Joint Scheduling of DER under Demand Charges: Structure and Approximation

TL;DR

The paper addresses joint scheduling of behind-the-meter DER comprising flexible loads, renewables, and battery storage under NEM tariffs with demand charges, formulated as a stochastic dynamic program. It proves the optimal policy has a threshold structure but exact DP is computationally intractable due to strong temporal coupling, motivating an efficient LSPS approximation that relaxes storage constraints and optimizes peak demand with linear horizon complexity $O(T)$. Case studies on HouseZero and BDGP show LSPS yielding near-optimal performance, closely tracking a theoretical upper bound and outperforming baselines including a reinforcement learning approach. The work offers a practical framework for DER co-optimization under complex tariffs, enabling scalable, interpretable strategies that reduce peak charges and improve tariff arbitrage in real-world settings.

Abstract

We study the joint scheduling of behind-the-meter distributed energy resources (DERs), including flexible loads, renewable generation, and battery energy storage systems, under net energy metering tariffs with demand charges. The problem is formulated as a stochastic dynamic program aimed at maximizing expected operational surplus while accounting for renewable generation uncertainty. We analytically characterize the optimal control policy and show that it admits a threshold-based structure. However, due to the strong temporal coupling of the storage and demand charge constraints, the number of conditional branches in the policy scales combinatorially with the scheduling horizon, as it requires a look-ahead over future states. To overcome the high computational complexity in the general formulation, an efficient approximation algorithm is proposed, which searches for the peak demand under a mildly relaxed problem. We show that the algorithm scales linearly with the scheduling horizon. Extensive simulations using two open-source datasets validate the proposed algorithm and compare its performance against different DER control strategies, including a reinforcement learning-based one. Under varying storage and tariff parameters, the results show that the proposed algorithm outperforms various benchmarks in achieving a relatively small solution gap compared to a theoretical upper bound.

Figures (8)

• Figure 1: DER setup with flexible demand $d \in \mathbb{R}+$, renewable generation $g \in \mathbb{R}+$, storage operation $e \in \mathbb{R}$, and net consumption $z \in \mathbb{R}$. The illustrated NEM tariff includes both energy and demand charges, with costs associated with net consumption, net generation, and the peak load recorded over the daily billing period.
• Figure 2: Daily net demand distributions for HouseZero and BDGP over the training and testing period.
• Figure 3: Comparison of daily surplus gaps to theoretical upper bound for different control strategies with varying parameters using HouseZero (top row) and BDGP (bottom row) test data. The cases include (a,e) battery capacities, (b,f) salvage value rates, (c,g) electricity export rates, and (d,h) peak demand prices.
• Figure 4: Typical day battery and demand actions comparison between different control methods for test building HouseZero.
• Figure 5: Computational time comparison between LSPS and deterministic optimization.

Theorems & Definitions (18)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Theorem 1
• proof
• Theorem 2
• proof