⚡ electrical engineering

Price-Based Distributed Scheduling of Flexible Demands in Energy Communities

This paper proposes a robust and computationally efficient Threshold Pricing Rule (TPR) for price-based distributed scheduling in energy communities, which guarantees revenue adequacy and individual rationality while achieving asymptotic optimality as community size increases.

Original authors: Minjae Jeon, Lang Tong, Qing Zhao

Published 2026-07-20

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CC BY 4.0

Original authors: Minjae Jeon, Lang Tong, Qing Zhao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a neighborhood where everyone has a little power plant on their roof, like a solar panel, and everyone also has a hungry electric car that needs charging. In the old days, if you had extra power, you sold it back to the big utility company for a low price, and if you needed power, you bought it from them for a high price. It was a bit like a one-way street: you either paid full price or got a tiny discount. But what if neighbors could trade with each other? If your neighbor has a sunny roof and your car is empty, you could buy their extra sun-power for a price that's better than what the big company charges, but still fair for them. This is the world of "energy communities," a hot topic in how we manage electricity. The big challenge is figuring out the perfect price to charge at every single moment so that everyone saves money, the community doesn't lose cash, and no one feels tricked into joining. It's a massive, moving puzzle involving math, weather, and human habits.

This paper tackles that puzzle by introducing a clever, simple rule called the "Threshold Pricing Rule" (TPR). The authors, Minjae Jeon, Lang Tong, and Qing Zhao, treat the energy community like a giant game of "hot potato" with electricity. They realized that the best way to manage the community isn't to try to solve a super-complex math problem for every single house every second (which is too hard and slow). Instead, they looked at what a "perfect" central boss would do if they knew everything. They found that this perfect boss follows a "procrastination policy": if you have enough solar power right now, use it. If you're desperate and might miss your deadline (like your car not being ready for school), buy the bare minimum from the grid. If you have a huge surplus, sell it.

The magic of this paper is that they turned this complex "perfect boss" strategy into a simple three-zone price tag that a coordinator can broadcast to everyone. Imagine the community's total solar power as a water level in a giant tank.

The Low Zone (Net-Consuming): When the water level is low (not enough sun for everyone), the price is set high, matching the expensive utility rate. This tells people: "Don't buy extra yet; wait or sell your own solar to neighbors who are desperate."
The High Zone (Net-Producing): When the water level is super high (too much sun), the price drops to the low utility rate. This tells people: "Go ahead and charge your cars! It's cheap because we have a surplus."
The Middle Zone (Net-Zero): When the water is just right, the price is a mix, acting like the standard utility bill.

The authors proved that if everyone follows these simple price signals, the whole community ends up acting just like that "perfect boss" would. They showed that this system is fair: no one pays more than they would if they were alone with the utility company (individual rationality), and the community always has enough money to pay the utility company (revenue adequacy).

The paper also ran simulations to see how this works in the real world. They found that as the community gets bigger—imagine growing from a few houses to a whole neighborhood—the simple TPR rule becomes almost perfect, matching the results of the super-complex, impossible-to-calculate "perfect" solution. In fact, in their computer tests with 14 households, the simple rule saved people significantly more money than other complicated scheduling methods. The paper suggests that this approach is robust, meaning it works well even if the weather or charging habits aren't exactly what the model predicted. It's a way to turn a chaotic, unpredictable energy grid into a smooth, cooperative neighborhood game where everyone wins by sharing the sun.

Technical Summary: Price-Based Distributed Scheduling of Flexible Demands in Energy Communities

Problem Formulation
The paper addresses the challenge of distributed demand scheduling within an energy community comprising $N$ households. Each household possesses renewable generation, deferrable loads (specifically Electric Vehicle charging with deadlines), and non-deferrable loads (e.g., thermostatically controlled HVAC). The community interacts with a distribution utility under a regulated Net Energy Metering (NEM) tariff, characterized by a retail purchase rate $\pi^+$ and a lower compensation rate $\pi^-$ for net exports.

The core problem is formulated as a bilevel stochastic dynamic program:

Upper Level (Coordinator): A coordinator broadcasts electricity prices to optimize community welfare (minimizing total energy costs) while satisfying operational constraints, revenue adequacy, and individual rationality.
Lower Level (Households): Individual households act as price-takers, solving stochastic dynamic programs to maximize their consumption benefits (or minimize costs) given the broadcast prices and their private constraints (e.g., EV deadlines, renewable availability).

The authors note that solving this bilevel problem directly is computationally prohibitive due to the curse of dimensionality in the stochastic dynamic programs and the complexity of coordinating decentralized agents.

Methodology
To overcome computational intractability, the authors first analyze the structure of the optimal centralized scheduling policy (where a central entity controls all decisions). They establish that the optimal policy follows a "Procrastination Policy" characterized by a two-threshold structure on the aggregate net renewable generation ( $g_t$ ):

Net-Consuming Zone: When $g_t$ falls below a lower threshold $m_t$ , the community imports the minimum necessary energy from the grid to meet urgent deadlines.
Net-Producing Zone: When $g_t$ exceeds an upper threshold $M_t$ , the community exports surplus energy, and all EVs charge to their maximum feasible rate.
Net-Zero Zone: When $g_t$ lies between $m_t$ and $M_t$ , the community neither imports nor exports; local renewables are allocated to meet demand.

Leveraging this structural insight, the authors propose the Threshold Pricing Rule (TPR). TPR is a simple, piecewise-linear pricing policy that maps the three scheduling zones to specific price signals:

In the Net-Consuming Zone, the community price is set to the utility's retail rate $\pi^+$ .
In the Net-Producing Zone, the price is set to the utility's compensation rate $\pi^-$ .
In the Net-Zero Zone, the standard NEM tariff (using both $\pi^+$ and $\pi^-$ ) is applied.

Crucially, TPR is independent of the specific parameters of the underlying stochastic dynamic programs (e.g., arrival rates, specific utility functions), relying only on the known utility rates and the calculated thresholds.

Key Contributions

Structural Characterization: The paper proves that the optimal centralized scheduling policy for deadline-constrained demand exhibits a threshold structure that partitions the state space into three distinct zones. This allows the isolation of computational complexity to the net-zero zone, where the optimal allocation is intractable.
Threshold Pricing Rule (TPR): The authors derive TPR as a distributed pricing mechanism that induces the optimal centralized behavior in the net-consuming and net-producing zones through simple price signals. TPR requires only linear computational cost relative to the community size.
Theoretical Guarantees:
- Individual Rationality: The paper proves that under TPR, every household's cost is no greater than if they operated as a standalone customer under the utility's NEM tariff. This ensures community stability by preventing members from leaving.
- Revenue Adequacy: The mechanism ensures the coordinator's revenue covers payments to the utility and to community members exporting surplus energy, preventing deficits.
- Asymptotic Optimality: Under light-traffic conditions (where the EV arrival rate is lower than the aggregate renewable generation capacity), the paper demonstrates that TPR becomes asymptotically optimal as the community size $N \to \infty$ . In this regime, the probability of the community falling into the suboptimal net-zero zone vanishes.
Extension to Price-Elastic Demand: The framework is extended to include non-deferrable demands that are price-elastic (e.g., HVAC). A modified TPR ( $\tilde{\chi}_{TPR}$ ) is shown to preserve individual rationality (in terms of surplus) and revenue adequacy.

Results
Numerical simulations validate the theoretical findings:

Asymptotic Optimality: The optimality gap between TPR and an "Oracle" policy (which has perfect foresight) decays exponentially as the community size increases, outperforming complex centralized heuristics like Least-Laxity-First (LLF) and Model Predictive Control (MPC).
Cost Savings: TPR yields significant cost savings for individual members compared to standalone NEM operation. The benefits are most pronounced when renewable generation is decentralized (private rooftop solar), allowing members with deficits to buy surplus from neighbors at $\pi^-$ , while members with surplus sell at $\pi^+$ (or avoid buying at $\pi^+$ ).
Robustness: Because TPR depends only on the utility's fixed rates and aggregate thresholds, it is robust against modeling uncertainties regarding household demand patterns and renewable generation distributions.

Significance
The paper claims significance in providing a computationally tractable and robust solution to the bilevel stochastic dynamic programming problem in energy communities. By decoupling the complex coordination problem into a simple pricing rule based on aggregate renewable states, TPR achieves near-optimal social welfare without requiring a central scheduler to know private household information or solve intractable dynamic programs. The work bridges the gap between theoretical optimal control and practical implementation, offering a mechanism that guarantees economic stability (individual rationality and revenue adequacy) while leveraging the efficiency of shared renewable resources. The authors position TPR as a practical alternative to iterative peer-to-peer trading mechanisms, which are often difficult to implement and analyze.

Technical Summary: Price-Based Distributed Scheduling of Flexible Demands in Energy Communities

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