Formulation and Experimental Validation of Price-Based Control of Flexible Prosumers in Distribution Grids with the Alternating Direction Method of Multipliers

TL;DR

The paper tackles the challenge of coordinating price-based control for flexible prosumers in distribution grids while respecting grid constraints. It introduces an ADMM-based distributed OPF formulation that interprets Lagrange multipliers as dynamic price signals, enabling privacy-preserving coordination between the DSO and prosumers. Key contributions include a distributed optimization framework with a novel interpretation as price-based control, receding-horizon and real-time control schemes to handle uncertainty, and experimental validation on a 9-node LV testbed with BESS and curtailable PV. The results demonstrate convergence of ADMM, effective voltage-support through dynamic tariffs, and practical viability for real-world deployment, while outlining future work on uncertainty handling and fairness.

Abstract

This paper describes a method for computing price signals for prosumers, incentivizing them to adjust their consumption according to the constraints of the distribution grids to which they are connected, thereby preventing voltage violations and line congestion. The proposed method leverages an interpretation of the Alternating Direction Method of Multipliers (ADMM), which enables the extraction of a price signal to coordinate the operations of prosumers and the distribution grid's constraints while limiting the sharing of sensitive information among them. The method can be used by Distribution System Operators (DSOs) to dynamically adjust a pre-existing retail electricity tariff (e.g., a constant or time-of-use tariff), thereby triggering grid-support actions from prosumers. The method is validated experimentally in a 9-node low-voltage distribution grid laboratory with real components (lines and controllable power converters). The experiments validate the algorithm's performance in terms of convergence and operational efficiency, demonstrating its viability in a real-life setting.

Figures (8)

• Figure 1: Exchange of information between the DSO and the prosumers during the phases of ADMM. At iteration $k$, The DSO advertises to prosumer $i$ the price signal $\mathcal{C}_i^k(\mathbf{x}_i)$, whose coefficients depend on (i) the sensitivity matrix $A^k_i$ of the DSO constraints with respect to the demand $\mathbf{x}_i$ of the prosumer, (ii) the marginal price $\mathbf{y}^k_i$ of the constraint with respect to $\mathbf{x}_i$, (iii) the contribution $\mathbf{z}^k_i$ of the prosumer in the grid constraints, and (iv) the penalty term $\rho^k$ on the satisfaction of the constraints. The prosumer responds with the optimal decision $\mathbf{x}^{k+1}_i$ that minimizes the price signal subject to the prosumer's constraints.
• Figure 2: Grid topology for the experimental validation. The emulated prosumers are connected to nodes N3, N4, N5, N7, and N9. N1 is the connection point with the upper grid.
• Figure 3: Simulation results with no DSO-prosumers coordination. (a) Electricity tariff, (b) SoC of the BESSs, (c) PV production, and (d) nodal voltage magnitudes, which violate the upper limit in the central part of the day.
• Figure 4: Simulation results with DSO-prosumers coordination. (a) Electricity tariff, now different for each consumer, (b) SoC of the BESSs, (c) PV production, showing one unit being curtailed, and (d) nodal voltage magnitudes, all of which now fall within limits.
• Figure 5: Primal and dual residuals as a function of the number of iterations.