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Optimal Scheduling of Integrated Demand Response-Enabled Community Integrated Energy Systems in Uncertain Environments

Yang Li, Bin Wang, Zhen Yang, Jiazheng Li, Guoqing Li

arXiv:2108.08055v1eess.SYeess.SPmath.OC

TL;DR

CIES scheduling must better integrate multi-energy demand response, renewable uncertainty, and spinning reserves. The paper formulates a chance-constrained scheduling model and converts it into a solvable MILP, reducing total operating costs by 12.3% without renewable curtailment while balancing economy and reliability.

  • Problem

    Prior CIES studies insufficiently integrate electricity-gas-heat demand response, electric vehicles, spinning reserves, and multiple renewable uncertainties in one scheduling problem.

  • Method

    The paper uses chance-constrained programming with integrated demand response, P2G, MT, and SOT-based linearization to formulate a solvable MILP.

  • Results

    12.3% lower total system operating cost is achieved under a scheduling cycle with no renewable power curtailments.

  • Takeaways & Limitations

    Setting an appropriate spinning-reserve confidence level balances CIES operating economy and reliability, while P2G and MT improve flexibility and user satisfaction.

Abstract

from arXiv · show

The community integrated energy system (CIES) is an essential energy internet carrier that has recently been the focus of much attention. A scheduling model based on chance-constrained programming is proposed for integrated demand response (IDR)-enabled CIES in uncertain environments to minimize the system operating costs, where an IDR program is used to explore the potential interaction ability of electricity-gas-heat flexible loads and electric vehicles. Moreover, power to gas (P2G) and micro-gas turbine (MT), as links of multi-energy carriers, are adopted to strengthen the coupling of different energy subsystems. Sequence operation theory (SOT) and linearization methods are employed to transform the original model into a solvable mixed-integer linear programming model. Simulation results on a practical CIES in North China demonstrate an improvement in the CIES operational economy via the coordination of IDR and renewable uncertainties, with P2G and MT enhancing the system operational flexibility and user comprehensive satisfaction. The CIES operation is able to achieve a trade-off between economy and system reliability by setting a suitable confidence level for the spinning reserve constraints. Besides, the proposed solution method outperforms the Hybrid Intelligent Algorithm in terms of both optimization results and calculation efficiency.

I. INTRODUCTION · II. STRUCTURE MODELING OF CIES · A. Probabilistic Wind Turbine Model

The paper proposes a chance-constrained scheduling strategy for IDR-enabled CIES under renewable and load-related uncertainties, integrating flexible multi-energy loads, electric vehicles, and spinning reserves. It models CIES components and probabilistic wind-turbine output, then uses SOT and linearization to obtain a solvable MILP whose simulations improve economic, flexibility, satisfaction, and reliability outcomes.

  • I. INTRODUCTION: I. INTRODUCTION — Scenario-based uncertainty methods depend heavily on scenario generation and reduction quality.
  • I. INTRODUCTION: I. INTRODUCTION — Prior studies insufficiently explore natural-gas and heat-load demand response and often omit spinning reserves induced by prediction errors.
  • I. INTRODUCTION: I. INTRODUCTION — The proposed CCP scheduling strategy minimizes operating costs by coordinating electricity-gas-heat flexible loads, electric vehicles, and spinning reserves from storage and the power grid.
  • I. INTRODUCTION: I. INTRODUCTION — SOT converts chance constraints into deterministic equivalents, while linearization produces a solvable MILP model.
  • I. INTRODUCTION: I. INTRODUCTION — North China simulations show that coordinating IDR with renewable uncertainties reduces operating costs, while confidence-level selection balances economy and system reliability.
  • II. STRUCTURE MODELING OF CIES: II. STRUCTURE MODELING OF CIES — The CIES comprises PV and WT units, an EB, EV charging station, P2G, an MT unit, energy storage devices, and loads, with hydrogen as an intermediate P2G product.
  • A. Probabilistic Wind Turbine Model: A. Probabilistic Wind Turbine Model — WT output depends on wind speed and rated output, with wind speed modeled by a Weibull distribution and characterized by scale and shape factors.

B. Probabilistic Photovoltaic Model · C. Electric Vehicle Model

The paper models photovoltaic output probabilistically through Beta-distributed solar irradiance and its linear relationship with PV power. It models EV charging from probabilistic return times and daily mileage, deriving charging loads through Monte Carlo simulation and load aggregation.

  • B. Probabilistic Photovoltaic Model: Solar irradiance approximately follows a Beta distribution, while PV power output has a linear relationship with solar irradiance.The PV power probability density function is formulated from this relationship.
  • B. Probabilistic Photovoltaic Model: The PV power density formulation uses the maximum PV power, two shape factors, the Gamma function, and actual and maximum solar irradiance.The parameters are defined as PV P maximum value, λ1 and λ2 shape factors, Γ as the Gamma function, and ξ and ξmax as actual and maximum irradiance.
  • C. Electric Vehicle Model: EV charging is assumed to commence when the EV’s final return ends, with final return time and daily mileage represented by probability density functions.The PDFs are given as equations (3) and (4).
  • C. Electric Vehicle Model: The EV distributions are parameterized by means and standard deviations for arrival time and daily mileage.μs and σs describe EV arrival time, while μd and σd describe daily mileage.
  • C. Electric Vehicle Model: The EV state of charge at the start of charging is calculated from each vehicle’s daily mileage.The formulation uses the daily mileage of EV n to determine its initial charging SOC.
  • C. Electric Vehicle Model: Each EV’s charging time is calculated from its charging requirements and charging characteristics.The charging-time formulation is introduced after calculating the starting SOC.
  • C. Electric Vehicle Model: Because daily driving distance and starting charging time are independent, Monte Carlo simulation derives individual EV charging loads and superimposes them into the total charging load.The resulting disorderly-charging daily load is depicted in Fig. 2.

D. Modeling of Load

The load-modeling framework represents electric, gas, and heat demand flexibility for CIES scheduling. It incorporates thermal comfort and user comprehensive satisfaction to capture the effects of integrated demand response on users.

  • Electric Load Model: Electric demand is divided into fixed and flexible loads, with time-shiftable electric load and interruptible electric load modeled through scheduling constraints.Load shifting and interruption are associated with user subsidies because they affect user experience.
  • Gas Load Model: Natural-gas demand response is modeled analogously to electric demand using time-shiftable and interruptible gas loads.The gas-load formulation is specified by equations (11)-(14).
  • Heat Load Model: Heat demand modeling uses building thermal inertia to reduce heat load within an acceptable thermal comfort range.The model defines actual heat load, introduces the Predictive Mean Vote (PMV) index, and sets PMV limits according to ISO 7730.
  • Heat Load Model: A user comprehensive satisfaction measure is designed to quantify the impact of integrated demand response on user experience.The satisfaction formulation aggregates the effects of load adjustments across modeled demand types.

E. Electric Boiler Model … III. OPTIMAL SCHEDULING MODEL OF CIES

The CIES scheduling model represents electric boilers, energy storage, P2G, and micro-gas turbines through component-specific energy-conversion and storage relationships. These components support the stated objective of minimizing CIES operating costs.

  • E. Electric Boiler Model: Electric boilers are modeled as electro-thermal coupling units that produce no pollutant emissions.Their output relationship links electric-boiler power, heat output, and efficiency.
  • F. Energy Storage Device Model: Energy storage is divided into electricity storage devices and heat storage devices.The storage model specifies charging, discharging, losses, capacity, and time-step effects.
  • G. Power to Gas Model: P2G converts water into hydrogen and oxygen through electrolysis, then synthesizes hydrogen and carbon dioxide into methane through the Sabatier process.The model relates P2G-produced natural gas to electricity consumption.
  • G. Power to Gas Model: The P2G formulation expresses produced-gas energy using electricity consumption, production terms, and higher heating values.This relationship is given in the P2G equations.
  • H. Micro-Gas Turbine Model: The micro-gas turbine model describes the relationship between its input power and output power.The formulation includes electrical output, heat output, efficiency, losses, and gas-consumption components.
  • III. OPTIMAL SCHEDULING MODEL OF CIES: The proposed CIES scheduling approach seeks to minimize operating costs.The paper introduces the scheduling components after stating this objective.

A. Objective Function · B. Constraint Conditions

The model minimizes total operating cost, incorporating energy transactions, spinning reserve, maintenance, environmental, and IDR compensation costs. Its constraints enforce multi-energy balance, renewable consumption, storage and device operating limits, EV feasibility, and chance-constrained spinning reserves.

  • A. Objective Function: The objective function minimizes total operating cost.The formulation includes energy transaction, spinning reserve, maintenance, environmental, and IDR compensation costs.
  • B. Constraint Conditions: Energy balance constraints prevent supply–demand imbalance across electricity, heat, and gas subsystems.The electricity and heat balances include system components such as ESD, MT, EVs, renewable generation, and load shedding; the gas balance includes P2G and MT.
  • B. Constraint Conditions: The renewable consumption constraint requires expected joint renewable outputs to satisfy the power balance.The renewable-output relationship combines RG contributions with electricity, P2G, gas, heat, and load-shedding terms.
  • B. Constraint Conditions: Storage constraints limit charging and discharging power and require equal starting and ending capacities in each scheduling cycle.The equal-boundary condition ensures identical initial conditions across scheduling cycles.
  • B. Constraint Conditions: Operating constraints bound electric-boiler output and restrict P2G input power and ramp rate.The P2G constraints include both input-power limits and a ramp-rate inequality.
  • B. Constraint Conditions: Micro-gas-turbine constraints impose bounds and ramp-rate limits on its input.The MT input must satisfy minimum and maximum operating limits together with a ramp constraint.
  • B. Constraint Conditions: EV constraints limit charging-station power and keep EV capacity within its minimum and maximum bounds.The charging-capacity relation accounts for charging power and efficiency over each time interval.
  • B. Constraint Conditions: Spinning-reserve constraints model reserve provision from ESD and the grid using a chance-constraint form under extreme renewable-output conditions.The formulation considers cases where renewable generation may be zero and imposes reserve requirements on grid and system resources.

IV. MODEL CONVERSION AND SOLUTION

The chance-constrained scheduling model is converted into a deterministic equivalent using sequence operation theory, then linearized into a solvable mixed-integer linear program and solved with CPLEX.

  • Model conversion: Sequence operation theory converts the chance constraint into its deterministic equivalent form.The resulting equivalent model is then transformed using linearization methods.
  • Solution: Linearization methods transform the equivalent model into a solvable MILP model, which is solved by CPLEX.

A. Probabilistic Sequence of RG Outputs · B. Deterministic Conversion of Chance Constraints

PV and WT outputs are discretized into probabilistic sequences, which determine renewable-generation output distributions over each period. Sequence operation theory then converts the renewable-output chance constraint into a deterministic equivalent using the joint-output probability sequence and Boolean variables.

  • A. Probabilistic Sequence of RG Outputs: PV and WT outputs are modeled as random variables and discretized into period-wise probability sequences.The PV and WT probability sequences are represented separately for each period.
  • A. Probabilistic Sequence of RG Outputs: PV discretization uses a step size q over output states from 0 through the maximum possible PV output.The discretized PV sequence contains N_PV^t + 1 states.
  • A. Probabilistic Sequence of RG Outputs: Each discretized PV state is assigned a corresponding probability, forming the PV output sequence shown in Table Ⅱ.The table lists power states and their associated probabilities.
  • A. Probabilistic Sequence of RG Outputs: The WT probabilistic sequence is obtained using the same discretization method as the PV sequence.The PV and WT probability series determine renewable-generation output E_RG^t in each period.
  • B. Deterministic Conversion of Chance Constraints: The chance-constraint conversion requires the distribution of the combined renewable-output variable Z_t = P_PV^t + P_WT^t.The source distribution is formed from two random variables with different distributions.
  • B. Deterministic Conversion of Chance Constraints: Because the inverse transform F_Z^-1 is difficult for the complex PDFs and may yield multiple solutions, SOT is used to obtain the deterministic constraint class.SOT handles the probability distribution of Z during the transformation.
  • B. Deterministic Conversion of Chance Constraints: The joint renewable-output sequence combines the PV and WT sequences, with length N_ct = N_at + N_bt and step size q.Its probability sequence for E_RG^t is presented in Table Ⅲ.
  • B. Deterministic Conversion of Chance Constraints: Boolean variables identify joint-output states satisfying the reserve inequality, allowing the chance constraint to be simplified into a deterministic equivalent form.The Boolean-state formulation is based on Table Ⅲ and precedes the deterministic reformulation of (44).

C. Linearization Methods · 1) Piecewise Function Linearization

The linearization methods transform nonlinear or non-MILP expressions into equivalent linear forms using binary and auxiliary variables. Piecewise constraints and minimum operators are reformulated so the deterministic equivalent becomes solvable as a MILP.

  • 1) Piecewise Function Linearization: The original expression cannot be directly solved using MILP, motivating its transformation into a piecewise linear formulation.The transformation begins from equation (50) and introduces a large positive number χ.
  • 1) Piecewise Function Linearization: A binary variable and a small positive parameter τ encode the piecewise condition while preserving the meaning of the original constraint.The binary variable is 1 under the specified condition and 0 otherwise, making the reformulated constraint equivalent to (50).
  • 1) Piecewise Function Linearization: Auxiliary variables are introduced to eliminate minimum operators in term C5 of (27).The method uses min{P_TSE_t, 0} as the illustrative case.
  • 1) Piecewise Function Linearization: Continuous auxiliary variables w1, w2, w3 and binary auxiliary variables z1, z2, z3 convert the minimum expression into linear constraints.These variables are used to convert equation (53) into linear form.
  • 1) Piecewise Function Linearization: The same linearization method is applied to min{Q_TSQt, 0}.This extends the auxiliary-variable reformulation beyond the illustrative P_TSE_t case.
  • C. Linearization Methods: The resulting deterministic equivalent is reformulated as a solvable mixed-integer linear programming equation.The final reformulation follows the linear treatment of both minimum operators.

D. Solution Process

The solution process builds device and IDR models, formulates a chance-constrained scheduling problem, and transforms renewable-generation uncertainty into a solvable MILP. It then sets the reserve-capacity confidence level, solves iteratively with CPLEX, and obtains the scheduling strategy when the stop criterion is satisfied.

  • Model and IDR formulation: The process first establishes models for each CIES device and designs an IDR mechanism for electricity-gas-heat flexible loads and electric vehicles.These are Steps 1 and 2 of the solution process.
  • Chance-constrained model: A CCP-based CIES scheduling model is established, with renewable-generation output PDFs and the discrete step q provided as inputs.These are Steps 3 and 4.
  • Uncertainty processing: Renewable-generation output PDFs are discretized, probabilistic sequences are generated, and SOT obtains expected joint outputs with corresponding probability sequences.These are Steps 5 and 6.
  • Model conversion: The chance constraint is converted into deterministic form, and linearization methods transform the deterministic equivalent model into MILP form.These are Steps 7 and 8.
  • Iterative solution: System parameters and the reserve-capacity confidence level are input, CPLEX solves the model, and the confidence level is modified until the stop criterion is satisfied before obtaining the scheduling strategy.Steps 9–13 define the iterative solution procedure.

V. CASE STUDY · A. Description of Testing System · B. Results and Analysis

A North China CIES case study evaluates three scheduling scenarios with different levels of IDR, P2G, and MT participation. Results show improved operational economy, renewable utilization, flexibility, and user satisfaction when these components are coordinated.

  • V. CASE STUDY: The testing system is a North China CIES simulated on a PC with two 2.8 GHz Intel Core dual-core CPUs and 16 GB RAM.
  • A. Description of Testing System: The CIES includes renewable generation, an EB, P2G and MT units, storage devices, and an EV charging station.
  • B. Results and Analysis: Three scenarios compare operation without IDR, P2G, and MT; with IDR alone; and with all three components in the proposed method.
  • B. Results and Analysis: Reserve capacities are analyzed under five confidence levels to select an appropriate spinning-reserve confidence level for scenario 3.
  • B. Results and Analysis: IDR improves energy-utilization efficiency while producing peak-shaving and valley-filling effects.
  • B. Results and Analysis: P2G absorbs electricity during 1:00-7:00, MT operates during 1:00-20:00, and both couple subsystems to improve operational flexibility.
  • B. Results and Analysis: 6697.68 ￥ total operating costs and 0 kWh renewable curtailment occur in scenario 3, compared with 7981.1 ￥ and 66.1 kWh in scenario 1.
  • B. Results and Analysis: Scenario 3 generally exceeds scenario 2 in comprehensive user satisfaction, while MT and P2G better satisfy load demands through added flexibility.

C. Comparison with Hybrid Intelligent Algorithm · VI. CONCLUSION

The proposed scheduling method outperforms HIA in operating cost and computation time, while the IDR-enabled CIES improves economy, flexibility, satisfaction, and reliability under uncertainty. The study also identifies modeling limitations and future extensions involving degradation, EV interaction, load uncertainty, and game theory.

  • C. Comparison with Hybrid Intelligent Algorithm: The proposed method achieves lower operating costs and computation time than HIA under different confidence levels.HIA combines particle swarm optimization with Monte Carlo simulations, using a population size of 100.
  • VI. CONCLUSION: IDR implements peak shaving and valley filling, decreasing total system operating cost by 12.3% with no renewable power curtailments.The result applies to a scheduling cycle without renewable power curtailments.
  • VI. CONCLUSION: P2G and MT enhance system operational flexibility and user comprehensive satisfaction through multi-energy complementary benefits.They function as links between multiple energy carriers.
  • VI. CONCLUSION: Chance-constrained spinning reserves from ESD and the power grid balance CIES economy and reliability when an appropriate confidence level is selected.The constraints account for uncertainties from multiple renewable generators.
  • VI. CONCLUSION: SOT and linearization convert the CCP-based scheduling framework into a solvable MILP model solved by CPLEX, surpassing HIA in cost and calculation efficiency.The conclusion attributes the approach’s advantage to lower operating costs and higher calculation efficiency.
  • VI. CONCLUSION: The study ignores battery degradation, EVs interaction, and load uncertainty, which should be considered in more realistic scheduling scenarios.The paper also proposes integrating IDR and Game theory into future IES scheduling.
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