Source-linked AI summary
Three-Party Energy Management With Distributed Energy Resources in Smart Grid
Wayes Tushar, Bo Chai, Chau Yuen, David B. Smith, Kristin L. Wood, Zaiyue Yang, H. Vincent Poor
TL;DR
The paper addresses energy management for DER-equipped residential units and a shared facility controller, especially where units lack storage. It formulates their trading as a non-cooperative Stackelberg game and extends it with SFC storage operation. The resulting equilibrium is unique and strategy-proof, the distributed algorithm reaches it, and numerical cases report substantial SFC cost reductions.
Problem
Energy-management research has largely assumed DER-equipped users also have storage, while this paper targets smart communities where residential units trade generated energy without storage.
Method
The paper models residential units and a shared facility controller as followers and leader in a non-cooperative Stackelberg game, with a distributed equilibrium algorithm and an SFC storage charging-discharging scheme.
Results
The proposed game has a unique, strategy-proof Stackelberg equilibrium, its distributed algorithm is guaranteed to reach it, and storage further lowers SFC energy-purchase cost.
Takeaways & Limitations
At equilibrium, DER use benefits both the SFC and residential units, while the storage strategy further improves the SFC’s cost outcome.
Abstract
from arXiv · showhide
In this paper, the benefits of distributed energy resources (DERs) are considered in an energy management scheme for a smart community consisting of a large number of residential units (RUs) and a shared facility controller (SFC). A non-cooperative Stackelberg game between RUs and the SFC is proposed in order to explore how both entities can benefit, in terms of achieved utility and minimizing total cost respectively, from their energy trading with each other and the grid. From the properties of the game, it is shown that the maximum benefit to the SFC in terms of reduction in total cost is obtained at the unique and strategy proof Stackelberg equilibrium (SE). It is further shown that the SE is guaranteed to be reached by the SFC and RUs by executing the proposed algorithm in a distributed fashion, where participating RUs comply with their best strategies in response to the action chosen by the SFC. In addition, a charging-discharging scheme is introduced for the SFC's storage device (SD) that can further lower the SFC's total cost if the proposed game is implemented. Numerical experiments confirm the effectiveness of the proposed scheme.
I. INTRODUCTION
DERs can reduce emissions, grid dependence, and electricity costs, but prior work largely assumes users have storage. The paper addresses this gap with a three-party energy-management scheme for residential units and a shared facility controller.
- DERs are motivated by their potential to reduce greenhouse-gas emissions and electricity-purchase costs while decreasing dependence on the main grid.
- Prior energy-management research has mostly considered users with DERs that also possess storage devices, leaving non-storage settings less studied.The paper identifies appropriate, practically feasible, and beneficial models and protocols as a key challenge in such settings.
- The proposed scheme models a smart community with DER-equipped residential units and a shared facility controller that trades energy with both the units and the grid.The shared facility provides public services such as maintaining lifts in community apartments.
- A non-cooperative Stackelberg game represents the independent decisions of the SFC and RUs, with the SFC setting buying prices and RUs responding to optimize their payoffs.The game is designed for decentralized energy management with limited communication between the SFC and each RU.
- The paper proves a unique, strategy-proof Stackelberg equilibrium, provides a distributed algorithm guaranteed to reach it, and adds an SFC storage charging-discharging strategy.The storage strategy is based on the main grid’s price and is intended to further improve the SFC’s daily energy-purchase cost.
III. SYSTEM MODEL
The system comprises DER-equipped residential units and a shared facility controller that obtains energy from the units or the grid. Their coupled decisions balance RU consumption and revenue against the SFC’s purchasing cost.
- The smart community contains residential units, a main power grid, and an SFC serving shared equipment such as lifts, pumps, gates, and lights.The SFC has no generation capability and must purchase all required energy from RUs or the grid.
- Each RU generates energy with DERs and chooses consumption so that excess generation can be sold to the SFC or the grid.RUs may be individual residences or groups connected through an aggregator.
- An RU must retain at least its essential load, while participating units sell remaining energy after satisfying their own consumption.A unit whose generation equals its essential load cannot sell energy and therefore cannot participate.
- The SFC sets a price between the grid’s buying and selling prices so RUs have an incentive to sell to the SFC while the SFC buys below the grid’s selling price.If RU energy is insufficient, the SFC purchases the remainder from the grid.
- The RU utility combines logarithmic consumption utility with sales revenue, whereas the SFC cost combines purchases from RUs and any required grid energy.The SFC’s cost function also enforces that total procurement does not exceed its required demand.
- As the SFC’s payment price increases, an RU’s maximum utility shifts left because it reduces consumption and sells more energy to the SFC.A price that is too low reduces RU sales; a price near the grid’s selling price can significantly increase the SFC’s cost.
A. Objective of the RU
Because RU utility and SFC cost are coupled through RU consumption and the SFC’s payment price, each RU selects consumption in response to the SFC’s offer. Higher offers encourage greater sales to the SFC.
- Without storage, each RU seeks to sell its excess generated energy after adjusting consumption at a suitable SFC payment price.
- The RU’s first-order condition links its consumption decision to the price offered by the SFC while respecting its essential-load constraint.The preference parameter must be sufficiently large for the resulting consumption to remain positive and at least the essential load.
- RU consumption is inversely proportional to the SFC’s payment price, so a higher offer makes the RU reduce consumption and sell more energy.
B. Objective of the SFC
The SFC minimizes its total energy-purchasing cost by choosing a buying price for RU energy, while privacy constraints motivate a distributed mechanism.
- The SFC minimizes the total cost of purchasing energy from RUs and the grid by selecting its own buying price.
- The optimal SFC price depends on the number of RUs selling energy and their DER generation during the considered period.
- The grid price affects the SFC’s price, while an added price margin is proposed to encourage RUs to sell excess energy.
- The SFC could optimize its price centrally if it had access to each RU’s private generation and parameter information.
- Because private RU information may be inaccessible to protect user privacy, the pricing mechanism must be distributed.
C. Non-cooperative Stackelberg game
The paper models energy management as a non-cooperative Stackelberg game in which the SFC leads through pricing and RUs respond through energy consumption decisions.
- The SFC is the leader and RUs are followers whose decisions respond to the SFC’s buying price.
- Each RU selects an energy consumption strategy from its feasible strategy set and seeks to maximize its utility.
- The SFC’s cost accounts for energy trading with RUs and the main grid, and its objective is cost minimization.
- A Stackelberg equilibrium gives the SFC an optimal price given followers’ best responses, with no player benefiting from unilateral deviation.
- At equilibrium, the SFC cannot reduce cost by lowering its price, and no RU can improve utility by changing its energy choice.
D. Existence and Uniqueness of SE
The proposed game has a unique Stackelberg equilibrium, supported by the RUs’ concave utility functions and the SFC’s convex cost function; a distributed algorithm is designed to reach it.
- A unique Stackelberg equilibrium always exists in the proposed game between the SFC and RUs.
- Each RU has a unique utility-maximizing energy choice because its utility is strictly concave over a bounded strategy range.
- Given RU energy choices, the SFC’s cost is strictly convex in its price, yielding a unique optimal per-unit price.
- The paper proposes a distributed algorithm to reach the unique equilibrium without requiring private RU information at the SFC.
E. Distributed Algorithm
The distributed algorithm alternates RU best responses and SFC price optimization until equilibrium conditions are met, and its convergence to the unique equilibrium is guaranteed.
- The algorithm iteratively has each RU choose energy consumption in response to the SFC price, then has the SFC optimize its price using RU energy information.
- The interaction continues until the equilibrium conditions are satisfied, producing the Stackelberg equilibrium.
- The SFC’s strict cost convexity makes its equilibrium price minimize total cost.
- Each RU selects a best response that maximizes its concave utility for the SFC’s current price.
- The proposed algorithm is guaranteed to converge to the game’s unique Stackelberg equilibrium.
1) Strategy-Proof Property:
The proposed algorithm is strategy-proof: no residential unit can improve its position by misreporting the energy it promises after reaching the Stackelberg equilibrium.
- No RU can sell more or less than promised when the SFC and other RUs follow Algorithm 1.
- The strategy-proof result applies when all other players, including the SFC and remaining RUs, adopt Algorithm 1.
- Algorithm 1 produces the Stackelberg-equilibrium consumption amounts for all RUs.
V. ENERGY MANAGEMENT WITH STORAGE
The SFC combines Stackelberg energy trading with storage operation based on grid time-of-use prices. It charges during lower-price periods and discharges during higher-price periods to reduce trading cost.
- The storage scheme is designed to further reduce the SFC’s total energy-purchase cost when combined with the Stackelberg game.DER output can be abundant or scarce, changing how much energy the SFC must buy from the grid.
- The SFC uses announced grid time-of-use prices to determine charging and discharging periods.It selects minimum and maximum price thresholds from the announced price list.
- The charging duration Tchg and discharging duration Tdis are selected according to the grid price.Their choices are illustrated in Fig. 3.
- During charging, the SFC sets a target SOC and allocates charging across time slots according to price differences.The storage efficiency σ and maximum charging rate constrain the charging process.
- During discharging, the SFC allocates discharge across selected slots while preventing storage drainage beyond equipment requirements.The negative sign in the discharge expression denotes discharging during Tdis.
- Charging at lower prices and discharging at higher prices reduces the SFC’s energy-trading cost.Two thresholds also permit distinct charging, discharging, and idle periods.
VI. CASE STUDY
The case studies show that the distributed Stackelberg scheme reduces SFC costs through RU energy trading, approaches centralized performance, and converges to the SE. Adding storage further reduces costs, with savings depending on storage capacity and operating conditions.
- Convergence and equilibrium: After 34 iterations, the SFC reaches its equilibrium price and minimum total energy-purchase cost for five RUs.The RUs simultaneously reach their best utilities in response to the SFC’s offered price.
- Effect of the number of RUs: 58.2% average cost reduction is achieved versus the baseline as the number of RUs varies.The proposed scheme benefits from buying more energy from RUs at lower prices, while the DER-free baseline remains dependent on the grid.
- Effect of SFC energy requirements: 74.9% lower average SFC cost is reported than the baseline when the SFC’s required energy changes.The proposed scheme spends less to buy the same amount of energy because it trades with RUs’ DERs.
- Distributed versus centralized control: The distributed scheme’s average social cost is only 7.07% and 6.75% higher than the centralized scheme at grid prices of 85 and 60 cents/kWh, respectively.This comparison covers networks growing from 5 to 25 RUs; the centralized controller has access to private RU information.
- Storage-device evaluation: 53.8% average cost reduction is obtained when an SFC with storage plays the game compared with an SFC with storage that does not.During peak hours, storage reduces grid purchases and RU trading provides energy at a cheaper rate than the grid.
- Storage-device evaluation: 54.02% and 58.1% average daily savings are reported for the proposed case versus no game and versus neither game nor storage, respectively.For a fixed charging rate, savings increase as storage capacity increases.
VII. CONCLUSION
The paper presents a non-cooperative Stackelberg-game energy management scheme whose unique, strategy-proof equilibrium benefits both the SFC and RUs. Future work includes discriminatory pricing, grid-price thresholds, and quantifying interaction-related inconvenience.
- The scheme uses a non-cooperative Stackelberg game for energy management in a smart community.
- A unique, strategy-proof Stackelberg equilibrium is shown to exist, benefiting both the SFC and RUs through DER use.
- Future work includes evaluating discriminatory pricing among RUs and determining the threshold for the grid’s price.
- Quantifying the inconvenience that the SFC and RUs face during their interaction is identified as another possible investigation.