WO2021164454A1 - 一种用于综合能源***调度的供热网络水路建模方法 - Google Patents
一种用于综合能源***调度的供热网络水路建模方法 Download PDFInfo
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/08—Fluids
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/14—Pipes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Definitions
- the application relates to a heating network waterway modeling method for integrated energy system scheduling, which belongs to the technical field of operation control of integrated energy systems.
- thermoelectric coupling system can give full play to the coupling characteristics of heat and electricity and improve the efficiency of comprehensive energy utilization. It has received extensive attention and research from scholars at home and abroad. At present, a series of applications such as combined heat and power flow calculation, combined economic dispatch of heat and power, combined heat and power planning, and combined state estimation of heat and power have been developed, all of which are based on the modeling and analysis of power and heating networks. Among them, the analysis of power network based on circuit theory has formed a mature AC power flow model and DC power flow model, while the heating network has not yet formed a unified theory and model. Regarding the hydraulic analysis of the heating network, the steady-state modeling method is generally used in engineering at present, which breaks the connection between the hydraulic dynamics and the steady-state, and there are deficiencies in which the physical meaning is not clear.
- the purpose of this application is to propose a heating network waterway modeling method for integrated energy system scheduling, unify the hydraulic analysis model of the heating network in the integrated energy system with the power network model, and establish hydraulic dynamics and hydraulic stability. To complete the degradation of dynamic hydraulic network equations to steady-state hydraulic network equations.
- the heating network waterway modeling method for integrated energy system scheduling proposed in this application includes the following steps:
- ⁇ , v, and p are the density, flow rate, and pressure of water, respectively, ⁇ , D, and ⁇ are the friction coefficient, inner diameter, and inclination of the thermal pipe, g is the acceleration of gravity, and t and x are time and space, respectively;
- step (1-1-3) Ignore the convection term in the momentum conservation equation of step (1-1-1) which is And the resistance term
- the square of the velocity term in is approximated by incremental linearization, that is, v 2 ⁇ 2v base vv base 2 , where v base is the base value of the water velocity in the thermal pipeline, and the value is the velocity in the design working condition;
- step (1-1-4) Substituting step (1-1-2) and step (1-1-3) into step (1-1-1), the following equation is obtained:
- dG is the flow difference between the two ends of the thermal pipe micro-element
- dp is the pressure drop at both ends of the thermal pipe micro-element
- thermal pipeline micro-element dx is represented as a section of water path including 3 elements, and then the entire thermal pipeline is represented as a distributed parameter water path;
- R is the water resistance in the lumped parameter waterway of the heating pipe
- L is the water feel in the lumped parameter waterway of the heating pipe
- E is the water pressure source in the lumped parameter waterway of the heating pipe
- l is the heat The length of the pipe
- p 0 and G 0 are the pressure and flow rate at the head end of the heat pipe, and p l and G l are the pressure and flow rate at the end of the heat pipe;
- k v is the opening coefficient of the valve, and G is the mass flow of water
- step (1-2-2) define the water resistance R v and water pressure source E v of the flow control valve.
- the calculation equations of R v and E v are as follows:
- k p1 , k p2 and k p3 are the inherent coefficients of the booster pump, which are obtained from the factory nameplate of the booster pump or obtained by external characteristic test and fitting.
- ⁇ p is the rotation frequency of the booster pump;
- R p -(2k p1 G base +k p2 ⁇ p )
- step (1) Based on the model of thermal pipeline, flow control valve and booster pump established in step (1), establish the characteristic equation of the hydraulic branch of the heating network:
- G b y b (p b -E b )
- G b is the mass flow base value corresponding to the base value of the flow velocity in the hydraulic branch
- p b is the water pressure difference between the two ends of the hydraulic branch
- y b is the branch formed by the water resistance and water sense in the hydraulic branch.
- Admittance, E b is the sum of water pressure sources in the hydraulic branch;
- G b y b (p b -E b )
- G b , p b and E b are the column vectors composed of the mass flow of water in all hydraulic branches in the heating network, the water pressure difference at both ends of the branch and the water pressure source, respectively, and y b is the total value of the heating network.
- (3-1) Define the node-branch association matrix A h in the heating network, which is a matrix with n rows and m columns, where n is the number of nodes in the heating network, and m is the number of nodes in the heating network.
- Use (A h ) i,j 1 to indicate that branch j flows out of node i
- use (A h ) i,j -1 to indicate that branch j flows into node i;
- p n is a column vector composed of the water pressure value of each node
- G′ n G n +A h y b E b
- the steady-state waterway model is the heating network waterway model for integrated energy system control.
- This application is used for the heating network waterway modeling method of integrated energy system scheduling, unifies the hydraulic analysis model of the heating network in the integrated energy system with the power network model, and establishes the connection between the hydraulic dynamics and the hydraulic steady state.
- the method of this application is based on the characteristic equations of thermal pipelines, flow control valves and booster pumps, and abstracts water resistance, water sense and water pressure source and other water circuit component models.
- the hydraulic branch characteristics of the heating network are established, based on the class Kirchhoff's laws of voltage and current, establish the hydraulic topology constraints of the heating network, and combine the above-mentioned hydraulic branch characteristics and hydraulic topology constraints to establish the dynamic hydraulic network equation of the heating network (ie, the dynamic water model of the heating network), Complete the degradation of dynamic hydraulic network equations to steady-state hydraulic network equations.
- the method of this application has a clear physical meaning, covers various equipment of thermal pipelines, flow control valves, and booster pumps, fully considers the branch characteristics and topology constraints of the heating network, and the modeling method has strong applicability.
- Figure 1 is a schematic diagram of the distributed parameter waterway of the thermal pipeline involved in the method of the present application, where (a) is the distributed parameter waterway of the entire thermal pipeline, (b) is the distributed parameter waterway of the dx length in the thermal pipeline.
- Figure 2 is a schematic diagram of the lumped parameter equivalent water circuit of the thermal pipeline.
- the heating network waterway modeling method for integrated energy system control proposed in this application includes the following steps:
- ⁇ , v, and p are the density, flow rate, and pressure of water, respectively, ⁇ , D, and ⁇ are the friction coefficient, inner diameter, and inclination of the thermal pipe, g is the acceleration of gravity, and t and x are time and space, respectively;
- step (1-1-3) Ignore the convection term in the momentum conservation equation of step (1-1-1) which is And the resistance term
- the square of the velocity term in is approximated by incremental linearization, that is, v 2 ⁇ 2v base vv base 2 , where v base is the base value of the water velocity in the thermal pipeline, and the value is the velocity in the design working condition;
- step (1-1-4) Substituting step (1-1-2) and step (1-1-3) into step (1-1-1), the following equation is obtained:
- dG is the flow difference between the two ends of the thermal pipe micro-element
- dp is the pressure drop at both ends of the thermal pipe micro-element
- the thermal pipeline micro-element dx is represented as a section of water path including three elements, and the entire thermal pipeline is represented as a distributed parameter water path.
- the distributed parameter water path of the entire thermal pipeline and the distributed parameter water path of the thermal pipe micro-element dx are shown in Figure 1. Show;
- thermo pipeline lumped parameter water circuit (1-1-7) According to the component parameters of the thermal pipeline distribution parameter water circuit in (1-1-6), establish the thermal pipeline lumped parameter water circuit.
- the thermal pipeline lumped parameter water circuit is shown in Figure 2. The component parameters:
- R is the water resistance in the lumped parameter waterway of the heating pipe
- L is the water feel in the lumped parameter waterway of the heating pipe
- E is the water pressure source in the lumped parameter waterway of the heating pipe
- l is the heat The length of the pipe
- p 0 and G 0 are the pressure and flow rate at the head end of the heat pipe, and p l and G l are the pressure and flow rate at the end of the heat pipe;
- k v is the opening coefficient of the valve, and G is the mass flow of water
- step (1-2-2) define the water resistance R v and water pressure source E v of the flow control valve.
- the calculation equations of R v and E v are as follows:
- k p1 , k p2 and k p3 are the inherent coefficients of the booster pump, which are obtained from the factory nameplate of the booster pump or obtained by external characteristic test and fitting.
- ⁇ p is the rotation frequency of the booster pump;
- R p -(2k p1 G base +k p2 ⁇ p )
- step (1) Based on the model of thermal pipeline, flow control valve and booster pump established in step (1), establish the characteristic equation of the hydraulic branch of the heating network:
- G b y b (p b -E b )
- G b is the mass flow base value corresponding to the base value of the flow velocity in the hydraulic branch
- p b is the water pressure difference between the two ends of the hydraulic branch
- y b is the branch formed by the water resistance and water sense in the hydraulic branch.
- Admittance, E b is the sum of water pressure sources in the hydraulic branch;
- G b y b (p b -E b )
- G b , p b and E b are the column vectors composed of the mass flow of water in all hydraulic branches in the heating network, the water pressure difference at both ends of the branch and the water pressure source, respectively, and y b is the total value of the heating network.
- (3-1) Define the node-branch association matrix A h in the heating network, which is a matrix with n rows and m columns, where n is the number of nodes in the heating network, and m is the number of nodes in the heating network.
- Use (A h ) i,j 1 to indicate that branch j flows out of node i
- use (A h ) i,j -1 to indicate that branch j flows into node i;
- p n is a column vector composed of the water pressure value of each node
- G′ n G n +A h y b E b
- the above hydraulic network equation describes the hydraulic dynamics of the heating network, and has a unified form with the network equation of the power network;
- the steady-state waterway model can be used as a heating network waterway model for integrated energy system control.
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Abstract
一种用于综合能源***调度的供热网络水路建模方法,水力分析模型与电力网络模型相统一,并建立起水力动态与水力稳态之间的联系。本方法基于热力管道、流量控制阀和增压泵的特性方程,抽象出水阻、水感和水压源等水路元件模型,基于上述水路元件,建立供热网络的水力支路特性,基于类基尔霍夫电压、电流定律,建立供热网络的水力拓扑约束,结合上述水力支路特性与水力拓扑约束,最后建立稳态水力网络方程。
Description
相关申请的交叉引用
本申请基于申请号为202010109315.5、申请日为2020年02月22日的中国专利申请“一种用于综合能源***调度的供热网络水路建模方法”提出,并要求上述中国专利申请的优先权,上述中国专利申请的全部内容在此引入本申请作为参考。
本申请涉及一种用于综合能源***调度的供热网络水路建模方法,属于综合能源***的运行控制技术领域。
热电耦合***作为综合能源***的典型代表,能够充分发挥热力和电力的耦合特性,提高综合能源利用效率,得到了国内外学者的广泛关注与研究。目前已经发展出热电联合潮流计算、热电联合经济调度、热电联合规划和热电联合状态估计等一系列应用,这些工作均以电力网络和供热网络的建模和分析为基础。其中,电力网络的分析基于电路理论已形成了成熟的交流潮流模型与直流潮流模型,而供热网络尚未形成与之相统一的理论与模型。针对供热网络的水力分析,目前工程上普遍采用稳态建模的方法,割裂了水力动态与稳态之间的联系,同时存在物理意义不明确的不足。
发明内容
本申请的目的是提出一种用于综合能源***调度的供热网络水路建模方法,将综合能源***中供热网络的水力分析模型与电力网络模型相统一,并建立起水力动态与水力稳态之间的联系,以完成动态水力网络方程向稳态水力网络方程的退化。
本申请提出的用于综合能源***调度的供热网络水路建模方法,包括以下步骤:
(1)建立供热网络的设备模型,包括以下步骤:
(1-1)建立供热网络中热力管道模型,包括以下步骤:
(1-1-1)建立描述水在热力管道中一维流动过程的质量守恒方程和动量守恒方程:
上式中,ρ、v和p分别为水的密度、流速和压力,λ、D和θ分别为热力管道的摩擦 系数、内径和倾角,g为重力加速度,t和x分别表示时间和空间;
(1-1-2)根据水为不可压缩流体,建立水的密度关于时间和空间的微分方程:
(1-1-3)忽略步骤(1-1-1)的动量守恒方程中的对流项
即
并将阻力项
中的流速平方项进行增量线性化近似,即令v
2≈2v
basev-v
base
2,式中v
base为热力管道中水的流速基值,取值为设计工况中的流速;
(1-1-4)将步骤(1-1-2)和步骤(1-1-3)代入步骤(1-1-1)中,得到以下方程:
上式中,G为水的质量流量,G=ρvA,A为热力管道的横截面积,G
base为流速基值对应的质量流量基值,即G
base=ρv
baseA;
(1-1-5)根据步骤(1-1-4),建立热力管道微元dx两端的流量差和压力降方程:
dG=0
上式中,dG为热力管道微元的两端流量差,dp为热力管道微元的两端压降;
(1-1-6)根据步骤(1-1-5)的热力管道微元dx两端的流量差和压力降方程,得到热力管道中的水阻R
h、水感L
h和水压源E
h,R
h、L
h和E
h的计算方程如下:
R
h=λG
base/(ρA
2D)
L
h=1/A
E
h=ρg sinθ-λG
base
2/(2ρA
2D)
从而,将热力管道微元dx表示为一段包括3个元件的水路,进而整个热力管道表示为一个分布参数水路;
(1-1-7)根据(1-1-6)的热力管道分布参数水路的元件参数,建立热力管道集总参数水路的元件参数:
R=R
hl
L=L
hl
E=E
hl
上式中,R为热力管道的集总参数水路中的水阻,L为热力管道的集总参数水路中的水感,E为热力管道的集总参数水路中的水压源,l为热力管道的长度;
(1-1-8)将热力管道集总参数水路的激励进行傅里叶变换,分解为多个不同频率的正弦稳态激励,建立正弦稳态激励中的每一个频率分量ω对应的集总参数频域水路的代数方程:
p
l=p
0-(R+jωL)G
0-E
G
l=G
0
上式中,p
0和G
0分别为热力管道首端的压力和流量,p
l和G
l是热力管道末端的压力和流量;
(1-2)建立供热网络中流量控制阀模型,包括以下步骤:
(1-2-1)建立流量控制阀两侧压差p和质量流量G之间的方程:
p=k
vG
2
上式中,k
v为阀门的开度系数,G为水的质量流量;
p=2k
vG
base·G-k
vG
base
2
(1-2-3)根据步骤(1-2-2),定义流量控制阀的水阻R
v和水压源E
v,R
v和E
v的计算方程如下:
R
v=2k
vG
base
E
v=-k
vG
base
2
(1-3)建立供热网络中增压泵模型,包括以下步骤:
(1-3-1)建立在给定转速下增压泵两侧的压差p和水的质量流量G之间的方程:
上式中,k
p1、k
p2和k
p3为增压泵固有的系数,由增压泵出厂铭牌获取或进行外特性测试并拟合获取,ω
p是增压泵的旋转频率;
(1-3-2)对步骤(1-3-1)中的质量流量平方项G
2进行增量线性化近似,即G
2=2G
baseG-G
base
2,从而将步骤(1-3-1)转化为下式:
(1-3-3)根据步骤(1-3-2),定义增压泵的水阻R
p和水压源E
p,R
p和E
p的计算方程如下:
R
p=-(2k
p1G
base+k
p2ω
p)
(2)建立供热网络的水力支路特性,包括以下步骤:
(2-1)基于步骤(1)中建立的热力管道、流量控制阀和增压泵的模型,建立供热网络的水力支路的特性方程:
G
b=y
b(p
b-E
b)
式中,G
b为水力支路中与流速基值对应的质量流量基值,p
b为水力支路两端的水压差,y
b为水力支路中的水阻和水感构成的支路导纳,E
b是水力支路中水压源的总和;
(2-2)将供热网络中所有水力支路的水力支路方程写成矩阵形式如下:
G
b=y
b(p
b-E
b)
式中,G
b、p
b和E
b分别为供热网络中所有水力支路中水的质量流量、支路两端的水压差和水压源组成的列向量,y
b是供热网络所有支路的导纳组成的对角矩阵;
(3)建立供热网络的水力拓扑约束,包括以下步骤:
(3-1)定义供热网络中的节点-支路关联矩阵A
h,该矩阵是一个n行、m列的矩阵,其中n为供热网络中的节点数,m为供热网络中的支路数,用(A
h)
i,j表示(A
h)
i,j中第i行、第j列的元素,用(A
h)
i,j=0表示支路j与节点i不相连,用(A
h)
i,j=1表示支路j从节点i流出,用 (A
h)
i,j=-1表示支路j流入节点i;
(3-2)根据类基尔霍夫电流定律,建立供热网络的节点质量守恒方程:
A
hG
b=G
n
上式中,G
n为由每个节点的水流注入构成的列向量,若供热网络为闭式网络,则G
n=0;
(3-3)根据类基尔霍夫电压定律,建立供热网络的回路压降方程:
上式中,p
n为由每个节点的水压值构成的列向量;
(4)建立供热网络的动态水力网络方程,包括以下步骤:
(4-1)将步骤(3-2)和步骤(3-3)建立的水力拓扑约束代入步骤(2-2)建立的支路特性方程,得到未约简形式的供热网络水力网络方程如下:
(4-2)定义广义节点导纳矩阵Y
h和广义节点注入向量G′
n如下:
G′
n=G
n+A
hy
bE
b
(4-3)将步骤(4-2)中定义的Y
h和G′
n代入步骤(4-1)中的未约简形式的供热网络水力网络方程,得到以下形式的供热网络中水力网络方程如下::
Y
hp
n=G′
n
上述水力网络方程描述了供热网络的水力动态;
(5)删除供热网络水路模型中的水感元件,按照步骤(4)重新计算广义节点导纳矩阵Y
h,并只取频域中的零频率分量,使动态水路模型退化为稳态水路模型,该稳态水路模型即为用于综合能源***控制的供热网络水路模型。
本申请提出的用于综合能源***调度的供热网络水路建模方法,其优点是:
本申请用于综合能源***调度的供热网络水路建模方法,将综合能源***中供热网络的水力分析模型与电力网络模型相统一,并建立起水力动态与水力稳态之间的联系。本申请方法基于热力管道、流量控制阀和增压泵的特性方程,抽象出水阻、水感和水压源等水路元件模型,基于上述水路元件,建立供热网络的水力支路特性,基于类基尔霍夫电压、 电流定律,建立供热网络的水力拓扑约束,结合上述水力支路特性与水力拓扑约束,建立供热网络的动态水力网络方程(即,供热网络的动态水路模型),完成动态水力网络方程向稳态水力网络方程的退化。本申请方法物理意义明确,涵盖了热力管道、流量控制阀和增压泵各类设备,全面考虑了供热网络支路特性和拓扑约束,建模方法适用性强。同时,通过抽象出水阻、水感和水压源等水路元件,使得供热网络水路模型与电力网络模型在数学形式上高度统一,因此本申请方法有助于热和电两种异质能流***的统一调度。
图1是本申请方法中涉及的热力管道的分布参数水路示意图,其中(a)是整个热力管道的分布参数水路,(b)是热力管道中dx长度的微元的分布参数水路。
图2是热力管道的集总参数等值水路示意图。
本申请提出的用于综合能源***控制的供热网络水路建模方法,包括以下步骤:
(1)建立供热网络的设备模型,包括以下步骤:
(1-1)建立供热网络中热力管道模型,包括以下步骤:
(1-1-1)建立描述水在热力管道中一维流动过程的质量守恒方程和动量守恒方程:
上式中,ρ、v和p分别为水的密度、流速和压力,λ、D和θ分别为热力管道的摩擦系数、内径和倾角,g为重力加速度,t和x分别表示时间和空间;
(1-1-2)根据水为不可压缩流体,建立水的密度关于时间和空间的微分方程:
(1-1-3)忽略步骤(1-1-1)的动量守恒方程中的对流项
即
并将阻力项
中的流速平方项进行增量线性化近似,即令v
2≈2v
basev-v
base
2,式中v
base为热力管道中水的流速基值,取值为设计工况中的流速;
(1-1-4)将步骤(1-1-2)和步骤(1-1-3)代入步骤(1-1-1)中,得到以下方程:
上式中,G为水的质量流量,G=ρvA,A为热力管道的横截面积,G
base为流速基值对应的质量流量基值,即G
base=ρv
baseA;
(1-1-5)根据步骤(1-1-4),建立热力管道微元dx两端的流量差和压力降方程:
dG=0
上式中,dG为热力管道微元的两端流量差,dp为热力管道微元的两端压降;
(1-1-6)根据步骤(1-1-5)的热力管道微元dx两端的流量差和压力降方程,得到热力管道中的水阻R
h、水感L
h和水压源E
h,R
h、L
h和E
h的计算方程如下:
R
h=λG
base/(ρA
2D)
L
h=1/A
E
h=ρg sinθ-λG
base
2/(2ρA
2D)
从而,将热力管道微元dx表示为一段包括3个元件的水路,进而整个热力管道表示为一个分布参数水路,整个热力管道的分布参数水路和热力管道微元dx的分布参数水路如图1所示;
(1-1-7)根据(1-1-6)的热力管道分布参数水路的元件参数,建立热力管道集总参数水路,该热力管道集总参数水路如图2所示,的元件参数:
R=R
hl
L=L
hl
E=E
hl
上式中,R为热力管道的集总参数水路中的水阻,L为热力管道的集总参数水路中的水感,E为热力管道的集总参数水路中的水压源,l为热力管道的长度;
(1-1-8)将热力管道集总参数水路的激励进行傅里叶变换,分解为多个不同频率的正弦稳态激励,建立正弦稳态激励中的每一个频率分量ω对应的集总参数频域水路的代数方程:
p
l=p
0-(R+jωL)G
0-E
G
l=G
0
上式中,p
0和G
0分别为热力管道首端的压力和流量,p
l和G
l是热力管道末端的压力和流量;
(1-2)建立供热网络中流量控制阀模型,包括以下步骤:
(1-2-1)建立流量控制阀两侧压差p和质量流量G之间的方程:
p=k
vG
2
上式中,k
v为阀门的开度系数,G为水的质量流量;
(1-2-2)对步骤(1-2-1)中的质量流量平方项G
2进行增量线性化近似,即G
2=2G
baseG-G
base
2,从而将步骤(1-2-1)的流量控制阀两侧压差p和质量流量G之间的方程转化为下式:
p=2k
vG
base·G-k
vG
base
2
(1-2-3)根据步骤(1-2-2),定义流量控制阀的水阻R
v和水压源E
v,R
v和E
v的计算方程如下:
R
v=2k
vG
base
E
v=-k
vG
base
2
(1-3)建立供热网络中增压泵模型,包括以下步骤:
(1-3-1)建立在给定转速下增压泵两侧的压差p和水的质量流量G之间的方程:
上式中,k
p1、k
p2和k
p3为增压泵固有的系数,由增压泵出厂铭牌获取或进行外特性测试并拟合获取,ω
p是增压泵的旋转频率;
(1-3-2)对步骤(1-3-1)中的质量流量平方项G
2进行增量线性化近似,即G
2=2G
baseG-G
base
2,从而将步骤(1-3-1)转化为下式:
(1-3-3)根据步骤(1-3-2),定义增压泵的水阻R
p和水压源E
p,R
p和E
p的计算方程如 下:
R
p=-(2k
p1G
base+k
p2ω
p)
(2)建立供热网络的水力支路特性,包括以下步骤:
(2-1)基于步骤(1)中建立的热力管道、流量控制阀和增压泵的模型,建立供热网络的水力支路的特性方程:
G
b=y
b(p
b-E
b)
式中,G
b为水力支路中与流速基值对应的质量流量基值,p
b为水力支路两端的水压差,y
b为水力支路中的水阻和水感构成的支路导纳,E
b是水力支路中水压源的总和;
(2-2)将供热网络中所有水力支路的水力支路方程写成矩阵形式如下:
G
b=y
b(p
b-E
b)
式中,G
b、p
b和E
b分别为供热网络中所有水力支路中水的质量流量、支路两端的水压差和水压源组成的列向量,y
b是供热网络所有支路的导纳组成的对角矩阵;
(3)建立供热网络的水力拓扑约束,包括以下步骤:
(3-1)定义供热网络中的节点-支路关联矩阵A
h,该矩阵是一个n行、m列的矩阵,其中n为供热网络中的节点数,m为供热网络中的支路数,用(A
h)
i,j表示(A
h)
i,j中第i行、第j列的元素,用(A
h)
i,j=0表示支路j与节点i不相连,用(A
h)
i,j=1表示支路j从节点i流出,用(A
h)
i,j=-1表示支路j流入节点i;
(3-2)根据类基尔霍夫电流定律,建立供热网络的节点质量守恒方程:
A
hG
b=G
n
上式中,G
n为由每个节点的水流注入构成的列向量,若供热网络为闭式网络,则G
n=0;
(3-3)根据类基尔霍夫电压定律,建立供热网络的回路压降方程:
上式中,p
n为由每个节点的水压值构成的列向量;
(4)建立供热网络的动态水力网络方程,包括以下步骤:
(4-1)将步骤(3-2)和步骤(3-3)建立的水力拓扑约束代入步骤(2-2)建立的支路特性方程,得到未约简形式的供热网络水力网络方程如下:
(4-2)定义广义节点导纳矩阵Y
h和广义节点注入向量G′
n如下:
G′
n=G
n+A
hy
bE
b
(4-3)将步骤(4-2)中定义的Y
h和G′
n代入步骤(4-1)中的未约简形式的供热网络水力网络方程,得到以下形式的供热网络中水力网络方程如下::
Y
hp
n=G′
n
上述水力网络方程描述了供热网络的水力动态,并具有和电力网络的网络方程相统一的形式;
(5)删除供热网络水路模型中的水感元件,按照步骤(4)重新计算广义节点导纳矩阵Y
h,并只取频域中的零频率分量,使动态水路模型退化为稳态水路模型。当不需要考虑短暂的水力动态过程时,可采用该稳态水路模型作为用于综合能源***控制的供热网络水路模型。
Claims (1)
- 一种用于综合能源***调度的供热网络水路建模方法,其特征在于,该方法包括以下步骤:(1)建立供热网络的设备模型,包括以下步骤:(1-1)建立供热网络中热力管道模型,包括以下步骤:(1-1-1)建立描述水在热力管道中一维流动过程的质量守恒方程和动量守恒方程:上式中,ρ、v和p分别为水的密度、流速和压力,λ、D和θ分别为热力管道的摩擦系数、内径和倾角,g为重力加速度,t和x分别表示时间和空间;(1-1-2)根据水为不可压缩流体,建立水的密度关于时间和空间的微分方程:(1-1-3)忽略步骤(1-1-1)的动量守恒方程中的对流项 即 并将阻力项 中的流速平方项进行增量线性化近似,即令v 2≈2v basev-v base 2,式中v base为热力管道中水的流速基值,取值为设计工况中的流速;(1-1-4)将步骤(1-1-2)和步骤(1-1-3)代入步骤(1-1-1)中,得到以下方程:上式中,G为水的质量流量,G=ρvA,A为热力管道的横截面积,G base为流速基值对应的质量流量基值,即G base=ρv baseA;(1-1-5)根据步骤(1-1-4),建立热力管道微元dx两端的流量差和压力降方程:dG=0上式中,dG为热力管道微元的两端流量差,dp为热力管道微元的两端压降;(1-1-6)根据步骤(1-1-5)的热力管道微元dx两端的流量差和压力降方程,得到热力管道中的水阻R h、水感L h和水压源E h,R h、L h和E h的计算方程如下:R h=λG base/(ρA 2D)L h=1/AE h=ρg sinθ-λG base 2/(2ρA 2D)从而,将热力管道微元dx表示为一段包括3个元件的水路,进而整个热力管道表示为一个分布参数水路;(1-1-7)根据(1-1-6)的热力管道分布参数水路的元件参数,建立热力管道集总参数水路的元件参数:R=R hlL=L hlE=E hl上式中,R为热力管道的集总参数水路中的水阻,L为热力管道的集总参数水路中的水感,E为热力管道的集总参数水路中的水压源,l为热力管道的长度;(1-1-8)将热力管道集总参数水路的激励进行傅里叶变换,分解为多个不同频率的正弦稳态激励,建立正弦稳态激励中的每一个频率分量ω对应的集总参数频域水路的代数方程:p l=p 0-(R+jωL)G 0-EG l=G 0上式中,p 0和G 0分别为热力管道首端的压力和流量,p l和G l是热力管道末端的压力和流量;(1-2)建立供热网络中流量控制阀模型,包括以下步骤:(1-2-1)建立流量控制阀两侧压差p和质量流量G之间的方程:p=k vG 2上式中,k v为阀门的开度系数,G为水的质量流量;(1-2-2)对步骤(1-2-1)中的质量流量平方项G 2进行增量线性化近似,即 G 2=2G baseG-G base 2,从而将步骤(1-2-1)的流量控制阀两侧压差p和质量流量G之间的方程转化为下式:p=2k vG base·G-k vG base 2(1-2-3)根据步骤(1-2-2),定义流量控制阀的水阻R v和水压源E v,R v和E v的计算方程如下:R v=2k vG baseE v=-k vG base 2(1-3)建立供热网络中增压泵模型,包括以下步骤:(1-3-1)建立在给定转速下增压泵两侧的压差p和水的质量流量G之间的方程:上式中,k p1、k p2和k p3为增压泵固有的系数,由增压泵出厂铭牌获取或进行外特性测试并拟合获取,ω p是增压泵的旋转频率;(1-3-2)对步骤(1-3-1)中的质量流量平方项G 2进行增量线性化近似,即G 2=2G baseG-G base 2,从而将步骤(1-3-1)转化为下式:(1-3-3)根据步骤(1-3-2),定义增压泵的水阻R p和水压源E p,R p和E p的计算方程如下:R p=-(2k p1G base+k p2ω p)(2)建立供热网络的水力支路特性,包括以下步骤:(2-1)基于步骤(1)中建立的热力管道、流量控制阀和增压泵的模型,建立供热网络的水力支路的特性方程:G b=y b(p b-E b)式中,G b为水力支路中与流速基值对应的质量流量基值,p b为水力支路两端的水压差,y b为水力支路中的水阻和水感构成的支路导纳,E b是水力支路中水压源的总和;(2-2)将供热网络中所有水力支路的水力支路方程写成矩阵形式如下:G b=y b(p b-E b)式中,G b、p b和E b分别为供热网络中所有水力支路中水的质量流量、支路两端的水压差和水压源组成的列向量,y b是供热网络所有支路的导纳组成的对角矩阵;(3)建立供热网络的水力拓扑约束,包括以下步骤:(3-1)定义供热网络中的节点-支路关联矩阵A h,该矩阵是一个n行、m列的矩阵,其中n为供热网络中的节点数,m为供热网络中的支路数,用(A h) i,j表示(A h) i,j中第i行、第j列的元素,用(A h) i,j=0表示支路j与节点i不相连,用(A h) i,j=1表示支路j从节点i流出,用(A h) i,j=-1表示支路j流入节点i;(3-2)根据类基尔霍夫电流定律,建立供热网络的节点质量守恒方程:A hG b=G n上式中,G n为由每个节点的水流注入构成的列向量,若供热网络为闭式网络,则G n=0;(3-3)根据类基尔霍夫电压定律,建立供热网络的回路压降方程:上式中,p n为由每个节点的水压值构成的列向量;(4)建立供热网络的动态水力网络方程,包括以下步骤:(4-1)将步骤(3-2)和步骤(3-3)建立的水力拓扑约束代入步骤(2-2)建立的支路特性方程,得到未约简形式的供热网络水力网络方程如下:(4-2)定义广义节点导纳矩阵Y h和广义节点注入向量G′ n如下:G′ n=G n+A hy bE b(4-3)将步骤(4-2)中定义的Y h和G′ n代入步骤(4-1)中的未约简形式的供热网络水力网络方程,得到以下形式的供热网络中水力网络方程如下::Y hp n=G′ n上述水力网络方程描述了供热网络的水力动态;(5)删除供热网络水路模型中的水感元件,按照步骤(4)重新计算广义节点导纳矩阵Y h,并只取频域中的零频率分量,使动态水路模型退化为稳态水路模型,该稳态水路模型即为用于综合能源***控制的供热网络水路模型。
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