[Paper Review] Control of Energy Storage in Home Energy Management Systems: Non-Simultaneous Charging and Discharging Guarantees

Kaitlyn Garifi, Kyri Baker+2 more|arXiv (Cornell University)|Apr 30, 2018

Smart Grid Energy Management23 references19 citations

TL;DR

This paper proposes a convex optimization formulation for model predictive control (MPC)-based home energy management systems (HEMS) that guarantees non-simultaneous charging and discharging in linear energy storage system (ESS) models. By leveraging Karush-Kuhn-Tucker (KKT) optimality conditions, the method ensures suboptimal solutions do not involve simultaneous ESS charging and discharging under various pricing schemes, including time-of-use (TOU) and net metering, even when efficiency losses are modeled.

ABSTRACT

In this paper we provide non-simultaneous charging and discharging guarantees for a linear energy storage system (ESS) model for a model predictive control (MPC) based home energy management system (HEMS) algorithm. The HEMS optimally controls the residential load and residentially-owned power sources, such as photovoltaic (PV) power generation and energy storage, given residential customer preferences such as energy cost sensitivity and ESS lifetime. Under certain problem formulations with a linear ESS model, simultaneous charging and discharging can be observed as the optimal solution when there is high penetration of PV power. We present analysis for a proposed HEMS optimization formulation that ensures non-simultaneous ESS charging and discharging operation for a linear ESS model that captures both charging and discharging efficiency of the ESS. The energy storage system model behavior guarantees are shown for various electricity pricing schemes such as time of use (TOU) pricing and net metering. Simulation results demonstrating desirable ESS behavior are provided for each electricity pricing scheme.

Motivation & Objective

• Address the problem of simultaneous ESS charging and discharging in MPC-based HEMS, which can arise in convex formulations despite being physically infeasible.
• Provide theoretical guarantees that simultaneous operation is suboptimal under realistic electricity pricing schemes such as TOU and net metering.
• Ensure non-simultaneous ESS operation without resorting to non-convex or restrictive ESS models, preserving computational tractability.
• Demonstrate that including ESS lifetime penalties in the cost function enhances non-simultaneous operation guarantees, especially when electricity is free during off-peak periods.
• Validate the proposed formulation through simulations across multiple pricing scenarios, showing consistent and physically plausible ESS behavior.

Proposed method

• Formulate a convex MPC-based HEMS optimization problem with a linear ESS model that captures both charging and discharging efficiency using parameters $\eta_c$ and $\eta_d$.
• Incorporate time-of-use (TOU) pricing and net metering into the cost function via electricity prices $c_e^{(t)}$, with $c_e^{(t)} = 0$ during off-peak hours.
• Introduce penalty terms $\alpha \cdot P_{\rm ch}$ and $\beta \cdot P_{\rm dis}$ in the objective function to discourage simultaneous ESS charging and discharging.
• Apply Karush-Kuhn-Tucker (KKT) conditions to the optimization problem, analyzing both primal and dual variables to prove that simultaneous operation is suboptimal.
• Use the KKT analysis to derive conditions under which any solution with simultaneous ESS charging and discharging cannot be optimal, thus guaranteeing non-simultaneous behavior.
• Validate the theoretical findings through simulation of power profiles, ESS state of charge, and charging/discharging behavior under various TOU and net metering scenarios.

Experimental results

Research questions

• RQ1 Under what conditions is simultaneous ESS charging and discharging suboptimal in a convex MPC-based HEMS formulation with a linear ESS model?
• RQ2 How do different electricity pricing schemes—specifically TOU and net metering—affect the optimality of simultaneous ESS operation?
• RQ3 Can penalty terms in the objective function ensure non-simultaneous ESS operation without introducing non-convexity or restrictive ESS models?
• RQ4 What role does ESS lifetime modeling play in enhancing the non-simultaneous operation guarantees, particularly when electricity is free during off-peak periods?
• RQ5 Can the KKT optimality conditions be used to formally prove that simultaneous ESS charging and discharging is not part of any optimal solution under realistic HEMS constraints?

Key findings

• Simultaneous ESS charging and discharging is suboptimal under all studied scenarios, including TOU pricing and net metering, as proven via KKT conditions.
• The inclusion of ESS lifetime penalty terms ($\alpha$ and $\beta$) in the objective function is necessary to ensure non-simultaneous operation when electricity prices are zero during off-peak periods.
• Under TOU pricing with no export allowed, the ESS charges during off-peak and shoulder periods when solar exceeds load and discharges during on-peak to avoid grid usage, demonstrating non-simultaneous behavior.
• Under net metering with zero-cost off-peak electricity, the ESS charges during off-peak hours when power is free and discharges during on-peak, while excess solar is exported, confirming non-simultaneous operation.
• Simulation results show consistent non-simultaneous ESS charging and discharging across all cases, with ESS state of charge (SoC) dynamically adjusting based on pricing and solar availability.
• The proposed formulation avoids the need for non-convex or non-smooth ESS models, preserving computational efficiency while ensuring physically realistic ESS dynamics.