CN115221693A - Heating system observable state judgment method considering quasi-dynamic pipeline temperature - Google Patents
Heating system observable state judgment method considering quasi-dynamic pipeline temperature Download PDFInfo
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Abstract
The invention discloses a method for judging an observable state of a heat supply system by considering quasi-dynamic pipeline temperature, which comprises the following steps: s1, determining input parameters of an observable state judgment model of a heating system; s2, establishing a heat supply system observable state judgment model according to the input parameters; and S3, solving the established heat supply system observable state judgment model to obtain the observable state of the system. When the quasi-dynamic state of the pipeline temperature is considered, the propagation speed of the temperature depends on the water flow, and the time-lag characteristic exists in the propagation process of the temperature. At the moment, the thermodynamic equation of the heating system and the estimation result of the flow influence each other, which causes that the traditional observable state judgment method is difficult to be applied to the heating system. Aiming at the problem, the invention provides a method for judging the observable state based on multiple time-lag scenes, which can ensure that the acquired observable state is effective under the scenes.
Description
Technical Field
The invention relates to the technical field of observable analysis of a heating system, in particular to a method for judging an observable state of the heating system by considering the quasi-dynamic state of pipeline temperature.
Background
In practical applications, it is necessary to perform state estimation on the heating system to monitor the operation state. Before performing state estimation, the observability of the system needs to be analyzed to obtain input measurements for the state estimation. The observable state decision problem, which is the first problem to be addressed in observability analysis, determines the set of states that the system can observe under the collected measurements. The existing observable state judgment method mainly adopts a numerical method, needs to determine the specific form of a measurement equation, and cannot directly solve the problem of observable state judgment of a heating system. In heating systems, the temperature is carried in pipes by water. Temperature propagation in a pipe has a time-lag characteristic due to the time required for water to flow from the head end of the pipe to the tail end of the pipe. When the quasi-dynamic characteristic of the temperature of the pipeline of the heat supply system is considered, the thermal dynamic equation of the heat supply system is related to a time-lag scene, and the time-lag scene is determined by the estimation result of the water flow, so that the thermal dynamic equation and the estimation result are mutually influenced, the exact form of the thermal dynamic equation cannot be determined when the observable state is judged, and the conventional numerical method cannot be directly applied to the heat supply system.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art and provides a method for judging the observable state of a heating system by considering the quasi-dynamic state of the pipeline temperature. The method solves the problem that the thermodynamic equation of the heating system and the estimation result influence each other, and can provide a reliable observable analysis result for the heating system.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a heat supply system observable state judgment method considering pipeline temperature quasi-dynamic state is disclosed, wherein the heat supply system is composed of a heat source, a heat load, a water supply pipeline and a water return pipeline, and comprises the following steps:
s1, determining input parameters of a heat supply system observable state judgment model, including a collected measurement equation set
State set of heating system
Set of considered time-lapse scenarios
Measuring equation j and correlation coefficient a of system state i under time-lag scene (gamma, phi) ij，(γ，φ) Measurement equation j is
Individual scenarios involving a union of states
Number n of heating system nodes Node Set of considered time periods
Set of time period t heating system flow continuity equations
S2, establishing a target function and a constraint condition of the observable state judgment model of the heating system according to the input parameters, and performing linearization processing on a nonlinear term in the constraint condition;
and S3, solving the processed observable state judgment model of the heat supply system by using a solver to obtain the observable state of the system.
Further, the step S1 includes:
determining a set of collected metrology equations
It is derived from real-time measurement acquired by a measuring instrument and a state equation of a system; the real-time measurement comprises pipeline flow measurement, node temperature measurement, heat source heat supply measurement and heat load heat consumption measurement; the system's equation of state includes flow continuity equation, loop pressure drop equation and pipeline temperature snapAn equation of state;
determining a set of states of a heating system
The temperature of all nodes of the heating system and the flow of all pipelines are contained;
determining a set of considered time-lapse scenarios
The flow estimation method can be obtained by calculating the flow estimation results of pseudo measurement and historical time periods of the pipeline flow;
determining a correlation coefficient a of a measurement equation j and a system state i under a time-lag scene (gamma, phi) ij，(γ，φ) Measurement equation j is
Individual scenarios involving a union of states
By using
Representing a system state set related to a measurement equation j under a time-lag scene (gamma, phi); if the system status i belongs to
The correlation coefficient is assigned a ij，(γ，φ) =1; if the system status i does not belong to
The correlation coefficient is assigned a ij，(γ，φ) ＝0；
Can pass through
And calculating to obtain:
determining the number n of heating system nodes Node Set of considered time periods
Set of flow continuity equations of heat supply system for time period t
They can be obtained by analyzing the system structure.
Further, the step S2 includes the steps of:
s201, establishing an objective function of the heat supply system observable state judgment model according to the input parameters, wherein the number of observable states is maximized:
in the formula, n i Is a variable from 0 to 1, if state i is observable, the variable is 1, otherwise the variable is 0;
s202, establishing a constraint condition of a heat supply system observable state judgment model according to the input parameters, wherein the constraint condition is ensured to be in
In each scene, a group of basic measurement equations consisting of related measurement equations can be found, wherein the related measurement equations refer to
The basic measurement equation refers to a group of independent equations capable of solving the observable state; the established constraints specifically include:
the dependent metrology equations involve observability constraints on states that ensure that the states involved in the dependent metrology equations are
In each sceneAre all observable:
in the formula, w j Is a 0-1 variable, if the measurement equation j is relevant, the variable is 1, otherwise the variable is 0;
the source constraint of the basic measurement equations ensures that all basic measurement equations are related measurement equations:
in the formula, v j，(γ，φ) Is a variable of 0-1, if the measurement equation j is a basic measurement equation under a time-lag scene (gamma, phi), the variable is 1, otherwise the variable is 0;
the independence constraint of the basic metrology equations, which ensures that all basic metrology equations involving multiple states are independent of each other:
the mapping constraint between the observable state and the basic measurement equation ensures that the observable state and the basic measurement equation have a one-to-one mapping relationship, which is a condition that the basic measurement equation can solve the observable state and needs to meet:
in the formula, y ij，(γ，φ) Is a variable of 0 to 1, if the state i and the measurement equation j have a one-to-one correspondence relationship in a time-lag scene (gamma, phi), the variable is 1, otherwise the variable is 0;
s203, carrying out linearization processing on the nonlinear terms in the constraint conditions; in the constraints (2), (6) there are non-linear terms multiplied by a plurality of decision variables, using
Represents the k-th nonlinear term:
in the formula (I), the compound is shown in the specification,
a set of decision variables referred to for the k-th nonlinear term; x is a radical of a fluorine atom l Is the l decision variable;
the linear treatment is carried out on the formula (7) to obtain:
in the formula (I), the compound is shown in the specification,
the number of decision variables involved for the k-th nonlinear term.
Further, the step S3 includes the steps of:
s301, solving the processed observable state judgment model of the heat supply system by using a solver;
s302, acquiring an observable state of the system; the solving result of the heat supply system observable state judgment model contains a variable n i Represents the observability of state i, if n i If =1, it is indicated that state i is observable.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the method provided by the invention considers the quasi-dynamic characteristic of the pipeline temperature in the heating system, provides the observable state judgment method based on the multi-time-lag scene, and ensures that the acquired observable state is effective in the scenes. The method can solve the problem that the thermal dynamic equation and the estimation result in the heat supply system are mutually influenced, and provides a reliable observable state result while considering the dynamic characteristic of the heat supply system.
2. The traditional observable state judgment method needs to clearly determine the specific form of a measurement equation, and can only obtain an observable state result in a time-lag scene each time. Compared with a method for judging observable states one by one for each time lag scene, the method provided by the invention considers observable judgment problems under a plurality of time lag scenes, and has the advantages of less decision variables and constraint conditions for establishing the model, smaller calculation scale and higher solving efficiency.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a classification diagram of measurement equations in the observable state determination problem.
FIG. 3 is a schematic diagram of real-time measurements collected at various time intervals in case one.
FIG. 4 is a schematic diagram of the real-time measurements collected at each time interval in case two.
Fig. 5 is a schematic diagram of real-time measurements collected at each time interval in case three.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
As shown in fig. 1, this embodiment provides a method for determining an observable state of a heat supply system considering quasi-dynamic pipeline temperature, where the heat supply system is composed of a heat source, a heat load, a water supply pipeline, and a water return pipeline, and the method for determining an observable state specifically includes the following steps:
s1, determining input parameters of a heat supply system observable state judgment model, including a collected measurement equation set
State set of heating system
Set of considered time-lapse scenarios
Measuring equation j and correlation coefficient a of system state i under time-lag scene (gamma, phi) ij，(γ，φ) Measurement equation j is
Individual scenarios involving a union of states
Number n of heating system nodes Node Set of considered time periods
Set of flow continuity equations of heat supply system for time period t
The method comprises the following specific steps:
determining a set of collected metrology equations
The system is derived from real-time measurement acquired by a measuring instrument and a state equation of the system; the real-time measurement comprises pipeline flow measurement, node temperature measurement, heat source heat supply measurement and heat load heat consumption measurement; the state equation of the system comprises a flow continuity equation, a loop pressure drop equation and a pipeline temperature quasi-dynamic equation;
determining a set of states of a heating system
The temperature of all nodes of the heating system and the flow of all pipelines are contained;
determining a set of considered time-lapse scenarios
The flow estimation method can be obtained by calculating the flow estimation results of pseudo measurement and historical time periods of the pipeline flow;
determining a correlation coefficient a of a measurement equation j and a system state i under a time-lag scene (gamma, phi) ij，(γ，φ) Measurement equation j is in
Individual scenarios involving a union of states
By using
Representing a system state set related to a measurement equation j under a time-lag scene (gamma, phi); if the system status i belongs to
The correlation coefficient is assigned a ij，(γ，φ) =1; if the system status i does not belong to
The correlation coefficient is assigned a ij，(γ，φ) ＝0；
Can pass through
And calculating to obtain:
determining the number n of heating system nodes Node Set of considered time periods
Set of flow continuity equations of heat supply system for time period t
They can be obtained by analyzing the system structure.
S2, establishing a target function and a constraint condition of the observable state judgment model of the heating system according to the input parameters, and carrying out linearization treatment on a nonlinear term in the constraint condition, wherein the concrete steps are as follows:
s201, establishing an objective function of the heat supply system observable state judgment model, wherein the number of observable states is maximized:
in the formula, n i Is a variable from 0 to 1, if state i is observable, the variable is 1, otherwise the variable is 0;
s202, establishing constraint conditions of an observable state judgment model of the heating system, wherein the constraint conditions are ensured to be in
In each scene, a group of basic measurement equations consisting of related measurement equations can be found, wherein the related measurement equations refer to
The basic measurement equation refers to a set of independent equations (as shown in fig. 2) capable of solving the observable state; the constraints established specifically include:
the dependent metrology equation involves an observability constraint of the state that ensures that the state involved in the dependent metrology equation is at
Observable in each scene:
in the formula, w j Is a variable of 0-1, if the measurement equation j is relevant, the variable is 1, otherwise the variable is 0;
the source constraints of the basic measurement equations ensure that all the basic measurement equations are related measurement equations:
in the formula, v j，(γ，φ) The variable is 0-1, if the measurement equation j is a basic measurement equation under a time-lag scene (gamma, phi), the variable is 1, otherwise, the variable is 0;
the independence constraint of the basic metrology equations, which ensures that all basic metrology equations involving multiple states are independent of each other:
the mapping constraint between the observable state and the basic measurement equation ensures that the observable state and the basic measurement equation have a one-to-one mapping relationship, which is a condition that the basic measurement equation can solve the observable state and needs to satisfy:
in the formula, y ij，(γ，φ) Is a variable of 0 to 1, if the state i and the measurement equation j have a one-to-one correspondence relationship in a time-lag scene (gamma, phi), the variable is 1, otherwise the variable is 0;
s203, carrying out linearization processing on the nonlinear terms in the constraint conditions; in the constraints (2), (6) there are non-linear terms multiplied by a plurality of decision variables, using
Represents the k-th nonlinear term:
in the formula (I), the compound is shown in the specification,
a set of decision variables referred to for the k-th nonlinear term; x is a radical of a fluorine atom l Is the l decision variable;
the linearization processing of the formula (7) can obtain:
wherein the content of the first and second substances,
the number of decision variables involved for the k-th nonlinear term.
S3, solving the processed heat supply system observable state judgment model by using a solver to obtain the observable state of the system, wherein the method comprises the following specific steps:
s301, solving an observable state judgment model of the heating system by using a solver;
s302, acquiring an observable state of the system; the solving result of the heat supply system observable state judgment model contains a variable n i Represents the observability of state i, if n i =1, state i is observable.
For a better understanding of the effectiveness of the invention and the advantages thereof over the prior art, reference should be made to the following examples which are set forth to illustrate, but are not to be construed as limiting the scope of the invention.
And setting the performance of the observable state judgment model of the heat supply system by using different cases. All observable state judgment models are solved by a Gurobi solver.
1. Validity of observable state judgment result
The validity of the invention is verified by the observable state judgment result of case one. In case of a 4-node heating system, taking into account 3 time intervals, the real-time measurements collected by the system at each time interval are shown in fig. 3. In case one, the time lag coefficients of all pipelines are the same, and the time lag coefficient set is considered
Are { (0, 1), (1, 1), (0, 2), (1, 2), (2, 2) }. The inventors compared the present invention with
The results of the unobservable states in each scene illustrate the effectiveness of the invention. The detailed comparison results are shown in Table 1, where the last action is the result of the invention, T 3，t-2 Representing the temperature state of node 3, T, over time period T-2 3，t-1 Representing the temperature state of node 3 for time period t-1 and 'x' representing a non-observable state.
TABLE 1 results of unobservable states under different time-lag scenarios
| Time-lag scene (gamma, phi) | T 3，t-2 | T 3，t-1 |
| (0，1) | x | |
| (1，1) | x | |
| (0，2) | x | x |
| (1，2) | x | x |
| (2，2) | x | |
| Consider all of the above scenarios (invention) | x | x |
As can be seen from Table 1, the unobservable state determined by the present invention is
The union of the unobservable states in each scene. It follows that the observable state found by the present invention is
The intersection of the observable states in each scene. Thus, the observable state found by the present invention is
Each scene is observable. In addition, for an unobservable state, which is obtained by the present invention, it is always possible to
To find a scene in such a way that the state is not observable. Therefore, the number of unobservable states found by the present invention is the smallest and the number of observable states found is the largest. These results demonstrate the effectiveness of the present invention.
2. Comparison with existing methods
The performance of the present invention is illustrated by the results of the observable state determinations in case two and case three. Case two and case three are 12-node heating systems. In case two, the number of time segments considered is 3, and the real-time measurements collected for each time segment are shown in fig. 4. By using
Representing the set of time lag coefficients considered by pipe b during time period t. Case two assumes that the symmetrical water supply pipeline and the water return pipeline have the same time lag coefficient, so the considered time lag coefficient set
Time lag coefficient of 5 groups related to time period t and 5 water supply pipelines
The Cartesian product of (A), which are all taken as { (1, 1), (1, 2), (2, 2) }.
A total of 243 time-lapse scenarios are included. In case three, the number of considered time periods is 6. The heating system is complete in measurement configuration from time t-5 to time t-3, and the system state can be observed; the real-time measurements collected by the system from time t-2 to time t are shown in FIG. 5. Case three assumes that the time lag coefficients of the symmetrical water supply pipeline and the water return pipeline are the same, so the considered time lag coefficient set
Time lag coefficients of 15 groups of water supply pipelines related to time period t-2 to time period t and 5 water supply pipelines
The cartesian products of (a) and their arrangement are shown in table 2.
A total of 216 time-lag scenarios are included.
Table 2 three time lag coefficient sets considered by water supply pipeline
The existing observable state judgment method needs to clearly determine the specific form of a measurement equation, so that an observable state result under a time-lag scene can be obtained each time. Under the solution strategy based on a multi-time-lag scene, the existing method can only analyze one by one
The observable state under each scene judges the problem and will
And taking the intersection of the observable states obtained in each scene as a final result. The inventors illustrate the advantages of the present invention by comparing the results of the present invention with the prior methods in case two and case three. Specific comparison results are shown in Table 3, T 8，t-2 Representing the temperature state of node 8, T, over time period T-2 9，t-2 Indicating the temperature state of node 9, T, over time period T-2 8，t-1 Representing the temperature state of node 8, T, over time period T-1 9，t-1 Indicating the temperature state of node 9, T, over time period T-1 8，t Indicating the temperature state of node 8 for time period t.
TABLE 3 comparison of results of different solving methods
As can be seen from Table 3, the method can obtain the same observable state judgment result as the existing method, and has shorter solving time. The existing method only can analyze the observable state judgment problem under different time-delay scenes one by one, but the method considers the observable state judgment problem under a plurality of time-delay scenes simultaneously, has fewer decision variables and constraint conditions for establishing the model, and has smaller scale for establishing the model, so the method has higher calculation efficiency than the existing method.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (4)
1. A heat supply system observable state judgment method considering pipeline temperature quasi-dynamic state is characterized by comprising a heat source, a heat load, a water supply pipeline and a water return pipeline, and comprises the following steps:
s1, determining input parameters of a heat supply system observable state judgment model, including a collected measurement equation set
State set of heating system
Set of considered time-lapse scenarios
Measuring equation j and correlation coefficient a of system state i under time-lag scene (gamma, phi) ij,(γ,φ) Measurement equation j is in
Each scenario involves a union of states
Number n of heating system nodes Node Set of considered time periods
Set of flow continuity equations of heat supply system for time period t
S2, establishing a target function and a constraint condition of the observable state judgment model of the heating system according to the input parameters, and performing linearization processing on a nonlinear term in the constraint condition;
and S3, solving the processed heat supply system observable state judgment model by using a solver to obtain the observable state of the system.
2. A method for determining an observable state of a heating system considering quasi-dynamic state of pipe temperature according to claim 1, wherein the step S1 includes:
determining a set of collected metrology equations
It is derived from real-time measurement acquired by a measuring instrument and a state equation of a system; the real-time measurement comprises pipeline flow measurement, node temperature measurement, heat source heat supply measurement and heat load heat consumption measurement; the state equation of the system comprises a flow continuity equation, a loop pressure drop equation and a pipeline temperature quasi-dynamic equation;
determining a set of states of a heating system
The temperature of all nodes of the heating system and the flow of all pipelines are contained;
determination testSet of filtered time-lag scenarios
The flow estimation method can be obtained by calculating the flow estimation results of pseudo measurement and historical time periods of the pipeline flow;
determining a correlation coefficient a of a measurement equation j and a system state i under a time-lag scene (gamma, phi) ij,(γ,φ) Measurement equation j is
Each scenario involves a union of states
By using
Representing a system state set related to a measurement equation j under a time-lag scene (gamma, phi); if the system status i belongs to
The correlation coefficient is assigned a ij,(γ,φ) =1; if the system status i does not belong to
The correlation coefficient is assigned a ij,(γ,φ) ＝0；
Can pass through
And calculating to obtain:
determining the number n of heating system nodes Node Set of considered time periods
Set of time period t heating system flow continuity equations
They can be obtained by analyzing the system structure.
3. A method for determining observable states of a heating system in consideration of quasi-dynamic pipeline temperature according to claim 1, wherein the step S2 comprises the steps of:
s201, establishing an objective function of the heat supply system observable state judgment model according to the input parameters, wherein the number of observable states is maximized:
in the formula, n i Is a variable from 0 to 1, if state i is observable, the variable is 1, otherwise the variable is 0;
s202, establishing a constraint condition of a heat supply system observable state judgment model according to the input parameters, wherein the constraint condition is ensured to be in
In each scene, a group of basic measurement equations consisting of related measurement equations can be found, wherein the related measurement equations refer to
The basic measurement equation refers to a group of independent equations capable of solving the observable state; the established constraints specifically include:
the dependent metrology equation involves an observability constraint of the state that ensures that the state involved in the dependent metrology equation is at
Observable in each scene:
in the formula, w j Is a variable of 0-1, if the measurement equation j is relevant, the variable is 1, otherwise the variable is 0;
the source constraints of the basic measurement equations ensure that all the basic measurement equations are related measurement equations:
in the formula, v j,(γ,φ) Is a variable of 0-1, if the measurement equation j is a basic measurement equation under a time-lag scene (gamma, phi), the variable is 1, otherwise the variable is 0;
the independence constraint of the basic metrology equations, which ensures that all basic metrology equations involving multiple states are independent of each other:
the mapping constraint between the observable state and the basic measurement equation ensures that the observable state and the basic measurement equation have a one-to-one mapping relationship, which is a condition that the basic measurement equation can solve the observable state and needs to meet:
in the formula, y ij,(γ,φ) Is a 0-1 variable, if state i is in a time-lag scenario (γ, φ)If the measurement equation j has a one-to-one correspondence relationship, the variable is 1, otherwise the variable is 0;
s203, carrying out linearization processing on the nonlinear terms in the constraint conditions; in the constraints (2), (6) there are non-linear terms multiplied by a plurality of decision variables, using
Represents the k-th nonlinear term:
in the formula (I), the compound is shown in the specification,
a set of decision variables referred to for the k-th nonlinear term; x is a radical of a fluorine atom l Is the l decision variable;
the linear treatment is carried out on the formula (7) to obtain:
in the formula (I), the compound is shown in the specification,
the number of decision variables involved for the k-th nonlinear term.
4. A method for determining observable states of a heating system in consideration of quasi-dynamic pipeline temperature according to claim 1, wherein the step S3 comprises the steps of:
s301, solving the processed observable state judgment model of the heat supply system by using a solver;
s302, obtainingTaking an observable state of the system; the solving result of the heat supply system observable state judgment model comprises a variable n i Represents the observability of state i if n i =1, state i is observable.
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