Greedy-VoI Time-Mesh Design for Rolling-Horizon EMS: Optimizing Block-Variable Granularity and Horizon under Compute Budgets

1. Introduction

Electric power systems are being reshaped into the smart grid paradigm, characterized by bidirectional power and information flows, the rapid expansion of variable renewable generation and distributed energy resources (DER) along the grid, together with the widespread deployment of advanced metering, sensing, communications, and automation technologies [1]. This transition offers a significant route to decarbonization, not only by displacing fossil fuel-based electric generation but also by electrifying end-uses—most notably space and water heating—where high-efficiency heat pumps can deliver low-carbon heat [2]. At the same time, the proliferation of behind-the-meter PV, storage, EV charge points, and electric flexible loads or consumption assets increases operational complexity in distribution grids, with documented concerns such as reverse power flows, voltage deviations/unbalance, and protection challenges under high PV penetration [3], as well as local grid congestions [4]. Consequently, system “flexibility”—the ability to shift or modulate generation, consumption, and storage in response to external signals—has become a central enabling resource for integrating high shares of variable renewables while preserving security of supply and compliance with network constraints [5,6]. In particular, demand-side management can convert electrified loads into controllable resources that follow price, carbon-intensity, or grid operator signals, ranging from tariff-driven load shaping to direct, real-time control of smart loads and DER portfolios [7]. Energy Management Systems provide the supervisory layer that operationalises such flexibility by acquiring field data, forecasting and optimally scheduling heterogeneous DER and controllable loads to meet multiple objectives—e.g., minimizing operating costs, maximizing self-consumption, or minimizing emissions—while respecting user preferences and grid/market constraints; this role is well established in microgrid supervisory control and is increasingly relevant in the emerging prosumer-centric market paradigm [8,9].

To take advantage of the flexibility and controllability of distributed energy resources presupposes a high degree of automation in monitoring, optimisation and actuation, because evidence from residential demand-response programmes shows that engagement is hindered by perceived complexity and effort, as well as concerns about risk and loss of control; accordingly, automation becomes an enabling condition when accompanied by transparency and user final control [10]. In line with these insights, the stakeholder-centric surveys conducted in the REEFLEX project report that only 39.8% of respondents currently use any energy management/monitoring tool and only 19% use a dedicated energy/flexibility management tool, while simultaneously revealing strong preferences—sometimes unanimous—for fully automated solutions with user override capabilities and for trust-building features such as long-term support and automatic security updates (with higher expectations of automatic control for critical loads) [11]. An EMS can therefore be defined as a supervisory hardware–software layer that acquires measurements and contextual data, forecasts relevant disturbances (e.g., weather, occupancy and prices) and solves an optimisation problem subject to technical and contractual constraints to schedule and dispatch controllable generation, flexible demand and storage, thereby meeting local objectives (cost, comfort or emissions) while enabling the provision of grid or market services [7,8]. Such EMS concepts span residential home EMS, commercial and tertiary Building EMS, industrial EMS, and microgrid/community controllers. Across these domains, Model Predictive Control (MPC) is widely adopted as a core algorithmic paradigm because its receding-horizon formulation explicitly embeds forecasts and operational constraints and has been extensively validated for both building HVAC energy management and microgrid operation optimisation [12,13].

In EMS/MPC based on deterministic optimisation techniques, the dominant sources of performance degradation are driven mainly by imperfect forecasts of exogenous inputs (e.g., weather, demand, renewable generation, and prices) and by discretisation of continuous dynamics and device operating modes into granular decisions on a fixed time grid [13,14,15,16]. The receding or rolling horizon principle partly mitigates forecast uncertainty by repeatedly updating the optimisation as new measurements and forecasts become available, thereby correcting operation schedules before prediction errors accumulate [14,15]; likewise, increasing the temporal granularity of the EMS (e.g., 15-min intervals instead of hourly steps) can reduce discretisation artefacts and better capture intra-hour variability, ramping behaviour, and constraint activation—although at the cost of a larger optimisation problem with higher computation needs [12,17]. However, finer granularity increases the number of decision variables and constraints roughly proportionally to the number of time steps. It can cause solve times to rise sharply with problem size, particularly in mixed-integer EMS formulations, where the combinatorial growth in binary variables is a significant factor [18]. In complex, large-scale deployments (e.g., microgrids or aggregated DER portfolios), this computational burden can make real-time operation impractical, leading to the paradox that the computation time exceeds the control interval so that the “optimal” solution becomes outdated before it can be applied [18].

To address the increasing computational needs that arise from complex EMS/MPC formulations, particularly when discretized at finer time steps, the literature has proposed several strategies. A proposed solution is to decompose long-horizon (some days) mixed-integer scheduling problems into a sequence of overlapping subproblems (a few hours) solved in a rolling-horizon manner, which can deliver substantial runtime reductions for large energy-hub Mixed Integer Linear Programming(MILP) formulations while preserving the quality of the resulting operating policies [19]. Beyond fixed periodic re-optimization, the rolling-horizon execution itself can also be made adaptive: [20] proposes a dynamic scheduling tool that selects informative start times for the rolling-horizon solves under uncertainty—rather than triggering them uniformly—thereby improving operational performance in a microgrid energy management case study. In parallel, temporal aggregation of input time series—via clustering into typical time steps or typical periods (e.g., typical days/weeks)—reduces the number of time steps and can be tuned to the mathematical structure of the optimization model (notably the presence of time-linking constraints such as storage); recent comparative studies formalize the accuracy–runtime trade-off as a Pareto frontier and provide methods to identify near-optimal aggregation configurations instead of relying on ad hoc choices [21,22]. Another alternative is multi-rate discretization, in which different decision variables and constraints are represented at distinct (and potentially time-varying) temporal resolutions according to their characteristic dynamics; the fully flexible temporal resolution formulation proposed by [23] explicitly enables per-variable resolutions and demonstrates computational-efficiency gains in large-scale co-optimization of investment and operational decisions (see Figure 1). Finally, the computational budget is also shaped by EMS design choices, such as the length of the optimization horizon. Multi-objective receding-horizon scheduling studies suggest that longer optimization horizons can enhance renewable utilization and operational outcomes, albeit at a higher computational cost, thereby reinforcing the motivation for adaptive update policies and multi-resolution modeling in practical EMS deployments [24]. More generally, variable-granularity schemes—where temporal resolution is adjusted during execution—are emerging as another approach to address the computational needs related to complex EMS/MPC formulations.

Variable temporal granularity (also referred to as flexible temporal resolution or multi-timescale discretization) can be defined as the deliberate use of non-uniform time steps along the optimization horizon—and, in some formulations, different time steps for different decision variables—so that fast dynamics and near-term decisions are represented with acceptable resolution. In contrast, slower trends and far-future decisions are represented more coarsely to reduce problem size. In EMS/MPC settings, this concept is especially natural because the controller is usually executed in a receding or rolling horizon structure, where forecasts and states are updated frequently and only the first portion of the computed optimal trajectory or operation set-points are implemented before re-optimizing; consequently, modelling fidelity is most valuable near the current time, whereas distant decisions mainly provide feasibility and boundary guidance. A basic justification for variable granularity is also offered by the exponential decay of sensitivity (EDS). Under suitable regularity conditions, the sensitivity of the optimal decision at stage i to perturbations at stage j can be bounded to decay exponentially with the temporal distance ∣i-j∣ [25]. In rolling-horizon EMS/MPC—where near-term actions are executed, and the horizon is repeatedly shifted—EDS implies that aggregating or coarsening far-future time steps may have limited impact on the current control action, while still capturing long-term constraints and dominant trends. This rationale is directly exploited in diffusing-horizon MPC, which constructs a discretization grid whose spacing becomes exponentially sparser as the horizon is extended, achieving substantial computational savings with limited closed-loop performance degradation [26].

Multi-timescale rolling operation schemes for building and integrated energy systems exemplify this idea by combining day-ahead schedules with progressively finer intraday and real-time refinements (e.g., hourly → 15-min → 5-min) [27], and by embedding horizons with increasing step size directly into MPC to balance economic performance, robustness, and runtime [28]. Closely related multi-horizon formulations also seek long look-ahead horizons without an explosion in variables, e.g., distributed MPC for networks of energy hubs [29] and multi-resolution approaches for storage control that explicitly trade temporal/state resolution against computation, allowing re-optimization to be performed more frequently [30]. Beyond EMS, flexible temporal resolution has recently become an explicit computational lever in large-scale MILP scheduling, such as network-constrained unit commitment with adaptive time-period aggregation [31] and cost-oriented time-adaptive UC formulations [32], reinforcing the broader observation—quantified in comparative studies of temporal-resolution selection—that higher temporal fidelity improves representation accuracy but can quickly render optimization impractical at scale [33].

Although temporal aggregation and resolution-selection have been studied in planning-oriented energy system models, the methodological development for operational microgrid EMS/MPC—where computational latency becomes a hard real-time constraint—remains comparatively limited [20]. Recent contributions nevertheless illustrate the potential of non-uniform temporal designs: [35] introduces an “optimal rolling-horizon strategy” (ORoHS) that explicitly partitions prediction/execution horizons to trade off dispatch cost and forecast accuracy under uncertainty. At the same time, diffusing-horizon MPC provides a constructive coarsening mechanism in which sampling points become progressively sparser (e.g., exponentially) as they move farther into the horizon, leveraging the fact that far-future perturbations have a weaker influence on near-term control actions [20]. In parallel, time-adaptive discretization is also emerging in large-scale mixed-integer scheduling problems (e.g., unit commitment), where cost-oriented temporal resolution seeks to retain fine granularity only where it is economically consequential [20]. However, most existing works either (i) evaluate a limited set of preselected discretizations, or (ii) prescribe coarsening rules tailored to a specific formulation, and they rarely provide general methods to compute an optimal variable-granularity design for a given microgrid and operating context; moreover, to the best of our knowledge, the coupled design problem of jointly selecting both a variable time-mesh and the rolling-horizon length in an integrated and systematic manner is still largely unaddressed in the EMS literature. Building on the above gaps, this work aims to take a step further by proposing a compute-budget-aware procedure that evaluates admissible optimization-horizon lengths, along with block-structured variable granularities tailored to the target market setting. Then, it employs a Greedy-Value-of-Information (Greedy-VoI) metaheuristic to generate and screen new mesh–horizon combinations. In doing so, the proposed methodology targets microgrid-specific near-optimal temporal designs that explicitly balance closed-loop economic performance, forecast uncertainty, and real-time solvability.

The remainder of this paper is organized as follows. Section 2 presents the proposed methodology, including the problem formulation, the design choices adopted for variable temporal granularity and optimization horizon selection, and the evaluation procedure. Section 3 reports the main results obtained across the considered case study. Section 4 discusses the findings, highlighting the observed practical implications and limitations. Finally, Section 5 summarizes the main conclusions and outlines directions for future research.

2. Materials and Methods

This section introduces the proposed methodology for optimal selection of a block-variable temporal discretization and an optimization horizon for rolling horizon EMS/MPC operation under explicit computational constraints. First, the microgrid modelling layer (objective function and constraints) and the market layer are outlined, which define the admissible settlement-aligned time steps and candidate horizon lengths. Next, the workflow is described in Figure 2, where a pool of market-consistent “baseline” discretizations is evaluated to build a comparable KPI benchmark, which is then used to guide a metaheuristic search. Finally, the high-level logic of the Greedy-VoI procedure is presented, which is used to generate and assess new discretization–horizon candidates, as well as the criteria used to select the final recommended configuration.

At a high level, the proposed procedure can be interpreted as a compute-aware time-mesh design layer placed on top of a conventional EMS optimizer. The starting point is a mathematical model of the prosumer microgrid, which includes electrical/physical constraints, as well as economic terms, along with a set of reference inputs (e.g., demand, PV generation, electricity prices, and device limits) representative of the operating period of interest. The market layer then provides the practical boundaries of the decision space: (i) a base/market granularity consistent with market clearing and settlement, and (ii) a base horizon that reflects how far ahead the EMS is expected to plan. These elements define the admissible combinations of “how often decisions are made” (temporal resolution) and “how far ahead the EMS looks” (horizon). At the same time, a compute budget constrains what is feasible to solve repeatedly in real time.

The workflow in Figure 2 proceeds in two stages. In the first stage, the method loads and executes a pool of predefined solutions, i.e., a curated set of block schedules and horizons that are directly compatible with the target market structure. Each candidate is run through the same evaluation pipeline: a rolling-horizon simulation (or repeated replanning procedure) is executed, only the first control action is applied at each step, and the process is repeated across the study horizon. For each candidate configuration, the framework computes comparative KPIs that capture both operational quality and computational practicality. The output of this stage is a consolidated results dataset that provides a transparent baseline and a cost–runtime reference for subsequent search.

In the second stage, the Greedy-VoI algorithm iteratively generates and evaluates new candidate discretizations beyond the predefined pool. Conceptually, Greedy-VoI explores local modifications of the time mesh—such as refining near-term blocks (where actions are executed) and coarsening far-term blocks (where decisions primarily provide boundary guidance)—and may also test alternative horizon lengths to ensure market alignment and computational limits at all times. After each candidate is generated, it is evaluated through the same execution and KPIs, and the best-performing configurations are retained according to the selected decision rule. The procedure finishes when the compute budget and/or stopping criteria are met, returning the selected optimal solution together with its recommended block schedule (granularity profile) and optimization horizon, ready to be deployed as the EMS planning configuration for the specific microgrid and market framework.

2.1. Mathematical definition of granularity, blocks, and optimisation horizon

This section provides a mathematical definition of the blocks that form the EMS/MPC optimisation horizon, as well as the parameters that characterise them and the equations they must satisfy. The pair defines each solution that makes up an optimisation horizon:

⟨B,H⟩,

(1)

Where $\mathbb{B}$, is a schedule of time blocks and $H$is the optimization horizon. A time-block schedule is an ordered list of blocks:

B={(n₁,Δt₁),…,(n_B,Δt_B)}

(2)

Where block $i$comprises $n_i\in {\mathbb{Z}}_{\ge 1}$consecutive time steps (granularities) of identical duration $\mathsf{\Delta }{t}_i>0$(minutes).

For auditability, the mesh signature is defined as:

sig(B,H)=[(n₁,Δt₁)…(n_B,Δt_B);H]

(3)

2.1.1. Optimization horizon

The optimization horizon (minutes) is

$$H=\sum _{i=1}^B{\mathrm{n}}_{\mathrm{i}}\ast \mathsf{\Delta }{\mathrm{t}}_{\mathrm{i}}$$

(4)

and the effective size of the discrete problem is

$$N=\sum _{i=1}^B{\mathrm{n}}_{\mathrm{i}}$$

(5)

2.1.2. Conditions that must be met by the combinations of values that define the optimization horizons.

Unless extended for a specific application (e.g., allowing 30′ in 15′ markets), there is a limited group or set of admissible time-step (granularities):

• {5, 15, 60} [minutes] for 15-minute settlement markets
• {15, 60, 120} [minutes] for 1-hour settlement markets
• Integer blocks and closure of the horizon:

$$\begin{gathered} H=\sum _{i=1}^B{\mathrm{n}}_{\mathrm{i}}\ast \mathsf{\Delta }{\mathrm{t}}_{\mathrm{i}} \\ \mathrm{W}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{B}\in \mathrm{Z}\ge 1,\mathrm{n}\mathrm{i}\in \mathrm{Z}\ge 1,\mathsf{\Delta }\mathrm{t}\mathrm{i}\in \mathsf{\Delta } \end{gathered}$$

(6)

This constraint ensures that the blocks tile the horizon exactly.

• Horizon domain:

H∈H, H={2880,4320} (2 or 3 days in minutes)

(7)

Project pre-defined horizon lengths are 2 or 3 days ($H\in \left[\mathrm{48,72}\right]$h), other works could propose other optimization horizons

• Model-size bound:

$$N=\sum _i{\mathrm{n}}_{\mathrm{i}}\le N_{max}$$

(8)

N_max is chosen from solver and hardware limits (e.g., 220–300 periods for MILP with mixed integer devices). It is the first control against intractable instances.

• Real-time calculations:

It is enforced a per-cycle compute budget $T_{\mathrm{m}\mathrm{a}\mathrm{x}}$(seconds) with

$$T_{max}\le \min \mathsf{\Delta }{\mathrm{t}}_{\mathrm{i}}$$

(9)

• Non-decreasing resolution:

Δt₁≤Δt₂≤…≤Δt_B

(10)

This avoids repeated switching fine→coarse→fine, which tends to generate unstable set points and redundant solver work.

2.1.3. Predefined pool of solutions

As previously indicated, some solutions adapted to the electric market environment have been defined and tested before applying the Greedy-VoI algorithm to ensure that these market solutions are evaluated. Table 1 presents this predefined market of solutions.