# Combined Heat and Power Dispatch Considering Heat Storage of Both Buildings and Pipelines in District Heating System for Wind Power Integration

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## Abstract

**:**

## 1. Introduction

- A novel CPB-CHPD model is proposed with special emphasis on the coordinating operation of both PDTP and BTI aiming at breaking the power and heat coupling to significantly improve the system operational flexibility without any additional investment.
- A physical model of the DHS is proposed. The pipeline model is built considering heat loss, temperature time delays and network topology characteristics in terms of single and network level. The building model is formulated based on buildings’ thermal equilibrium considering building characteristics’ diversity and outdoor temperature variation.
- The synergic benefits of both PDTP and BTI on reducing wind power curtailment and total operation cost are evaluated, which are better than considering only one or neither of them.

## 2. System Model of the DHS

#### 2.1. Heat Sources

#### 2.1.1. Electric and Heat Power Characteristics

#### 2.1.2. Operation Cost

#### 2.2. District Heating Pipelines Network

#### 2.2.1. Single Pipeline Level

#### 2.2.2. Pipeline Network Level

- Relationship between heat power and water temperatures:The heat power of the hot water, flowing into the inlet and flowing out of the outlet, of pipeline k at period t is expressed respectively as follows:$$\left(\right)open="\{"\; close>\begin{array}{c}{q}_{\mathrm{p},k,t}^{\mathrm{in}}={c}_{\mathrm{w}}{G}_{\mathrm{p},k}{T}_{\mathrm{p},k,t}^{\mathrm{in}}\hfill \\ {q}_{\mathrm{p},k,t}^{\mathrm{out}}={c}_{\mathrm{w}}{G}_{\mathrm{p},k}{T}_{\mathrm{p},k,t}^{\mathrm{out}}\hfill \end{array}$$
- Supply and return water temperature limits:The water temperatures in the water supply and return network should be kept within their limits:$${T}_{\mathrm{ps}}^{\mathrm{min}}\le {T}_{\mathrm{p},k,t}^{\mathrm{in}},{T}_{\mathrm{p},k,t}^{\mathrm{out}}\le {T}_{\mathrm{ps}}^{\mathrm{max}},\phantom{\rule{3.33333pt}{0ex}}\forall k\in {S}_{\mathrm{pipe}}^{\mathrm{SN}},\phantom{\rule{3.33333pt}{0ex}}t\in N$$$${T}_{\mathrm{pr}}^{\mathrm{min}}\le {T}_{\mathrm{p},k,t}^{\mathrm{in}},{T}_{\mathrm{p},k,t}^{\mathrm{out}}\le {T}_{\mathrm{pr}}^{\mathrm{max}},\phantom{\rule{3.33333pt}{0ex}}\forall k\in {S}_{\mathrm{pipe}}^{\mathrm{RN}},\phantom{\rule{3.33333pt}{0ex}}t\in N$$
- Mass flow rates’ continuity and limits:Similar to Kirchhoff’s current law, for each node in the pipeline network, the total mass flow rates of all pipelines connecting to this node is zero:$$\sum _{k\in {S}_{n}^{\mathrm{pipe},\mathrm{in}}}{G}_{\mathrm{p},k}=\sum _{k\in {S}_{n}^{\mathrm{pipe},\mathrm{out}}}{G}_{\mathrm{p},k}$$The mass flow rates at each period should not exceed their upper or lower limits:$${G}_{\mathrm{p},k}^{\mathrm{min}}\le {G}_{\mathrm{p},k}\le {G}_{\mathrm{p},k}^{\mathrm{max}},\phantom{\rule{3.33333pt}{0ex}}\forall k\in {S}^{\mathrm{pipe}}$$
- Node temperature characteristics:According to the energy conservation law, the water temperatures of all pipelines flowing into the same node are mixed at this node, and the water temperatures of all pipelines flowing out of this node are equal to the mixed temperature at this node, as described in Equation (15).$$\left(\right)$$

#### 2.3. Buildings

#### 2.3.1. Relationship between Indoor Temperatures and Heat Power Supplied

- $\Delta {Q}_{\mathrm{st},j,t}$ denotes the change rate of the heat energy of the building, as expressed in Equation (17). When the indoor temperature increases, i.e., $\mathrm{d}{T}_{\mathrm{id},j,t}/\mathrm{d}t>0$, the heat energy of the building increases, which means the building heat storage is charged. Oppositely, when the indoor temperature decreases, $\mathrm{d}{T}_{\mathrm{id},j,t}/\mathrm{d}t<0$, the building heat storage is discharged.
- On the right side of Equation (16), the two items in the first parenthesis denote the building total heat energy supplied, where ${H}_{\mathrm{hr},j,t}$ and ${H}_{\mathrm{td},j}$ are the heat power supplied by district heating pipelines and by internal heat gains (such as the effect of indoor lighting, persons, appliances, etc.), respectively. Here, the heat power supplied by internal heat gains is assumed as $3.8\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\mathrm{W}/{\mathrm{m}}^{2}$.
- On the right side of Equation (16), the two items in the second parenthesis denote the building total heat energy loss, where ${H}_{\mathrm{en},j,t}$ is the sum of the heat power transfer through each side of the building envelope structures including doors, windows, walls, floors, roofs, etc., as expressed in Equation (18). Meanwhile, the solar radiation is appended to the heat power transfer by orientation correction, and the outdoor cold wind speed effect is also appended by its additional correction. ${H}_{\mathrm{ca},j,t}$ is the building heat power loss by cold air infiltration through the windows and doors gaps, as well as cold air intrusion from the opening windows and doors, as expressed in Equation (19); ${S}^{\mathrm{bui}}$ is the index set of buildings.

#### 2.3.2. Indoor Temperatures Limits

#### 2.4. Interfaces among Heat Sources, Network and Loads

#### 2.4.1. Between Heat Sources and Pipelines Network

#### 2.4.2. Between Pipeline Network and Heat Loads

## 3. Optimization Model of the CPB-CHPD

#### 3.1. Decision Variables

#### 3.2. Objective Function

- The operation cost of the CHP unit ${C}_{i,t}^{\mathrm{chp}}$ is defined in Equation (4).
- The operation cost of the CON unit is expressed as a quadratic function of its electric power output [16]:$$\left(\right)$$
- The penalty cost of the wind farm is proportional to the wind power spillage:$${C}_{i,t}^{\mathrm{wind}}={\sigma}_{i}\xb7\left(\right)open="("\; close=")">{P}_{\mathrm{wind},i,t}^{\mathrm{max}}-{P}_{\mathrm{wind},i,t}$$

#### 3.3. Constraints

#### 3.3.1. EPS Constraints

- Electric power balance constraints:The system total electric power output and total electric loads are equal at each dispatch period:$$\sum _{i\in {S}^{\mathrm{chp}}}{P}_{\mathrm{chp},i,t}+\sum _{i\in {S}^{\mathrm{con}}}{P}_{\mathrm{con},i,t}+\sum _{i\in {S}^{\mathrm{wind}}}{P}_{\mathrm{wind},i,t}=\sum _{i\in {S}^{\mathrm{load}}}{P}_{\mathrm{load},i,t}$$
- Units’ operation constraints:
- Generation range constraints:The electric and heat power limits constraints of extraction condensing and back pressure turbine CHP units are defined in Equations (1)–(3).The electric power output of the CON units must be kept within their limits:$${P}_{\mathrm{con},i}^{\mathrm{min}}\le {P}_{\mathrm{con},i,t}\le {P}_{\mathrm{con},i}^{\mathrm{max}},\phantom{\rule{3.33333pt}{0ex}}\forall i\in {S}^{\mathrm{con}},\phantom{\rule{3.33333pt}{0ex}}t\in N$$The electric power output of the wind farms are limited by the maximum wind power:$$0\le {P}_{\mathrm{wind},i,t}\le {P}_{\mathrm{wind},i,t}^{\mathrm{max}},\phantom{\rule{3.33333pt}{0ex}}\forall i\in {S}^{\mathrm{wind}},\phantom{\rule{3.33333pt}{0ex}}t\in N$$
- Ramping constraints:

#### 3.3.2. DHS Consraints

- PDTP constraints:
- BTI constraints:

#### 3.3.3. Interfaces Constraints among Heat Sources, Network and Loads

## 4. Simulation Cases and Results Analysis

#### 4.1. Simulation System Description

#### 4.2. Cases Settings

- The differences between the constraints of the CED and CPB-CHPD models are in two aspects. One is that Equations (7)–(15) and (26) should be replaced by Equation (36). The other is that Equations (21)–(24) and (27) should be replaced by Equation (37).$${H}_{\mathrm{hs},i,t}=\sum _{j\in {S}_{\mathrm{chp},i}^{\mathrm{bui}}}{H}_{\mathrm{hr},j,t},\phantom{\rule{3.33333pt}{0ex}}\forall i\in {S}^{\mathrm{chp}},\phantom{\rule{3.33333pt}{0ex}}t\in N$$$$\left(\right)open="\{"\; close>\begin{array}{c}{H}_{\mathrm{hr},j,t}={\chi}_{\mathrm{b},j}\xb7\left(\right)open="("\; close=")">{T}_{\mathrm{id},j,t}-{T}_{\mathrm{od},j,t}\hfill \end{array}{T}_{\mathrm{id},j,t}={T}_{\mathrm{id},j}^{\mathrm{st}}\hfill ,\phantom{\rule{3.33333pt}{0ex}}\forall i\in {S}^{\mathrm{chp}},\phantom{\rule{3.33333pt}{0ex}}t\in N$$

#### 4.3. Results Analysis

#### 4.3.1. Case 1

#### 4.3.2. Case 2

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CHP | Combined heat and power |

CON | Condensing power |

EPS | Electric power system |

DHS | District heating system |

PDTP | Pipelines dynamic thermal performance |

BTI | Buildings thermal inertia |

CPB-CHPD | Combined heat and power dispatch considering both PDTP and BTI |

CP-CHPD | Combined heat and power dispatch only considering PDTP |

CB-CHPD | Combined heat and power dispatch only considering BTI |

CED | Conventional economic dispatch considering neither PDTP, nor BTI |

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**Figure 5.**Profiles of the typical day during the heating season: (

**a**) total electric loads and forecast wind power; (

**b**) outdoor temperature.

**Figure 6.**Electric power output of the thermal power units at each period in Case 1: (

**a**) the first CHP unit CHP1; (

**b**) the second CHP unit CHP2; (

**c**) the first CON unit CON1; (

**d**) the second CON unit CON2.

**Figure 7.**Heat power output of the CHP units at each period in Case 1: (

**a**) the first CHP unit CHP1; (

**b**) the second CHP unit CHP2.

**Figure 8.**Electric power output of the wind farm of the four dispatch models at each period, including the CPB-CHPD, CB-CHPD, CP-CHPD models (combined heat and power dispatch models considering both PDTP and BTI, only BTI, only PDTP, respectively) and the CED model (conventional economic dispatch model considering neither PDTP, nor BTI).

**Figure 9.**Profiles of indoor temperatures in Case 1 at each period: (

**a**) Building1; (

**b**) Building2; (

**c**) Building3; (

**d**) Building4; (

**e**) Building5 ; (

**f**) Building6.

**Figure 10.**Optimal result comparison of the four dispatch models, including the CPB-CHPD, CB-CHPD, CP-CHPD and CED models: (

**a**) abandoned wind power; (

**b**) operation cost savings.

Type | CHP Units | CON Units | ||
---|---|---|---|---|

Unit name | CHP1 | CHP2 | CON1 | CON2 |

Capacity ($\mathrm{MW}$) | 300 | 200 | 500 | 200 |

${P}_{\mathrm{chp},i}^{\mathrm{co},\mathrm{max}}$ ($\mathrm{MW}$) | 323 | 212 | / | / |

${P}_{\mathrm{chp},i}^{\mathrm{co},\mathrm{min}}$ ($\mathrm{MW}$) | 150 | 100 | 200 | 80 |

${H}_{\mathrm{chp},i}^{\mathrm{max}}$ ($\mathrm{MW}$) | 357 | 241 | / | / |

${c}_{\mathrm{v}1,i}$ | 0.23 | 0.21 | / | / |

${c}_{\mathrm{v}2,i}$ | 0 | 0 | / | / |

${c}_{\mathrm{m},i}$ | 0.45 | 0.44 | / | / |

Ramping rate ($\mathrm{MW}/\mathrm{h}$) | 80 | 50 | 100 | 50 |

No. | ${\mathit{L}}_{\mathbf{p},\mathit{k}}$ ($\mathbf{m}$) | ${\mathit{R}}_{\mathbf{p},\mathit{k}}$ ($\mathbf{m}$) | ${\mathit{\mu}}_{\mathbf{p},\mathit{k}}$ ($\mathbf{W}/({\mathbf{m}}^{2}{\xb7}^{\circ}\mathbf{C})$) |
---|---|---|---|

1, 2, 11, 12 | 3250 | 0.8 | 32 |

3, 4, 5, 6, 13, 14, 15, 16 | 1500 | 0.6 | 32 |

7, 8, 9, 10, 17, 18, 19, 20 | 1050 | 0.5 | 32 |

No. | ${\mathit{\chi}}_{\mathbf{bt},\mathit{j}}$ (${\mathbf{MW}/}^{\circ}\mathbf{C}$) | ${\mathit{t}}_{\mathbf{bs},\mathit{j}}$ ($1{0}^{4}\phantom{\rule{0.166667em}{0ex}}\mathbf{s}$) | Equivalent area ($1{0}^{6}\phantom{\rule{0.166667em}{0ex}}{\mathbf{m}}^{2}$) |
---|---|---|---|

1 | 1.85 | 16.20 | 1.32 |

2 | 2.45 | 12.60 | 1.74 |

3 | 2.95 | 10.08 | 2.09 |

4 | 1.45 | 13.68 | 1.16 |

5 | 1.75 | 10.44 | 1.40 |

6 | 1.95 | 8.64 | 1.56 |

**Table 4.**Wind power integration and operation cost savings of the four dispatch models including the CPB-CHPD, CB-CHPD, CP-CHPD and CED models.

Wind Power Integration ($\mathbf{MWh}$) | Total Operation Costs ($) | Cost Savings Based on CED ($) | Saving Proportion Based on CED | |
---|---|---|---|---|

CPB-CHPD | 5239.68 | 521,741 | 70,172.55 | 11.86% |

CB-CHPD | 5166.19 | 530,458 | 61,455.19 | 10.38% |

CP-CHPD | 4709.51 | 575,062 | 16,866.53 | 2.85% |

CED | 4549.97 | 591,929 | / | / |

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## Share and Cite

**MDPI and ACS Style**

Li, P.; Wang, H.; Lv, Q.; Li, W.
Combined Heat and Power Dispatch Considering Heat Storage of Both Buildings and Pipelines in District Heating System for Wind Power Integration. *Energies* **2017**, *10*, 893.
https://doi.org/10.3390/en10070893

**AMA Style**

Li P, Wang H, Lv Q, Li W.
Combined Heat and Power Dispatch Considering Heat Storage of Both Buildings and Pipelines in District Heating System for Wind Power Integration. *Energies*. 2017; 10(7):893.
https://doi.org/10.3390/en10070893

**Chicago/Turabian Style**

Li, Ping, Haixia Wang, Quan Lv, and Weidong Li.
2017. "Combined Heat and Power Dispatch Considering Heat Storage of Both Buildings and Pipelines in District Heating System for Wind Power Integration" *Energies* 10, no. 7: 893.
https://doi.org/10.3390/en10070893