# Optimal Scheduling of Thermoelectric Coupling Energy System Considering Thermal Characteristics of DHN

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## Abstract

**:**

## 1. Introduction

- (1)
- In TCES, a new thermal characteristic index (TCI) based on quantized heat storage capacity of DHN is proposed to measure the DHN’s heat endothermic and exothermic ability to improve the heat regulation flexibility of DHS.
- (2)
- By controlling confidence level K in the proposed probabilistic constraint of CHP’s spinning reserve capacity, the reliability of the TCES is improved.
- (3)
- This is the first time the wind power generation uncertainty and DHN’s heat storage capability have been addressed simultaneously in the TCES dispatching problem. Furthermore, this involved converting a non-linear model into a linear form by discretized step transformation and the CF-VT method for the overall problem-solving process.

## 2. Modeling of Thermoelectric Coupling Energy System

#### 2.1. Probabilistic Model of EPS Considering Confidence Level K

_{w}(P

^{w}) and the charging or discharging power ${P}_{t}^{EES}$ of EES at time t can be found in [24]. Moreover, the changing load injection P

^{L}is an important source of uncertainty in the actual power system. A widely used normal distribution model proposed in [9] is used to simulate load fluctuations in this paper. The PDF of power load injection ${f}_{l}({P}^{L})$ is also shown in [9]. In order to promote the combination of multiple random variables, the power of EL (equivalent load) is defined as the difference between the load power and the power output of WT (wind turbine), which is expressed as follows:

^{EL}denotes the power of the EL.

_{a,t}and N

_{b,t}represent the probability sequence length of ${P}_{t}^{w}$ and ${P}_{t}^{L}$, respectively. $a({i}_{a,t})$ and $b({i}_{b,t})$ are the probability sequence of ${P}_{t}^{w}$ and ${P}_{t}^{L}$, which are introduced in Appendix A. In some extreme cases, when ${P}_{t}^{w}$ is zero [25], sufficient rotating reserve capacity should be provided to maintain the continuity of the system, which will result in higher reserve costs.

#### 2.2. Model of DHS Considering a New Thermal Characteristic Index

#### 2.2.1. Heat Storage Characteristic of DHN

_{th}pipeline node is shown as follows:

_{1}, ω

_{2}) ≤ 1, which ω

_{1}+ ω

_{2}= 1, indicate the relative importance of each index for considering DHN. The choice of these factors mainly depends on the experiences and concerns of planners or decision makers. The equal weights are assumed for the proposed indices in this paper. In addition, TCI is used in the objective function of DHS in Section 3.1.

#### 2.2.2. Relationship between K and TCI in TCES

## 3. Coordinated Operation Optimization

#### 3.1. Objective Function

^{EPS}and J

^{DHS}. In EPS, J

^{EPS}consists of four parts, including the penalty cost of wind power curtailment, EES devices operation cost, fuel cost of CHP units, and spinning reserve cost. Besides, the first term is to prioritize the use of clean energy, the second term is to reduce the emission of pollutants, the third term is to decrease the operation cost of EES and the last term is to restrict the use of spinning reserve capacity. In DHS, J

^{DHS}is the compensation cost used to regulate the flexibility of system.

^{EPS}represents the weighted sum of the cost for the EPS, which is expressed as follows:

^{w}is the penalty factor of wind curtailment of the wind turbine, and ${\overline{P}}_{t}^{w}$ is the predicted available wind energy of the wind turbine at time t; the second term ${\phi}^{a}\times {P}_{t}^{EES,Max}+{\phi}^{b}\times SO{C}_{t}^{Max}+{\phi}^{e}\times {\displaystyle \sum _{t=1}^{T}\left|{P}_{t}^{EES}\right|}$ is EES device operation cost, φ

^{a}and φ

^{b}are the power-specific and energy-specific investment costs, respectively,${P}_{t}^{EES,Max}$ is the maximum output of EES devices at time t, $SO{C}_{t}^{Max}$ is the maximum storage capacity of EES at time t and φ

^{e}is the operating cost factor; the third term $\sum _{t=1}^{T}{\displaystyle {\sum}_{k=1}^{M}{\alpha}_{t}^{k}{c}_{k}}$ is the overall fuel cost of CHP unit, and the CHP model will be introduced in Section 3.2; the last term $\sum _{t=1}^{T}{\phi}^{r}{R}_{t}^{CHP}$ is the spinning reserve cost, and φ

^{r}is the spinning reserve pricing.

^{m}is the price compensation factor. In a word, the function of ${J}^{DHS}$ means that if the DHN has a higher heat regulation capacity, higher incentive compensation costs will be produced in DHS, and then ${J}^{DHS}$ will obtain more minimum and optimal value.

#### 3.2. Constraints

_{th}heat load in the building during time period t can be expressed by the lumped heat source term ${Q}_{a,t}^{HES}$.

_{b}and m

_{b}are the specific heat capacity and mass flow of indoor air, respectively. To reflect the actual situation, the product of c

_{b}and c

_{m}can be obtained by an engineering experiment. In this TCES, there are power and heat equilibrium as follows:

_{u}is the ratio of power to heat under extraction mode. If there is no need for reserve capacity, ${R}_{t}^{CHP}$ is set to zero.

#### 3.3. Solving Method of Nonlinear Constraints

_{c,t}q is discretized ${P}_{t}^{EL}$, which will be introduced in Appendix A in detail. When the inequality ${R}_{t}^{CHP}\ge {i}_{c,t}q-E\left({P}_{t}^{EL}\right)$ holds, Equation (23) is equal to the inequality $\chi \le {Z}_{{i}_{c,t}}\le 1+\chi $ (where $\chi $ is a small positive number), and at the same time ${Z}_{{i}_{c,t}}$ is a 0–1 variable. Thereby, this variable ${Z}_{{i}_{c,t}}$ can only be driven to 1. In a similar way, if the inequality ${R}_{t}^{CHP}\le {i}_{c,t}q-E\left({P}_{t}^{EL}\right)$ holds, Equation (23) is equal to the inequality $-\chi \le {Z}_{{i}_{c,t}}\le 1-\chi $, and hence ${Z}_{{i}_{c,t}}$ can only be equal to 0 for the same cause. Therefore, Equation (4) is simplified as follows:

## 4. Case Study

_{e}= 2.4 W/m·°C, γ

_{r}= 15 W/m

^{2}·°C, d

_{in}= 2 m, d

_{ex}= 2.114 m, χ = 0.1, γ

_{b}= 0.023 W/m·°C, R

_{e}= 0.049 m·°C/W, T

^{in,Min}= 20 °C, T

^{in,Max}= 24 °C, and T

^{in,ch}= 1 °C. Besides, Appendix B shows the profiles of total electric and heat load, as well as the forecast values and prediction intervals of available wind power.

#### 4.1. Comparative Tests with Different TCIs

#### 4.2. Comparative Tests with Different K

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Abbreviations | w | Wind Turbine | |

CHP | Combined heat and power | k | Corner point of CHP operation region |

DHN | District heating network | HS,S | Heat resource on the supply side |

EPS | Electric power system | HS,R | Heat resource on the return side |

DHS | District heating system | HES,S | Heat exchange station on the supply side |

TCES | Thermoelectric coupling energy system | HES,R | Heat exchange station on the return side |

CF-VT | Constant mass flow and variables temperature | in | Indoor temperature |

TCI | Thermal characteristic index | out | Outdoor temperature |

EES | Electric energy storage | NS | Node in supply pipeline |

EB | Electric boiler | NR | Node in return pipeline |

WT | Wind turbine | surf | Soil surface |

HES | Heat exchange station | Pipe,S | Supply pipelines |

HS | Heat resource | Pipe,R | Return pipelines |

EL | Equivalent load | surf | Soil surface |

Greek letters | Subscript | ||

K | Confidence level | t | Time moment s |

β | Electrothermal conversion efficiency | n_{1} | Node of HS |

Γ | Index set of pipes in the DHN | n_{2} | Node of HES |

λ | Factors of heat conduction | b | Building envelope |

ε | Factors of heat radiation | Roman letters | |

ν | Velocity of water flow | P | Power output MW |

γ | Coefficient of heat transformation | Q | Heat output MW |

μ | Additional factor of heat loss | R | Power reserve capacity MW |

φ | Penalty factor | ST | Operating status of EB |

ω | Weighting factor of DHN | T | Temperature ℃ |

Ψ | Weight coefficient | m | Mass flow t/h |

χ | Small positive number | Ramp | Ramp rate of CHP |

$\varpi $ | Large positive number | J | Objective function |

Superscripts | E | Expectation value of EL MW | |

L | Power load injections | Z | 0–1 variable |

## Appendix A

#### Appendix A.1. Serialization Modeling of Random Variables in EPS

^{w}and the load power P

^{L}are random variables, and they can be described by the corresponding probability sequences a(i

_{a,t}) and b(i

_{b,t}) by discretizing the continuous probability distribution. The length calculation formulas of the WT output and load power probability sequence N

_{a,t}and N

_{b,t}are as follows:

_{b,t}) can be obtained by analogy.

_{c,t}) is calculated by the subtraction-type-convolution (STC) operation.

^{EL}with the step size q and the length N

_{c,t}.

Power(MW) | 0 | q | … | i_{c,t}q | … | N_{c,t}q |
---|---|---|---|---|---|---|

Probability | c(0) | c(1) | … | c(i_{c,t}) | … | c(N_{c,t}) |

_{c,t}q, there is always a corresponding probability c(i

_{c,t}).

## Appendix B

#### Appendix B.1. Profiles of Electric and Heat Load and Wind Power Forecast

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1: | Model building: |

2: | Uncertainty model of EPS; |

3: | CF-VT modelling of DHN. |

4: | Model conversion: |

5: | Transform chance probability into deterministic MILP constraints; |

6: | Set the mass flow rates, and calculate the temperature of HS, HES, pipelines. |

7: | Model solving: |

8: | Enter the parameters of TCES; |

9: | Set the constraints and objective function; |

10: | Solve the model using Yamip and Cplex solvers; |

11: | If find a solution? |

12: | Output the optimal scheduling scheme; |

13: | Else if |

14: | Update K and TCI and return to Step 9. |

15: | End |

Test System | Electric Power System | District Heating Network | |||||||
---|---|---|---|---|---|---|---|---|---|

Bus | Line | CHP | WT | EES | EB | Node | Pipeline | HES | |

Number | 2 | 2 | 2 | 1 | 1 | 1 | 6 | 10 | 3 |

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**MDPI and ACS Style**

Li, G.; Tang, Q.; Hu, B.; Ma, M.
Optimal Scheduling of Thermoelectric Coupling Energy System Considering Thermal Characteristics of DHN. *Sustainability* **2022**, *14*, 9764.
https://doi.org/10.3390/su14159764

**AMA Style**

Li G, Tang Q, Hu B, Ma M.
Optimal Scheduling of Thermoelectric Coupling Energy System Considering Thermal Characteristics of DHN. *Sustainability*. 2022; 14(15):9764.
https://doi.org/10.3390/su14159764

**Chicago/Turabian Style**

Li, Guangdi, Qi Tang, Bo Hu, and Min Ma.
2022. "Optimal Scheduling of Thermoelectric Coupling Energy System Considering Thermal Characteristics of DHN" *Sustainability* 14, no. 15: 9764.
https://doi.org/10.3390/su14159764