CN110765577A - Radiation type heat supply network statistical characteristic obtaining method based on probability energy flow - Google Patents

Radiation type heat supply network statistical characteristic obtaining method based on probability energy flow Download PDF

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CN110765577A
CN110765577A CN201910891018.8A CN201910891018A CN110765577A CN 110765577 A CN110765577 A CN 110765577A CN 201910891018 A CN201910891018 A CN 201910891018A CN 110765577 A CN110765577 A CN 110765577A
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孙国强
王文学
卫志农
臧海祥
陈�胜
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Hohai University HHU
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Abstract

The invention discloses a method for acquiring statistical characteristics of a radiant heat supply network based on probability energy flow, which comprises the following steps: (1) acquiring parameter information of a radiation type heat supply network model, and establishing a heat supply network system model according to the parameter information; (2) setting the heat load in a heat supply network system model to obey independent normal distribution, obtaining the mean value and the variance of the flow of the pipeline adjacent to a heat source according to the heat supply network system model, obtaining the relation met by the mean value and the variance of the flow of the adjacent pipeline according to the heat supply network system model, and further obtaining the mean value and the variance of the flow of each pipeline; (3) the relation between the node temperature and the reciprocal of the pipeline flow is obtained through a heat supply network system model, and the correlation coefficient among the pipeline flows is obtained by combining a continuous random variable probability density function theory, so that the mean value and the variance of the node temperature are obtained. The method has the advantages of simple model and high calculation speed.

Description

Radiation type heat supply network statistical characteristic obtaining method based on probability energy flow
Technical Field
The invention relates to the calculation of the power flow of a heat supply network, in particular to a method for acquiring statistical characteristics of a radiation type heat supply network based on probability energy flow.
Background
With the global energy and environmental issues becoming more prominent, how to utilize energy cleanly and efficiently has become a hot point of research. The comprehensive energy system integrates various energy forms such as cold, heat, electricity, gas and the like, is the development direction of a modern energy supply system, and can realize comprehensive utilization and management of energy. With the increasing use of cogeneration, gas turbines and other energy conversion facilities, the degree of interdependence between different energy systems is increased.
The steady-state modeling and analysis of the comprehensive energy system are the basis of planning and operation, and the established comprehensive energy steady-state model is essentially deterministic analysis and cannot solve the problem of uncertainty in the comprehensive energy.
The comprehensive energy system comprises a large number of uncertain factors such as fluctuation of cold, heat, electricity and gas loads, intermittent energy output fluctuation, generator fault, line (pipeline) fault, market uncertainty and the like, different energy networks have mutual influence, and the operation characteristics of the comprehensive energy system in an uncertain environment are difficult to master only through a single energy network deterministic analysis method. The influence of the uncertain factors on the power network and the analysis method have been researched more, and in contrast, the research on the influence analysis of the uncertain factors on the comprehensive energy system is just started.
In the electric power system, the statistical characteristics of the output random variables can be obtained through probability load flow calculation according to the statistical characteristics of the input random variables, so that a foundation is laid for quantitative analysis and evaluation of the influence of uncertain factors on the electric power system. At present, probability trend is widely researched in an electric power system, but for probability trend analysis of a thermodynamic system, related research reports at home and abroad are few.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a method for acquiring statistical characteristics of a radiant heat supply network based on probability energy flow.
The technical scheme is as follows: the invention discloses a method for acquiring statistical characteristics of a radiant heat supply network based on probability energy flow, which comprises the following steps:
(1) acquiring parameter information of a radiation type heat supply network model, and establishing a heat supply network system model according to the parameter information;
(2) setting the heat load in a heat supply network system model to obey independent normal distribution, obtaining the mean value and the variance of the flow of the pipeline adjacent to a heat source according to the heat supply network system model, obtaining the relation met by the mean value and the variance of the flow of the adjacent pipeline according to the heat supply network system model, and further obtaining the mean value and the variance of the flow of each pipeline;
(3) the relation between the node temperature and the reciprocal of the pipeline flow is obtained through a heat supply network system model, and the correlation coefficient among the pipeline flows is obtained by combining a continuous random variable probability density function theory, so that the mean value and the variance of the node temperature are obtained.
Further, the parameter information of the radiant heat supply network model obtained in the step (1) comprises water supply temperature of each pipeline, heat source, return water temperature of heat load, heat load and fluctuation range thereof. The established heat supply network system model specifically comprises the following steps:
Am＝mq
Bhf＝0
hf＝Km|m|
Figure BDA0002208755230000021
Figure BDA0002208755230000023
Figure BDA0002208755230000024
Figure BDA0002208755230000025
Figure BDA0002208755230000027
in the formula: a is a heat supply network node-pipeline incidence matrix, m is heat supply network pipeline flow, m isqFor node incoming load traffic, B is the loop correlation matrix, hfFor the pipeline pressure drop caused by friction loss, K is the resistance coefficient of the pipeline, L is the length of the pipeline, D is the diameter of the pipeline, ρ is the water density, g is the acceleration of gravity, f is the friction coefficient, ε is the roughness of the pipeline, Re is the Reynolds number, and μ is the kinematic viscosity of the pipeline water;
Figure BDA0002208755230000028
for thermal load, TsThe temperature of water supplied To the node, To is the temperature of return water To the node, TstartFor the head end temperature of the pipeline, TendIs the temperature at the end of the pipe, TaIs the external ambient temperature, lambda is the heat transfer coefficient, CpIs the specific heat capacity of water, minFor pipe flow into the node, moutFor pipe flow out of the node, TinFor the temperature at the end of the input pipe, ToutIs the node mixing temperature;
Figure BDA0002208755230000029
and
Figure BDA00022087552300000210
respectively thermal load
Figure BDA00022087552300000211
Expectation and standard deviation.
Further, the step (2) specifically comprises:
(2.1) setting the heat load in the heat supply network system model to obey independent normal distribution, and obtaining the average value and the variance of the flow of the pipelines adjacent to the heat source as follows:
Figure BDA0002208755230000031
Figure BDA0002208755230000032
in the formula, m*Indicating the flow of the pipe adjacent to the heat source,represents m*The average value of the average value is calculated,
Figure BDA0002208755230000033
represents m*The variance of the measured values is calculated,
Figure BDA0002208755230000034
in order to be the thermal load of the node i,
Figure BDA0002208755230000035
representing the heat loss, σ, of the pipe adjacent to node i2Is composed of
Figure BDA0002208755230000036
Variance of (1), THIs the CHP heat source temperature, ToReturning the temperature for the load node;
(2.2) obtaining a relation satisfied by the mean value and the variance of the flow of the adjacent pipelines according to the heat supply network system model, wherein the relation is as follows:
Figure BDA0002208755230000037
Figure BDA0002208755230000038
in the formula (I), the compound is shown in the specification,
Figure BDA0002208755230000039
representing the flow variance of the first, second and nth tubes, respectively, branched off from the tube, n representing the number of tubes branched off from the tube,
Figure BDA00022087552300000310
respectively representing the average flow of the first, second and nth pipes branched from the pipe;
(2.3) obtaining the flow variance of all adjacent pipelines according to the relation satisfied by the mean value and the variance of the flow of the adjacent pipelines as follows:
Figure BDA00022087552300000312
……
Figure BDA00022087552300000313
in the formula (I), the compound is shown in the specification,
Figure BDA00022087552300000314
respectively representing the sum of all thermal loads flowing through the conduits 1,2, n,
Figure BDA00022087552300000315
respectively represent
Figure BDA00022087552300000316
The variance of (a);
the average value of the pipeline flow is the solution when the heat loads are averaged;
and (2.4) obtaining the flow mean value and the flow variance of each other pipeline according to the steps (2.2) and (2.3).
Further, the step (3) specifically comprises:
(3.1) obtaining the relation between the node temperature and the inverse of the pipeline flow through a heat supply network system model as follows:
Figure BDA0002208755230000042
……
Figure BDA0002208755230000043
THthe heat source temperature is adopted, the flow is sent out by a heat source H, and the number of a pipeline through which the flow flows between the heat source H and a node to be solved is x1、x2…xNThe temperature of the node flowing through is
Figure BDA0002208755230000047
N is the number of pipelines through which the flow between the heat source H and the node to be solved flows,
Figure BDA0002208755230000048
respectively representing a pipe x1、x2…xNOf flow rate of1、λ2...λNRespectively representing a pipe x1、x2…xNHeat transfer coefficient of (L)1、L2...LNRespectively representing a pipe x1、x2…xNThe length of the conduit of (a);
(3.2) calculating a correlation coefficient between any pipeline flow according to the pipeline flow variance by adopting the following formula:
Figure BDA0002208755230000044
wherein i, j, k represent any of various pipes, shaped as m#Representing the pipe # flow, in the form of p#·Represents m#And m·Is in the form of
Figure BDA0002208755230000045
Represents the flow rate m#Variance;
(3.3) establishing a covariance matrix xi of the node temperature normal distribution according to the calculated correlation coefficients:
Figure BDA0002208755230000046
(3.4) converting the relation in the step (3.1) into a matrix form as follows:
Figure BDA00022087552300000511
Figure BDA00022087552300000512
……
Figure BDA00022087552300000513
Figure BDA0002208755230000051
in the formula (I), the compound is shown in the specification,
Figure BDA00022087552300000514
respectively representing the corresponding coefficient vectors, of size 1 × N, whose elements respectively include 1,2, …, N1, and the remaining elements are 0,
(3.5) obtaining the flow rate according to the step (2)
Figure BDA00022087552300000515
Mean and variance of (1) to obtain
Figure BDA0002208755230000052
To obtain X, and thenmIn
Figure BDA0002208755230000053
Mean value of
Figure BDA00022087552300000516
Sum variance
Figure BDA0002208755230000054
(3.6) obtaining X according to step (3.5)mObeying an N-dimensional normal distribution N (μ, xi),
Figure BDA0002208755230000055
obtaining the node temperature
Figure BDA00022087552300000517
Obey normal distributions of
Figure BDA0002208755230000056
Figure BDA0002208755230000057
Namely the node
Figure BDA0002208755230000058
Respectively mean value of
Figure BDA0002208755230000059
Variance is respectively
Figure BDA00022087552300000510
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention establishes a radiation type heat supply network probability energy flow model based on the heat transfer theory and the pipe network basic theory, and has the advantages of simple model, small calculated amount, pure algebraic operation, high calculation speed and high solving precision. The probabilistic energy flow model provided by the invention can more comprehensively disclose the operating characteristics of the comprehensive energy system, so that information with higher reference value is provided for planning, optimizing operation, static safety analysis, risk assessment and the like of the comprehensive energy system.
Drawings
FIG. 1 is a schematic representation of a pipeline flow correlation coefficient;
fig. 2 is a 23-node radiant heat network system diagram.
Detailed Description
The embodiment provides a nonlinear analysis method for a radiant heat network probability energy flow, which comprises the following steps:
(1) acquiring radiation type heat supply network model parameter information, specifically comprising each pipeline parameter of the heat supply network, heat source water supply temperature, heat load return water temperature, heat load and fluctuation range thereof, and establishing a heat supply network system model according to the information, specifically comprising the following steps:
Am＝mq(1)
Bhf＝0 (2)
hf＝Km|m| (3)
Figure BDA0002208755230000061
Figure BDA0002208755230000062
Figure BDA0002208755230000063
Figure BDA0002208755230000064
Figure BDA0002208755230000065
Figure BDA0002208755230000067
in the formula: a is a heat supply network node-pipeline incidence matrix, m is heat supply network pipeline flow, m isqFor node incoming load traffic, B is the loop correlation matrix, hfFor the pipeline pressure drop caused by friction loss, K is the resistance coefficient of the pipeline, L is the length of the pipeline, D is the diameter of the pipeline, ρ is the water density, g is the acceleration of gravity, f is the friction coefficient, ε is the roughness of the pipeline, Re is the Reynolds number, and μ is the kinematic viscosity of the pipeline water;for thermal load, TsSupply water temperature to the node, ToIs the node return water temperature, TstartFor the head end temperature of the pipeline, TendIs the temperature at the end of the pipe, TaIs the external ambient temperature, lambda is the heat transfer coefficient, CpIs the specific heat capacity of water, minFor pipe flow into the node, moutFor pipe flow out of the node, TinFor the temperature at the end of the input pipe, ToutIs the node mixing temperature;and
Figure BDA00022087552300000610
respectively thermal load
Figure BDA00022087552300000611
Expectation and standard deviation.
The formulas (1) to (6) are heat supply network hydraulic models, the formula (1) is a node flow balance equation, the formula (2) is a loop pressure equation, the formula (3) is a head loss equation, and the joint type formulas (4) to (6) can obtain a pipeline resistance coefficient K. Equations (7) - (9) are thermal power network thermodynamic models, equation (7) is a thermal load power equation, equation (8) is a pipeline temperature drop equation, and equation (9) is a node power conservation equation. The heat load probability model is described by equation (10).
(2) Setting the heat load in the heat supply network system model to obey independent normal distribution, obtaining the mean value and the variance of the flow of the pipeline adjacent to the heat source according to the heat supply network system model, obtaining the relation met by the mean value and the variance of the flow of the adjacent pipeline according to the heat supply network system model, and further obtaining the mean value and the variance of the flow of each pipeline. The method specifically comprises the following steps.
(2.1) deducing the heat loss of the pipeline according to the heat supply network model
Figure BDA0002208755230000071
The formula of (1) is:
Figure BDA0002208755230000072
writing a thermal power balance equation for the heat source node H column comprises:
Figure BDA0002208755230000073
in the formula (I), the compound is shown in the specification,
Figure BDA0002208755230000074
in order to be the thermal load of the node i,
Figure BDA0002208755230000075
is the mean value of the flow of the pipes adjacent to the heat source node, THIs the CHP heat source temperature, ToReturning the temperature for the load node.
The average flow of the adjacent pipes to the heat source node can be obtained according to the formula (12) as follows:
Figure BDA0002208755230000076
introduction 1: if X is to N (mu, sigma)2) And a and b are real numbers, then aX + b N (a μ, (b σ)2)；
2, leading: if it is not
Figure BDA0002208755230000077
And
Figure BDA0002208755230000078
are statistically independent normal distribution random variables, then their sum also satisfies the normal distribution
Figure BDA0002208755230000079
In the formula (11), T is smaller in the value of λ L than in the value of thermal loadsCan be approximated as the CHP source temperature THThen, then
Figure BDA00022087552300000710
Is a fixed value, thereforeThe variance of (a) is 0.
Uniform clothes assuming thermal loadFrom the independent normal distribution, as can be seen from lemma 2,
Figure BDA00022087552300000712
also obeying normal distribution, and setting the standard deviation as sigma, and obtaining the pipe flow m from theorem 1*Standard deviation of (a)m*Comprises the following steps:
and 3, introduction: is provided with
Figure BDA00022087552300000714
Wherein rho is a correlation coefficient of random variables X and Y, and a non-zero linear combination aX + bY of X and Y still obeys normal distribution:
and (4) introduction: two-dimensional random variables, independent and uncorrelated, are equivalent.
(2.2) setting the flow m in FIG. 1iAnd mjCorrelation coefficient is rhoijDue to the flow rate miAnd mjFlow out of the same node, flow miAnd mjDepends mainly on the heat energy flowing through the pipes i and j, so miAnd mjThe correlation coefficient of (2) is small and can be approximated to 0. By theory of 4, miAnd mjCan be considered approximately independent of each other. In fig. 1, the flow balance equation for node k column has:
mk＝mi+mj(15)
from equation (15) and theorem 3, it can be seen that:
Figure BDA0002208755230000081
due to rhoij0, then equation (16) can be simplified as:
let the variance of the sum of all thermal loads flowing through pipe i in FIG. 2 beThe variance of the sum of all thermal loads flowing through pipe j is
Figure BDA0002208755230000084
Then there is
Figure BDA0002208755230000085
Similarly, the mean and variance of the flow of adjacent pipes satisfy the following relationship:
Figure BDA0002208755230000088
in the formula (I), the compound is shown in the specification,
Figure BDA0002208755230000089
representing the flow variance of the first, second and nth tubes, respectively, branched off from the tube, n representing the number of tubes branched off from the tube,
Figure BDA00022087552300000810
mean values of the flow rates of the first, second and nth tubes branched from the tube are shown, respectively.
(2.3) obtaining the flow variance of all adjacent pipelines according to the relation satisfied by the expressions (18) and (19) and the mean and variance of the flow of the adjacent pipelines as follows:
Figure BDA0002208755230000091
……
Figure BDA0002208755230000093
the pipeline flow mean is the solution when the thermal loads are all averaged.
(3) The relation between the node temperature and the reciprocal of the pipeline flow is obtained through a heat supply network system model, and the correlation coefficient among the pipeline flows is obtained by combining a continuous random variable probability density function theory, so that the mean value and the variance of the node temperature are obtained.
The step specifically includes the following steps.
(3.1) if
Figure BDA0002208755230000094
Represents the thermal power loss of the pipeline i, and the pipeline i is provided with:
Figure BDA0002208755230000096
the united type (23) to (24) can be obtained:
Figure BDA0002208755230000097
if the temperature of the node i to be solved is TiThe flow being generated by a heat source H, THThe number of the pipeline through which the flow flows from the heat source H to the node to be solved is x1、x2…xNThe temperature of the node flowing through is
Figure BDA0002208755230000099
N is the flow between the heat source H and the node to be solvedThe number of the pipelines is equal to that of the pipelines,
Figure BDA00022087552300000910
respectively representing a pipe x1、x2…xNOf flow rate of1、λ2...λNRespectively representing a pipe x1、x2…xNHeat transfer coefficient of (L)1、L2...LNRespectively representing a pipe x1、x2…xNThe length of the pipeline of (a) is then:
Figure BDA0002208755230000098
Figure BDA0002208755230000101
……
Figure BDA0002208755230000102
the joint type (26) to (28) parallel item arrangement can obtain:
Figure BDA0002208755230000103
and (5) introduction: let the continuous random variable X have a probability density function fX(x) Y ═ g (x) and monotonous conductance, and the inverse function is x ═ g ∞-1(Y) Y ═ g (x) is a continuous random variable whose probability density function is
Figure BDA0002208755230000104
Let normal distribution random variable x ═ miMean and variance are respectively μiAnd σiThe probability density function is:
Figure BDA0002208755230000105
from a leadingIn theory 5, y is 1/x is 1/miThe probability density function of (a) is:
Figure BDA0002208755230000106
the formula (31) is modified as follows:
Figure BDA0002208755230000107
taking 1/u as the mean value of y in the above formula in the form of normal distribution probability density functioniTaking the standard deviation (sigma)iy)/uiWherein y is 1/uiThen the standard deviation is
Figure BDA0002208755230000111
Then it can be obtained:
Figure BDA0002208755230000112
therefore, if the normal distribution is adopted, the random variable x is miRespectively, mean and variance ofiAnd σiAnd y is 1/x is 1/miApproximately obey normal distribution, and the mean and variance are 1/uiAnd
Figure BDA0002208755230000113
(3.2) setting the flow rate mkAnd miCorrelation coefficient is rhokiFlow rate mkAnd mjHas a correlation coefficient of rhokjThe derivation can be:
ρki 2+ρkj 2≈1 (34)
Figure BDA0002208755230000114
and (6) introduction: the pipeline A is adjacent to the pipeline B, and the flow rates of the pipelines are m respectivelyAAnd mBAnd m isAAnd mBHas a correlation coefficient of rhoABThe pipeline B is adjacent to the pipeline CFlow rates are respectively mBAnd mCAnd m isBAnd mCHas a correlation coefficient of rhoBCAnd there is only a unique path from pipe A to pipe C, then mAAnd mCHas a correlation coefficient of rhoAC＝ρAB·ρBC；
(3.3) if the temperature of the node i to be solved is TiThe flow being generated by a heat source H, THThe number of the pipeline through which the flow flows from the heat source H to the node to be solved is x1、x2…xNThe temperature of the node flowing through isN is the number of pipelines through which the flow between the heat source H and the node to be solved flows,
Figure BDA0002208755230000117
respectively representing a pipe x1、x2…xNThe flow rate of (1) can be numbered x by the following equations (34) to (35) and theorem 61、x2…xNThe correlation coefficient of the flow of any two pipelines. Let x1And x2Has a correlation coefficient of rho12Then there is ρ12＝ρ21And the other is the same, and its covariance matrix xi may be determined:
Figure BDA0002208755230000115
when the temperature of a node does not change greatly due to load fluctuation, the temperature T in the formula (29)H、
Figure BDA0002208755230000118
Taking the mean value, where the error is generally 10-4And the error is small and can be approximately ignored.
(3.4) converting equation (29) into a matrix form:
Figure BDA00022087552300001216
……
Figure BDA00022087552300001218
in the formula (I), the compound is shown in the specification,
Figure BDA0002208755230000122
respectively representing corresponding coefficient vectors with the size of 1 multiplied by N, wherein the elements respectively comprise 1,2, …, N1, and the rest elements are 0; for example,
Figure BDA0002208755230000123
(3.5) obtaining the flow rate according to the step (2)
Figure BDA00022087552300001215
Mean and variance of (1) to obtain
Figure BDA0002208755230000124
To obtain X, and thenmIn
Figure BDA0002208755230000125
Mean value of
Figure BDA0002208755230000126
Sum variance
The concrete solving method comprises the following steps: flow rate of pipeline
Figure BDA0002208755230000128
Following normal distribution, the variance of the pipe flow is obtained from equations (20) to (22), and is shown in equation (33)
Figure BDA0002208755230000129
Approximately follows normal distribution, and the denominator C in the expressions (26) to (28) is small in node temperature fluctuationpWhen 4182 is larger, then
Figure BDA00022087552300001210
Figure BDA00022087552300001211
The error is smaller when all the steady-state values are obtained, known from theory 1
Figure BDA00022087552300001212
Subject to a normal distribution, given their mathematical expectations respectively
Figure BDA00022087552300001213
The standard deviation sigma is respectively
Figure BDA00022087552300001214
And (3) introduction 7: if X is ═ X1,X2…Xn) Obeying an N-dimensional normal distribution N (μ, B), and C is an arbitrary m x N matrix, then Y ═ CX obeys an m-dimensional normal distribution N (C μ, CBC)T) Where μ and B are the mathematical expectation and covariance matrix, respectively, of the random variable X.
(3.6) obtaining X according to step (3.5)mObeying an N-dimensional normal distribution N (μ, xi),
Figure BDA0002208755230000131
obtaining the node temperature
Figure BDA0002208755230000132
Obey normal distributions of
Figure BDA0002208755230000133
Figure BDA0002208755230000134
Namely the node
Figure BDA0002208755230000135
Respectively mean value of
Figure BDA0002208755230000136
Variance is respectively
Figure BDA0002208755230000137
Is provided with
Figure BDA0002208755230000138
According to XmObeying the N-dimensional normal distribution N (μ, xi) and the theorem 7, the expression (37) is obtained
Figure BDA0002208755230000139
Respectively obey normal distribution
Figure BDA00022087552300001310
Figure BDA00022087552300001311
Obtaining the node temperature according to the theory 1
Figure BDA00022087552300001313
Obey normal distributions of
Figure BDA00022087552300001314
Figure BDA00022087552300001315
For example, if f is m + n, then by theorem 7, C is [1,1 ═ n]，
Figure BDA00022087552300001316
Wherein m and n are both subject to normal distribution, and mu is mathematically expected to be mu respectivelymAnd munThe standard deviation sigma is respectively sigmamAnd σnAnd the correlation coefficient of m and n is rhomnCorrelation coefficient of n with mIs rhonmAnd has ρmn＝ρnmThen the covariance matrix B is:
Figure BDA00022087552300001317
then
Figure BDA00022087552300001318
Figure BDA00022087552300001319
So f follows a normal distribution
The present embodiment is subjected to simulation verification as follows.
A23-node radiation type heat supply network system is selected, as shown in figure 2, wherein the temperature of the CHP source is constant at 100 ℃, the temperature of the load node return water is constant at 30 ℃, and the ambient temperature T is constantaIs 10 ℃.
Scenario in analysis 3: wherein, the Monte Carlo method (simulating 50000 times) and the flow mean value, the flow standard deviation, the temperature mean value and the temperature standard deviation obtained by the method are respectively measured by mum,mcs，σm,mcs，μT,mcs，σT,mcsAnd mum，σm，μT，σTAnd (4) showing. The error percentages of the flow mean, the flow standard deviation, the temperature mean and the temperature standard deviation are respectively deltaμ,m，δσ,m，δμ,TAnd deltaσ,TAnd (4) showing.
Scene 1: (1) if each pipe length is set to 300 meters, all thermal loads are set to 0.5MW and all thermal load fluctuations are within ± 10%. Typical piping was selected, and the calculated flow and temperature means and variances are shown in tables 1-2. (2) If each pipe length is set to 300 meters, all thermal loads are set to 0.5MW and all thermal load fluctuations are within ± 20%. Typical piping was selected, and the calculated flow and temperature means and variances are shown in tables 3-4.
TABLE 1 typical mean and standard deviation of pipeline flow
Figure BDA0002208755230000141
TABLE 2 typical nodal temperature mean and standard deviation
Figure BDA0002208755230000142
TABLE 3 typical mean and standard deviation of pipeline flow
TABLE 4 typical nodal temperature mean and standard deviation
Figure BDA0002208755230000144
Scene 2: (1) if each pipe length is set to 300 meters, all thermal loads are set to 0.5MW and all thermal load fluctuations are within ± 10%. Selecting a typical pipeline, wherein the temperature drop of the pipeline is shown in table 5; (2) if each pipe length is set to 300 meters, all thermal loads are set to 0.5MW and all thermal load fluctuations are within ± 50%. Selecting a typical pipeline, wherein the temperature drop of the pipeline is shown in table 6; (3) if each pipe length is set to 1000 meters, all thermal loads are set to 0.5MW and all thermal load fluctuations are within ± 50%. Selecting a typical pipeline, wherein the temperature drop of the pipeline is shown in a table 7;
TABLE 5 mean value and standard deviation of temperature drop of partial pipelines
Figure BDA0002208755230000152
TABLE 6 average and standard deviation of temperature drop of partial pipeline
Figure BDA0002208755230000153
TABLE 7 average and standard deviation of temperature drop of partial pipelines
Figure BDA0002208755230000154
Figure BDA0002208755230000161
Scene 3: when the thermal load fluctuation range is set to + -10% and the thermal load value is fixed, it is set to
Figure BDA0002208755230000163
The lengths of all pipelines are sequentially 100:100:2000 m, Monte Carlo simulation is carried out for 50000 times, the standard deviation of the flow of 20 groups of pipelines 1 can be obtained, and the average value is sigmam,mcsThe method obtains the standard deviation of the flow of the pipeline 1 and sets the standard deviation as sigmamThe standard error percentage of the flow of the pipeline 1 is set as deltaσ,mThe results are shown in Table 8. As can be seen from table 8, when the thermal load and the thermal load fluctuation range were not changed, the influence of the pipe length on the pipe flow standard deviation was small, and when the thermal load was increased, the pipe flow standard deviation was increased approximately linearly.
TABLE 8 standard error of flow for pipe 1 at different thermal loads
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (5)

1. A radiation type heat supply network statistical characteristic obtaining method based on probability energy flow is characterized by comprising the following steps:
(1) acquiring parameter information of a radiation type heat supply network model, and establishing a heat supply network system model according to the parameter information;
(2) setting the heat load in a heat supply network system model to obey independent normal distribution, obtaining the mean value and the variance of the flow of the pipeline adjacent to a heat source according to the heat supply network system model, obtaining the relation met by the mean value and the variance of the flow of the adjacent pipeline according to the heat supply network system model, and further obtaining the mean value and the variance of the flow of each pipeline;
(3) the relation between the node temperature and the reciprocal of the pipeline flow is obtained through a heat supply network system model, and the correlation coefficient among the pipeline flows is obtained by combining a continuous random variable probability density function theory, so that the mean value and the variance of the node temperature are obtained.
2. The method for acquiring statistical characteristics of a radiant heat network based on probability energy flow according to claim 1, wherein the radiant heat network model parameter information acquired in the step (1) comprises each pipeline, heat source water supply temperature, heat load water return temperature, heat load and fluctuation range thereof.
3. The method for acquiring statistical characteristics of a radiant heat supply network based on probability energy flow according to claim 1, wherein the heat supply network system model established in the step (1) is specifically as follows:
Am＝mq
Bhf＝0
hf＝Km|m|
Figure FDA0002208755220000011
Figure FDA0002208755220000012
Figure FDA0002208755220000014
Figure FDA0002208755220000015
(∑mout)Tout＝∑(minTin)
Figure FDA0002208755220000016
in the formula: a is a heat supply network node-pipeline incidence matrix, m is heat supply network pipeline flow, m isqFor node incoming load traffic, B is the loop correlation matrix, hfFor the pipeline pressure drop caused by friction loss, K is the resistance coefficient of the pipeline, L is the length of the pipeline, D is the diameter of the pipeline, ρ is the water density, g is the acceleration of gravity, f is the friction coefficient, ε is the roughness of the pipeline, Re is the Reynolds number, and μ is the kinematic viscosity of the pipeline water;
Figure FDA0002208755220000021
for thermal load, TsSupply water temperature to the node, ToIs the node return water temperature, TstartFor the head end temperature of the pipeline, TendIs the temperature at the end of the pipe, TaIs the external ambient temperature, lambda is the heat transfer coefficient, CpIs the specific heat capacity of water, minFor pipe flow into the node, moutFor pipe flow out of the node, TinFor the temperature at the end of the input pipe, ToutIs the node mixing temperature;
Figure FDA0002208755220000022
and
Figure FDA0002208755220000023
respectively thermal load
Figure FDA0002208755220000024
Expectation and standard deviation.
4. The method for acquiring statistical characteristics of a radiant heat network based on probability energy flow according to claim 3, wherein the step (2) specifically comprises:
(2.1) setting the heat load in the heat supply network system model to obey independent normal distribution, and obtaining the average value and the variance of the flow of the pipelines adjacent to the heat source as follows:
Figure FDA0002208755220000025
Figure FDA0002208755220000026
in the formula, m*Indicating the flow of the pipe adjacent to the heat source,
Figure FDA0002208755220000027
represents m*The average value of the average value is calculated,
Figure FDA0002208755220000028
represents m*The variance of the measured values is calculated,
Figure FDA0002208755220000029
in order to be the thermal load of the node i,
Figure FDA00022087552200000210
representing the heat loss, σ, of the pipe adjacent to node i2Is composed of
Figure FDA00022087552200000211
Variance of (1), THIs the CHP heat source temperature, ToReturning the temperature for the load node;
(2.2) obtaining a relation satisfied by the mean value and the variance of the flow of the adjacent pipelines according to the heat supply network system model, wherein the relation is as follows:
Figure FDA00022087552200000212
Figure FDA00022087552200000213
in the formula (I), the compound is shown in the specification,representing the flow variance of the first, second and nth tubes, respectively, branched off from the tube, n representing the number of tubes branched off from the tube,
Figure FDA00022087552200000215
respectively representing the average flow of the first, second and nth pipes branched from the pipe;
(2.3) obtaining the flow variance of all adjacent pipelines according to the relation satisfied by the mean value and the variance of the flow of the adjacent pipelines as follows:
Figure FDA00022087552200000216
……
Figure FDA0002208755220000032
in the formula (I), the compound is shown in the specification,
Figure FDA0002208755220000033
respectively representing the sum of all thermal loads flowing through the conduits 1,2, n,respectively represent
Figure FDA0002208755220000035
The variance of (a);
the average value of the pipeline flow is the solution when the heat loads are averaged;
and (2.4) obtaining the flow mean value and the flow variance of each other pipeline according to the steps (2.2) and (2.3).
5. The method for acquiring statistical characteristics of a radiant heat network based on probability energy flow according to claim 3, wherein the step (3) specifically comprises:
(3.1) obtaining the relation between the node temperature and the inverse of the pipeline flow through a heat supply network system model as follows:
Figure FDA0002208755220000036
Figure FDA0002208755220000037
……
THthe heat source temperature is adopted, the flow is sent out by a heat source H, and the number of a pipeline through which the flow flows between the heat source H and a node to be solved is x1、x2…xNThe temperature of the node flowing through is
Figure FDA0002208755220000039
N is the number of pipelines through which the flow between the heat source H and the node to be solved flows,
Figure FDA00022087552200000310
respectively representing a pipe x1、x2…xNOf flow rate of1、λ2...λNRespectively representing a pipe x1、x2…xNOfCoefficient, L1、L2...LNRespectively representing a pipe x1、x2…xNThe length of the conduit of (a);
(3.2) calculating a correlation coefficient between any pipeline flow according to the pipeline flow variance by adopting the following formula:
wherein i, j, k represent any of various pipes, shaped as m#Representing the pipe # flow, in the form of p#Denotes m#Correlation coefficient with m, in the form of
Figure FDA0002208755220000042
Represents the flow rate m#Variance;
(3.3) establishing a covariance matrix xi of the node temperature normal distribution according to the calculated correlation coefficients:
Figure FDA0002208755220000043
(3.4) converting the relation in the step (3.1) into a matrix form as follows:
Figure FDA0002208755220000044
Figure FDA0002208755220000045
……
Figure FDA0002208755220000046
in the formula (I), the compound is shown in the specification,
Figure FDA0002208755220000048
respectively representing corresponding coefficient vectors with the size of 1 multiplied by N, wherein the elements respectively comprise 1,2, …, N1, and the rest elements are 0;
(3.5) obtaining the flow rate according to the step (2)
Figure FDA0002208755220000049
Mean and variance of (1) to obtainTo obtain X, and thenmIn
Figure FDA00022087552200000411
Mean value of
Figure FDA00022087552200000412
Sum variance
Figure FDA00022087552200000413
(3.6) obtaining X according to step (3.5)mObeying an N-dimensional normal distribution N (μ, xi),
Figure FDA0002208755220000051
obtaining the node temperature
Figure FDA0002208755220000052
Obey normal distributions of
Figure FDA0002208755220000053
Figure FDA0002208755220000054
I.e. the node temperature
Figure FDA0002208755220000055
Respectively mean value of
Figure FDA0002208755220000056
Figure FDA0002208755220000057
Variance is respectively
Figure FDA0002208755220000058
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