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Optimal dispatch of low-carbon integrated energy system considering nuclear heating and carbon trading

Yang Li, Fanjin Bu, Jiankai Gao, Guoqing Lia

arXiv:2209.12025v1eess.SYcs.SY

TL;DR

Nuclear units can provide low-carbon energy, but their constant full-power operation challenges IES flexibility amid uncertain renewable output. This paper combines nuclear cogeneration and flexibility equipment with carbon trading, and uses discretized step transformation to convert chance constraints into a mixed-integer model. The authors report reduced CO₂ emissions and operating costs, improved flexibility, and expanded renewable-energy consumption.

  • Problem

    Nuclear units' constant full-power operation challenges IES flexibility, while distributed renewable output is uncertain.

    Source: §1 · pp. 2–3

  • Method

    The model coordinates nuclear units and carbon trading with heating renovation and ESS, HSS, and P2G, and converts chance constraints using discretized step transformation.

    Source: §1 · p. 4, §2.2 · pp. 5–6

  • Results

    The authors report that nuclear power and carbon trading together reduce CO₂ emissions and overall operating costs, while coordinated flexibility equipment improves system flexibility and renewable-energy consumption.

    Source: §6 · p. 26

  • Takeaways & Limitations

    The proposed scheduling approach is reported to yield economic and environmental benefits while improving flexibility and accommodating renewable energy.

    Source: §6 · p. 26

    Improving flexibility through loads and demand response is identified as a direction for future exploration.

    Source: §6 · p. 26

Abstract

from arXiv · show

The development of miniaturized nuclear power (NP) units and the improvement of the carbon trading market provide a new way to realize the low-carbon operation of integrated energy systems (IES). In this study, NP units and carbon trading mechanisms are introduced into the IES to build a new low-carbon scheduling model. In view of the decrease in system operation flexibility caused by the introduction of NP unit, on the one hand, the heating renovation of the NP unit is carried out to make it a cogeneration unit, to expand its operating range and improve its operating flexibility; on the other hand, auxiliary equipment such as electricity storage system, heat storage system and power to gas unit, which can carry out energy time translation or energy form conversion, are introduced into IES to jointly improve the flexibility of system operation. In the model-solving stage, the chance-constrained programming (CCP) model considering the uncertainty of the renewable energy (RE) output is converted into an equivalent mixed-integer linear programming (MILP) model using discretized step transformation. The test system built based on real data of an IES in North China shows that the proposed method has good economic and low-carbon environmental protection benefits.

NOMENCLATURE

The nomenclature defines abbreviations for the energy-system components and optimization methods, alongside symbols for unit outputs, storage, emissions, costs, and renewable-energy uncertainty.

Abbreviations

  • IES, NP, ESS, HSS, P2G, RE, and MILP denote the integrated system, generation and storage components, renewable energy, and optimization model.The list also defines CCP as chance-constrained programming and DST as discretized step transformation.Source: NOMENCLATURE · p. 1

Unit and conversion variables

  • NP and gas-cogeneration symbols specify electrical and heating power, including minimum and maximum operating bounds.The nomenclature also identifies nuclear equivalent electrical power and the P2G unit's power and gas volume.Source: NOMENCLATURE · pp. 1–2

Storage, emissions, and costs

  • Storage symbols cover ESS and HSS charging, discharging, capacity, and energy states, while other symbols describe emissions, carbon quotas, and operating costs.The nomenclature also lists renewable-output sequences and discretization-step length.Source: NOMENCLATURE · pp. 1–2

1 Introduction

The introduction frames nuclear power as a low-carbon supply option whose operating constraints complicate IES flexibility, especially amid renewable-output uncertainty. It proposes coordinating nuclear cogeneration, storage and P2G, carbon trading, and chance-constrained scheduling to address these challenges.

1 Introduction

  • Carbon trading can prioritize cleaner units but has limited effect on total emissions when operated independently; carbon capture and oxygen-enriched combustion face energy, cost, and retrofit barriers.The introduction therefore identifies a need to combine policy and technical measures.Source: §1 · pp. 3–4
  • Nuclear power emits no CO₂ during operation, but safety and economic considerations favor constant full-power operation over daily peak shaving, constraining IES flexibility.Frequent nuclear-unit power changes can affect reactor and primary-circuit stability and reduce economics; uncertain renewable output also raises flexibility demands.Source: §1 · pp. 2–3
  • The study combines nuclear power with stepped carbon pricing, which is intended to translate nuclear's low-carbon operation into economic advantages.The proposed mechanism is presented as promoting low-carbon IES development.Source: §1 · p. 4
  • Heating renovation expands nuclear units' operating range, while ESS, HSS, and P2G add flexibility through energy time shifting or form conversion.Prior work cited in the introduction describes storage as transferring energy across time to improve system flexibility.Source: §1 · p. 4
  • A chance-constrained IES model and discretized step transformation address renewable-output uncertainty by converting chance constraints into deterministic equivalents without distribution inverses.The introduction also reports testing the method on real-world IES data from northern China.Source: §1 · pp. 4–5

2 Low-carbon IES model

The IES combines renewable generation, thermal and cogeneration units, nuclear power, storage, and power-to-gas conversion. Heating renovation broadens nuclear cogeneration operation while maintaining constant equivalent electric power, and P2G converts electricity into gas.

2.1 System structure

  • The low-carbon IES combines photovoltaic and wind generation with thermal, nuclear, and gas cogeneration units, P2G, and energy storage.The system structure also includes auxiliary equipment.Source: §2.1 · p. 5

2.2 Nuclear cogeneration unit model

  • NP units operate at constant full power during the one-day dispatch period, while heating renovation expands their operating range from point A to line A-B.The renovated unit's equivalent electric power remains unchanged, maintaining the reactor at full power.Source: §2.2 · pp. 5–7
  • The study adopts steam extraction from the turbine for heating, rather than recovering post-generation waste heat.The text describes waste-heat recovery as suitable only for supplying heat to a small area near the plant.Source: §2.2 · p. 6

2.3 P2G unit model

  • P2G uses electricity to electrolyze water into hydrogen and oxygen, then converts hydrogen and CO₂ into methane and water.The process connects electricity and natural-gas systems through energy-form conversion.Source: §2.3 · p. 7

2.4 Energy storage system model

The model uses electrical and heat storage to buffer renewable output and load variation. ESS shifts electricity across time, while HSS works with cogeneration units to decouple heat and power production.

2.4 Energy storage system model

  • The model includes ESS and HSS as storage devices to suppress fluctuations from renewable-energy output and load variation.The passage introduces the two storage types as part of an energy storage and release strategy.Source: §2.4 · p. 7

2.4.1 Electric energy storage system model

  • ESS stores electricity when load is low or renewable output is high, then releases it when electric load is high.This shifts electricity across time and alleviates mismatches between production and consumption.Source: §2.4.1 · pp. 7–8

2.4.2 Heat storage system model

  • HSS and cogeneration units decouple heat and electricity: stored heat serves demand when electricity demand is high, allowing more electric output.When electricity demand is low, the cogeneration unit can reduce electric power and store heat instead.Source: §2.4.2 · p. 8

2.5 Gas cogeneration unit model

The GC unit is modeled as a cogeneration unit with linked electrical and heating operating limits. Its natural-gas consumption is calculated using a formula defined in terms of its thermoelectric ratio and heat loss.

2.5 Gas cogeneration unit model

  • GC units have higher thermal efficiency and a smaller footprint than coal-fired CHP units; at equal generation, GP units release less CO₂.The thermoelectric characteristics of GC units are described as matching those of ordinary CHP units.Source: §2.5 · p. 8
  • The GC operating domain is bounded by its electrical-power and heating-power limits.The figure passage identifies the shaded region as the GC unit's operating domain.Source: Figure 4 · p. 8, §2.5 · p. 9
  • The model calculates GC natural-gas consumption using a formula involving the unit's thermoelectric ratio and heat-loss rate.The passage introduces the consumption formula and defines those two quantities.Source: §2.5 · p. 9

2.6 Probabilistic model of photovoltaic and wind turbine output

The probabilistic output model represents photovoltaic and wind generation using probability distributions for solar irradiance and wind speed.

2.6 Probabilistic model of photovoltaic and wind turbine output

  • The model describes photovoltaic and wind-turbine output with probability density functions of solar irradiance and wind speed, respectively.It notes that prior studies indicate beta and Weibull distributions for solar irradiance and wind speed, respectively.Source: §2.6 · p. 9

2.7 Carbon trading model

The model assigns initial carbon quotas using a baseline method and prices emissions through a trading mechanism. Its stepped carbon price rises with emissions, while emissions accounting includes thermal and gas cogeneration emissions and P2G absorption.

2.7 Carbon trading model

  • Initial carbon quotas are allocated using a baseline method, and the free-quota coefficient can be adjusted according to the emissions-reduction target.Emissions above the free limit require purchasing allowances; emissions below it can be sold for profit.Source: §2.7 · p. 9
  • Carbon trading prices rise in steps as emissions increase, making higher emissions more costly and promoting low-carbon IES operation.The model contrasts its stepped pricing with traditional fixed carbon prices.Source: §2.7 · pp. 9–10
  • Actual emissions account for thermal-unit and gas-cogeneration emissions, minus the CO₂ absorbed by the P2G unit.The P2G absorption term is tied to its gas production and the natural-gas CO₂ factor.Source: §2.7 · p. 10

3.1 Objective function

The objective minimizes total IES operating cost, combining equipment operating costs with carbon-trading costs. The nuclear unit’s operating cost is treated as fixed under the stated full-power operating assumption.

3.1 Objective function

  • Total IES operating cost combines thermal and gas cogeneration costs, storage costs, nuclear-unit costs, and carbon-trading costs.The objective is to minimize the sum of these cost components.Source: §3.1 · p. 11
  • Thermal-unit cost includes power-related fuel costs and spinning-reserve costs, while gas cogeneration cost includes natural gas and reserve provision.The reserve-cost coefficients are specified for both unit types.Source: §3.1 · p. 11
  • The ESS cost accounts for charging, discharging, and reserve provision, while the nuclear unit’s operating cost is fixed.The nuclear unit maintains full power after startup and has scheduled nuclear-fuel replacement.Source: §3.1 · p. 12

3.2 Constraints

The constraints balance electricity, heat, and natural gas across the IES. They also bound equipment operation and reserve provision, including a chance constraint for renewable-output uncertainty.

3.2.1 Energy balance constraints

  • The IES constraints enforce electric, heating, and natural-gas balances across supply, storage, renewable power, and loads.The balance equations include absorbed renewable power and purchased natural gas.Source: §3.2.1 · p. 12

3.2.2 Equipment operation constraints

  • Thermal and gas cogeneration units must remain within operating limits and satisfy their specified power-ramp constraints.The passage also identifies upper and lower output bounds for the units.Source: §3.2.2 · pp. 12–13
  • Heating renovation expands the nuclear cogeneration unit’s operating range, subject to electric-output and heating-output limits.The constraints specify upper and lower electric-power bounds and an upper heating-power bound.Source: §3.2.2 · p. 13
  • P2G, electricity storage, and heat storage are bounded by operating, ramping, charge-discharge, capacity, or heat-transfer limits.The ESS also has a minimum capacity requirement to protect it and prolong its service life.Source: §3.2.2 · p. 13
  • The system’s spinning reserve must cover renewable-output deviations with a specified confidence level, avoiding reserve sizing for an extremely rare zero-output case.The authors frame the chance constraint as balancing reliability and economy.Source: §3.2.2 · p. 14

4 Model conversion and solution

The solution process discretizes renewable-output probabilities and uses DST to convert chance constraints into deterministic constraints, then linearizes the model as an MILP. It proceeds from model construction through optimization and application of the dispatch scheme.

4 Model conversion and solution

  • DST transforms the difficult chance constraints into equivalent deterministic constraints and linearizes the CCP model into a solvable MILP.The method is presented as the model-conversion step before solving.Source: §4 · p. 14

4.1.1 Probabilistic sequence of RE output

  • Wind and photovoltaic output distributions are discretized into probability sequences, which are combined by rolling sum to represent renewable output.Each discretized renewable-output value is associated with a probability.Source: §4.1.1 · pp. 14–15

4.1.2 Transformation of chance constraints into deterministic constraints

  • A binary indicator marks whether reserve exceeds the gap between expected renewable output and a discretized output state, forming the deterministic reserve constraint.The indicator is set to one when reserve exceeds the gap and zero otherwise.Source: §4.1.2 · p. 15

4.1.3 Linearization

  • The authors linearize the indicator-based expression because it cannot be solved directly by mixed-integer linear programming, completing the DST conversion to an MILP.The text identifies a large positive number in the linearization.Source: §4.1.3 · p. 16

4.2 Solution process

  • The workflow builds the nuclear cogeneration and carbon-trading models, formulates scheduling, discretizes renewable output, converts reserve constraints, solves the MILP, and applies the resulting schedule.CPLEX is used to find the optimization schedule; the workflow updates the confidence level if no solution is found.Source: §4.2 · p. 16

5 Case study

The North China IES case study compares operation without NP, with NP, and with NP converted to cogeneration. It assesses operating costs, emissions, renewable-energy use, flexibility, and carbon trading across these modes.

5.2 Cost and carbon emission analysis of each operating mode

  • Against mode 1, modes 2 and 3 reduce emissions by 3,105 t and 4,122 t, and operating costs by 455,526 ¥ and 984,961 ¥; without carbon trading, mode 3 has no clear economic advantage.The study excludes the cost of NP heating renovation.Source: §5.2 · pp. 18–19, Table 6 · p. 18

5.3.1 Analysis of consumption of renewable energy

5.3.2 Analysis of P2G unit operation

  • Mode 3's NP cogeneration units reduce dependence on P2G, which runs for fewer hours and at lower power than in mode 2.In mode 2, P2G operates near full power in early morning and at night to help balance electricity.Source: §5.3.2 · p. 21, Figure 13 · p. 21

5.4.1 ESS operation analysis

  • The ESS charges from 0:00–7:00 and discharges from 9:00–19:00, shifting electricity across the day to help balance supply and load.The authors describe this operation as peak shaving and valley filling that improves system economy and flexibility.Source: §5.4.1 · p. 22, Figure 14 · p. 22

5.4.2 HSS operation analysis

  • The HSS stores heat during 0:00–8:00 and 20:00–24:00 and releases it from 9:00–19:00, allowing NP electrical output to increase during high electrical demand.The authors attribute increased operational flexibility to storage and release of heat.Source: §5.4.2 · pp. 22–23, Figure 15 · p. 22

5.5.1 Analysis of the role of carbon trading price step changes

  • The stepped carbon-price model expands mode 3's operating-cost advantage over mode 1 from 471,700 ¥ to 984,961 ¥; mode 2 becomes cheaper than mode 1 at 105 ¥/t.The study reports that costs for all three modes rise as carbon trading prices increase.Source: §5.5.1 · p. 23, §5.5.3 · p. 25

5.5.2 Impact of carbon trading price on carbon emissions

  • As carbon trading prices increase, emissions decline below 200 ¥/t but remain unchanged above it; TP output decreases as GC output rises, until GC reaches maximum power above 200 ¥ and the output ratio stabilizes.Above 200 ¥/t, GC is already at full power and cannot replace more TP output, so emissions do not change.Source: §5.5.2 · p. 24, §5.5.4 · p. 25

5.6 Comparison of solution algorithms

  • Compared with SA and SAA, the proposed method has operating costs lower by 11,154 ¥ and 30,170 ¥, carbon emissions lower by 132 t and 211 t, and calculation times lower by 37.46 s and 15.16 s, respectively.Source: §5.6 · p. 26

6 Conclusions

The proposed low-carbon IES coordinates nuclear power units with carbon trading and flexibility measures, with simulations reporting lower emissions and operating costs. The study also identifies modeling and scope limitations for more realistic scenarios.

6 Conclusions

  • Coordinated carbon trading and nuclear power units greatly reduce total CO₂ emissions and overall operating costs in the newly constructed low-carbon IES.Source: §6 · p. 26
  • Renovating the nuclear unit improves its flexibility, while coordinated storage and P2G transfer or convert energy, alleviate supply-demand mismatch, and expand renewable-energy consumption space.Source: §6 · p. 26
  • The sequence-operation-theory solution converts the difficult chance-constrained model into a solvable mixed-integer programming model for quick and accurate scheduling.Source: §6 · p. 26
  • Nuclear cogeneration thermoelectric characteristics are simplified, and the cost of nuclear-unit heating renovation is omitted despite its relevance to more realistic scenarios.Source: §6 · p. 26
  • Flexible loads and demand response are identified as future directions for improving system flexibility.Source: §6 · p. 26
  • The study represents renewable power with probability density functions and identifies GAN-based renewable-scenario generation as a more realistic uncertainty-modeling direction.Source: §6 · p. 27
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