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Improving operational flexibility of integrated energy system with uncertain renewable generations considering thermal inertia of buildings
Yang Li, Chunling Wang, Guoqing Li, Jinlong Wang, Dongbo Zhao, Chen Chen
TL;DR
Traditional CHP heat-set operation limits IES flexibility and renewable consumption under uncertain renewable generation, particularly during winter heating periods. The paper develops a chance-constrained scheduling model with thermal-comfort and building-inertia-aware heating loads, solves it as MILP through SOT, and reports improved flexibility through coordinated auxiliary equipment.
Problem
Traditional CHP heat-set operation and uncertain renewable generation limit IES flexibility and renewable-energy consumption during winter heating periods.
Method
A chance-constrained minimum-generation-cost scheduling model represents probabilistic spinning reserves and heating loads incorporating building thermal comfort and inertia, then converts the model to MILP using SOT.
Results
The proposed model improves IES operational flexibility under uncertain renewable generation by leveraging building thermal inertia and auxiliary equipment.
Takeaways & Limitations
HST, EB, and BESS should be selected and coordinated according to electricity and heating demands to improve flexibility and energy-supply reliability.
Takeaways & Limitations
The study omits storage capacity losses, time delay, and transmission losses, which future realistic optimization should include.
Abstract
from arXiv · showhide
Insufficient flexibility in system operation caused by traditional "heat-set" operating modes of combined heat and power (CHP) units in winter heating periods is a key issue that limits renewable energy consumption. In order to reduce the curtailment of renewable energy resources through improving the operational flexibility, a novel optimal scheduling model based on chance-constrained programming (CCP), aiming at minimizing the lowest generation cost, is proposed for a small-scale integrated energy system (IES) with CHP units, thermal power units, renewable generations and representative auxiliary equipments. In this model, due to the uncertainties of renewable generations including wind turbines and photovoltaic units, the probabilistic spinning reserves are supplied in the form of chance-constrained; from the perspective of user experience, a heating load model is built with consideration of heat comfort and inertia in buildings. To solve the model, a solution approach based on sequence operation theory (SOT) is developed, where the original CCP-based scheduling model is tackled into a solvable mixed-integer linear programming (MILP) formulation by converting a chance constraint into its deterministic equivalence class, and thereby is solved via the CPLEX solver. The simulation results on the modified IEEE 30-bus system demonstrate that the presented method manages to improve operational flexibility of the IES with uncertain renewable generations by comprehensively leveraging thermal inertia of buildings and different kinds of auxiliary equipments, which provides a fundamental way for promoting renewable energy consumption.
1 Introduction
Renewable uncertainty and traditional CHP heat-set operation constrain IES flexibility, especially during winter heating periods. The paper proposes chance-constrained scheduling that combines thermal inertia, auxiliary equipment, and thermal-electric decoupling to improve flexibility and renewable consumption.
- 1. Introduction: Prior IES studies use HSTs, electric boilers, pumped hydro, and BESSs to improve CHP flexibility and reduce wind curtailment.These approaches motivate broader use of auxiliary equipment for coordinated electricity and heating operation.
- 1. Introduction: Winter heating demand and uncertain distributed-generation outputs require greater flexibility, while CHP heat-set operation compresses renewable accommodation space.Thermal-electric decoupling is identified as an urgent challenge for improving renewable consumption.
- 1. Introduction: The paper addresses gaps in modeling multiple renewable uncertainties, heating loads satisfying thermal comfort, and IES scheduling under these combined conditions.The authors identify limited prior treatment of customer thermal comfort and the difficulty of handling multiple renewable-generation uncertainties.
- 1.2 Contributions of this work: A chance-constrained scheduling model minimizes generation cost for a small-scale IES with uncertain renewable generation and auxiliary equipment.Probabilistic spinning reserves are represented through chance constraints, while building heating loads include thermal comfort and transient heat balance.
- 1.2 Contributions of this work: Sequence operation theory converts the chance-constrained model into MILP, which is solved using CPLEX.The deterministic equivalence class makes the original formulation computationally solvable.
- 1.2 Contributions of this work: Simulations indicate that thermal inertia and multiple auxiliary equipments improve IES flexibility, while confidence-level selection balances economy and reliability.Different charging and discharging periods also leave energy reserves that strengthen energy-supply reliability.
2 Structure modeling of integrated energy system
The IES integrates coupled heat and electricity components, including CHP units, renewable generators, thermal units, and auxiliary equipment. Its models represent CHP flexibility, renewable-output uncertainty, electric and heat storage, and building heating dynamics.
- Overall framework: The small-scale IES integrates wind, photovoltaic, thermal power, CHP, BESS, HST, and HB components across heat and electricity networks.The HB, CHP units, and building are electro-thermal coupling units.
- CHP unit model: HST installation expands CHP operating ranges and significantly reduces electro-thermal coupling at a given heating power.The heating range expands to [0, P_hc,max], while the electric range expands to [P_e,L, P_e,M].
- Electric boiler model: The electric boiler converts electricity into heat, reducing CHP heating requirements while increasing valley-period electric demand for peak regulation.Its electric-to-heat relation is P_EB,t = η_EB P_EB,t^r, and the stated heating efficiency can reach 95%.
- Battery energy storage system model: BESS operation shifts surplus electricity from off-peak charging to peak-period discharging and smooths distributed-generation fluctuations.Its capacity balance accounts for charge and discharge powers, efficiencies, and the time interval.
- Heat storage tank model: HST operation decouples CHP electricity and heat production by storing heat during low heating demand and releasing it when needed.Positive heat-storage power denotes release, whereas negative power denotes storage.
- Probabilistic renewable models: Wind and photovoltaic models represent renewable uncertainty using wind-speed and solar-irradiance distributions linked to generator outputs.Wind speed uses a PDF with scale and shape factors, while solar irradiance is approximated by a Beta distribution.
- Building heating-load model: The building heating model combines fuzzy thermal-comfort requirements with transient heat balance to connect heating power and indoor temperature.The model uses building heat capacity, indoor and outdoor temperatures, heat-transfer properties, and heating power.
3 Proposed scheduling model
The proposed CCP-based scheduling model minimizes the IES’s power generation cost while explicitly accounting for probabilistic spinning reserves.
- The model seeks the minimum power generation cost of the integrated energy system.
- It incorporates operational constraints into the scheduling formulation.
- Probabilistic spinning reserves are included explicitly in the model.
3.1 Chance constrained programming
The scheduling problem is formulated as a chance-constrained stochastic optimization model with deterministic and probabilistic constraints governed by confidence levels.
- IES scheduling is formulated as a stochastic optimization problem using chance-constrained programming.
- The formulation uses decision variables, random parameters, an objective function, and probabilistic constraints.
- Confidence levels specify the required probability for constraints and the objective function.
- Traditional deterministic constraints and probabilistic constraints are both represented in the general formulation.
3.2 Formulation of the scheduling model
The scheduling model is organized into an objective function and a set of operational constraints, which are detailed in the formulation.
- The scheduling model contains an objective function.
- The model includes various operational constraints.
- The objective and constraints form the two main parts of the proposed scheduling model.
3.2.1 Objective function
The objective minimizes IES generation cost by combining conventional generation, CHP, battery, and spinning-reserve costs. Investment and maintenance costs are excluded because they are fixed and do not affect scheduling.
- The objective function minimizes the IES’s minimum generation cost while accounting for uncontrollable distributed-generation outputs.
- Battery energy-storage costs include charge and discharge costs together with battery spinning-reserve costs.
- Thermal power-unit costs are included through their electric-power outputs, fuel-cost coefficients, and spinning-reserve costs.
- CHP costs account for electric output, total heating power with the heat storage tank, fuel-cost coefficients, and spinning-reserve costs.
- Investment and maintenance costs are excluded because they are fixed values that do not affect the scheduling result.
3.2.2 Operational constraints
The IES scheduling model enforces energy balance, equipment operating limits, storage constraints, renewable-consumption bounds, and probabilistic spinning-reserve requirements. These constraints represent both secure operation and flexibility under renewable-generation uncertainty.
- Energy balance: Electrical and heat demand must equal the corresponding system supply in each period.Renewable consumption, electric and heating loads, and equipment outputs appear in the balance equations.
- Generation units: Thermal units and CHP units are constrained by minimum and maximum outputs and ramp-rate limits.The constraints bound thermal generation, CHP electric and heat production, and interperiod output changes.
- Energy storage: HST and BESS operation is limited by charging, discharging, capacity, and cycle-end conditions.Storage capacities remain within bounds, while starting and ending capacities are matched for the next scheduling cycle.
- Auxiliary equipment and renewables: The EB output and renewable-energy consumption are bounded by their maximum operating or expected-generation values.Renewable consumption satisfies 0 ≤ P^c_t ≤ E_t, where E_t is the expected renewable output.
- Spinning reserves: Thermal units, CHP units, and the BESS provide spinning reserves to address deviations between expected and random renewable outputs.The formulation recognizes that extreme renewable shortfalls are possible but may have low probability, motivating probabilistic reserve constraints.
4 Model solving
The solution method discretizes uncertain wind and PV outputs into probabilistic sequences, combines them for distributed-generation scenarios, and uses SOT to convert chance constraints into a deterministic MILP. CPLEX then solves the resulting scheduling model.
- Probability serialization: SOT first generates probabilistic sequences from the probability distributions of wind-turbine and PV outputs.The sequences discretize continuous probability distributions into finite output states with associated probabilities.
- Probability serialization: PV output sequences contain finite states determined by the maximum possible output and discrete step size.The sequence length is defined using a ceiling operation, and the resulting states are listed with their probabilities.
- Joint renewable outputs: The wind and PV sequences are combined into a distributed-generation output sequence whose length is N^c_t = N^a_t + N^b_t.Each combined output corresponds to a probability and forms the sequence used for reserve conversion.
- Chance-constraint conversion: SOT avoids directly computing the difficult inverse distribution of combined renewable output by representing chance-constraint scenarios discretely.The inverse transformation is difficult because the wind and PV probability-density functions have complex forms.
- MILP solution: The proposed workflow ends by checking solution existence and outputting the optimal IES scheduling scheme.If no solution exists, the confidence level is updated before resolving the model.
5 Case studies
The proposed scheduling approach is evaluated on a modified IEEE 30-bus system using MATLAB and CPLEX on a specified PC platform.
- Experimental setup: The test system models electricity at distribution-network scale and heating at district level.All procedures use MATLAB R2016b with CPLEX, running on a PC with 8 GB RAM and two 2.4 GHz dual-core CPUs.
5.1 Introduction of the test system
The modified IEEE 30-bus test system replaces two generators with CHP units and integrates WT, PV, EB, BESS, and HST equipment. Six operating modes compare auxiliary-equipment use, renewable uncertainty, and building thermal inertia.
- Test-system configuration: Generators 1 and 2 are replaced by CHP units, while WT and PV connect to buses 6 and 17.The system also includes one EB, one BESS, and two HSTs with identical parameters.
- Parameter settings: The study specifies building, renewable-generation, storage, EB, and 24-hour scheduling parameters for the test system.The scheduling interval is 1 h, and the listed parameters include capacities, operating limits, efficiencies, and costs.
- Study assumptions: The simulations neglect losses in the BESS, HST, and transmission lines while comparing the six operating modes.The comparisons separately assess renewable uncertainty and building thermal inertia.
- Operating modes: Modes 4 and 6 use spinning reserves set to 20% of system net load when renewable generations are modeled deterministically.System net load is defined as original electric load minus expected distributed-generation output.
5.2 Results and analysis
The results compare operating modes, renewable consumption, auxiliary-equipment dispatch, and computational performance in the IES. Coordinated storage and electric-boiler operation improves flexibility, renewable utilization, and generation-cost performance.
- Cost comparison: $133431.02 is the minimum total generation cost in mode 3, decreasing by $61,729.55 versus mode 1 and $1808.15 versus mode 2.Mode 3 combines HST, BESS, and EB operation.
- Renewable consumption: Renewable resources are completely consumed during 8:00–20:00 in all three modes, while nighttime curtailment is completely absorbed in mode 3.Adding BESS in mode 2 raises flexibility, and adding HSTs and EB in mode 3 enhances it further.
- Auxiliary-equipment operation: BESS charges from 0:00–6:00 and discharges from 11:00–18:00, remaining unchanged at other times.It acts as a load when evening electricity demand is low and as a power source when daytime demand increases.
- Auxiliary-equipment operation: HSTs adjust CHP heating load without changing user-side heating load, expanding CHP electrical-output flexibility during nighttime electrical-load valleys.This can improve peak regulation when sufficient heat is stored during lower-heating-load periods.
- Computational performance: The proposed approach requires about 6.5 seconds across operating modes, meeting the stated real-time requirements of IES operation.The chance-constrained model is converted into a solvable MILP formulation for CPLEX.
6 Conclusion
The paper proposes chance-constrained IES scheduling to address flexibility limits from CHP heat-set operation under uncertain renewable generation. Results indicate that thermal inertia and coordinated auxiliary equipment improve flexibility and renewable consumption, while the study omits several practical operating effects.
- Model and contribution: The scheduling model uses chance-constrained programming with probabilistic spinning reserves and a heating-load model incorporating building thermal comfort and inertia.
- Main results: The presented model improves operational flexibility under uncertain renewable generation by leveraging building thermal inertia and auxiliary equipment.
- Solution approach: The SOT-based approach converts the chance-constrained scheduling model into a MILP formulation and solves it with CPLEX.
- Auxiliary equipment: HST, EB, and BESS have different flexibility effects, while complementary coordinated operation improves flexibility and energy-supply reliability.
- Scope boundary: The study does not consider storage capacity losses, time delay, or transmission losses, and future work will integrate renewable scheduling with demand response.