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 哈尔滨工程大学学报  2018, Vol. 39 Issue (9): 1485-1490  DOI: 10.11990/jheu.201706040 0

### 引用本文

GUO Dan, XIA Hong, YANG Bo. Modeling and control on dynamic water level of steam generator with natural circulation[J]. Journal of Harbin Engineering University, 2018, 39(9), 1485-1490. DOI: 10.11990/jheu.201706040.

### 文章历史

Modeling and control on dynamic water level of steam generator with natural circulation
GUO Dan, XIA Hong, YANG Bo
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin 150001, China
Abstract: In order to simulate the phenomenon of false water level caused by the contraction and expansion of bubbles at the bottom of water level in the steam generator during disturbance and weaken the corresponding effect on water-level control, in this paper, according to the three conservation laws, a fourth-order dynamic water-level mechanism model of steam generator with natural circulation, which can reflect the thermal characteristics and facilitate the design of control system, was established under reasonable assumptions and by using Lumped Parameter Method. The change process of the water level and the parameters affecting water level were analyzed for the time when load disturbance and heat disturbance occurred at different operating points, and the cascade PID controller was designed for the water level system. The simulation results indicate that, the main parameters of the steam generator changed reasonably following disturbance, the phenomenon of false level could be accurately simulated and the controller could also suppress the interference at low operating conditions.
Keywords: steam generator    contraction    expansion    false water level    lumped parameter method    thermal properties    control system    modeling    PID control

1 SG四阶动态水位模型的建立

 $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {{\rho _{\rm{s}}}{V_{{\rm{st}}}} + {\rho _{\rm{w}}}{V_{{\rm{wt}}}}} \right) = {W_{{\rm{fw}}}} - {W_{\rm{s}}}$ (1)

 $\frac{{{\rm{d}}\left( {{\rho _{\rm{s}}}{V_{{\rm{st}}}}{u_{\rm{s}}} + {\rho _{\rm{w}}}{V_{{\rm{wt}}}}{u_{\rm{w}}} + {m_{\rm{t}}}{C_{\rm{p}}}T} \right)}}{{{\rm{d}}t}} = Q + {W_{{\rm{fw}}}}{h_{{\rm{fw}}}} - {W_{\rm{s}}}{h_{\rm{s}}}$ (2)

 $u = h - \frac{P}{\rho }$ (3)

 $\begin{array}{*{20}{c}} {\frac{{{\rm{d}}\left( {{\rho _{\rm{s}}}{V_{{\rm{st}}}}{u_{\rm{s}}} + {\rho _{\rm{w}}}{V_{{\rm{wt}}}}{h_{\rm{w}}} - {V_{\rm{t}}}P + {m_{\rm{t}}}{C_{\rm{p}}}T} \right)}}{{{\rm{d}}t}} = }\\ {Q + {W_{{\rm{fw}}}}{h_{{\rm{fw}}}} - {W_{\rm{s}}}{h_{\rm{s}}}} \end{array}$ (4)

 ${V_{\rm{t}}} = {V_{{\rm{st}}}} + {V_{{\rm{wt}}}}$ (5)

 ${x_{\rm{m}}}\left( \xi \right) = x\xi$ (6)

 ${\beta _{\rm{v}}} = \frac{{{\rho _{\rm{w}}}{x_{\rm{m}}}}}{{{\rho _{\rm{s}}} + \left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right){x_{\rm{m}}}}}$ (7)

 $\begin{array}{*{20}{c}} {{{\bar \beta }_{\rm{v}}} = \int\limits_0^1 {{\beta _{\rm{v}}}\left( \xi \right){\rm{d}}\xi } = \frac{1}{x}\int\limits_0^x {{\beta _{\rm{v}}}\left( \xi \right){\rm{d}}\xi } = }\\ {\frac{{{\rho _{\rm{w}}}}}{{{\rho _{\rm{w}}} - {\rho _{\rm{s}}}}}\left( {1 - \frac{{{\rho _{\rm{s}}}}}{{\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)x}}\ln \left( {1 + \frac{{{\rho _{\rm{w}}} - {\rho _{\rm{s}}}}}{{{\rho _{\rm{s}}}}}x} \right)} \right)} \end{array}$ (8)

 $\frac{d}{{{\rm{d}}t}}\left( {{\rho _{\rm{s}}}{{\bar \beta }_{\rm{v}}}{V_{\rm{b}}} + {\rho _{\rm{w}}}\left( {1 - {{\bar \beta }_{\rm{v}}}} \right){V_{\rm{b}}}} \right) = {W_{{\rm{dc}}}} - {W_{\rm{b}}}$ (9)

 ${h_{\rm{m}}} = x{h_{\rm{s}}} + \left( {1 - x} \right){h_{\rm{w}}}$ (10)

 $\begin{array}{*{20}{c}} {\frac{{{\rm{d}}\left( {{\rho _{\rm{s}}}{{\bar \beta }_{\rm{v}}}{V_{\rm{b}}}{h_{\rm{s}}} + {\rho _{\rm{w}}}\left( {1 - {{\bar \beta }_{\rm{v}}}} \right){V_{\rm{b}}}{h_{\rm{w}}} - {V_{\rm{b}}}P + {m_{\rm{b}}}{C_{\rm{p}}}T} \right)}}{{{\rm{d}}t}} = }\\ {Q + {W_{{\rm{dc}}}}{h_{\rm{w}}} - {W_{\rm{b}}}{h_{\rm{m}}}} \end{array}$ (11)

 ${L_{\rm{r}}} = {L_{{\rm{dc}}}} - {L_{\rm{b}}}$ (12)

 $\begin{array}{*{20}{c}} {\frac{1}{2}k\frac{{{W_{{\rm{dc}}}}^2}}{{{A_{{\rm{dc}}}}^2{\rho _{\rm{w}}}}} = }\\ {{\rho _{\rm{w}}}g{L_{{\rm{dc}}}} - \left( {{{\hat \beta }_{\rm{v}}}{\rho _{\rm{s}}} + \left( {1 - {{\hat \beta }_{\rm{v}}}} \right){\rho _{\rm{w}}}} \right)g{L_{\rm{b}}} - {\rho _{\rm{w}}}g{L_{\rm{r}}}} \end{array}$ (13)

 $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {{\rho _{\rm{s}}}{V_{{\rm{sr}}}}} \right) = x{W_{\rm{b}}} - {W_{{\rm{sr}}}} - {W_{{\rm{cr}}}}$ (14)

 ${W_{{\rm{sr}}}} = x{W_{\rm{b}}} - \frac{{{\rho _{\rm{s}}}}}{{{t_{\rm{r}}}}}\left( {{V_{{\rm{sr0}}}} - {V_{{\rm{sr}}}}} \right)$ (15)
 $\begin{array}{*{20}{c}} {{W_{{\rm{cr}}}} = \frac{1}{{{h_{\rm{s}}} - {h_{\rm{w}}}}}\left[ {{\rho _{\rm{s}}}{V_{{\rm{sr}}}}\frac{{{\rm{d}}{h_{\rm{s}}}}}{{{\rm{d}}t}} + {\rho _{\rm{w}}}{V_{{\rm{wr}}}}\frac{{{\rm{d}}{h_{\rm{w}}}}}{{{\rm{d}}t}} - } \right.}\\ {\left. {\left( {{V_{{\rm{sr}}}} - {V_{{\rm{wr}}}}} \right)\frac{{{\rm{d}}P}}{{{\rm{d}}t}} + {m_{\rm{r}}}{C_{\rm{p}}}\frac{{{\rm{d}}T}}{{{\rm{d}}t}}} \right]} \end{array}$ (16)
 ${V_{{\rm{wr}}}} = {V_{{\rm{wt}}}} - {V_{{\rm{dc}}}} - \left( {1 - {{\bar \beta }_{\rm{v}}}} \right){V_{\rm{b}}}$ (17)

 $L = \frac{{{V_{{\rm{sr}}}} + {V_{{\rm{wr}}}}}}{{{A_{\rm{r}}}}} + {L_{\rm{b}}}$ (18)

 $\left\{ \begin{array}{l} {a_{11}}\frac{{{\rm{d}}{V_{{\rm{wt}}}}}}{{{\rm{d}}t}} + {a_{12}}\frac{{{\rm{d}}P}}{{{\rm{d}}t}} = {W_{{\rm{fw}}}} - {W_{\rm{s}}}\\ {a_{21}}\frac{{{\rm{d}}{V_{{\rm{wt}}}}}}{{{\rm{d}}t}} + {a_{22}}\frac{{{\rm{d}}P}}{{{\rm{d}}t}} = Q + {W_{{\rm{fw}}}}{h_{{\rm{fw}}}} - {W_{\rm{s}}}{h_{\rm{s}}}\\ {a_{32}}\frac{{{\rm{d}}P}}{{{\rm{d}}t}} + {a_{33}}\frac{{{\rm{d}}x}}{{{\rm{d}}t}} = Q - x{W_{{\rm{sc}}}}\left( {{h_{\rm{s}}} - {h_{\rm{w}}}} \right)\\ {a_{42}}\frac{{{\rm{d}}P}}{{{\rm{d}}t}} + {a_{44}}\frac{{{\rm{d}}{V_{{\rm{sr}}}}}}{{{\rm{d}}t}} = \frac{{{\rho _{\rm{s}}}}}{{{t_{\rm{r}}}}}\left( {{V_{{\rm{sr0}}}} - {V_{{\rm{sr}}}}} \right) \end{array} \right.$ (19)

 ${a_{11}} = {\rho _{\rm{w}}} - {\rho _{\rm{s}}}$
 ${a_{12}} = {V_{{\rm{wt}}}}\frac{{\partial {\rho _{\rm{w}}}}}{{\partial P}} - {V_{{\rm{st}}}}\frac{{\partial {\rho _{\rm{s}}}}}{{\partial P}}$
 ${a_{21}} = {\rho _{\rm{w}}}{h_{\rm{w}}} - {\rho _{\rm{s}}}{h_{\rm{s}}}$
 $\begin{array}{l} {a_{22}} = {V_{{\rm{wt}}}}\left( {{h_{\rm{w}}}\frac{{\partial {\rho _{\rm{w}}}}}{{\partial P}} + {\rho _{\rm{w}}}\frac{{\partial {h_{\rm{w}}}}}{{\partial P}}} \right) + \\ \;\;\;\;\;\;\;\;{V_{{\rm{st}}}}\left( {{h_{\rm{s}}}\frac{{\partial {\rho _{\rm{s}}}}}{{\partial P}} + {\rho _{\rm{s}}}\frac{{\partial {h_{\rm{s}}}}}{{\partial P}}} \right) - {V_{\rm{t}}} + {m_{\rm{t}}}{C_{\rm{p}}}\frac{{\partial T}}{{\partial P}} \end{array}$
 $\begin{array}{l} {a_{32}} = \left( {{\rho _{\rm{w}}}\frac{{\partial {h_{\rm{w}}}}}{{\partial P}} - x\left( {{h_{\rm{s}}} - {h_{\rm{w}}}} \right)\frac{{\partial {\rho _{\rm{w}}}}}{{\partial P}}} \right)\left( {1 - {{\bar \beta }_{\rm{v}}}} \right){V_{\rm{b}}} + \\ \;\;\;\;\;\;\;\;\left( {{\rho _{\rm{s}}}\frac{{\partial {h_{\rm{s}}}}}{{\partial P}} - \left( {1 - x} \right)\left( {{h_{\rm{s}}} - {h_{\rm{w}}}} \right)\frac{{\partial {\rho _{\rm{s}}}}}{{\partial P}}} \right){{\bar \beta }_{\rm{v}}}{V_{\rm{b}}} + \\ \;\;\;\;\;\;\;\;\left( {{\rho _{\rm{s}}} + x\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)} \right)\left( {{h_{\rm{s}}} - {h_{\rm{w}}}} \right)\frac{{\partial {{\bar \beta }_{\rm{v}}}}}{{\partial P}}{V_{\rm{b}}} - {V_{\rm{b}}} + \\ \;\;\;\;\;\;\;\;{m_{\rm{r}}}{C_{\rm{p}}}\frac{{{\rm{d}}T}}{{{\rm{d}}P}} \end{array}$
 ${a_{33}} = \left( {\left( {1 - x} \right){\rho _{\rm{s}}} + x{\rho _{\rm{w}}}} \right)\left( {{h_{\rm{s}}} - {h_{\rm{w}}}} \right){V_{\rm{b}}}\frac{{\partial {{\bar \beta }_{\rm{v}}}}}{{\partial x}}$
 $\begin{array}{l} {a_{42}} = {V_{{\rm{sr}}}}\frac{{\partial {\rho _{\rm{s}}}}}{{\partial P}} + \frac{1}{{{h_{\rm{s}}} - {h_{\rm{w}}}}}\left( {{\rho _{\rm{s}}}{V_{{\rm{sr}}}}\frac{{{\rm{d}}{h_{\rm{s}}}}}{{{\rm{d}}P}} + {\rho _{\rm{w}}}{V_{{\rm{wr}}}}\frac{{{\rm{d}}{h_{\rm{w}}}}}{{{\rm{d}}P}} - } \right.\\ \;\;\;\;\;\;\;\;\left. {\left( {{V_{{\rm{sr}}}} + {V_{{\rm{wr}}}}} \right) + {m_{\rm{r}}}{C_{\rm{p}}}\frac{{{\rm{d}}T}}{{{\rm{d}}P}}} \right) \end{array}$
 ${a_{44}} = {\rho _{\rm{s}}}$
 $\begin{array}{*{20}{c}} {\frac{{\partial {{\bar \beta }_{\rm{v}}}}}{{\partial P}} = \frac{{\left( {{\rho _{\rm{w}}}\frac{{{\rm{d}}{\rho _{\rm{s}}}}}{{{\rm{d}}P}} - {\rho _{\rm{s}}}\frac{{{\rm{d}}{\rho _{\rm{w}}}}}{{{\rm{d}}P}}} \right)}}{{{{\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)}^2}}} \cdot \left( {1 + \frac{{{\rho _{\rm{w}}}}}{{x{\rho _{\rm{w}}} + \left( {1 - x} \right){\rho _{\rm{s}}}}} - } \right.}\\ {\left. {\frac{{{\rho _{\rm{w}}} + {\rho _{\rm{s}}}}}{{x\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)}}\ln \left( {x{p_{\rm{w}}} + \frac{{\left( {1 - x} \right){p_s}}}{{{\rho _{\rm{s}}}}}} \right)} \right)} \end{array}$
 $\begin{array}{*{20}{c}} {\frac{{\partial {{\bar \beta }_{\rm{v}}}}}{{\partial x}} = {\rho _{\rm{w}}}\left[ {\frac{{{\rho _{\rm{s}}}}}{{x\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)}}\ln \left( {\frac{{x{\rho _{\rm{w}}} + \left( {1 - x} \right){\rho _{\rm{s}}}}}{{{\rho _{\rm{s}}}}}} \right) - } \right.}\\ {\left. {\frac{{{\rho _{\rm{s}}}}}{{x{\rho _{\rm{w}}} + \left( {1 - x} \right){\rho _{\rm{s}}}}}} \right]/x\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)} \end{array}$
 $\begin{array}{l} {W_{\rm{b}}} = {W_{{\rm{dc}}}} - {V_{\rm{b}}}\left[ {{{\bar \beta }_{\rm{v}}}\frac{{{\rm{d}}{\rho _{\rm{s}}}}}{{{\rm{d}}P}} + \left( {1 - {{\bar \beta }_{\rm{v}}}} \right)\frac{{{\rm{d}}{\rho _{\rm{w}}}}}{{{\rm{d}}P}} + } \right.\\ \;\;\;\;\;\;\;\left. {\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)\frac{{\partial {{\bar \beta }_{\rm{v}}}}}{{\partial P}}} \right]\frac{{{\rm{d}}P}}{{{\rm{d}}t}} + {V_{\rm{b}}}\left( {{\rho _{\rm{w}}} - {\rho _{\rm{s}}}} \right)\frac{{\partial {{\bar \beta }_{\rm{v}}}}}{{\partial x}}\frac{{{\rm{d}}x}}{{{\rm{d}}t}} \end{array}$

$\frac{{\partial {h_{\rm{s}}}}}{{\partial p}}$为例，本文中热工参数关于饱和压力的导数在间隔取的极小的情况下，偏导数可以用$\frac{{\partial {h_{\rm{s}}}}}{{\partial p}} = \frac{{{h_{{{\rm{s}}_2}}} - {h_{{{\rm{s}}_1}}}}}{{{p_2} - {p_1}}}$来近似(下标1、2分别代表前一时刻值与后一时刻值)。

2 仿真结果分析

2.1 蒸汽流量扰动

 Download: 图 1 蒸汽流量扰动时各参量动态响应曲线 Fig. 1 Dynamic response curve of each parameter with steam flow diaturbance

 Download: 图 2 不同工况水位响应对比曲线 Fig. 2 The water level response contrast curves in different conditions

2.2 换热量扰动

 Download: 图 3 换热量扰动时各参量动态响应曲线 Fig. 3 Dynamic response curve of each parameter with heat exchange diaturbance

 Download: 图 4 不同工况相同换热量水位响应对比曲线 Fig. 4 The water level response contrast curves of the same heat exchange in different conditions

3 SG串级PID控制与仿真结果 3.1 控制系统结构与原理

 Download: 图 5 SG串级PID控制结构图 Fig. 5 The cascade PID control structure diagram of SG

3.2 控制系统仿真结果 3.2.1 蒸汽流量扰动

 Download: 图 6 蒸汽流量扰动水位响应曲线 Fig. 6 The water level response curve with steam flow disturbance

3.2.2 换热量扰动

 Download: 图 7 换热量扰动水位响应曲线 Fig. 7 The water level response curve with heat exchange diaturbance

4 结论

1) 本文成功建立了一种既能反映一定热工特性又便于控制系统设计的自然循环蒸汽发生器四阶动态水位机理模型，为后期控制系统设计提供了很大便利。

2) 当引入负荷扰动及热量扰动时，蒸汽发生器主要参数都表现出合理的变化趋势，准确的模拟出了虚假水位现象。

3) 验证了串级PID控制系统基本上能满足蒸汽发生器水位控制的要求。

4) 由于计算机技术和信息技术的迅猛发展，导致控制理论与控制技术不断向前推进，一些尖端的控制策略不断被提出，在低工况、大扰动下，水位特性参数变化大，控制效果不佳，控制器参数难以整定，因此本文对后期研究更为先进的控制方法有重要的指导意义。

 [1] 彭敏俊. 船舶核动力装置[M]. 哈尔滨: 原子能出版社, 2011. PENG Minjun. Marine nuclear power plant[M]. Harbin: Atomic Energy Press, 2011. (0) [2] BAO Jie, SUN Baozhi, ZHANG Guolei. Simulation and analysis of steam generator water level based on nonlinear level model[C]//2012 Asia-Pacific Power and Energy Engineering Conference. Shanghai, China, 2012: 1-4. (0) [3] ZHAO Futao, OU Jing, DU Wei. Simulation modeling of nuclear steam generator water level process-a case study[J]. ISA transactions, 2000, 39(2): 143-151. DOI:10.1016/S0019-0578(00)00015-X (0) [4] BASHER A M H. Development of a robust model-based water level controller for U-tube steam generator[R]. ORNL Oak Ridge National Laboratory (US), 2001. (0) [5] ZHOU Gang, ZHANG Dafa, YANG Shiben. Simulation and analysis on dynamics characteristic for nuclear steam generator water level process[J]. Journal of system simulation, 2006, 18(12): 3383-3386. (0) [6] 蒸汽发生器编写组. 蒸汽发生器[M]. 北京: 原子能出版社, 1982. (0) [7] ÅSTRÖM K J, BELL R D. Drum-boiler dynamics[J]. Automatic, 2000, 36(3): 363-378. DOI:10.1016/S0005-1098(99)00171-5 (0) [8] KIM H, CHOI S. A model on water level dynamics in natural circulation drum-type boilers[J]. International communications in heat and mass transfer, 2005, 32(6): 786-796. DOI:10.1016/j.icheatmasstransfer.2004.10.010 (0) [9] 史达明, 马文智. 自然循环锅炉蒸发区动态数学模型[J]. 中国电机工程学报, 1990, 10(1): 68-72. SHI Daming, MA Wenzhi. The mathematical model of evaporation zone of nature circulation boiler[J]. Proceedings of the CSEE, 1990, 10(1): 68-72. (0) [10] 郭广跃, 袁景淇, 袁嘉婧, 等. 自然循环锅炉汽水系统动态模型的建立[J]. 控制工程, 2010, 17(S2): 39-41. GUO Guangyue, YUAN Jingqi, YUAN Jiajing, et al. Modeling for the steam-water system of the natural circulation boilers in the power plant[J]. Control engineering of China, 2010, 17(S2): 39-41. (0) [11] 王卓, 付冬梅, 刘德军. 锅炉汽包水位控制系统的研究[J]. 自动化仪表, 2006, 27(11): 51-52, 56. WANG Zhuo, FU Dongmei, LIU Dejun. The study on drum water level control system for boiler[J]. Process automation instrumentation, 2006, 27(11): 51-52, 56. DOI:10.3969/j.issn.1000-0380.2006.11.016 (0) [12] IRVING E, MIOSSEC C, TASSART J. Towards efficient full automatic operation of the PWR steam generator with water level adaptive control[C]//Proceedings of the 2nd International Conference on Boiler Dynamics and Control in Nuclear Power Stations 2. London: British Nuclear Energy Society, 1980. (0) [13] 刘金琨. 先进PID控制MATLAB仿真[M]. 北京: 电子工业出版社, 2004. (0)