Distributed Stochastic Model Predictive Control with Temporal Aggregation for the Joint Dispatch of Cascaded Hydropower and Renewables

TL;DR

The paper tackles real-time joint dispatch of cascaded hydropower and renewable generation under inflow, renewable, and price uncertainties within a day-ahead market. It introduces a temporally aggregated, distributed stochastic MPC framework that uses time-series aggregation on the horizon tail and consensus ADMM to decompose across assets and scenarios, alongside McCormick relaxations for hydro nonconvexities and formal bounds on approximation error. Key contributions include the TSA-based centralized MPC formulation, its ADMM-based distributed implementation, and upper/lower bounds ($F^{\mathrm{UB}}$, $F^{\mathrm{LB}}$) with an algorithm to certify optimality gaps; simulations on a real CH-vRES case show a 42% speedup over centralized full-scale MPC. The work advances scalable, risk-aware dispatch for hybrid hydro–renewable systems, enabling real-time decisions with provable performance guarantees in day-ahead trading contexts.

Abstract

This paper addresses the real-time energy dispatch of a hybrid system comprising cascaded hydropower plants, wind, and solar units, jointly participating in the day-ahead energy market under inflow, renewable generation, and price uncertainties. Traditional scenario-based stochastic model predictive control (MPC) faces severe computational bottlenecks due to the complexity arising from the temporal, asset, and scenario dimensions of this control problem. To address this, we propose a novel control scheme that combines time series aggregation (TSA) with distributed stochastic MPC. TSA is applied exclusively to the tail of the MPC prediction horizon to preserve real-time accuracy, while distributed optimization enables decomposition across assets and scenarios. Notably, the controller offers a formal performance guarantee through theoretically validated bounds on its approximation error. Simulations on a real-world case study confirm the controller's effectiveness, achieving a 42% reduction in execution time compared to centralized full-scale MPC.

Figures (7)

• Figure 1: Illustration of the McCormick approximation.
• Figure 2: Illustration of the proposed TSA method.
• Figure 3: The proposed decomposition in \ref{['eq:consensus_ADMM_prob']}, with $|\boldsymbol{N}|=3$ and $|\boldsymbol{\Omega}|=2$.
• Figure 4: Boxplots of hourly uncertainty realizations. Each boxplot characterizes the distribution of values observed at a given hour: the box spans the interquartile range, the blue line indicates the median, the whiskers extend to the 10th and 90th percentiles, and outliers are shown as individual points.
• Figure 5: Objective function bounds computed via Algorithm \ref{['alg:dis_sto_MPC']}.