Data-Driven Distributionally Robust Scheduling of Community Integrated Energy Systems with Uncertain Renewable Generations Considering Integrated Demand Response

Yang Li; Meng Han; Mohammad Shahidehpour; Jiazheng Li; Chao Long

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Data-Driven Distributionally Robust Scheduling of Community Integrated Energy Systems with Uncertain Renewable Generations Considering Integrated Demand Response

Yang Li, Meng Han, Mohammad Shahidehpour, Jiazheng Li, Chao Long

arXiv:2301.08861v2Jan 21, 2023eess.SY

TL;DR

CIES scheduling must manage renewable-generation uncertainty while coordinating demand response and maintaining economical, robust operation. The paper proposes a data-driven two-stage DRO model using a comprehensive norm, WGAN-GP scenarios, and thermal-flexibility modeling. On an actual North China CIES, the approach balances economy and robustness and outperforms commonly used DRO methods in economy, curtailment, and computational efficiency.

Problem
CIES scheduling needs to coordinate integrated demand response with uncertain renewable generation, while existing heat-demand models often omit thermal-comfort ambiguity.
Method
The paper constructs a data-driven two-stage DRO model using a 1-norm and infinity-norm information set, WGAN-GP scenario generation, and PMV-based thermal-comfort and building-inertia modeling.
Results
The proposed DRO model balances system economy and robustness and outperforms commonly used DRO methods in operational economy, renewable-power curtailment rate, and computational efficiency.
Takeaways & Limitations
The approach provides stronger adaptability for CIES scheduling while promoting renewable-energy consumption through integrated demand response.
Takeaways & Limitations
The presented work does not take data privacy protection into account, although more realistic applications should preserve data privacy.

Abstract

from arXiv · show

A community integrated energy system (CIES) is an important carrier of the energy internet and smart city in geographical and functional terms. Its emergence provides a new solution to the problems of energy utilization and environmental pollution. To coordinate the integrated demand response and uncertainty of renewable energy generation (RGs), a data-driven two-stage distributionally robust optimization (DRO) model is constructed. A comprehensive norm consisting of the 1-norm and infinity-norm is used as the uncertainty probability distribution information set, thereby avoiding complex probability density information. To address multiple uncertainties of RGs, a generative adversarial network based on the Wasserstein distance with gradient penalty is proposed to generate RG scenarios, which has wide applicability. To further tap the potential of the demand response, we take into account the ambiguity of human thermal comfort and the thermal inertia of buildings. Thus, an integrated demand response mechanism is developed that effectively promotes the consumption of renewable energy. The proposed method is simulated in an actual CIES in North China. In comparison with traditional stochastic programming and robust optimization, it is verified that the proposed DRO model properly balances the relationship between economical operation and robustness while exhibiting stronger adaptability. Furthermore, our approach outperforms other commonly used DRO methods with better operational economy, lower renewable power curtailment rate, and higher computational efficiency.

1 Introduction

The paper develops a data-driven two-stage DRO scheduling model for CIESs that coordinates renewable-generation uncertainty with integrated demand response. It combines WGAN-GP scenario generation, thermal-comfort and building-inertia modeling, and a comprehensive norm to improve practical scheduling.

Existing stochastic programming and robust optimization methods address uncertainty in CIES operation, but renewable-generation uncertainty can reduce operational stability and renewable-energy consumption.
Previous demand-response studies often simplified controllable heat loads and did not model ambiguity in users' thermal comfort.
The proposed model uses a data-driven two-stage DRO formulation with a 1-norm and infinity-norm information set, requiring simple linearization instead of complex mathematical conversions.
WGAN-GP generates renewable-generation scenarios that better represent worst-case probability distributions and space-time characteristics than the original GAN.
The integrated demand-response mechanism models thermal-comfort ambiguity and building thermal inertia to promote renewable-energy consumption.
Simulations on an actual CIES in North China indicate that the proposed DRO model balances economical operation and robustness with stronger adaptability than traditional methods.

2 RGs scenario generation and reduction

The paper uses GAN-based learning to generate renewable-generation scenarios and WGAN-GP to improve distribution estimation. K-means++ then reduces the generated scenarios, with DBI and SC used to evaluate clustering quality.

WGAN-GP scenario generation: A GAN learns the distribution of historical renewable-generation data by training a generator and discriminator in an adversarial process.The generator maps noise vectors to samples, while the discriminator distinguishes generated samples from real data.
WGAN-GP scenario generation: WGAN replaces Jensen-Shannon distance with Wasserstein distance, while WGAN-GP adds a gradient penalty to constrain the discriminator's gradient norm.
Scenario reduction: K-means++ clusters large numbers of WGAN-GP-generated scenarios to reduce them for scheduling-model construction and computational efficiency.The number of clusters affects clustering quality, model construction, and computational efficiency.
Scenario reduction: The Davies-Bouldin index and silhouette coefficient provide quantitative measures for selecting the number of scenario clusters.DBI uses intra-cluster and inter-cluster distances, while SC compares within-cluster and outside-cluster distances.

3 Physical model of CIES

The CIES couples electric and thermal subsystems with renewable generation, storage, and flexible loads. Its physical model represents electrical shifting and interruption, thermal comfort, building heat dynamics, and interruptible heating.

Overall CIES structure: The CIES supplies electricity through MTGs, wind turbines, photovoltaic units, and the main grid, while MTGs and electric boilers supply heat.ESS and HSD provide buffering for safe, flexible, and economical operation.
Electric load model: Time-shiftable loads adjust consumption periods under total-demand balance to support peak shaving and valley filling.
Electric load model: Electrical interruptible loads can be reduced during high-demand periods, with the maximum interruption assumed to equal 10% of each period's electrical demand.
Thermal flexible load: PMV quantifies users' thermal-comfort perception, with different allowable PMV ranges assigned to daytime and nighttime periods.The study sets |PMV| ≤ 0.9 from 1:00–7:00 and 20:00–24:00, and |PMV| ≤ 0.5 from 8:00–19:00.
Thermal flexible load: A transient building heat-balance equation relates heating power to indoor temperature while accounting for building heat-transfer and indoor-air properties.Assuming outdoor temperature remains unchanged over a short time allows the equation to be linearized.
Thermal flexible load: Interruptible heating is bounded by its maximum value and equals the difference between heat-load demand before and after reduction.

4.1 Two-stage objective function

The two-stage objective separates commitment-related costs from scenario-dependent operating costs. The model accounts for generation, grid exchange, storage, curtailment, emissions, and demand-response costs.

First-stage objective function: The first-stage objective minimizes gas-turbine startup and shutdown costs over the scheduling horizon.The horizon is 24 h, and binary startup and shutdown variables indicate corresponding micro-gas-turbine transitions.
Second-stage objective function: The second-stage objective includes MTG operation, grid power purchase, ESS, HSD, renewable curtailment, CO2 penalties, electricity sales, and demand-response costs.
Second-stage objective function: Wind and photovoltaic output differences are penalized as renewable-power curtailment, while demand-response actions incur compensation costs.
Second-stage objective function: MTG and grid power outputs contribute to operating and emissions costs, while purchased and sold grid electricity are represented separately.
Second-stage objective function: ESS and HSD charging and discharging powers enter the second-stage cost through their respective operating costs.

4.2 Constraints

The CIES constraints coordinate MTG, ESS, HSD, EB, grid-interactive, and electric–thermal operations while enforcing output, capacity, and state restrictions.

ESS constraints: ESS constraints regulate charging and discharging states, power limits, remaining capacity, and equal end-of-period and initial capacity.Boolean variables prevent simultaneous charging and discharging, while the terminal-capacity condition keeps each scheduling period starting from the same state.
Power balance constraints: Power-balance constraints require electricity supply and demand to balance across renewable generation, storage, EB, MTG, loads, and grid transactions.The CIES may purchase electricity when internal supply is insufficient and sell excess electricity, subject to upper bounds.
Electric–thermal balance constraints: Heat demand is supplied by MTGs, EBs, and HSD, with the EB constrained by its heating-power rating and performance coefficient.The EB performance coefficient represents the ratio of heating power to electricity consumption.
HSD constraints: HSD constraints regulate heat storage and release states, charging and discharging powers, capacity evolution, and allowable capacity bounds.Boolean operating-state variables distinguish heat storage, heat release, and inactivity.

4.3 Data-driven distributed robust framework

The data-driven framework uses two-stage decisions and an ambiguity set over clustered renewable-generation scenario probabilities to represent uncertainty without requiring complex probability densities.

Two-stage decisions: First-stage decisions schedule discrete MTG, ESS, and HSD states, while second-stage decisions adjust equipment outputs, renewable generation, grid purchases, and sales after uncertainty is revealed.The first stage determines startup–shutdown and storage states; the second stage formulates corresponding dispatch decisions.
Scenario representation: The model represents clustered renewable-generation scenarios with an initial probability distribution and a set of admissible probability distributions.The scenario set contains s_N clustered scenarios, with coefficient matrices defining the optimization constraints.
Distributional ambiguity set: The uncertainty confidence set is centered on the initial scenario distribution and restricts deviations using a composite 1-norm and ∞-norm.The two norms impose separate allowable probability-deviation limits controlled by θ_1 and θ_∞.
Linearization: The composite-norm probability constraints are converted into a tractable form by introducing binary auxiliary variables and positive or negative probability offsets.The actual scenario probability distribution is represented after the norm constraints are linearized.

5 Model solution

The solution procedure combines WGAN-GP scenario generation with column-and-constraint generation, iteratively linking a master problem and a worst-distribution subproblem.

WGAN-GP scenario generation: WGAN-GP trains a generator and discriminator iteratively so generated renewable-generation samples resemble historical samples.Random noise enters the generator, while generated and historical samples are evaluated by the discriminator before network weights are updated.
Iterative CCG solution: Column-and-constraint generation is selected because it offers few iterations and high accuracy for solving the proposed DRO model.The model-solving process is presented as a master-problem and subproblem iteration.
Problem decomposition: The two-stage DRO model is decomposed into a master problem containing first-stage decisions and a subproblem identifying the worst scenario probability distribution.The master problem uses the current worst distribution, while the subproblem is solved under the master problem’s first-stage solution.
Iterative CCG solution: The subproblem’s worst probability distribution is fed back to the master problem, which updates the second-stage variables and related constraints across iterations.The process continues until the upper- and lower-bound gap satisfies the prescribed convergence accuracy.

6 Case study

The case study evaluates WGAN-GP scenario generation and the proposed DRO scheduling model in an actual North China CIES. Results examine renewable-generation clustering, electrical and heat scheduling, integrated demand response, and operating modes.

6.1 Simulation system and data: Two years of 15-minute PV and WT output data from North China were split into 80% training and 20% testing for WGAN-GP evaluation.The simulation used MATLAB R2016b with IBM ILOG CPLEX Optimizer; the WGAN-GP learning rate was 0.0002.
6.2 Performance Evaluation of the WGAN-GP: WGAN-GP training progressively makes generated RG samples more similar to historical data as the Wasserstein distance decreases.The generator adjusts its weights while the discriminator improves its ability to distinguish real and generated samples.
6.3 RG scenario clustering: The optimal clustering numbers are 2 for PV outputs and 4 for WT outputs.DBI is minimized at the best classification effect, while silhouette values closer to 1 indicate better clustering.
6.4 Analysis of Scheduling Results in Typical RG Scenarios: During sufficient RG output, renewable energy entirely supplies electric load in some periods, while ESS, MTG, and the grid cover peak-period vacancies.The scheduling prioritizes RG consumption and uses bidirectional ESS flows to reduce electricity curtailment and power-supply pressure.
6.5 Analysis of IDR Scheduling Results: IDR smooths electric load through peak shaving and valley filling while allowing heat-load reductions during nighttime periods of lower comfort sensitivity.Users shift or interrupt electricity consumption during peak periods and increase consumption during low-price periods.
6.6 Comparison of different operating modes: 125.09¥ and 182.58¥ are the operating-cost reductions from Mode 1 to Mode 3 and from Mode 2 to Mode 4, respectively.The corresponding costs decrease from 3039.65¥ to 2914.56¥ and from 2879.36¥ to 2696.78¥ after applying IDR.

6.7 Sensitivity analysis of ambiguity set parameters

The sensitivity analysis varies historical-data volume, confidence levels, ambiguity-set norms, and CCG iterations. It shows how these choices affect operating cost, conservatism, uncertainty characterization, and computational effort.

Historical-data sensitivity: Increasing the number of historical data gradually decreases total CIES operating cost, with smaller reductions after reaching a certain data volume.More historical data bring the initial RG scenario distribution closer to real outputs and reduce the worst-case probability shift.
Confidence-level sensitivity: Higher confidence levels enlarge the confidence interval, increasing modeled uncertainty and producing more robust operating schemes.The analysis evaluates operating costs under different confidence levels with M=5000.
Ambiguity-set norm comparison: The comprehensive-norm confidence interval is less conservative and closer to real RG output scenarios than the compared single-norm formulation.The comprehensive norm combines 1-norm and infinity-norm constraints in the ambiguity-set comparison.
CCG computational complexity: Four iterations are sufficient for the CCG objective function to meet the prescribed iteration accuracy.The MP–SP decomposition avoids direct coupling between scenario probabilities and second-stage variables, reducing transformation complexity.
Comparison with traditional methods: The proposed DRO has lower operating cost than robust optimization but higher cost than stochastic programming, reflecting an intermediate robustness level.Stochastic programming does not consider worst cases, whereas robust optimization focuses heavily on extreme RG scenarios and becomes conservative.
Comparison with other DRO methods: The proposed DRO outperforms MDRO and WDRO in operating cost, renewable power curtailment rate, and calculation time.The comparison is reported in Table 10 for commonly used moment-based and Wasserstein-based DRO methods.

7 Conclusions

The paper develops a data-driven two-stage DRO scheduling model that coordinates renewable-generation uncertainty with integrated demand response in CIESs. Its WGAN-GP scenarios, comprehensive-norm confidence set, thermal-comfort modeling, and CCG solution support economical, robust operation while leaving data privacy for future work.

Contributions: The proposed model uses a comprehensive norm combining the 1-norm and ∞-norm to define the probability distribution confidence set.The solving stage applies a CCG algorithm iteratively, avoiding strong-duality or KKT transformations and reducing solution complexity.
Contributions: WGAN-GP generates renewable-generation scenarios from historical outputs while addressing gradient vanishing and mode collapse in original GANs.The approach avoids requiring traditional probability-density information and provides more stable training.
Contributions: The integrated demand response mechanism introduces PMV to represent ambiguity in users’ thermal comfort and supports peak shaving, valley filling, and reduced CIES operating costs.These mechanisms are designed to promote renewable-energy consumption.
Conclusions: Larger historical renewable-generation datasets produce smaller uncertainty-set confidence intervals and less conservative scheduling plans.The comprehensive norm is reported as closer to real renewable-generation output scenarios and more economical than using only the ∞-norm or 1-norm.
Conclusions: Simulations on an actual CIES in North China show that the proposed DRO model balances system economy and robustness and outperforms moment-based and Wasserstein-based DRO methods.Compared with those DRO methods, it achieves better operational economy, lower renewable-power curtailment, and higher computational efficiency.
Limitations: The study does not address data privacy protection, and future CIES scheduling should consider resilience to cyber-attacks such as false data injection.The authors identify privacy preservation and attack-resilient scheduling as directions for more realistic applications.