# Multistage Economic Scheduling Model of Micro-Energy Grids Considering Flexible Capacity Allocation

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## Abstract

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## 1. Introduction

#### 1.1. Application Scenarios of Micro-Energy Grid

#### 1.2. Construction of Micro-Energy Grid Optimization Scheduling Models

#### 1.3. Operation Strategy of Micro-Energy Grids

- (1)
- Building a basic structural framework model of the micro-energy grid and explaining the mathematical model of the essential physical components;
- (2)
- Building a three-level scheduling optimization model for micro-energy grids, which is divided into three stages: (a) day-ahead capacity configuration; (b) intraday system scheduling; (c) real-time system scheduling.
- (3)
- Using the FCM-CCQ algorithm to describe the uncertainty of wind power and photovoltaics, the typical scenarios were obtained. The optimization calculation was carried out based on the typical scenarios.
- (4)
- Based on CVaR theory, the risk value of the micro-energy grid system participating in spot market transactions was evaluated.

## 2. The Three-Stage Collaborative Optimization Operation Mechanism for a Micro-Energy Grid

#### 2.1. The Three-Stage Collaborative Optimization Framework of a Micro-Energy Grid

#### 2.2. The Connection Mechanism of the Three Different Stage Models

## 3. Construction of a Three-Stage Scheduling Optimization Model for the Micro-Energy Grid

#### 3.1. Uncertain Handling of Wind Power and Photovoltaic Output

#### 3.2. The Construction of a Three-Stage Scheduling Optimization Model for Micro-Energy Grids

#### 3.2.1. The First-Stage Model

- (1)
- The Objective functionIn the day-ahead capacity allocation, since the electricity transaction process is not involved, it is only necessary to control the total cost of the micro-energy grid in the day-ahead capacity allocation stage. Therefore, the target aims to minimize the day-ahead capacity allocation cost. The objective function is shown in Equation (1):$$min{C}_{co}={\displaystyle \sum _{t=1}^{T}\left[\left({C}_{GT,t}+{C}_{BESS,t}+{C}_{DR,t}\right)+\left({C}_{spiil}\left({P}_{W,t}^{spill}+{P}_{pv,t}^{spill}\right)\right)\right]}$$$${C}_{GT,t}={C}_{{}_{GT}}^{startup}{u}_{GT,t}^{startup}+{C}_{{}_{GT}}^{stop}{u}_{GT,t}^{stop}+{C}_{GT}^{RD}{R}_{GT,t}^{D}+{C}_{GT}^{RU}{R}_{GT,t}^{U}$$$${C}_{BESS,t}={C}_{BESS,t}^{D}{P}_{dis,t}+{C}_{BESS,t}^{C}{P}_{chr,t}$$$${C}_{DR,t}=a+b{P}_{DR,t}$$It can be seen from the objective function that the total cost (${C}_{co}$) can be divided into three parts: gas turbine capacity allocation cost (${C}_{GT,t}$), energy storage capacity allocation cost (${C}_{BESS,t}$), and demand response capacity allocation cost (${C}_{DR,t}$). Among them, the gas turbine capacity allocation cost includes the startup and shutdown cost of the unit, as well as the spare capacity cost.
- (2)
- System constraints
- (a)
- Gas turbine$${P}_{GT,min}\le {P}_{GT,t}-{R}_{GT,t}^{D}$$$${P}_{GT,t}+{R}_{GT,t}^{U}\le {P}_{GT,max}$$$${R}_{GT,t}^{D}\ge 0,{R}_{GT,t}^{U}\ge 0$$The functional relationship between the natural gas consumption and power generation of the gas turbine is shown in Equation (8):$${F}_{GT,t}=\frac{a{P}_{GT,t}+b{u}_{GT,t}}{{\eta}_{GT}\cdot LHV}$$In the above formula, $a$ and $b$ are the gas-to-electricity conversion coefficients, is the power generation efficiency of the gas turbine, $LHV$ is the low calorific value of natural gas, and ${u}_{GT,t}$ is a 0–1 variable: take 0 to mean gas turbine shutdown; take 1 to mean startup.In addition, the power output constraints and ramp rate constraints of the gas turbine need to be considered. The mathematical expressions are shown in Equations (9) and (10):$${u}_{GT,t}{P}_{GT}^{\mathrm{min}}\le {P}_{GT,t}\le {u}_{GT,t}{P}_{GT}^{\mathrm{max}}$$$${u}_{GT,t}Ram{p}_{GT}^{down}\le {P}_{GT,t}-{P}_{GT,t-1}\le {u}_{GT,t}Ram{p}_{GT}^{up}$$Considering that the gas turbine also produces heat energy while generating electricity, and the thermoelectric power relationship curve is generally a nonlinear relationship, in order to facilitate the solution, this paper adopts the idea of piecewise linearization to linearize the thermoelectric power output relationship and convert it into a general mixed-integer programming problem [26]. The mathematical expressions are shown in Equations (11)–(14).$${P}_{GT,t}={u}_{GT,t}{M}_{GT}^{1}+{\displaystyle \sum _{k=1}^{l}{D}_{GT,t}^{k}}$$$${u}_{GT,t}={\displaystyle \sum _{k=1}^{l}{z}_{GT,t}^{k}}$$$$\sum _{m=k+1}^{l}{z}_{GT,t}^{m}}\le \frac{{D}_{GT,t}^{k}}{{M}_{GT}^{k+1}-{M}_{GT}^{k}}\le {\displaystyle \sum _{m=k}^{l}{z}_{GT,t}^{m}$$$${H}_{he}={u}_{GT,t}{N}_{GT}^{1}+{\displaystyle \sum _{k=1}^{l}{c}_{GT}^{k}{D}_{GT,t}^{k}}$$
- (b)
- Energy storage battery operation constraints$${E}_{t+1}^{BESS}=(1-{\eta}_{L}^{BESS}){E}_{t}^{BESS}-\frac{{P}_{dis,t}^{}\Delta t}{{\eta}_{D}}+{\eta}_{C}{P}_{chr,t}^{}\Delta t,t=0,1,2\dots $$$${E}_{\mathrm{min}}^{BESS}\le {E}_{t}^{BESS}\le {E}_{\mathrm{max}}^{BESS}$$$$0\le {P}_{chr,t}^{}\le {u}_{chr,t}^{BESS}{P}_{chr,\mathrm{max}}^{}$$$$0\le {P}_{dis,t}^{}\le {u}_{dis,t}^{BESS}{P}_{dis,\mathrm{max}}^{}$$$${u}_{chr,t}^{BESS}+{u}_{dis,t}^{BESS}\le 1;{u}_{chr,t}^{BESS},{u}_{dis,t}^{BESS}\in \left\{0,1\right\}$$Equation (15) represents the state transition equation of the energy storage battery. ${E}_{t}^{BESS}$ represents the electrical energy stored by the energy storage battery in the time period $t$. ${\eta}_{C}$,${\eta}_{D}$, and ${\eta}_{L}$ represent the charge and discharge efficiency of the energy storage battery and its self-discharge rate. ${u}_{chr,t}^{BESS}$ and ${u}_{dis,t}^{BESS}$ are the 0–1 state variables of the charging and discharging of the energy storage battery in the period $t$, respectively; 0 means that the behavior does not occur, and 1 means that the behavior occurs. ${P}_{chr,t}^{}$ and ${P}_{dis,t}^{}$ are the corresponding charging and discharging power of the energy storage battery in the period.
- (c)
- Demand response capacity constraints$$0\le {P}_{DR,t}^{}\le {P}_{DR,max}^{}$$
- (d)
- Abandon wind power and photovoltaic output power constraints$$0\le {P}_{W,t}^{spill}\le {\tilde{P}}_{W,t}^{}$$$$0\le {P}_{pv,t}^{spill}\le {\tilde{P}}_{pv,t}^{}{}_{}$$
- (e)
- System rotation reserve constraints:Reference [27] proposed that, in a distribution network with a high proportion of large-scale wind power, photovoltaics, and other highly volatile renewable energy units connected, the scheduling optimization model must consider the system spinning reserve constraints in the micro-energy grid. This constraint also needs to be considered. When there is a deviation in wind power and photovoltaic output, the reserved reserve capacity is enough to balance the deviation.$$\{\begin{array}{l}{R}_{GT,t}^{U}+{P}_{dis,t}+{P}_{DR,t}\ge {\tilde{P}}_{W,t}-{P}_{W,t}^{D}+{\tilde{P}}_{pv,t}-{P}_{pv,t}^{D}\\ {R}_{GT,t}^{D}+{P}_{chr,t}\ge {P}_{W,t}^{U}-{\tilde{P}}_{W,t}+{P}_{pv,t}^{D}-{\tilde{P}}_{pv,t}\end{array}$$
- (f)
- System total reserve constraints:In the day-ahead stage, the total system reserve should be reserved for the intraday scheduling operation stage to ensure that the basic load requirements of cooling, heating, and electricity are met.$${\eta}_{ec}{P}_{ec,t}+{Q}_{D,t}^{IT}-{Q}_{C,t}^{IT}+{\eta}_{ac}{Q}_{ac,t}\ge \left(1+{\phi}_{c}\right){Q}_{c,t}$$$${\eta}_{hc}\left({Q}_{boiler,t}+{Q}_{rec,t}+{Q}_{dis,t}-{Q}_{chr,t}-{Q}_{ac,t}\right)\ge \left(1+{\phi}_{h}\right){Q}_{h,t}$$$${P}_{pv,t}-{P}_{pv,t}^{spill}+{P}_{W,t}-{P}_{W,t}^{spill}+{P}_{GT,t}-{P}_{ec,t}\ge \left(1+{\phi}_{e}\right){P}_{e,t}-{P}_{DR,t}$$

#### 3.2.2. The Second-Stage Model

- (1)
- The Objective functionThe second-stage model considers two objectives, and the specific indicators can be reflected in the total cost of system operation and the CO
_{2}emissions of the micro-energy grid. However, due to the difference between the two target dimensions, this paper converts the CO_{2}emissions into penalty costs to measure the economy of the micro-energy grid operation. These two goals can be expressed together, as shown in Equations (27)–(31):$$min{f}_{ID}={\displaystyle \sum _{t=1}^{T}\left({C}_{fuel,t}+{C}_{grid,t}+{C}_{rm,t}+{C}_{ce,t}\right)}$$$${C}_{fuel}=fp(Fb+FGT)$$$${C}_{grid}={p}_{M+}{P}_{M+}-{p}_{M-}{P}_{M-}$$$$\begin{array}{l}{C}_{rm}=r{m}_{gt}{P}_{GT}+r{m}_{ec}{P}_{ec}+r{m}_{rec}{Q}_{rec}+r{m}_{b}{Q}_{b}+r{m}_{bess}({P}_{dis}+{P}_{chr})\\ \text{\hspace{1em}\hspace{1em}}+r{m}_{tst}({Q}_{dis}+{Q}_{chr})+r{m}_{it}({Q}_{D}^{IT}+{Q}_{C}^{IT})+r{m}_{s}{P}_{s}+r{m}_{w}{P}_{w}\end{array}$$$${C}_{ce}={\displaystyle \sum _{t=1}^{T}pc({c}_{gt}{P}_{GT}+{c}_{boiler}{Q}_{b}+{c}_{grid}{P}_{M+})}$$_{2}emission penalty cost in the micro-energy grid. $Fb$ and $FGT$ represent the natural gas consumption of the gas turbine and gas boiler, respectively. $fp$ refers to the real-time purchase cost of natural gas. ${P}_{M+}$ and ${P}_{M-}$ decibels indicate the purchase and sale of electricity. ${c}_{g}$, ${c}_{boiler}$, and ${c}_{grid}$ represent the CO_{2}emission intensity coefficients of gas turbines, gas boilers, and electricity purchased from the grid, respectively. $pc$ is the penalty coefficient. $r{m}_{gt}$, $r{m}_{ec}$, $r{m}_{rec}$, $r{m}_{b}$, $r{m}_{bess}$, $r{m}_{tst}$, $r{m}_{it}$, $r{m}_{s}$, and $r{m}_{w}$ represent the operation and maintenance costs per unit of electricity for gas turbines, electric refrigerators, waste heat boilers, gas boilers, batteries, heat storage tanks, ice storage machines, photovoltaics, and wind power, respectively. - (2)
- System constraints$${u}_{GT,t}^{*}{P}_{GT}^{\mathrm{min}}\le {P}_{GT,t}-{R}_{GT,t}^{D*}\le {u}_{GT,t}^{*}{P}_{GT}^{\mathrm{max}}$$$${C}_{ce}={\displaystyle \sum _{t=1}^{T}pc({c}_{gt}{P}_{GT}+{c}_{boiler}{Q}_{b}+{c}_{grid}{P}_{M+})}$$$${u}_{GT,t}^{*}(Ram{p}_{GT}^{down}-{R}_{GT,t}^{D*})\le {P}_{GT,t}-{P}_{GT,t-1}\le {u}_{GT,t}(Ram{p}_{GT}^{up}-{R}_{GT,t}^{U*})$$$${F}_{GT,t}=\frac{a{P}_{GT,t}+b{u}_{GT,t}}{{\eta}_{GT}\cdot LHV}$$$${P}_{GT,t}={u}_{GT,t}^{*}{M}_{GT}^{1}+{\displaystyle \sum _{k=1}^{l}{D}_{GT,t}^{k}}$$$${H}_{he}={u}_{GT,t}^{*}{N}_{GT}^{1}+{\displaystyle \sum _{k=1}^{l}{c}_{GT}^{k}{D}_{GT,t}^{k}}$$$${u}_{GT,t}^{*}={\displaystyle \sum _{k=1}^{l}{z}_{GT,t}^{k}}$$$$\sum _{m=k+1}^{l}{z}_{GT,t}^{m}}\le \frac{{D}_{GT,t}^{k}}{{M}_{GT}^{k+1}-{M}_{GT}^{k}}\le {\displaystyle \sum _{m=k}^{l}{z}_{GT,t}^{m}$$
- (3)
- Subsection
- (a)
- Gas turbineCompared to the expression of the gas turbine in the first-stage model, more variables are added here. Among them, ${u}_{GT,t}^{*},{R}_{GT,t}^{D*},{R}_{GT,t}^{U*}$ are the clearing results of the first stage, which are directly substituted here as boundary conditions.
- (b)
- Gas boiler$${Q}_{boiler}^{\mathrm{min}}\le {Q}_{boiler,t}\le {Q}_{boiler}^{\mathrm{max}}$$$${F}_{b,t}=\frac{{Q}_{boiler,t}\Delta t}{{\eta}_{b}\cdot LHV}$$
- (c)
- Heat storage tankSimilar to the energy storage battery, the heat storage tank also has a thermal energy state transfer equation, charge/discharge power constraints, and charge and discharge state constraints, as shown in Equations (42)–(46):$${Q}_{tst,t+1}^{}=(1-{\eta}_{L}^{TST}){Q}_{tst,t}^{}-\frac{{Q}_{D,t}^{TST}\Delta t}{{\eta}_{D}^{TST}}+{\eta}_{C}^{TST}{Q}_{C,t}^{TST}\Delta t,t=0,1,2\dots $$$${Q}_{tst}^{\mathrm{min}}\le {Q}_{tst,t}^{}\le {Q}_{tst}^{\mathrm{max}}$$$$0\le {Q}_{C,t}^{TST}\le {u}_{chr,t}^{TST}{Q}_{C}^{TST,\mathrm{max}}$$$$0\le {Q}_{D,t}^{TST}\le {u}_{dis,t}^{TST}{Q}_{D}^{TST,\mathrm{max}}$$$${u}_{chr,t}^{TST}+{u}_{dis,t}^{TST}\le 1$$
- (d)
- Ice CoolerIn the same way, the operating constraints of the ice-cold storage machine are as follows:$${E}_{t+1}^{ISS}=(1-{\eta}_{L}^{ISS}){E}_{t}^{ISS}-\frac{{P}_{dis,t}^{ISS}\Delta t}{{\eta}_{D}}+{\eta}_{C}{P}_{chr,t}^{ISS}\Delta t,t=0,1,2\dots $$$${E}_{\mathrm{min}}^{ISS}\le {E}_{t}^{ISS}\le {E}_{\mathrm{max}}^{ISS}$$$$0\le {P}_{chr,t}^{ISS}\le {u}_{chr,t}^{ISS}{P}_{chr,\mathrm{max}}^{ISS}$$$$0\le {P}_{dis,t}^{ISS}\le {u}_{dis,t}^{ISS}{P}_{dis,\mathrm{max}}^{ISS}$$$${u}_{chr,t}^{ISS}+{u}_{dis,t}^{ISS}\le 1;{u}_{chr,t}^{ISS},{u}_{dis,t}^{ISS}\in \left\{0,1\right\}$$
- (e)
- Other energy conversion equipmentThe micro-energy grid also includes three types of equipment: electric cooling, gas heating, and thermal cooling. Electric refrigeration equipment converts electrical energy into cold energy, and gas heating generates thermal energy by burning natural gas. These energy conversion devices have different energy efficiencies when switching energy types. For simplicity, this paper uses the form of a matrix to represent the energy conversion process, as shown in Equation (52):$$\left[\begin{array}{c}{Q}_{ec,t}\\ {Q}_{rec,t}\\ {Q}_{h,t}\end{array}\right]=\left[\begin{array}{ccc}{P}_{ec,t}& 0& 0\\ 0& {H}_{he,t}& 0\\ 0& 0& {Q}_{hc,t}\end{array}\right]\left[\begin{array}{c}{\eta}_{ec}\\ {\eta}_{rec}\\ {\eta}_{hc}\end{array}\right]$$
- (f)
- Power balance constraints$${\eta}_{ec}{P}_{ec,t}+{Q}_{D,t}^{IT}-{Q}_{C,t}^{IT}={Q}_{c,t}$$$${Q}_{rec,t}={\eta}_{rec}{H}_{he}$$$${Q}_{h,t}={\eta}_{hc}\left({Q}_{boiler,t}+{Q}_{rec,t}+{Q}_{dis,t}-{Q}_{chr,t}\right)$$$${P}_{solar,t}+{P}_{wind,t}+{P}_{GT,t}-{P}_{ec,t}+{P}_{dis,t}-{P}_{chr,t}+{P}_{M-,t}-{P}_{M+,t}={P}_{l,t}$$

#### 3.2.3. The Third-Stage Model

#### 3.3. The Solution Method for the Three-Level Dispatch Optimization Model for the Micro-Energy Grid

## 4. Example Analysis

#### 4.1. Parameter Setting

#### 4.2. Analysis of Results of Clearing the Day before

#### 4.3. Analysis of Intraday Economic Dispatch Results

#### 4.4. Analysis of Clustering Results

#### 4.5. Analysis of Real-Time Stage-Clearing Results

#### 4.6. Sensitivity Analysis

_{2}emissions under different penalty prices are obtained, as shown in Figure 20. As the government increases penalties for CO

_{2}emissions, micro-energy grids will gradually come to control CO

_{2}emissions; they will not always decline, but rather, gradually slow down and tend toward a stable value. Further analysis shows that CO

_{2}emissions in the micro-energy grid are closely related to the combustion of natural gas and the purchase of electricity from the main grid. It can be seen that, when the electricity and consumption purchased by external users reach a certain functional constraint, CO

_{2}emissions will not increase because the functional requirements set by the system will have been fully satisfied.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

CVaR | Conditional value at risk | ${C}_{fuel}$ | The fuel cost of the gas turbine |

CCHP | Combined Cooling Heating and Power | ${C}_{grid}$ | The power interaction cost between the micro-energy grid and the main grid |

PV | Photovoltaic | ${C}_{rm}$ | The operation and maintenance cost of the micro-energy grid |

BESS | Battery energy storage system | ${C}_{ce}$ | The CO_{2} emission penalty cost in the micro-energy grid |

MT | Microturbine | $Fb$ | The natural gas consumption of gas boiler |

GA | Genetic algorithm | $FGT$ | The natural gas consumption of gas turbine |

CARIMA | Controlled autoregressive moving average | $fp$ | The real-time purchase cost price of natural gas |

RES | Renewable energy systems | ${P}_{M+}$ | The purchase of electricity |

ESS | Energy storage systems | ${P}_{M-}$ | The sale of electricity |

FCM-CCQ | Fuzzy c-means-clustering comprehensive quality | ${c}_{g}$ | The CO_{2} emission intensity coefficients of gas turbine |

FCM | Fuzzy C-means | ${c}_{boiler}$ | The CO_{2} emission intensity coefficients of gas boilers |

ACQS | Average comprehensive quality score | ${c}_{grid}$ | The CO_{2} emission intensity coefficients of electricity purchased from the grid |

${C}_{co}$ | The total cost | $pc$ | The penalty coefficient |

${C}_{GT,t}$ | Gas turbine capacity allocation cost | $r{m}_{gt}$ | The operation and maintenance costs per unit of electricity for gas turbines |

${C}_{BESS,t}$ | Energy storage capacity allocation cost | $r{m}_{ec}$ | The operation and maintenance costs per unit of electricity for electric refrigerators |

${C}_{DR,t}$ | Demand response capacity allocation cost | $r{m}_{rec}$ | The operation and maintenance costs per unit of electricity for waste heat boilers, |

${P}_{GT,max}$ | The maximum power of the gas turbine | $r{m}_{b}$ | The operation and maintenance costs per unit of electricity for gas boilers |

${P}_{GT,min}$ | The minimum power of the gas turbine | $r{m}_{bess}$ | The operation and maintenance costs per unit of electricity for batteries |

${R}_{GT,t}^{U}$ | The upper reserves of the gas turbine | $r{m}_{tst}$ | The operation and maintenance costs per unit of electricity for heat storage tanks |

${R}_{GT,t}^{D}$ | The lower reserves of the gas turbine | $r{m}_{it}$ | The operation and maintenance costs per unit of electricity for the ice storage machine |

${P}_{GT,t}$ | The actual gas turbine power | $r{m}_{s}$ | The operation and maintenance costs per unit of electricity for photovoltaic |

$LHV$ | The low calorific value of natural gas | $r{m}_{w}$ | The operation and maintenance costs per unit of electricity for wind power |

${u}_{GT,t}$ | The 0–1 variable | ${Q}_{boiler,t}$ | The thermal power output of the gas boiler at time t |

${P}_{GT}^{\mathrm{min}}$ | The lower limits of the gas turbine output | ${Q}_{boiler}^{\mathrm{max}}$ | The upper limits of the output thermal power of the gas boiler |

${P}_{GT}^{\mathrm{max}}$ | The upper limits of the gas turbine output | ${Q}_{boiler}^{\mathrm{min}}$ | The lower limits of the output thermal power of the gas boiler |

$Ram{p}_{GT}^{down}$ | Lower boundary value of gas turbine ramping power | ${F}_{b,t}$ | The natural gas consumption of the gas boiler |

$Ram{p}_{GT}^{up}$ | Upper boundary value of gas turbine ramping power | ${\eta}_{b}$ | The energy conversion efficiency coefficient of the gas boiler |

${M}_{GT}^{k}$ | The endpoint electric power value of each segment after the piecewise linearization of the thermoelectric curve | ${Q}_{ec,t}$ | The cooling power generated by the electric refrigeration at time t |

${z}_{GT,t}^{m}$ | A binary variable | ${Q}_{rec,t}$ | The thermal power generated by the gas boiler at time t |

${c}_{GT}^{k}$ | The slope of the linear function of the k segment | ${Q}_{h,t}$ | the thermal power generated by the heating coil at time t |

${H}_{he}$ | The heat produced by the gas turbine | ${P}_{ec,t}$ | The electricity consumption of the electric refrigerator at time t |

${E}_{t}^{BESS}$ | The electrical energy stored by the energy storage battery in the time period t | ${H}_{he,t}$ | The electricity consumption of the gas boiler at time t |

${\eta}_{C}$ | The charge efficiency of the energy storage battery | ${Q}_{hc,t}$ | The heat of the heating coil at time t |

${\eta}_{D}$ | The discharge efficiency of the energy storage battery | ${P}_{ec,t}$ | The electric power consumed by the electric refrigerator at time t |

${\eta}_{L}$ | Its self-discharge rate | ${\eta}_{ec}$ | The conversion coefficient of the electric refrigeration machine to cold |

${u}_{chr,t}^{BESS}$ | The 0–1 state variables of the charging of the energy storage battery in the period t | ${Q}_{D,t}^{IT}$ | The cooling power of the ice-cold storage machine at all times |

${u}_{dis,t}^{BESS}$ | The 0–1 state variables of the discharging of the energy storage battery in the period t | ${Q}_{C,t}^{IT}$ | The charging power of the ice-cold storage machine at all times |

${P}_{chr,t}^{}$ | The corresponding charging power of the energy storage battery in the period t | ${Q}_{c,t}$ | The cooling load in the system at the moment t |

${P}_{dis,t}^{}$ | The corresponding discharging power of the energy storage battery in the period t | ${Q}_{h,t}$ | The heating load in the system at the moment t |

${P}_{DR,t}^{}$ | The actual demand response reserve capacity signed with the power user during the $t$ period | ${P}_{l,t}$ | The electrical load in the system at the moment t |

${P}_{DR,max}^{}$ | The maximum corresponding capacity | ${\rho}_{k}$ | The probability of scenario occurrence |

${P}_{pv,t}^{spill}$ | The power generation of abandoned wind | ${f}_{ID}$ | The total cost function of intraday economic dispatch |

${P}_{pv,t}^{spill}$ | The power generation of abandoned photovoltaic | $\alpha $ | The confidence level |

${\tilde{P}}_{W,t}^{}$ | The predicted values of wind power output | $\lambda $ | The weight coefficient |

${\tilde{P}}_{pv,t}^{}$ | The predicted values of photovoltaic output | $\mathsf{\Omega}$ | The joint scenario set in the micro-energy grid |

${\phi}_{c}$ | The reserve coefficients of the cooling of the micro-energy grid | $k$ | The k-th scenario |

${\phi}_{h}$ | The reserve coefficients of the heating of the micro-energy grid | ${\rho}_{k}$ | The probability of occurrence of the k-th scenario |

${\phi}_{e}$ | The reserve coefficients of the electric load of the micro-energy grid |

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**Figure 14.**Curve comparison of the actual and predicted output of wind power and photovoltaic power.

Gas Turbine Spare Capacity Cost | Demand Response Spare Capacity Compensation Costs | Cost of Energy Storage Backup Capacity | Total Reserve Capacity Cost | ||
---|---|---|---|---|---|

Up Spare Capacity Costs | Down Spare Capacity Costs | Discharge Capacity Cost | Charging Capacity Cost | ||

14,579.893 | 11,065.679 | 9181.017 | 2147.625 | 2379.639 | 39,353.854 |

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**MDPI and ACS Style**

Liu, H.; Wang, Y.; Nie, S.; Wang, Y.; Chen, Y.
Multistage Economic Scheduling Model of Micro-Energy Grids Considering Flexible Capacity Allocation. *Sustainability* **2022**, *14*, 9013.
https://doi.org/10.3390/su14159013

**AMA Style**

Liu H, Wang Y, Nie S, Wang Y, Chen Y.
Multistage Economic Scheduling Model of Micro-Energy Grids Considering Flexible Capacity Allocation. *Sustainability*. 2022; 14(15):9013.
https://doi.org/10.3390/su14159013

**Chicago/Turabian Style**

Liu, Hang, Yongcheng Wang, Shilin Nie, Yi Wang, and Yu Chen.
2022. "Multistage Economic Scheduling Model of Micro-Energy Grids Considering Flexible Capacity Allocation" *Sustainability* 14, no. 15: 9013.
https://doi.org/10.3390/su14159013