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A Conditional Value-at-Risk Based Planning Model for Integrated Energy System with Energy Storage and Renewables

Ang Xuan, Xinwei Shen, Qinglai Guo, Hongbin Sun

arXiv:2104.10862v1eess.SYcs.SY

TL;DR

Complexity in integrated energy systems makes risk assessment an important planning challenge. The paper proposes a two-stage energy-hub planning model that uses CVaR and incorporates renewables and storage. The reported case studies indicate a trade-off between investment cost and operational risk, and benefits from RES and ESS.

  • Problem

    IES planning faces a risk-assessment challenge because of system complexity, while existing risk indices lack a unified standard and CVaR-based IES planning remains unstudied.

    Source: A. Background and Motivation · p. 2, §II · p. 3

  • Method

    The paper proposes a two-stage IES planning model that uses CVaR to assess operational risk and integrates RES and ESS investment and operation decisions.

    Source: NOMENCLATURE · p. 1, §II · p. 3, §V · p. 9

  • Results

    As risk parameter β increases, load shedding cost fell by 83.27% and 93.94%, while CVaR at β=0.9 fell to 66.24% of its β=0.1 level.

    Source: B. Analysis of investment strategies · p. 7

  • Takeaways & Limitations

    The case studies indicate that ESS can support peak-valley load shifting and energy arbitrage, while higher risk parameters can benefit planning by eliminating load shedding caused by load and renewable uncertainty.

    Source: §V · p. 9

Abstract

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Owing to the potential higher energy supply efficiency and operation flexibility, integrated energy system (IES), which usually includes electric power, gas and heating/cooling systems, is considered as one of the primary forms of energy carrier in the future. However, with the increasing complexity of multiple energy devices and systems integration, IES planning is facing a significant challenge in terms of risk assessment. To this end, an energy hub (EH) planning model considering renewable energy sources (RES) and energy storage system (ESS) integration is proposed in this paper, in which the risk is measured by Conditional Value-at-Risk (CVaR). The proposed IES planning model includes two stages: 1) investment planning on equipment types and capacity (e.g., energy converters, distributed RES and ESS) and 2) optimizing the potential risk loss in operation scenarios along with confidence level and risk preference. The problem solving is accelerated by Benders Decomposition and Improved Backward Scenario Reduction Method. The numerical results illustrate the effectiveness of proposed method in balancing the potential operation risk and investment cost. Moreover, the effectiveness of reducing potential operation risk by introducing ESS and RES are also verified.

NOMENCLATURE

The section defines the notation for IES planning and storage, then situates the work in the broader challenge of managing risk in integrated energy systems. Prior work addresses IES operation, planning, and uncertainty, but CVaR-based IES planning remains an open area.

NOMENCLATURE

  • The nomenclature identifies device, RES, and ESS indices and decision variables, including candidate options, scenario and hour indices, and ESS charge/discharge states.It also defines device output, ESS charging and discharging power, and EH output.Source: NOMENCLATURE · pp. 1–2
  • Cost and risk notation includes investment cost, scenario probability, confidence level, annualization, discount rate, and lifetime.The list also names gas and electricity prices, maintenance and load-shedding unit costs, and wind-speed thresholds.Source: NOMENCLATURE · p. 1
  • The remaining notation covers ESS capacity, charging and discharging efficiency, EH coupling, output limits, and load demand.The abbreviations include IES, EH, ESS, RES, and the investment, operating, trading, maintenance, and load-shedding costs.Source: NOMENCLATURE · pp. 1–2

A. Background and Motivation

  • IES combines different energy systems for potential efficiency and flexibility, while energy storage and renewable sources are framed as relevant to fluctuations and environmental concerns.The background notes storage services including peak shaving, uninterruptible power supply, and energy arbitrage.Source: A. Background and Motivation · p. 2
  • IES risk assessment and reduction are challenging because of system complexity, and prior risk indices lack a unified standard and are described as relatively rough.Existing IES planning work is described as emphasizing investment-operation co-optimization rather than risk management.Source: A. Background and Motivation · p. 2

B. Literature Review

  • Prior IES research includes coupled power-gas operation, interconnected energy hubs, regional coordination, and expansion or capacity planning.Uncertainty studies use stochastic or robust optimization for sources such as load, wind, and energy demand.Source: B. Literature Review · p. 2
  • CVaR applications in power systems mainly address operational risk, while CVaR-based IES planning is identified as unstudied.The cited applications include load variation and renewable-energy uncertainty.Source: B. Literature Review · pp. 2–3

C. Problem Identification and Main Contributions

The paper addresses the limited treatment of risk management in IES planning by applying CVaR to operation uncertainty within a two-stage investment-operation planning model. CVaR evaluates losses beyond a confidence-level threshold, and the approach supports a risk-cost trade-off while incorporating RES and ESS.

C. Problem Identification and Main Contributions

  • The paper applies CVaR to model uncertainty-driven IES operational risk as a basis for investment risk management.For IES planning, scenario loss is described as operating cost, including electricity and gas consumption.Source: C. Problem Identification and Main… · p. 3, §II · p. 3
  • The proposed two-stage CVaR-based IES planning method measures operational risk from renewable generation and load variation and supports investment choices that trade off risk and cost.Decision-makers can use confidence level and risk preference to select investment strategies.Source: C. Problem Identification and Main… · p. 3
  • The proposed model includes ESS to improve operational flexibility and reports it as cost-effective.It also applies an improved backward reduction method to reduce scenarios and Benders Decomposition to accelerate solution convergence.Source: C. Problem Identification and Main… · p. 3

II. PRELIMINARIES OF CONDITIONAL VALUE AT RISK

  • VaR defines a loss threshold at a specified confidence level, while CVaR averages extreme losses beyond that cutoff.The paper adopts CVaR because it describes VaR as limited for risk estimation.Source: §II · p. 3, Figure 1 · p. 3
  • The CVaR formulation is presented for multi-scenario losses, with scenario probabilities and investment decisions determining the loss distribution.The paper notes that a CVaR formulation can be used for general loss distributions.Source: §II · p. 3

III. MODEL FORMULATION

The model plans a regional IES energy hub with multi-energy devices, renewables, and storage. Investment choices are made in the first stage, while operational strategies are optimized in the second, with first-stage capacities affecting the second-stage decisions.

III. MODEL FORMULATION

  • The regional planning model includes CCHP, gas boilers, air conditioners, transformers, photovoltaics, wind turbines, and battery, heating, and cooling storage.It is presented as an approach for balancing system risk and economy.Source: §III · p. 4

A. Two-stage Planning Model for Investment-Operation Co-optimization

  • The first stage chooses investment decisions, and the second stage optimizes operating strategies from the system operator’s perspective.The model’s two-stage structure is depicted in Fig.2.Source: A. Two-stage Planning Model for… · p. 4, Figure 2 · p. 4
  • First-stage decisions include binary choices for multi-energy device options and integer choices for RES and ESS sizing.ESS charge/discharge scheduling variables are included in the second-stage problem.Source: A. Two-stage Planning Model for… · p. 4
  • Second-stage variables include operating power, load shedding, and other continuous operating quantities across scenarios and hours.The first-stage equipment and storage capacities constrain or affect these operating decisions.Source: A. Two-stage Planning Model for… · p. 4
  • The first-stage capacities of energy devices and RES, plus ESS capacity and maximum charging and discharging power, affect second-stage operation.Benders Decomposition is cited as a technique used to solve the two-stage optimization.Source: A. Two-stage Planning Model for… · p. 4
  • Fig.2 presents the structure of the two-stage planning-operation optimization problem.The prose distinguishes investment decisions from optimized operation strategies.Source: Figure 2 · p. 4, A. Two-stage Planning Model for… · p. 4

B. Objective Function

The objective combines annualized investment and expected operating costs, then adds a CVaR-weighted risk term to tune the trade-off between operating cost and scenario risk loss.

B. Objective Function

  • Binary variables select device capacity options, while integer variables size the RES and ESS modules.Investment cost is annualized over equipment lifetime.Source: B. Objective Function · p. 4
  • Expected operating cost aggregates scenario trading, maintenance, and load-shedding costs using scenario probabilities.Trading costs reflect electricity and gas use; maintenance costs include device, RES, and ESS charging/discharging operation.Source: B. Objective Function · p. 4

1) Investment logic constraints

Investment constraints encode equipment choices and require core hub devices and positive RES/ESS module counts. Renewable output is weather-dependent and capped by installed module capacity.

1) Investment logic constraints

  • Investment logic requires at least one CCHP and TX device and a positive number of RES and ESS modules.Binary and integer decisions represent equipment investments and module counts.Source: 1) Investment logic constraints · p. 5

2) RES constraints

  • Wind and PV outputs depend on weather conditions, with each renewable technology’s output limit scaled by its installed module count.The wind and PV formulas use weather variables and module parameters; constraints (15) and (17) impose the resulting output limits.Source: 2) RES constraints · p. 5

3) ESS constraints

ESS constraints govern charging, discharging, and state of charge, while energy-hub constraints limit multi-energy device power through investment decisions.

3) ESS constraints

  • ESS charge and discharge states cannot both be active, and their powers are bounded by the installed module capacity.The SOC is limited by the number of ESS modules and per-module capacity, evolves with charging and discharging, and returns to its initial value at scenario end.Source: 3) ESS constraints · p. 5

4) Energy hub constraints

5) Additional constraints

The constraints cap load shedding and renewable capacity, enforce energy balances, and address the computational burden of scenario-rich planning through reduction and other acceleration options.

5) Additional constraints

  • The model caps load shedding at total load and limits planned RES capacity to an operator-set share of total IES energy capacity.The RES share is chosen based on operator experience and case conditions to avoid instability from renewable intermittence.Source: 5) Additional constraints · p. 5

6) Power balance constraints

D. Solution Strategy

  • Benders decomposition, looser gap tolerance, and larger operation-stage time steps are listed as options for reducing computational time.Source: D. Solution Strategy · p. 6
  • The improved backward scenario reduction method aggregates scenarios using Kantorovich distances and transfers removed-scenario probability to a nearby retained scenario.The paper compares its clustering results with traditional k-means.Source: D. Solution Strategy · p. 6

IV. CASE STUDIES

The case study plans an energy hub serving an industrial park with electricity, heating, and cooling loads, using specified energy-price and device assumptions.

A. Basic Settings

  • The energy hub represents an industrial park with electricity, heating, and cooling loads, plus electricity and natural-gas inputs.Dotted lines in the model mark investment options to be planned and connected.Source: A. Basic Settings · p. 6, Figure 3 · p. 6
  • Planning uses 8,760 hours of annual load data and wind-speed and light-intensity records from China’s meteorological data service.The load-demand setting is based on an industrial park in Hebei Province, China.Source: A. Basic Settings · p. 6
  • Gas costs 3.4 RMB/m³ and is held constant, while electricity uses the local government’s hourly peak-valley price.No heating or cooling power is consumed at the energy hub’s input ports.Source: A. Basic Settings · p. 6
  • The candidate supply facilities include five types of each multi-energy device, and ESS maximum charging and discharging power is set to 50% of planned capacity.PV and wind-turbine candidate module parameters are also specified.Source: A. Basic Settings · p. 6, Table I · p. 6, Table II · p. 7

B. Analysis of investment strategies

Across coupling conditions, the results report lower trading, maintenance, and load-shedding costs with RES and ESS than with multi-energy devices alone. In risk-preference cases, greater risk aversion is associated with increased investment and reduced shedding and CVaR.

B. Analysis of investment strategies

  • Higher confidence-level and risk-parameter requirements tend to bring more investment, with risk-seeking investors favoring heating and cooling facilities and risk-averse investors adding electric facilities.Multi-energy devices and ESSs often appear together among additional investments.Source: B. Analysis of investment strategies · p. 7, Figure 4 · p. 7
  • Load-shedding cost falls by 83.27% and 93.94% as β increases, while investment cost rises by 7.97% and 10.73%, and CVaR at β=0.9 falls to 66.24% of its β=0.1 level.The passage attributes OC and CVaR variation mainly to load-shedding cost.Source: B. Analysis of investment strategies · p. 7, Table III · p. 7
  • Cooling-load shedding decreases to nearly zero when β≥0.8 as risk aversion increases.The passage relates the reduction to planning against adverse effects of extreme fluctuations under load uncertainty.Source: B. Analysis of investment strategies · p. 7, Figure 5 · p. 7

C. Analysis of different coupling conditions

  • Trading, maintenance, and load-shedding costs are lower in Cases 2–4 than Case 1, and CVaR and VaR show similar reductions with RES and ESS aggregation.Table IV compares the different coupling conditions.Source: C. Analysis of different coupling… · p. 8, Table IV · p. 8
  • In Cases 3 and 4, BESS charging raises electricity purchases during valley hours (23:00–7:00), followed by lower purchases in other periods; Cases 2 and 4 purchase less than Cases 1 and 3 due to wind and solar use.These comparisons describe the reported daily scheduling and energy-arbitrage patterns.Source: C. Analysis of different coupling… · p. 8

D. Analysis of computational speed and accuracy

The analysis reports faster convergence from Benders decomposition and smaller benchmark deviations from improved backward scenario reduction. The conclusions connect CVaR-based IES planning with RES and ESS benefits while noting a remaining speed-versus-deviation tradeoff.

D. Analysis of computational speed and accuracy

V. CONCLUSIONS

  • The two-stage model co-optimizes IES investment and operation with CVaR risk assessment and maintenance, trading, and load-shedding costs.Source: §V · p. 9
  • ESS can support operation through peak-valley load shifting and energy arbitrage, while increasing the risk parameter can benefit planning by eliminating uncertainty-related load shedding.Source: §V · p. 9
  • The authors identify balancing convergence speed against planning-result deviations as a direction for further research.Source: §V · p. 9
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