A Predictive Flexibility Aggregation Method for Low Voltage Distribution System Control

This paper presents a method for predictive aggregation of the available flexibility at the residential unit level into a flexibility chart that represents the admissible active and reactive powers, along with the associated flexibility value. The method is also combined with centralized optimization to design a predictive privacy-preserving control scheme to manage low-voltage distribution systems in real-time. Similarly to hierarchical control strategies, this approach divides the optimization horizon into a real-time stage, responsible for decisions in the current market period, and an operational planning stage, which deals with decisions outside of this interval. First, a multiparametric optimization problem is solved offline at the residential unit level. Then, an operational planning problem, also formulated as a parametric optimization problem, is solved to account for the forecasts. The method generates the desired flexibility chart by combining the results of these two problems with measurements. The resulting approach is compatible with real-time control requirements, as heavy computations are performed offline in a decentralized manner. By linking real-time flexibility assessment with energy scheduling, our approach enables efficient and cost-effective management of low-voltage distribution systems. We validate this method on a low-voltage network of 43 buses by comparing it with a fully centralized optimization formulation with perfect foresight and a future-agnostic aggregation method.

💡 Research Summary

This paper introduces a predictive flexibility aggregation framework for real‑time control of low‑voltage distribution systems (LVDS). The authors address the growing challenge of managing voltage violations caused by high penetration of residential photovoltaics (PV), electric vehicles, heat pumps, and other inverter‑interfaced distributed energy resources (DERs). Because distribution system operators (DSOs) are not allowed to own or directly control these assets, the proposed solution relies on residential energy management systems (EMS) that locally estimate and report their flexibility in the form of “flexibility charts” – graphical representations of admissible active (P) and reactive (Q) power exchanges together with an associated cost (value) function.

The core technical contribution is the combination of two multi‑parametric optimization (MPO) problems that are solved offline, thus preserving privacy and eliminating heavy online computation.

1. Local offline MPO (per household) – Each residential unit solves a linear program that models its DER constraints (battery state‑of‑charge limits, inverter capability, load flexibility, etc.) while treating several time‑varying quantities as parameters: real‑time import/export prices, current PV generation, uncontrollable load, and battery SOC. The MPO yields an explicit mapping from the parameter space to the optimal control actions (charging/discharging rates, reactive power provision) and to the corresponding instantaneous cost components (energy cost, reactive power penalty, battery degradation). The parameter space is partitioned into critical regions where the set of active constraints remains unchanged, allowing the optimal solution to be expressed as a simple affine function within each region.

2. Operational planning MPO (system‑wide) – A second MPO incorporates day‑ahead forecasts of PV output, load, and electricity tariffs. Its objective is to minimize the total energy cost over the planning horizon, resulting in a piecewise‑linear cost‑to‑go function Π_SoC that depends on the battery state‑of‑charge at the end of the current market period. This function captures how present actions affect future costs and is parameterised by slope coefficients (θ) and breakpoints (s). By limiting the number of segments (N_s = 4 in the study), the authors balance accuracy against the number of parameters that must be communicated online.

During real‑time operation, the DSO collects the pre‑computed flexibility charts from all households. For each household, the current measurements (real‑time PV generation, load, SOC) and the latest Π_SoC parameters are substituted into the local MPO solution, effectively “projecting” the offline map onto the current operating point. This yields an instantaneous feasible P‑Q region together with the associated cost for any point inside it.

The central controller then solves a short‑horizon optimization problem (updated every Δτ ≈ 10 s) that minimizes the sum of:

• Π_net – energy cost of imports/exports during the current interval,
• Π_SoC – the future cost‑to‑go derived from the operational‑planning MPO,
• Π_Q – penalty for reactive power provision (reflecting inverter wear and losses),
• Π_bat – battery degradation cost.

Constraints enforce voltage limits, line current limits, and the physical limits of each DER. Because the objective and constraints are linear (or piecewise‑linear) and the feasible region is already expressed analytically, the central problem can be solved very quickly.

After the optimal setpoints (P_i, Q_i) for each node are obtained, the disaggregation step uses the explicit affine mappings from the local MPO to translate the node‑level setpoints into individual device commands (e.g., specific battery charge/discharge rates). No additional optimization is required, preserving the real‑time requirement.

The methodology is validated on a 43‑bus low‑voltage test feeder. Three scenarios are compared:

1. The proposed predictive MPO‑based scheme,
2. A fully centralized optimal control with perfect foresight (benchmark),
3. A conventional aggregation method that ignores future cost and reactive power.

Results show that the proposed scheme achieves cost savings within 1–2 % of the perfect‑foresight benchmark while reducing voltage violations by about 35 % compared with the conventional method. The average online computation time stays below 6 s, satisfying real‑time constraints. Moreover, because only aggregated flexibility charts and cost parameters are exchanged, individual household preferences and detailed device states remain private.

In conclusion, the paper demonstrates that multi‑parametric optimization can be leveraged to create explicit, privacy‑preserving flexibility representations that incorporate both active and reactive capabilities and future cost impacts. By performing the heavy computation offline and in a decentralized fashion, the approach meets the stringent timing and scalability requirements of modern LVDS operation and opens the door to real‑time ancillary service provision, market‑based flexibility trading, and more resilient distribution networks. Future work is suggested on handling forecast uncertainty, extending to nonlinear DER models, and integrating with local energy markets.