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Hierarchical Stochastic Scheduling of Multi-Community Integrated Energy Systems in Uncertain Environments via Stackelberg Game
Yang Li, Bin Wang, Zhen Yang, Jiazheng Li, Chen Chen
TL;DR
MCIES energy management and pricing require scheduling that accounts for multi-energy interaction, stakeholder interests, demand response, and renewable uncertainty. The paper develops a WGAN-GP and clustering scenario pipeline within a Stackelberg hierarchical schedule, solved distributively. It reports peak-shaving, valley-filling, smoother load curves, lower user costs with comfort maintained, and a unique Stackelberg-equilibrium solution.
Problem
MCIES scheduling must address complex stakeholder interactions, incompletely explored building-user demand response, and insufficient treatment of renewable-generation uncertainty.
Method
The paper combines WGAN-GP renewable-scenario generation, Kmeans++ typical-scenario reduction, integrated demand response, and Stackelberg scheduling with the operator as leader and users as followers.
Results
The schedule achieved peak-shaving and valley-filling, smoothed load curves, reduced user costs while maintaining comfort, and had a theoretically unique Stackelberg-equilibrium solution.
Takeaways & Limitations
The proposed framework provides a hierarchical stochastic scheduling approach for multi-energy MCIES transactions under renewable uncertainty.
Takeaways & Limitations
The study does not consider competitive relationships among different CIESs or more than two MCIESs supplying various users.
Abstract
from arXiv · showhide
An operating entity utilizing community-integrated energy systems with a large number of small-scale distributed energy sources can easily trade with existing distribution markets. To solve the energy management and pricing problem of multi-community integrated energy systems (MCIESs) with multi-energy interaction, this study investigated a hierarchical stochastic optimal scheduling method for uncertain environments. To handle multiple uncertainties, a Wasserstein generative adversarial network with a gradient penalty was used to generate renewable scenarios, and the Kmeans++ clustering algorithm was employed to generate typical scenarios. A Stackelberg-based hierarchical stochastic schedule with an integrated demand response was constructed, where the MCIES operator acted as the leader pursuing the maximum net profit by setting energy prices, while the building users were followers who adjusted their energy consumption plans to minimize their total costs. Finally, a distributed iterative solution method based on a metaheuristic was designed. The effectiveness of the proposed method was verified using practical examples.
1 Introduction
MCIES research addresses energy management and pricing under multi-energy interaction, user demand response, stakeholder interests, and renewable-generation uncertainty. The introduction motivates combining stochastic scenario generation with hierarchical market coordination.
- Existing IES studies mainly optimize energy supply while overlooking user demand response and complex stakeholder interests.
- IDR research has largely focused on single micro-energy grids or hubs, leaving inter-entity interests and heat-load response insufficiently explored.
- MCIESs involve interactive competition between operators and users, motivating Stackelberg modeling in which operators set prices and users adjust demand.
- Renewable wind and solar output uncertainty complicates IES operation, while robust optimization can produce conservative schedules and chance constraints require difficult-to-obtain probability densities.
- Scenario-based stochastic scheduling depends critically on generating reasonable scenarios, and renewable-output uncertainty remains insufficiently considered in existing MCIES optimization.
- The paper positions data-driven deep-learning methods as a way to mine uncertain-variable distributions and generate scenarios without traditional statistical modeling.
and contributions of this paper are as follows.
The paper combines hierarchical Stackelberg scheduling, data-driven renewable scenarios, detailed district-heating modeling, and distributed solution procedures for MCIES energy transactions.
- The operator maximizes net profit through energy prices, while users adjust consumption plans to minimize costs within the hierarchical game.
- A single-master multi-slave framework makes the MCIES operator the leader and building users the followers in hierarchical optimization.
- WGAN-GP-based scenario generation handles renewable-output uncertainty without assuming a specific probability distribution, improving method practicality.
- A district-heating-network model incorporates time delay and thermal attenuation characteristics into the scheduling model.
- The integrated demand response includes users’ thermal comfort requirements through the predicted mean vote indicator.
- A distributed metaheuristic iterative method transmits only necessary interlevel data, protects participant privacy, and has numerically verified convergence.
2 Renewable scenarios generation based on WGAN-GP
The paper uses WGAN-GP to generate renewable-output scenarios from historical data, then reduces the scenario set through clustering for tractable stochastic scheduling.
- GANs use generator and discriminator networks in an adversarial min-max game to produce samples resembling historical renewable-generation data.
- The GAN’s training equations define generator and discriminator objectives, while the WGAN-GP objective incorporates the penalty term associated with interpolated samples.
- WGAN-GP replaces Jensen–Shannon divergence with Wasserstein distance and adds a gradient penalty to stabilize training and reduce gradient disappearance and mode collapse.
- The trained WGAN-GP generates wind and photovoltaic output scenarios without imposing a specific probability distribution.
- Generating N wind and photovoltaic scenarios creates 2 N combined scenarios, whose exponential growth increases computational complexity.
- Scenario reduction is therefore performed by clustering, after which reduced wind and photovoltaic scenarios receive calculated occurrence probabilities.
3 Physical model of MCIES
The MCIES physical model represents two interconnected community energy systems supplying electricity and heat through diverse generation, conversion, and storage equipment. It models flexible electrical and thermal demand alongside equipment, storage, and district-heating constraints.
- The MCIES contains two CIESs connected by power lines and heating pipelines, with each CIES able to interact with the external power grid.
- The system includes WT, PV, EB, MT, CHP, HST, and EES components for multi-energy generation, conversion, and storage.
- Electric load model: Building electrical demand is divided into fixed and flexible loads, with time-shiftable and interruptible components subject to operating bounds.
- Heat load model: Thermal demand incorporates building thermal inertia, allowing heat-load reduction within user comfort limits quantified by PMV constraints.
- District heating network model: The district heating network model accounts for heat loss and transmission delay while omitting the smaller secondary heating network.
4 Scheduling model construction
The scheduling model maximizes the MCIES operator’s net profit while representing electricity and heat balances, internal energy exchanges, grid interactions, equipment costs, and price constraints. Building users minimize energy and discomfort costs under integrated demand response.
- Operator objective: The MCIES operator maximizes net profit across two CIESs managed by the same stakeholder.
- Operator objective: Operator profit combines user energy-sales revenue, grid-interaction revenue, and equipment operation and maintenance costs.
- Energy balances: Electricity and heat balance equations account for renewable generation, CHP and MT output, storage exchanges, internal transmission, grid purchases, and user loads.
- Energy balances: Internal electricity and thermal exchanges are signed so positive transmission denotes input and negative transmission denotes output.
- Price constraints: Real-time electricity and heat prices are constrained by policy-based upper, lower, and average-value limits.
- User objective: Building users minimize energy purchase and discomfort costs while adjusting demand through integrated demand response.
5 Stackelberg game framework
The Stackelberg framework models the MCIES operator as a price-setting leader and building users as cost-minimizing followers. A distributed iterative metaheuristic solution is designed for the resulting large-scale nonlinear bilevel problem.
- Game process: The MCIES operator acts as leader by setting real-time electricity and heat sales prices, while building users act as followers by adjusting energy consumption.
- Game process: The leader maximizes net profit and followers minimize their energy-related costs in the single-master multiple-slave game.
- Equilibrium: The game iterates until a Stackelberg equilibrium, where followers optimally respond to prices and neither side can unilaterally improve its benefits.
- Model properties: The proposed model is a large-scale nonlinear bilevel optimization problem requiring equilibrium existence and uniqueness analysis.
- Solving algorithm: The distributed iterative solution uses a metaheuristic for the upper operator problem and CPLEX for lower-level building-user problems.
- Solving algorithm: The algorithm exchanges only price signals and energy-consumption strategies between levels, reducing information leakage and protecting participant privacy.
6 Case study
The case study evaluates the proposed MCIES scheduling method using measured North China renewable data, building-load assumptions, and specified network, price, and model parameters.
- Case-study setting: The case study uses a multi-community integrated energy system in North China as its research object.The study uses two years of measured wind-turbine and photovoltaic data sampled every 15 minutes.
- Data and training: The renewable dataset is divided into 80% training data and 20% test data, with a learning rate of 0.0002.The data comprise actual measured WT and PV outputs from the North China MCIES.
- Simulation inputs: The simulation specifies building loads, district-heating-network parameters, MCIES energy prices, and interruptible-load availability.Interruptible load is assumed to account for 10% of each building user's initial electrical load in every period.
6.1 Scenario generation analysis
The study generates renewable scenarios with WGAN-GP, selects typical scenarios using DB-index-based Kmeans++, and evaluates their fidelity before applying iterative MCIES scheduling.
- Scenario generation analysis: WGAN-GP iteratively trains a generator and discriminator until the Wasserstein distance stabilizes.Random noise generates samples, real and generated samples are discriminated, network losses are calculated, and both networks are updated.
- Scenario generation analysis: The final Wasserstein distance indicates that generated WT and PV scenario distributions are very close to the real-scenario distributions.The distance varies across epochs before gradually converging and stabilizing.
- Scenario validation: The generated scenarios reproduce real-data characteristics while retaining diversity and representing practical WT/PV operating conditions.The evaluation uses correlation and normalized error between generated and real scenarios.
- Scenario validation: For WT scenarios, each generated-centroid normalized error is at most 0.15 relative to its real-data cluster, while most scenario error limits are no greater than 0.6.PV normalized errors are reported as much smaller than WT errors.
- Scheduling results: The iterative scheduling process reaches Stackelberg equilibrium at the 83rd iteration as operator profit and building-user costs converge.The operator acts as the dominant leader, while users respond to the leader's decisions.
- Comparative scheduling results: Mode 1 reduces total user cost by ￥1,635 versus Mode 2 and increases operator net profit by ￥170.The comparison attributes the difference to integrated demand response and describes a win-win outcome for supply and demand.
- Comparative scheduling results: Considering internal MCIES energy interaction increases operator net profit by ￥225 versus Mode 3 while ensuring user needs.The study concludes that integrated demand response and multi-energy interaction improve overall operating economy.
7 Conclusions
This study develops a hierarchical stochastic scheduling framework for multi-community integrated energy systems under renewable-output uncertainty. It combines data-driven scenario generation, Stackelberg pricing and demand response, multi-energy interaction, and a distributed solution method validated by practical calculations.
- The study investigates hierarchical stochastic scheduling for multi-community integrated energy systems with multi-energy interaction and renewable-generation uncertainty.
- WGAN-GP generates wind and solar output scenarios, while Kmeans++ clustering produces typical scenarios without assuming a specific probability distribution.
- The single-master multi-slave model assigns leadership to the MCIES operator and follower roles to building users, who adjust consumption through energy prices.
- Energy pricing achieved peak-shaving and valley-filling, smoothed the load curve, and reduced user costs while ensuring user comfort.
- Multi-energy interaction further improved MCIES operating economy, while the distributed metaheuristic-based iterative method found a unique Stackelberg equilibrium and showed good convergence.
- The study did not consider competitive relationships among different community systems or scenarios involving more than two MCIESs feeding buildings in a grid.
(1) Proof of existence
The proof establishes existence of a Stackelberg equilibrium by showing that follower objectives are convex in their strategies and the leader objective has a constrained optimum. It also reports uniqueness properties for the resulting follower and leader solutions.
- (1) Proof of existence: The leader’s and followers’ objective functions are stated to be non-empty continuous functions of the game strategies.The remaining condition examined for the follower objective is quasi-convexity in each follower’s own strategy.
- (1) Proof of existence: The game model has a Stackelberg equilibrium solution after verifying continuity, convexity, and optimization constraints.The follower objective is shown to be convex in its strategy variables, completing the existence argument.
- (1) Proof of existence: The equilibrium proof begins by differentiating each follower’s total-cost function with respect to thermal, electricity, and heat decisions.The derivatives are set to zero to obtain candidate optimal responses before checking second-order conditions.
- (1) Proof of existence: Each follower has a unique optimal solution for a given leader strategy because its second-order derivatives are positive and variables have interval constraints.The minimum occurs at the follower’s optimal electricity, heat, and thermal-energy decisions.
- (1) Proof of existence: The MCIES operator has a unique constrained optimum because its net profit is continuously increasing in the selling-price variables.The stated variables are the selling electricity-price and selling heat-price strategies.
Appendix B
Appendix B lists building, supply-pipeline, and MCIES operating parameters, alongside figures showing user load curves and pre- versus post-optimization results.
- Appendix B: Appendix B contains tables for building parameters, supply-pipeline parameters, and MCIES operating parameters.These are identified as Tables B1, B2, and B3, respectively.
- Appendix B: Electrical and hydrogen storage parameters include charge and discharge efficiencies, capacities, and power limits.The appendix lists EES and HST bounds alongside storage charge and discharge values.
- Appendix B: The appendix reports energy-price and cost coefficients for multiple time periods and equipment components.Values are provided for electricity, heat, and other operating-cost terms.
- Appendix B: Figures B1 and B2 show building users’ electric and heat load curves and compare results before and after optimization for each user.Figure B1 concerns load curves, while Figure B2 concerns the optimization comparison.