State estimation method for heating network in steady state based on bilateral equivalent model

Abstract

A state estimation method for a heat supply network in a steady state based on a bilateral equivalent model is provided. The method includes: establishing the bilateral equivalent model based on a mass flow rate in each supply branch of the heating network, a mass flow rate in each return branch of the heating network, a mass flow rate in each connecting branch of the heating network, a pressure and a temperature of each node in the heating network, wherein each heat source is configured as a connecting branch and each heat load is configured as a connecting branch; and repeatedly performing a state estimation on the heating network based on the bilateral equivalent model, until a coverage state estimation result is acquired.

Description

FIELD

The present disclosure relates to a state estimation method for a heating network in a steady state based on a bilateral equivalent model, belonging to the technical field of the operation and control of comprehensive energy systems.

BACKGROUND

According to different heating mediums, heating networks can be divided into two categories: hot-water heat-supply networks and steam heat-supply networks. At present, most of China's industrial heating supply uses medium or high pressure steam heat supply networks, and civil heating supply mostly uses hot-water heat-supply networks. In the present disclosure, the hot-water heat-supply network is taken for analysis. According to whether there is a return network, the heating network can be divided into two types: an open network and a closed network.

For the open network, only the supply network of the heating network needs to be analyzed, while for the closed network, it is necessary to study both the supply network and the return network. Generally speaking, for the closed network, the supply network and the return network have the same topological structure. In the prior art, when analyzing the supply network and the return network individually, it is considered that the mass flow rate of each pipeline in the supply network and the return network is approximately the same. Therefore, only the hydraulic operating conditions of the supply network are analyzed, and on this basis, the thermal operating conditions of the supply network and the return network are analyzed. However, this method cannot handle asymmetry circumstances between the supply network and the return network. For example, when a line in the supply network or the return network fails or is being repaired, it will inevitably lead to the asymmetry between the supply network and the return network. On the other hand, the purpose of state estimation is to monitor the operation of the entire network. If the symmetric processing is simply performed, the operating conditions of the return network cannot be monitored.

SUMMARY

The purpose of the present disclosure is to propose a state estimation method for a heating network in a steady state based on a bilateral equivalent model. The method may include: establishing the bilateral equivalent model based on a mass flow rate in each supply branch of the heating network, a mass flow rate in each return branch of the heating network, a mass flow rate in each connecting branch of the heating network, a pressure and a temperature of each node in the heating network, in which each heat source is configured as a connecting branch and each heat load is configured as a connecting branch; and repeatedly performing a state estimation on the heating network based on the bilateral equivalent model, until a coverage state estimation result is acquired.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic structural diagram of a heating network involved in a method of the present disclosure.

FIG. 2 is a schematic structural view of a heating network components after equivalent processing involved in a method of the present disclosure.

DETAILED DESCRIPTION

The state estimation method for steady state operation of a heating network based on a bilateral equivalent model proposed by the present disclosure includes the following steps.

(1) Anode-branch incidence matrix for the bilateral equivalent model of the heating network is established, which includes followings.

The structure of the heating network involved in the method of the present disclosure is illustrated in FIG. 1, in which the solid lines represent supply branches in the heating network, and the dashed lines represent return branches in the heating network. In the bilateral equivalent model of the heating network, both the supply branches and the return branches of the heating network are taken into consideration, and a heat source and a heat load are equivalent to connecting branches which are represented by dashed lines in FIG. 2. For a heating network composed of N nodes and B branches, the following matrix representing the relationship among the nodes and branches is formed.

(1-1) a node-branch incidence matrix A:

The node-branch incidence matrix A represents the topological relationship among nodes and branches in the network. The matrix A consists of three elements: 0, 1, and −1. The elements in the matrix A are defined as follows:

$A_{\mathrm{ij}}=\{\begin{array}{cc}1& \begin{array}{c}\mathrm{representing}\mathrm{that}\mathrm{node}i\mathrm{is}a\mathrm{headend}\\ \mathrm{node}\mathrm{of}\mathrm{branch}j\end{array}\\ -1& \begin{array}{c}\mathrm{representing}\mathrm{that}\mathrm{node}i\mathrm{is}a\mathrm{tailend}\\ \mathrm{node}\mathrm{of}\mathrm{branch}j\end{array}\\ 0& \begin{array}{c}r\mathrm{epresenting}\mathrm{that}\mathrm{node}i\mathrm{is}\mathrm{not}\mathrm{an}\mathrm{end}\mathrm{of}\\ \mathrm{branch}j\end{array}\end{array}$

where i represents any node in the heating network, and j represents any branch in the heating network, i=1, 2, . . . , N, and j=1, 2, . . . , B. As shown in FIG. 2, the nodes are represented by n, and the branches are represented by b.

(1-2) a positive node-branch incidence matrix A_ƒ:

The positive node-branch incidence matrix A_ƒ represents the relationship among the headend nodes of the respective branches and the branches, A_ƒ={A|A_ij>0}, and the elements in the matrix A_ƒ are defined as follows:

$A_{\mathrm{fij}}=\{\begin{array}{cc}1& \begin{array}{c}\mathrm{representing}\mathrm{that}\mathrm{node}i\mathrm{is}a\mathrm{headend}\\ \mathrm{node}\mathrm{of}\mathrm{branch}j\end{array}\\ 0& \begin{array}{c}\mathrm{representing}\mathrm{that}\mathrm{node}i\mathrm{is}\mathrm{not}a\mathrm{headend}\\ \mathrm{node}\mathrm{of}\mathrm{branch}j\end{array}\end{array}$

where i=1, 2, . . . , N, and j=1, 2, . . . , B.

(1-3) a negative node-branch incidence matrix A_t:

The negative node-branch incidence matrix A_t represents the relationship among the tailend nodes of the respective branches and the branches, A_t={−A|A_ij<1}, and the elements in the matrix A_t are defined as follows:

$A_{\mathrm{tij}}=\{\begin{array}{cc}1& \begin{array}{c}\mathrm{representing}\mathrm{that}\mathrm{node}i\mathrm{is}a\mathrm{tailend}\\ \mathrm{node}\mathrm{of}\mathrm{branch}j\end{array}\\ 0& \begin{array}{c}\mathrm{representing}\mathrm{that}\mathrm{node}i\mathrm{is}\mathrm{not}a\mathrm{tailend}\\ \mathrm{node}\mathrm{of}\mathrm{branch}j\end{array}\end{array}$

where i=1, 2, . . . , N, and j=1, 2, . . . , B.

(2) A state estimation is performed on the heating network in steady state operation based on the bilateral equivalent model.

(2-1) A convergence accuracy δ and a maximum number of cycles d of the state estimation for the heating network are set, and a number of cycles a is set to 0 during initialization.

(2-2) The real-time measured operation data of the heating network at a time point t is obtained from a supervisory control and data acquisition system of the heating network, including a pressure H of each node in the heating network, a mass flow rate m of a branch between any two nodes, and a head-end temperature T_ƒ and a tailend temperature T_t of a branch between two nodes, a thermal power ϕ^q of connecting branches (as illustrated by the dashed lines in FIG. 2) which are equivalent from a heat source and a heat load, in which the superscript q represents a connecting branch. The above operation data constitutes a column vector z_h of measurement values.

(2-3) A column vector x_h is constituted by all the state values to be estimated for the heating network, including a pressure Ĥ of each node in the heating network, a headend temperature and a tailend temperature of the branch between any two nodes.

(2-4) A measurement function ƒ(x) describing a relation between a measurement value and a state value of the heating network is established, in which ƒ(x)=ƒ(x_h), and ƒ(x_h) is a group of equations describing the thermal system flow, including the following equations:

(2-4-1) a branch pressure loss equation:

The branch pressure loss equation represents a pressure difference between the nodes at the two ends of the branch. The branch pressure loss equation is represented in a matrix form as follows.A^TH=ΔH−H_p

where H represents a column vector composed of the pressures of the nodes in the heating network in the above step (2-2), A^T represents a transposed matrix of the node-branch incidence matrix A in the above step (1-1), and H_p represents a column vector composed of lifts of pumps on the branches, in which H_p=amp_p²+bm_p+c, where a, b, and c are pump parameters, which are obtained from the product nameplate of the pumps, m_p represents a mass flow rate of the branch where the pump is located, and ΔH represents a column vector composed of pressure losses of respective branches in the heating network, in which ΔH is calculated with the following equation.ΔH=K·m·|m|

where K represents a friction coefficient of the branch in the heating network, which ranges from 10 to 500 Pa/(kg/s)², and m represents a mass flow rate of any branch in the heating network.

(2-4-2) a thermal power equation of a connecting branch:

The thermal power equation represents the headend-to-tailend temperature relation of a connecting branch q, which is expressed by the following equation.ϕ^q=C_pm^q(T_ƒ^q−T_t^q)

where the superscript q represents the connecting branch, ϕ^q represents a heating power of the connecting branch, the value of the heating power at the heat load is positive, the value of the heating power at the heat source is negative, and C_p is a specific heat capacity of a heating medium, which is obtained from a physical parameter table of fluid, m^q represents a mass flow rate of the connecting branch, T_ƒ^q represents a temperature at a headend of the connecting branch, and T_t^q represents a temperature at a tailend of the connecting branch.

(3) According to the measurement values of the above step (2-2), an objective function of state estimation for steady state operation of a heating network is established as follows.min J(x_h)=min{[z_h−ƒ(x_h)]^TW[z_h−ƒ(x_h)]}

where W represents a covariance matrix of the measurement values, the superscript T represents matrix transposition, and J(x_h) is an expression of the objective function.

(4) Constraint conditions c(x_h) for the steady state operation of the heating network is established, including followings.

(4-1) Mass flow continuity constraints for all nodes are established, and the mass flow continuity constraints are expressed in a matrix form as follows.AM=0

where M represents a column vector composed of mass flow rates of respective branches in the heating network. The supply branch and the return branch are uniformly equivalent to an ordinary branch, which is represented by the superscript p, and the connecting branch is equivalent to a special branch, which is represented by the superscript q. Thus, M is represented by the following equation.

$M=\left[\begin{array}{c}{M}^p\\ M^q\end{array}\right]$

where M^p represents a sub-vector composed of mass flow rates of the ordinary branches (i.e., the supply branch and the return branch), and M^q represents a sub-vector composed of the mass flow rates of the connecting branch.

(4-2) Temperature mixing constraints for all nodes in the heating network are established.(Σm_out)T_n=Σ(m_inT_in)

where m_out represents a mass flow rates of the heating medium in a branch flowing out of a node, m_in represents a mass flow rates of the heating medium in a branch flowing into a node, T_n represents a temperature of the heating medium after being mixed at the node, and T_in represents a temperature of the heating medium in different branches before being mixed at the node.

The temperature T_in of the heating medium in branches before being mixed at the node is replaced by the tailend temperature T_t of different branches, then the temperature mixing constraints for nodes may be represented in a matrix form as follows.diag(A_ƒM)T_n=A_t diag(M)T_t

where A_ƒ and A_t represent the positive node-branch incidence matrix in the above step (1-2) and the negative node-branch incidence matrix in the above step (1-3) respectively, and diag(⋅) represents a diagonal matrix.

(4-3) Branch temperature drop constraints are established for all ordinary branches in the heating network. The branch temperature drop constraints are represented in a matrix form as follows.

$T_t^p-T_a=\left(T_f^p-T_a\right)e^{-\frac{\lambda L}{C_p{M}^p}}$

where T_a represents an ambient temperature, T_t^p represents a tailend temperature of the ordinary branch, T_ƒ^p represents a headend temperature of the ordinary branch, L represents a length of the ordinary branch, and λ represents a heat transfer coefficient of the ordinary branch in the heating network, the heat transfer coefficients of different materials are different, and the value of the heat transfer coefficient ranges from zero to a few hundreds, which may be obtained in the corresponding data manual, e is the natural logarithm, C_p represents a specific heat capacity of a heating medium, and M^p represents a sub-vector composed of mass flow rates of the ordinary branches (i.e., the supply branch and the return branch).

(5) A Lagrangian function is constituted with the objective function in the above step (3) and the constraints in the above step (4) using a Lagrangian multiplier method, which is represented as follows.L(x_h,ω)=J(x_h)+ω^Tc(x_h)

where J(x_h) represents the objective function in the above step (3), ω represents a Lagrangian multiplier, c(x_h) represents the constraint conditions for the steady state operation of the heating network established in the above step (4), and the superscript T represents matrix transposition.

The Newton-Raphson method in the optimization theory is used to solve the Lagrangian function for the steady state operation of the heating network to obtain a state estimation result for the steady state operation of the heating network.

(6) A convergence judgment is performed on the state estimation result in the above step (5).

If the number of cycles a reaches a preset number of cycles d, that is, a≥d, the current state estimation result is determined as a state estimation result for steady state operation of the heating network based on the bilateral equivalent model at a time point t.

If the number of cycles a does not reach the preset number of cycles d, that is, a<d, the convergence judgement is further performed on the state estimation result according to the accuracy δ of the state estimation for the heating network. If a difference between estimation values x_a and x_a-1 of state variables in two latest state estimation results is smaller than the accuracy δ of the state estimation, that is, max|x_a−x_a-1|<δ, the current state estimation result is determined as the state estimation result for steady state operation of the heating network based on the bilateral equivalent model at the time point t. If the difference between estimation values x_a and x_a-1 of state variables in two latest state estimation results is greater than or equal to the accuracy δ of the state estimation, that is, max|x_a−x_a-1≥δ, the state variables are updated, and the pressure of the node in the heating network and the headend temperature and the tailend temperature of the branch are updated according to the temperature obtained by the current state estimation, a=a+1 is set, and a process of the current state estimation is continued by returning to step (4).

Claims

1. A state estimation method for a heating network in a steady state based on a bilateral equivalent model, comprising: establishing the bilateral equivalent model based on a mass flow rate in each supply branch of the heating network, a mass flow rate in each return branch of the heating network, a mass flow rate in each connecting branch of the heating network, a pressure and a temperature of each node in the heating network, wherein each heat source is configured as a connecting branch and each heat load is configured as a connecting branch;repeatedly performing a state estimation on the heating network based on the bilateral equivalent model, until a coverage state estimation result is acquired, comprising: setting a convergence accuracy δ and a maximum number of cycles d of the state estimation, and initializing a number of cycles a to 0;performing a state estimation calculation on an objective function and constraint conditions by utilizing a Lagrange multiplier method and a Newton-Raphson method to acquire a state estimation result xa,if a≥d, determining the state estimation result xa as the coverage state estimation result for the heating network; andif a<d, determining whether a difference between two state estimation results xa and xa-1 is smaller than the convergence accuracy δ, if max|xa−xa-1|<δ, determining the state estimation result xa as the coverage state estimation result, and if max|xa−xa-1≤δ, updating the pressure and the temperature of each node in the heating network according to estimated values obtained in the state estimation calculation and updating the constraint conditions based on the updated temperature and the updated pressure of each node, setting a=a+1, and performing the state estimation calculation on the objective function and the updated constraint conditions; andmonitoring an operating condition of the heating network based on the coverage state estimation result.

2. The method of claim 1, wherein establishing the bilateral equivalent model based on the mass flow rate in each supply branch of the heating network, the mass flow rate in each return branch of the heating network and the mass flow rate in each connecting branch of the heating network, the pressure and the temperature of each node in the heating network comprises: establishing a node-branch incidence matrix of the heating network, in which the node-branch incidence matrix represents relations between nodes and branches in the heating network;establishing a measurement function describing relations between measurement values and state values of the heating network based on the node-branch incidence matrix of the heating network;establishing the objective function for the heating network based on the measurement function and the measurement values; andestablishing the constraint conditions for the heating network based on the mass flow rate in the supply branch, the mass flow rate in the return branch and the mass flow rate in the connecting branch, the temperature of each node in the heating network.

3. The method of claim 2, wherein establishing a node-branch incidence matrix of the heating network comprises: establishing a node-branch incidence matrix A representing topological relations between the nodes and the branches, in which,

4. The method of claim 2, wherein establishing the measurement function describing relations between the measurement values and the state values of the heating network based on the node-branch incidence matrix of the heating network comprises: acquiring operation data of the heating network at a time point t to constitute a column vector zh of the measurement values, wherein the operation data comprises a pressure H of each node in the heating network, a mass flow rate m of a branch between two nodes in the heating network, and a headend temperature Tƒ and a tailend temperature Tt of the branch, a thermal power ϕq of each connecting branch, in which q represents the connecting branch;constituting a column vector xh of the state values to be estimated for the heating network, wherein the state values to be estimated comprise a to-be-estimated pressure Ĥ of each node in the heating network, a to-be-estimated headend temperature and a to-be-estimated tailend temperature of the branch between two nodes in the heating network, andestablishing the measurement function ƒ(x) based on the column vector zh, the column vector xh and the node-branch incidence matrix, in which ƒ(x)=ƒ(xh), and ƒ(xh) represents a group of equations comprising a branch pressure loss equation and a thermal power equation of the connecting branch.

5. The method of claim 4, wherein the branch pressure loss equation represents a pressure difference between nodes at two ends of a branch, and is represented as: ATH=ΔH−Hp where H represents a column vector composed of pressures of the nodes in the heating network, AT represents a transposed matrix of the node-branch incidence matrix A, and Hp represents a column vector composed of lifts of pumps on the branches, in which Hp=ampp2+bmp+c, where a, b, and c represents pump parameters, mp represents a mass flow rate of the branch where a pump is located, and ΔH represents a column vector composed of pressure losses of the branches in the heating network, in which ΔH is calculated by an equation of: ΔH=K·m·|m|where K represents a friction coefficient of the branch in the heating network, and ranges from 10 to 500 Pa/(kg/s)2, and m represents a mass flow rate of the branch in the heating network.

6. The method of claim 4, wherein the thermal power equation of the connecting branch represents a headend-to-tailend temperature relation of the connecting branch, and is represented as: ϕq=Cpmq(Tƒq−Ttq)where q represents the connecting branch, ϕq represents a heating power of the connecting branch, the value of the heating power at the heat load is positive, the value of the heating power at the heat source is negative, and Cp represents a specific heat capacity of a heating medium, mq represents a mass flow rate of the connecting branch, Tƒq represents a headend temperature of the connecting branch, and Ttq represents a tailend temperature of the connecting branch.

7. The method of claim 4, wherein the objective function is represented as: min J(xh)=min{[zh−ƒ(xh)]TW[zh−ƒ(xh)]}where W represents a covariance matrix of the measurement values, the superscript T represents matrix transposition, and J(xh) represents an expression of the objective function.

8. The method of claim 2, wherein the constraint conditions comprise: a mass flow continuity constraint for the nodes in the heating network, a temperature mixing constraint for the nodes in the heating network, and a branch temperature drop constraint for the supply branches and the return branches in the heating network.

9. The method of claim 8, wherein the mass flow continuity constraint is represented as: AM=0where M represents a column vector composed of mass flow rates of the branches in the heating network, and M is represented by an equation of:

10. The method of claim 8, wherein the temperature mixing constraint is represented as: (Σmout)Tn=Σ(minTin)where mout represents an outgoing mass flow rate of a branch through which heating medium flows out of a node, min represents an incoming mass flow rate of a branch through which the heating medium flows into a node, Tn represents a temperature of the heating medium after being mixed at the node, and Tin represents a temperature of the heating medium from distinct branch before being mixed at the node.

11. The method of claim 8, wherein the branch temperature drop constraint is represented as:

12. The method of claim 10, wherein the temperature Tin of the heating medium from distinct branch before being mixed at the node is replaced by a tailend node temperature Tt of the branch, then the temperature mixing constraint is represented as: diag(AƒM)Tn=At diag(M)Tt where Aƒ and At represent a positive node-branch incidence matrix and a negative node-branch incidence matrix respectively, and diag(⋅) represents a diagonal matrix.

13. The method of claim 1, wherein performing the state estimation calculation on the objective function and the constraint conditions by utilizing the Lagrange multiplier method and the Newton-Raphson method to acquire the state estimation result xa comprises: constituting a Lagrangian function with the objective function and the constraint conditions using the Lagrangian multiplier method, which is represented as: L(xh,ω)=J(xh)+ωTc(xh)where J(xh) represents the objective function, ω represents a Lagrangian multiplier, c(xh) represents the constraint conditions, and T represents matrix transposition; andsolving the Lagrangian function using the Newton-Raphson method to obtain the state estimation result xa.