilibrium solutions are obtained by iteratively solving the profit maximization problem of each market player. Numerical tests on a CIGRE benchmark network show that coordination schemes enabling distribution resources to provide ancillary services to the transmission system can significantly increase system costs when congestion occurs in the transmission network.

math.OC↗

arXiv2025

Asset liability management under sequential stochastic dominance constraints

We consider a financial intermediary managing assets and liabilities exposed to several risk sources and seeking an optimal portfolio strategy to minimise the initial capital invested and the total risk associated with investment losses and financial debt. We formulate the problem as a multistage stochastic programming model, with a time-consistent dynamic risk measure in the objective function to control the investment risk. To ensure that the intermediary's financial equilibrium is preserved, we introduce a funding constraint in the model by enforcing in a time-consistent manner a sequential second-order stochastic dominance (SSD) of the portfolio return distribution over the liability distribution. We demonstrate that imposing the SSD constraint at the last-but-one stage is sufficient to enforce the SSD ordering at each stage. To deal with the computational burden of associated MSP, we develop a novel decomposition scheme integrating, for the first time in the literature, time-consistent dynamic risk measures and sequential stochastic dominance constraints. The proposed methodology is computationally validated on a case study developed on a property and casualty ALM problem.

math.OC↗

arXiv2025

A Stochastic Programming Model for Anticipative Planning of Integrated Electricity and Gas Systems with Bidirectional Energy Flows under Fuel and CO2 Price Uncertainty

A two-stage multi-period mixed-integer linear stochastic programming model is proposed to assist qualified operators in long-term generation and transmission expansion planning of electricity and gas systems to meet policy objectives. The first-stage decisions concern investments in new plants, new connections in the electricity and gas sectors, and the decommissioning of existing thermal power plants; the second-stage variables represent operational decisions, with uncertainty about future fuel and CO2 prices represented by scenarios. The main features of the model are: (i) the bidirectional conversion between electricity and gas enabled by Power-to-Gas and thermal power plants, (ii) a detailed representation of short-term operation, crucial for addressing challenges associated with integrating large shares of renewables in the energy mix, and (iii) an integrated planning framework to evaluate the operation of flexibility resources, their ability to manage non-programmable generation, and their economic viability. Given the computational complexity of the proposed model, in this paper we also implement a solution algorithm based on Benders decomposition to compute near-optimal solutions. A case study on the decarbonisation of the Italian integrated energy system demonstrates the effectiveness of the model. The numerical results show: (i) the importance of including a detailed system representation for obtaining reliable results, and (ii) the need to consider price uncertainty to design adequate systems and reduce overall costs.

math.OC↗