^{1}

^{2}

^{2}

^{1}

^{1}

In recent years, Combined electro-thermal system has developed rapidly. In order to provide the initial data for the analysis of the combined electro-thermal system, a practical energy flow calculation method for the combined electro-thermal system is proposed in this paper. Based on the detailed analysis of the topology structure of the heating network and its hydraulic and thermodynamic model, the forward-backward sweep method for the heat flow of the heating network is established, which is more suitable for the actual radial heating network. The electric and thermal coupling model for heating source, such as thermoelectric unit and electric boiler is established, and the heat flow of heating network and the power flow of power grid are calculated orderly, thus a fast calculation method for the combined electro-thermal system is formed. What’s more, a combined electro-thermal system with two-stage peak-shaving electric boiler is used as the example system. This paper validates the effectiveness and rapidity of this method through the example system, and analyzes the influence for the energy flow of combined electro-thermal system caused by the operating parameters such as the installation location of electric boiler, the outlet water temperature of heat source and the outlet flow rate, etc.

Heating network uses the heating pipes to transport steam or hot water, so as to achieve the purpose of transmitting energy. Heating source can use fossil fuels, renewable energy, electricity, cogeneration source, etc, so that it has great flexibility. Heating network and power grid are coupled into a system when cogeneration sources or electric boilers are used as heating source, thus a combined electro-thermal system is formed. The combined electro-thermal system is a typical multi-energy flow network system, which is also an important part of the energy of Internet [

Power flow calculation is very mature, derived out a variety of power flow calculation methods, such as Newton Raphson method, PQ decomposition method and so on [

The heating network consists of the water supply network and backwater network which are the same topology [

There are three variates in the heating network, including the pressure of each node h_{i}, the load demand water L_{i}, the water flow pipe m_{ij}. Due to pipe roughness, hot water in the pipes have to overcome the wall during the heat transfer process, coupled with the pipe heat dissipation outside, the hot water transferring

from the heating source to the heat load node will have heat loss. In the heat load node i, the hot water provides users with heat through the heat exchanger, and then the cooling water return to heating source through the return network, and the next heating process will start. The pipe water flow of supply or return network is almost the same. As the water temperature in the two networks is different from each other, it will affect the water density, viscosity, Reynolds number [

The hydrodynamic model of the heating network determines the water flow of each pipe (m_{ij}) and the injected water flow of each node (L_{i}). The topology of water supply network is the same as the backwater network, so only the water supply network is analyzed. There are water continuity of flow equation and pressure loss equation in hydraulic model, respectively corresponding to KCL and KVL which are belong to electrical power system [

1) Continuity of Flow Equation

The continuity of flow is expressed as: the water flow that enters into a node is equal to the water flow that leaves the node plus the flow consumption at the node. For the entire hydraulic network, the continuity of flow is expressed as

where A is the network incidence matrix that relates the nodes to the branches; m is the vector of the water flow (kg/s) within each pipe; m_{q} is the vector of the water flow (kg/s) through each node injected from a source or discharged to a load.

2) Pressure Loss Equation

The pressure loss equation is used to characterize the relationship between pressure loss and water flow in the pipe [

where K is the vector of the resistance coefficients of each pipe. K generally depends largely on the diameter of a pipe. The specific formula is

where ε is the absolute roughness value of each pipe; D is the diameter of each pipe.

Hydraulic model can be regarded as a common water pipe network, there are two basic methods of solving the water network, that is, pressure method [

Thermodynamic model is used to determine the temperature of nodes in heating network. The heating network node contains three temperature information (_{s}); the return (load output) temperature of node (T_{o}) and the return mixing temperature (T_{r}). The return temperature of node (T_{o}) is the temperature at which the water flow leaves the junction where the heat load node does not meet the confluence duct. If there is no confluence pipe in the thermal circuit, the return temperature of node (T_{o}) is the same as the return mixing temperature. The main factors that affect the node return temperature are: the supply temperature of node (T_{s}), the natural temperature of the outside surrounding (T_{a}) and the size of the heat load.

To sum up, using the hydraulic model to calculate the water flow data of each pipe, the three temperature information of the heating network nodes are determined by the thermal model considering the heating network relation, heat transfer and heat loss.

The heating network could be get by integrating hydraulic model and thermodynamic model. The variates relations in the heating network model are

The relationship for heat load, temperature, and water flow is

where _{p} is the specific heat capacity of water.

The return temperature of node is

The supply temperature of node is

where λ is the transmission impedance per meter of the pipe_{ij} the pipe transmission distance (m).

The pressure of water supply (h) can be deduced by Equation (4).

From Equation (6), Equation (7), we can see that the greater the pipe water flow, the less heat loss in the pipe, the higher the temperature of the destination node.

The thermodynamic model determines the temperature data of each node, the hydraulic model determines the water flow of each pipe, and the output data of the two systems are input to each other. For the heat flow calculation, the thermodynamic model and the hydraulic model are indispensable.

The combined electro-thermal system can be regarded as the coupling of the heating network and the electrical network through the energy conversion equipment (thermoelectric unit, electric boiler, etc.)

The purpose of heat flow calculation is to determine the water flow in the pipeline, the supply temperature of nodes and the return temperature of nodes, and finally determine the total heat supply of the heating source.

In actual production, each heating source (such as a thermoelectric unit) is fixedly supplied with a specific area heat load. The heating sources are either not connected or connected but the pipes are normally closed, which makes the heating network similar to power distribution network which is typical radial structure (

The actual heating network control method is divided into two kinds which are qualitative conditioning and volume conditioning. Qualitative conditioning

remains the heating source node outlet water flow rate unchanged, by adjusting the heating source outlet water temperature to adapt to heat load changes. Volume conditioning is to maintain the heating source outlet water temperature unchanged, by adjusting the heating source node outlet water flow rate to adapt to the heat load changes. The valve in volume conditioning acts frequently so that there will be more loss of the valve. Therefore, it is generally to take the method of qualitative conditioning.

Considering the characteristics of the heating network model and the actual structure of the heating network, the following recursive heat flow network model can be obtained.

From the above analysis, the actual heating network structure and its model are similar to the power distribution network, so the forward-backward sweep method can be used to calculate the heating flow.

Forward: using the load information of each node, the water flow of each pipe and the injected water flow of each node is determined by using Equation (9) forward from the terminal node against the hot water transfer direction.

Backward: according to the direction of hot water transfer, starting at the heating source node, Equation (10) is used to determine the supply temperature, return temperature, pressure and other information of each heat load node, which the water flow information could be obtained by the forward process.

1) Initialize all node supply temperature and outlet water flow rate.

2) Forward calculation: calculate the heat load node injected water flow, the water flow of each pipe.

3) Backward calculation: the calculation of the heat load node supply temperature, return temperature and node pressure.

4) Calculate the return temperature of the heating source node.

5) Iterative convergence judgment. The process would output outcome if the error is within the allowable range, otherwise return to the second step.

6) Calculate the heating power of each heating source.

After using extraction condensing turbine, electric boilers and other energy conversion equipment, power grid and heating network are tightly coupled.

1) The extraction condensing turbine can be equal to the back pressure turbine coupling with straight condensing turbine, the equivalent back pressure turbines are the main heating source. The relationship between electrical power and thermal power which are generated by back pressure turbine is expressed as

where _{B} is the electrical power generated by back pressure turbine; C_{m} is a constant which are the ratio between heat production and electricity.

2) As a supplementary heating source (such as peaking heat), electric boiler produces heat energy by using electrical power which are provide by power grid.

where P_{EB} is the power consumption by electric boiler;

After heat flow calculation, we could get the power generated by back pressure turbine and the power consumed by electric boiler by Equation (11) and Equation (12). Then, the Newton-Raphson method is used to calculate the power flow. Since the Newton-Raphson method is very mature [

Combined electro-thermal system with peak-shaving electric boiler installed in secondary heating network is to install electric boiler at the secondary network side of each heat exchange station. The main heating source is thermoelectric unit (extraction condensing turbine), satisfied the basic heat load, and the electric boiler is the supplementary heating source, satisfied the peak heat load [

The heating network of the example system consists of two independent heating networks, as shown in

The outlet water temperature of the heating source nodes is set at 130˚C, and the outlet water flow rates of pipes No. 2 and No. 11 are 2.3, 3.4 (kg/s). Since the two heating networks are independent of each other, the trend of heat flow is similar when the operating conditions changed. Therefore, this paper only lists the heat flow calculation results of S1 heating source network.

We can see from

The electric boiler is installed in the head end of the heating network (No. 2, 11

Pipe Number | Water Flow (kg/s) |
---|---|

1 | 0.39177 |

2 | 2.29978 |

3 | 2.12806 |

4 | 0.6184 |

5 | 0.30792 |

6 | 0.31048 |

7 | 0.30734 |

8 | 0.91262 |

9 | 0.31024 |

10 | 0.30994 |

Node Number | Ts (˚C) | Tr (˚C) | H (bar) |
---|---|---|---|

1 | 127.86704 | 62.57447 | 0.82847 |

2 | 129.18023 | 61.93836 | 0.80884 |

3 | 128.63193 | 62.20238 | 0.7862 |

4 | 128.17752 | 62.4229 | 0.78314 |

5 | 125.99947 | 63.50195 | 0.78196 |

6 | 125.65829 | 63.67437 | 0.78194 |

7 | 126.07824 | 63.46228 | 0.78502 |

8 | 128.21202 | 62.4061 | 0.78204 |

9 | 125.69018 | 63.65822 | 0.78083 |

10 | 125.72992 | 63.63809 | 0.78084 |

Branch Number | Branch Power Flow (MW) | Branch Number | Branch Power Flow (MW) |
---|---|---|---|

1 | 0.31597 | 11 | −0.01911 |

2 | 0.31496 | 12 | 0.01138 |

3 | 0.02641 | 13 | −0.00672 |

4 | 0.30096 | 14 | 0.05673 |

5 | 0.25339 | 15 | 0.22078 |

6 | 0.27921 | 16 | 0.02625 |

7 | −0.19902 | 17 | 0.02419 |

8 | 0.31558 | 18 | 0.01639 |

9 | 0.16035 | 19 | −0.02332 |

10 | 0.33724 | 20 | −0.00862 |

node), middle (No. 7, 16 nodes) and the end (No. 9, 19 nodes) in turn, and these electric load is borne by nodes No. 1 and No. 2 in the power grid respectively.

Remaining peak shaving ratio and heating source output temperature unchanged, the results of the combined system energy flow calculation compared with control group was shown in

In

The heating network adopts the qualitative conditioning, and in the case that the outlet water flow rate of the heating source node is kept constant, the heat balance of the heating network is realized by adjusting the outlet water temperature. Assuming that the outlet water temperatures are 110˚C, 120˚C, and 130˚C, the results are shown in

It can be seen from

deviation is only about 3 decimal places. Using qualitative conditioning limit heating source outlet water flow rate to a certain numerical value, in order to meet the balance of heating network can only be achieved by changing the heating source return temperature. We can see from

In

Assumed that the water temperature at the outlet of the heating source is constant, the effect of the outlet water flow on the combined system energy flow is studied. The outlet water flow rates of pipes No. 2 is set to 2.3, 2.8 and 3.3 (kg/s), and the other conditions are kept unchanged. The results of comparison with the control group are obtained as shown in

In

In

Outlet Water Temperature of Heating Souce (˚C) | Return Temperature of Heating Source (˚C) |
---|---|

130 | 61.546143 |

120 | 52.040796 |

110 | 42.516155 |

Water Flow of Heating Source (kg/s) | Return Temperature of Heating Source (˚C) |
---|---|

2.3 | 61.546143 |

2.8 | 73.512743 |

3.3 | 81.918498 |

transmission process. The active power output of the thermoelectric unit will be changed, which will affect the power flow, and the greater the variation of the outlet water flow rate, the greater the deviation of the power flow.

1) In the past few years, the thermoelectric unit, electric boiler and other energy conversion equipment have make the power grid and heat network be closed to each other, so it’s necessary to analysis the power flow and the heat flow together.

2) The forward and backward calculation of the heating network can conveniently handle the multi-branch radial heating network without complex network number and no admittance matrix. What’s more, there is also has less iterations in the new method. Therefore, the proposed method is simple and fast.

3) The example analysis shows that the electric boiler installation location, the heat source outlet water flow rate and the outlet water temperature affect the water flow distribution of the heating network, and changing the water temperature and flow rate of the heat source outlet will also affect the power flow results.

This paper was sponsored by the science and technology program called “Research and Application of Key Technology for Combined Electric-thermal System Optimizing Dispatching Considering Safety and Economy” which belong to State Grid Corporation of China.

Liu, S.X., Dai, S., Ding, Q., Hu, L.X. and Wang, Q.X. (2017) Fast Calculation Method of Energy Flow for Combined Electro-Thermal System and Its Application. Energy and Power Engineering, 9, 376-389. https://doi.org/10.4236/epe.2017.94B043