CN106294961A - A kind of meter and the central heating system modeling method of pipe network heat accumulation benefit - Google Patents

Abstract

The present invention relates to a kind of meter and the central heating system modeling method of pipe network heat accumulation benefit, belong to the system modelling field of multiple-energy-source coupling.The central heating system model of the present invention includes cogeneration units model, water circulating pump model, heat exchange station model and four submodels of heating network model, and each submodel is made up of respective constraints.The present invention is in the model set up, it is contemplated that the time of heat supply network pipe network intends dynamic characteristic, therefore can reflect the heat accumulation characteristic of heat supply network pipe network well.The model that the present invention is set up is suitably employed in the combined dispatching decision-making of heat supply network and electrical network.

Description

Central heating system modeling method considering heat storage benefits of pipe network

Technical Field

The invention belongs to the field of multi-energy coupling system modeling, and particularly relates to a centralized heating system modeling method considering heat storage benefits of a pipe network.

Background

The heat supply network has good heat storage characteristics, namely, has strong time delay for heat change of the heat supply network, and the heat storage characteristics are reflected on macroscopic time. In the central heating areas in the north of China, the main mode of heating in winter is large-scale cogeneration central heating. At present, the cogeneration units in northern China mainly adopt a model of 'fixing electricity by heat' to operate, namely, the power generation output of the cogeneration units depends on the heat supply load, so that the heat-electricity output is restricted, and the heat-electricity mandatory relationship is reflected. Under the 'electricity by heat' operation mode, the cogeneration unit is limited by the minimum power supply output to ensure that the heat supply meets the heat load requirement. In winter heat supply period, in order to ensure that heat supply requirements are met, a large number of cogeneration units operate in a state of minimum technical output. Limited by the mode of 'fixing power with heat', the peak regulation capacity of the cogeneration unit is very limited, so that the downward rotation reserve capacity of the system is insufficient, and a downward regulation space is difficult to provide for the consumption of wind power.

In the traditional economic dispatching and unit combination problems of the power system, the central heating system is not considered by modeling. The temperature variation of the heat supply pipe network has high time delay, i.e. heat is stored in the pipe network. By applying the heat storage benefit of the heat supply pipe network, the heat-electricity mandatory relation under the mode of 'fixing electricity by heat' can be relaxed. As an infrastructure for many northern cities, a district central heating network can provide additional flexibility for the operation of cogeneration units. The regional centralized heating network of actual scale is composed of thousands of heat-insulating pipelines, and has huge heat storage capacity. In order to reasonably utilize the energy storage characteristics of the pipe network, the research on a detailed model of the heat supply pipe network of the central heating system is necessary.

Disclosure of Invention

The invention aims to fill the blank of the prior art and provides a method for modeling a centralized heating system considering heat storage benefits of a pipe network. The method of the invention well reflects the heat storage characteristic of the heat supply network. The established model is suitable for being applied to the joint scheduling decision of the heat supply network and the power grid.

The invention provides a centralized heating system modeling method considering heat storage benefits of a pipe network, which is characterized in that a centralized heating system model comprises a cogeneration unit model, a circulating water pump model, a heat exchange station model and a heating network model, wherein each submodel consists of respective constraint conditions; the method specifically comprises the following steps:

1) building combined heat and power generation unit model

The cogeneration unit model contains the following constraints:

1.1) Heat supply and Power supply relationship constraints

The constraints of the power supply output and the heat supply output of the cogeneration unit are described by adopting a convex combination of poles of a polygonal region, as shown in formula (1):

wherein,

in the formula (1), p_i,tThe power supply output h of the ith unit in the t scheduling period_i,tFor the heating output of the ith cogeneration unit in the t-th scheduling period,operating the kth pole of the feasible region approximate polygon for the ith cogeneration unit,a convex combination coefficient, NK, corresponding to the kth pole for the operation point of the ith cogeneration unit in the t scheduling period_iThe number of poles of the approximate polygon of the operation feasible region of the ith cogeneration unit,is a subscript set of the cogeneration unit,subscript sets for scheduling periods;

1.2) circulating Water heating constraints

The heat supply output of the cogeneration unit is used for heating the circulating water flow in the heat supply network, as shown in formula (3):

wherein c is the specific heat capacity of water,the quality of circulating water flowing through the jth heating power station in the tth scheduling period, namely the circulating water flow rate;respectively the water supply temperature and the water return temperature of the nth node in the heat supply network in the t scheduling period,is a set of subscripts for the thermal station,a node subscript connected with the jth heating power station in the heating network;

1.3) Heat supply network node temperature constraints

The temperature of the heat supply network node is controlled within a reasonable range to ensure the heat supply quality and prevent the circulating water from vaporizing, as shown in formula (4):

wherein,andthe lower limit and the upper limit of the temperature of the nth node of the heating network are respectively set;

2) building circulating water pump model

The circulating water pump model contains the following constraints:

2.1) electric Power constraints on circulating Water Pump consumption

The electric power consumed by the circulating water pump is proportional to the supply and return water pressure difference of the heat supply network node and the circulating water flow, as shown in formula (5):

wherein,in order to circulate the electric power consumed by the water pump,respectively representing the water supply pressure and the water return pressure of the nth node of the heat supply network in the t scheduling period,the rho is the water density of the working efficiency of the circulating water pump;

2.2) the upper and lower limits of the circulating water electric power are restricted, as shown in formula (6):

wherein,andrespectively representing the upper limit and the lower limit of the electric power of the circulating water pump;

3) building heat exchange station model

The heat exchange station model contains the following constraints:

3.1) restriction of relationship between supply and return water temperature and heat exchange amount

The relation between the supply and return water temperature and the heat exchange amount of the heat exchange station is shown as the formula (7):

wherein,the circulating water flow rate for the ith heat exchange station in the t scheduling period,the heat load power for the ith heat exchange station at the t-th scheduling period,for a set of index numbers of the heat exchange stations,node subscript connected with the first heat exchange station in the heat supply network;

3.2) node supply and return water pressure restraint

The pressure difference of the supply water and the return water of the node at the heat exchange station is higher than a certain level to maintain the circulating water flow, as shown in the formula (8):

wherein,the minimum water supply and return pressure difference of the first heat exchange station is obtained;

3.3) Return Water temperature constraint

The return water temperature of the heat exchange station is kept within a certain temperature range, as shown in formula (9):

wherein,andrespectively representing the upper limit and the lower limit of the return water temperature of the heat exchange station;

4) building heat supply network model

In the heating network:the index set of the heat supply pipeline with the ith heat supply network node as the terminal point is shown,representing a set of heating pipeline indices starting from the ith heating network node,respectively showing the temperature of the head end and the tail end of the water supply pipeline of the mth dispatching time interval,respectively represents the temperature of the head end and the tail end of the b-th water return pipeline in the t-th scheduling period,respectively representing the water flow of the b-th water supply pipeline and the water return pipeline in the t-th scheduling period; the heating network model contains the following constraints:

4.1) flow continuity constraints

The sum of the water flows entering the same node is zero, as shown in formulas (10) and (11):

wherein,a subscript set of heating network nodes;

4.2) temperature mixing constraint

The temperature of the water flows from different pipelines after being mixed at the same network node meets the following equations as shown in the formulas (12) and (13):

4.3) network node temperature constraints

The temperature of the water flowing out of the network node is equal to the temperature of the network node, as shown in equations (14) and (15):

4.4) flow restriction constraints

The circulating water flow is limited within a certain range to prevent the vibration of the pipeline, as shown in equations (16) and (17):

wherein,is the upper limit of the water flow speed of the b-th heat supply pipeline,a heat supply pipeline subscript set;

4.4) pressure loss constraint

The pressure loss along the pipe due to the friction of the water flow against the inner wall of the pipe is proportional to the square of the flow velocity, as shown in equation (18):

wherein, mu_bThe pressure loss coefficient of the b-th heat supply pipeline,subscripts of the head end node and the tail end node of the b-th heat supply pipeline are respectively provided;

4.5) Water temperature Change delay constraint and along-tube Heat loss constraint

This constraint is divided into two steps:

4.5.1) estimate the duct outlet temperature neglecting heat loss along the tube using the duct inlet temperature over the past period, as shown by equations (19) and (20):

wherein,andneglecting the pipeline outlet temperature of heat loss along the pipeline in the t scheduling period for the b-th heat supply pipeline respectively;

variable K_b,t,kThe value of (a) is determined by the circulating water flow rate, as shown in formula (21):

$K_{b,t,k}=\left\{\begin{array}{c}({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t-S_{b,t}+{\mathrm{\ρA}}_b{L}_b)/({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t),k=t-{\mathrm{\φ}}_{b,t}\\ ({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t)/({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t),k=t-{\mathrm{\φ}}_{b,t}+1,\mathrm{...},t-{\mathrm{\γ}}_{b,t}-1\\ (R_{b,t}-{\mathrm{\ρA}}_b{L}_b)/({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t),k=t-{\mathrm{\γ}}_{b,t}\\ 0,otherwise\end{array}\right.---\left(21\right)$

where Δ t is the time interval between adjacent scheduling periods, A_bIs the cross-sectional area, L, of the b-th heat supply pipeline_bThe length of the b-th heat supply pipeline;

in the formulae (19) to (21), the integer variable φ_b,tAnd gamma_b,tRespectively represent the number of scheduling time periods related to the water temperature change delay, as shown in equation (22) and equation (23):

r in the formula (21)_b,tAnd S_b,tThe expressions are respectively shown in formula (24) and formula (25):

$R_{b,t}=\underset{k=0}{\overset{{\mathrm{\γ}}_{b,t}}{\Σ}}({\mathrm{ms}}_{b,t-k}^{pipe}\·\mathrm{\Δ}t)---\left(24\right)$

$S_{b,t}=\left\{\begin{array}{c}\underset{k=0}{\overset{{\mathrm{\φ}}_{b,t}-1}{\Σ}}({\mathrm{ms}}_{b,t-k}^{pipe}\·\mathrm{\Δ}t),{\mathrm{if\φ}}_{b,t}\≥{\mathrm{\γ}}_{b,t}+1\\ R_{b,t},otherwise\end{array}\right.---\left(25\right)$

4.5.2) performing heat loss correction on the outlet temperature of the pipeline, as shown in the formulas (26) and (27):

${\mathrm{\τ}}_{b,t}^{PS,out}={\mathrm{\τ}}_t^{am}+({\mathrm{\τ}}_{b,t}^{\′PS,out}-{\mathrm{\τ}}_t^{am})\exp \[-\frac{{\mathrm{\λ}}_b\mathrm{\Δ}t}{A_b\mathrm{\ρ}c}\left({\mathrm{\γ}}_{b,t}+\frac{1}{2}+\frac{S_{b,t}-R_{b,t}}{{\mathrm{ms}}_{b,t-{\mathrm{\γ}}_{b,t}}^{pipe}\mathrm{\Δ}t}\right)\]---\left(26\right)$

${\mathrm{\τ}}_{b,t}^{PR,out}={\mathrm{\τ}}_t^{am}+({\mathrm{\τ}}_{b,t}^{\′PR,out}-{\mathrm{\τ}}_t^{am})\exp \[-\frac{{\mathrm{\λ}}_b\mathrm{\Δ}t}{A_b\mathrm{\ρ}c}({\mathrm{\γ}}_{b,t}+\frac{1}{2}+\frac{S_{b,t}-R_{b,t}}{{\mathrm{ms}}_{b,t-{\mathrm{\γ}}_{b,t}}^{pipe}\mathrm{\Δ}t})\]---\left(27\right)$

wherein,for the ambient temperature of the t-th scheduling period, λ_bThe heat loss coefficient of the b-th heat supply pipeline along the pipe is obtained;

5) and finishing the construction of the central heating system model.

The invention has the characteristics and beneficial effects that:

the modeling method of the centralized heating system considering the heat storage benefits of the pipe network, which is provided by the invention, is used for sequentially modeling the cogeneration unit, the circulating water pump, the heat exchange station and the heating network according to the characteristics of the regional heating network. In the established model, the time quasi-dynamic characteristic of a heat supply network is considered, the heat storage characteristic of the central heating system is accurately described, and the method is suitable for being applied to the operation scheduling of the power system so as to fully utilize the scheduling flexibility introduced by the central heating system.

Drawings

FIG. 1 is a block flow diagram of the method of the present invention.

Fig. 2(a) is a schematic diagram of the feasible region of the output operation of the back-pressure cogeneration unit.

Fig. 2(b) is a schematic diagram of the operable range of the output power of the extraction condensing cogeneration unit.

DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION

The invention provides a method for modeling a centralized heating system considering heat storage benefits of a pipe network, which is further described in detail by combining the attached drawings and specific embodiments.

The invention provides a centralized heating system modeling method considering heat storage benefits of a pipe network, a flow diagram is shown in figure 1, a centralized heating system model comprises a cogeneration unit model, a circulating water pump model, a heat exchange station model and a heating network model, and each submodel consists of respective constraint conditions; the method specifically comprises the following steps:

1) building combined heat and power generation unit model

The cogeneration unit model contains the following constraints:

1.1) Heat supply and Power supply relationship constraints

The cogeneration units are divided into two types, namely a back pressure type cogeneration unit and a drainage and condensation type cogeneration unit, and the output operation of the two types of units is feasible, namely the relationship between heat supply and power supply output, as shown in fig. 2, wherein fig. 2(a) is the back pressure type cogeneration unit, and fig. 2(b) is the drainage and condensation type cogeneration unit. The abscissa of the two graphs is the heat supply output of the unit, and the ordinate is the power supply output of the unit. The back pressure cogeneration unit in fig. 2(a) has a linear relationship between the power supply output and the heat supply output, and the extraction and condensation unit in fig. 2(b) has a convex quadrilateral feasible region between the power supply output and the heat supply output. The constraints of the power supply output and the heat supply output of the cogeneration unit are described by adopting a convex combination of poles of a polygonal region, as shown in formula (1):

wherein,

in the formula (1), p_i,tThe power supply output h of the ith unit in the t scheduling period_i,tFor the heating output of the ith cogeneration unit in the t-th scheduling period,operating the kth pole of the feasible region approximate polygon for the ith cogeneration unit,a convex combination coefficient, NK, corresponding to the kth pole for the operation point of the ith cogeneration unit in the t scheduling period_iThe number of poles of the approximate polygon of the operation feasible region of the ith cogeneration unit,is a subscript set of the cogeneration unit,subscript sets for scheduling periods;

1.2) circulating Water heating constraints

The heating output of the cogeneration unit is used for heating the circulating water flow in the heating network as shown in formula (3):

wherein c is the specific heat capacity of water, the specific value is measured according to an actual water quality experiment,for the quality of the circulating water flowing through the jth thermal station during the tth scheduling period (for convenience, hereinafter referred to as circulating water flow rate),respectively the water supply temperature and the water return temperature of the nth node in the heat supply network in the t scheduling period,is a set of subscripts for the thermal station,a node subscript connected with the jth heating power station in the heating network;

1.3) Heat supply network node temperature constraints

The temperature of the heat supply network node is controlled within a reasonable range to ensure the heat supply quality and prevent the circulating water from vaporizing, as shown in formula (4):

wherein,andthe lower limit and the upper limit of the temperature of the nth node of the heating network are respectively set;

2) building circulating water pump model

The circulating water pump model contains the following constraints:

2.1) electric Power constraints on circulating Water Pump consumption

The electric power consumed by the circulating water pump is proportional to the supply and return water pressure difference of the heat supply network node and the circulating water flow, as shown in formula (5):

wherein,in order to circulate the electric power consumed by the water pump,respectively representing the water supply pressure and the water return pressure of the nth node of the heat supply network in the t scheduling period,the rho is the water density of the working efficiency of the circulating water pump;

2.2) the upper and lower limits of the circulating water electric power are restricted, as shown in formula (6):

wherein,andrespectively representing the upper limit and the lower limit of the electric power of the circulating water pump;

3) building heat exchange station model

The heat exchange station model contains the following constraints:

3.1) restriction of relationship between supply and return water temperature and heat exchange amount

In a heat transfer system, a heat exchange station may be considered a heat load; the relation between the supply and return water temperature and the heat exchange amount of the heat exchange station is shown as the formula (7):

wherein,the circulating water flow rate for the ith heat exchange station in the t scheduling period,the heat load power for the ith heat exchange station at the t-th scheduling period,for a set of index numbers of the heat exchange stations,node subscript connected with the first heat exchange station in the heat supply network;

3.2) node supply and return water pressure restraint

The pressure difference of the supply water and the return water of the node at the heat exchange station is higher than a certain level to maintain the circulating water flow, as shown in the formula (8):

wherein,the minimum water supply and return pressure difference of the first heat exchange station is obtained;

3.3) Return Water temperature constraint

The return water temperature of the heat exchange station is kept within a certain temperature range, as shown in formula (9):

wherein,andrespectively representing the upper limit and the lower limit of the return water temperature of the heat exchange station;

4) building heat supply network model

The following variables in the heating network are defined:the index set of the heat supply pipeline with the ith heat supply network node as the terminal point is shown,representing a set of heating pipeline indices starting from the ith heating network node,respectively showing the temperature of the head end and the tail end of the water supply pipeline of the mth dispatching time interval,respectively represents the temperature of the head end and the tail end of the b-th water return pipeline in the t-th scheduling period,respectively shows the water flow of the b-th water supply pipeline and the water return pipeline in the t-th scheduling period. It is worth noting that the water supply and return temperature of the ith node in the heating network in the t-th scheduling periodRefers to the steady-state temperature of the water flows flowing into the node after the water flows are mixed with each other, and the head and tail end temperatures of the water supply pipeline and the water return pipeline in the t scheduling periodRefers to the temperature of the water stream prior to mixing at the corresponding location within the pipe.

The heating network model contains the following constraints:

4.1) flow continuity constraints

According to the law of conservation of mass, since water is an incompressible fluid, the sum of the water flows entering the same node is zero, as shown in equations (10) and (11):

wherein,a subscript set of heating network nodes;

4.2) temperature mixing constraint

According to the law of conservation of energy, the temperature of the water flows from different pipelines after being mixed at the same network node satisfies the following equations as shown in formulas (12) and (13):

4.3) network node temperature constraints

The temperature of the water flowing out of the network node is equal to the temperature of the network node, as shown in equations (14) and (15):

4.4) flow restriction constraints

The circulating water flow is limited within a certain range to prevent the vibration of the pipeline, as shown in equations (16) and (17):

wherein,is the upper limit of the water flow speed of the b-th heat supply pipeline,a heat supply pipeline subscript set;

4.4) pressure loss constraint

According to the Darcy-Weisbach equation, the pressure loss along the pipe due to water flow rubbing against the inner wall of the pipe is proportional to the square of the flow velocity, as shown in equation (18):

wherein, mu_bThe pressure loss coefficient of the b-th heat supply pipeline,subscripts of the head end node and the tail end node of the b-th heat supply pipeline are respectively provided;

4.5) Water temperature Change delay constraint and along-tube Heat loss constraint

The method is described by adopting a node method, and the constraint comprises two steps:

4.5.1) estimate the duct outlet temperature neglecting heat loss along the tube using the duct inlet temperature over the past period, as shown by equations (19) and (20):

wherein,andneglecting edges of the b-th heat supply pipeline in the t-th scheduling periodPipe exit temperature of pipe heat loss;

variable K_b,t,kThe value of (a) is determined by the circulating water flow rate, as shown in formula (21):

$K_{b,t,k}=\left\{\begin{array}{c}({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t-S_{b,t}+{\mathrm{\ρA}}_b{L}_b)/({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t),k=t-{\mathrm{\φ}}_{b,t}\\ ({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t)/({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t),k=t-{\mathrm{\φ}}_{b,t}+1,\mathrm{...},t-{\mathrm{\γ}}_{b,t}-1\\ (R_{b,t}-{\mathrm{\ρA}}_b{L}_b)/({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t),k=t-{\mathrm{\γ}}_{b,t}\\ 0,otherwise\end{array}\right.---\left(21\right)$

where Δ t is the time interval between adjacent scheduling periods, A_bIs the cross-sectional area, L, of the b-th heat supply pipeline_bThe length of the b-th heat supply pipeline;

in the formulae (19) to (21), the integer variable φ_b,tAnd gamma_b,tRespectively represent the number of scheduling time periods related to the water temperature change delay, as shown in equation (22) and equation (23):

r in the formula (21)_b,tAnd S_b,tThe expressions are respectively shown in formula (24) and formula (25):

$R_{b,t}=\underset{k=0}{\overset{{\mathrm{\γ}}_{b,t}}{\Σ}}({\mathrm{ms}}_{b,t-k}^{pipe}\·\mathrm{\Δ}t)---\left(24\right)$

$S_{b,t}=\left\{\begin{array}{c}\underset{k=0}{\overset{{\mathrm{\φ}}_{b,t}-1}{\Σ}}({\mathrm{ms}}_{b,t-k}^{pipe}\·\mathrm{\Δ}t),{\mathrm{if\φ}}_{b,t}\≥{\mathrm{\γ}}_{b,t}+1\\ R_{b,t},otherwise\end{array}\right.---\left(25\right)$

4.5.2) performing heat loss correction on the outlet temperature of the pipeline, as shown in the formulas (26) and (27):

${\mathrm{\τ}}_{b,t}^{PS,out}={\mathrm{\τ}}_t^{am}+({\mathrm{\τ}}_{b,t}^{\′PS,out}-{\mathrm{\τ}}_t^{am})\exp \[-\frac{{\mathrm{\λ}}_b\mathrm{\Δ}t}{A_b\mathrm{\ρ}c}\left({\mathrm{\γ}}_{b,t}+\frac{1}{2}+\frac{S_{b,t}-R_{b,t}}{{\mathrm{ms}}_{b,t-{\mathrm{\γ}}_{b,t}}^{pipe}\mathrm{\Δ}t}\right)\]---\left(26\right)$

${\mathrm{\τ}}_{b,t}^{PR,out}={\mathrm{\τ}}_t^{am}+({\mathrm{\τ}}_{b,t}^{\′PR,out}-{\mathrm{\τ}}_t^{am})\exp \[-\frac{{\mathrm{\λ}}_b\mathrm{\Δ}t}{A_b\mathrm{\ρ}c}({\mathrm{\γ}}_{b,t}+\frac{1}{2}+\frac{S_{b,t}-R_{b,t}}{{\mathrm{ms}}_{b,t-{\mathrm{\γ}}_{b,t}}^{pipe}\mathrm{\Δ}t})\]---\left(27\right)$

wherein,for the ambient temperature of the t-th scheduling period, λ_bThe heat loss coefficient of the b-th heat supply pipeline along the pipe is obtained.

5) And finishing the construction of the central heating system model.

Claims (1)

1. A centralized heating system modeling method considering heat storage benefits of a pipe network is characterized in that a centralized heating system model comprises a cogeneration unit model, a circulating water pump model, a heat exchange station model and a heating network model, wherein each submodel is composed of respective constraint conditions; the method specifically comprises the following steps:

1) building combined heat and power generation unit model

The cogeneration unit model contains the following constraints:

1.1) Heat supply and Power supply relationship constraints

The constraints of the power supply output and the heat supply output of the cogeneration unit are described by adopting a convex combination of poles of a polygonal region, as shown in formula (1):

wherein,

in the formula (1), p_i,tThe power supply output h of the ith unit in the t scheduling period_i,tFor the heating output of the ith cogeneration unit in the t-th scheduling period,operating the kth pole of the feasible region approximate polygon for the ith cogeneration unit,a convex combination coefficient, NK, corresponding to the kth pole for the operation point of the ith cogeneration unit in the t scheduling period_iThe number of poles of the approximate polygon of the operation feasible region of the ith cogeneration unit,is a subscript set of the cogeneration unit,subscript sets for scheduling periods;

1.2) circulating Water heating constraints

The heat supply output of the cogeneration unit is used for heating the circulating water flow in the heat supply network, as shown in formula (3):

wherein,c is the specific heat capacity of water,the quality of circulating water flowing through the jth heating power station in the tth scheduling period, namely the circulating water flow rate;respectively the water supply temperature and the water return temperature of the nth node in the heat supply network in the t scheduling period,is a set of subscripts for the thermal station,a node subscript connected with the jth heating power station in the heating network;

1.3) Heat supply network node temperature constraints

The temperature of the heat supply network node is controlled within a reasonable range to ensure the heat supply quality and prevent the circulating water from vaporizing, as shown in formula (4):

wherein,andthe lower limit and the upper limit of the temperature of the nth node of the heating network are respectively set;

2) building circulating water pump model

The circulating water pump model contains the following constraints:

2.1) electric Power constraints on circulating Water Pump consumption

The electric power consumed by the circulating water pump is proportional to the supply and return water pressure difference of the heat supply network node and the circulating water flow, as shown in formula (5):

wherein,in order to circulate the electric power consumed by the water pump,respectively representing the water supply pressure and the water return pressure of the nth node of the heat supply network in the t scheduling period,the rho is the water density of the working efficiency of the circulating water pump;

2.2) the upper and lower limits of the circulating water electric power are restricted, as shown in formula (6):

wherein,andrespectively representing the upper limit and the lower limit of the electric power of the circulating water pump;

3) building heat exchange station model

The heat exchange station model contains the following constraints:

3.1) restriction of relationship between supply and return water temperature and heat exchange amount

The relation between the supply and return water temperature and the heat exchange amount of the heat exchange station is shown as the formula (7):

wherein,the circulating water flow rate for the ith heat exchange station in the t scheduling period,the heat load power for the ith heat exchange station at the t-th scheduling period,for a set of index numbers of the heat exchange stations,node subscript connected with the first heat exchange station in the heat supply network;

3.2) node supply and return water pressure restraint

The pressure difference of the supply water and the return water of the node at the heat exchange station is higher than a certain level to maintain the circulating water flow, as shown in the formula (8):

wherein,the minimum water supply and return pressure difference of the first heat exchange station is obtained;

3.3) Return Water temperature constraint

The return water temperature of the heat exchange station is kept within a certain temperature range, as shown in formula (9):

wherein,andrespectively represents the return water temperature of the heat exchange stationThe upper and lower limits of (d);

4) building heat supply network model

In the heating network:the index set of the heat supply pipeline with the ith heat supply network node as the terminal point is shown,representing a set of heating pipeline indices starting from the ith heating network node,respectively showing the temperature of the head end and the tail end of the water supply pipeline of the mth dispatching time interval,respectively represents the temperature of the head end and the tail end of the b-th water return pipeline in the t-th scheduling period,respectively representing the water flow of the b-th water supply pipeline and the water return pipeline in the t-th scheduling period; the heating network model contains the following constraints:

4.1) flow continuity constraints

The sum of the water flows entering the same node is zero, as shown in formulas (10) and (11):

wherein,a subscript set of heating network nodes;

4.2) temperature mixing constraint

The temperature of the water flows from different pipelines after being mixed at the same network node meets the following equations as shown in the formulas (12) and (13):

4.3) network node temperature constraints

The temperature of the water flowing out of the network node is equal to the temperature of the network node, as shown in equations (14) and (15):

4.4) flow restriction constraints

The circulating water flow is limited within a certain range to prevent the vibration of the pipeline, as shown in equations (16) and (17):

wherein,is the upper limit of the water flow speed of the b-th heat supply pipeline,a heat supply pipeline subscript set;

4.4) pressure loss constraint

The pressure loss along the pipe due to the friction of the water flow against the inner wall of the pipe is proportional to the square of the flow velocity, as shown in equation (18):

wherein, mu_bThe pressure loss coefficient of the b-th heat supply pipeline,subscripts of the head end node and the tail end node of the b-th heat supply pipeline are respectively provided;

4.5) Water temperature Change delay constraint and along-tube Heat loss constraint

This constraint is divided into two steps:

4.5.1) estimate the duct outlet temperature neglecting heat loss along the tube using the duct inlet temperature over the past period, as shown by equations (19) and (20):

wherein,andneglecting the pipeline outlet temperature of heat loss along the pipeline in the t scheduling period for the b-th heat supply pipeline respectively;

variable K_b,t,kThe value of (a) is determined by the circulating water flow rate, as shown in formula (21):

$K_{b,t,k}=\left\{\begin{array}{c}\left({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t-S_{b,t}+{\mathrm{\ρA}}_b{L}_b\right)/\left({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t\right),k=t-{\mathrm{\φ}}_{b,t}\\ \left({\mathrm{ms}}_{b,k}^{pipe}\·\mathrm{\Δ}t\right)/\left({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t\right),k=t-{\mathrm{\φ}}_{b,t}+1,...,t-{\mathrm{\γ}}_{b,t}-1\\ \left(R_{b,t}-{\mathrm{\ρA}}_b{L}_b\right)/\left({\mathrm{ms}}_{b,t}^{pipe}\·\mathrm{\Δ}t\right),k=t-{\mathrm{\γ}}_{b,t}\\ 0,otherwise\end{array}\right.---\left(21\right)$

where Δ t is the time interval between adjacent scheduling periods, A_bIs the cross-sectional area, L, of the b-th heat supply pipeline_bThe length of the b-th heat supply pipeline;

in the formulae (19) to (21), the integer variable φ_b,tAnd gamma_b,tRespectively represent the number of scheduling time periods related to the water temperature change delay, as shown in equation (22) and equation (23):

r in the formula (21)_b,tAnd S_b,tThe expressions are respectively shown in formula (24) and formula (25):

$R_{b,t}=\underset{k=0}{\overset{{\mathrm{\γ}}_{b,t}}{\mathrm{\Σ}}}({\mathrm{ms}}_{b,t-k}^{pipe}\·\mathrm{\Δ}t)---\left(24\right)$

$S_{b,t}=\left\{\begin{array}{c}\underset{k=0}{\overset{{\mathrm{\φ}}_{b,t}-1}{\mathrm{\Σ}}}\left({\mathrm{ms}}_{b,t-k}^{pipe}\·\mathrm{\Δ}t\right),{\mathrm{if\φ}}_{b,t}\≥{\mathrm{\γ}}_{b,t}+1\\ R_{b,t},otherwise\end{array}\right.---\left(25\right)$

4.5.2) performing heat loss correction on the outlet temperature of the pipeline, as shown in the formulas (26) and (27):

${\mathrm{\τ}}_{b,t}^{PS,out}={\mathrm{\τ}}_t^{am}+({\mathrm{\τ}}_{b,t}^{\′PS,out}-{\mathrm{\τ}}_t^{am})\exp \[-\frac{{\mathrm{\λ}}_b\mathrm{\Δ}t}{A_b\mathrm{\ρ}c}({\mathrm{\γ}}_{b,t}+\frac{1}{2}+\frac{S_{b,t}-R_{b,t}}{{\mathrm{ms}}_{b,t-{\mathrm{\γ}}_{b,t}}^{pipe}\mathrm{\Δ}t})\]---\left(26\right)$

${\mathrm{\τ}}_{b,t}^{PR,out}={\mathrm{\τ}}_t^{am}+({\mathrm{\τ}}_{b,t}^{\′PR,out}-{\mathrm{\τ}}_t^{am})\exp \[-\frac{{\mathrm{\λ}}_b\mathrm{\Δ}t}{A_b\mathrm{\ρ}c}({\mathrm{\γ}}_{b,t}+\frac{1}{2}+\frac{S_{b,t}-R_{b,t}}{{\mathrm{ms}}_{b,t-{\mathrm{\γ}}_{b,t}}^{pipe}\mathrm{\Δ}t})\]---\left(27\right)$

wherein,for the ambient temperature of the t-th scheduling period, λ_bThe heat loss coefficient of the b-th heat supply pipeline along the pipe is obtained;

5) and finishing the construction of the central heating system model.