﻿ 大扰动下船舶柴油发电机组非线性建模与仿真
 舰船科学技术  2018, Vol. 40 Issue (4): 77-81 PDF

1. 大连海事大学 轮机工程学院，辽宁 大连 116026;
2. 青岛远洋船员职业学院 机电系，山东 青岛 266071

Non-linear modeling and dynamic simulation of diesel engine generator system under large disturbance
MA Chuan1,2, LI Di-yang2, LIU Yan-cheng1, JIANG Meng2
1. School of Marine Engneering, Dalian Maritime University, Dalian 116026, China;
2. Qingdao Ocean Shipping Mariners College, Qingdao 266071, China
Abstract: In view of the low order mathematical model of the marine diesel generator, it will cause big error in the analysis under large disturbance. Based on the analysis of the marine diesel generator. The seven order nonlinear mathematical model of synchronous generator, diesel engine, speed regulation system and excitation system is established and solved. At the same time, simulation curve of speed and voltage are drawn. Then, we analysis and comparison of the indicators of the curve, the results show that the nonlinear mathematical model fulfills specification requirements.
Key words: diesel generator set     large disturbance     non-linear model     implicit trapezoidal integration method
0 引　言

1 船舶柴油发电机组系统

 图 1 船舶柴油发电机组系统框图 Fig. 1 System diagram of marine diesel generator
2 船舶柴油发电机组非线性建模 2.1 同步发电机数学模型

1）电压方程

 $\left\{ \begin{array}{l}{u_d} = \displaystyle\frac{{\rm d}}{{{\rm d}{t_{}}}}{\varPsi _d} - {\omega _{}}{\varPsi _q} - {r_a}{i_d}\text{，}\\{u_q} = \displaystyle\frac{{\rm d}}{{{\rm d}{t_{}}}}{\varPsi _q} + {\omega _{}}{\varPsi _d} - {r_a}{i_q}\text{，}\\{u_0} = \displaystyle\frac{{\rm d}}{{{\rm d}{t_{}}}}{\varPsi _0} - {r_a}{i_0}\text{。}\end{array} \right.$ (1)
 $\left\{ \begin{array}{l}{u_f} = \displaystyle\frac{{\rm d}}{{{\rm d}t}}{\varPsi _f} + {r_f}{i_f}\text{，}\\{u_D} = \displaystyle\frac{{\rm d}}{{{\rm d}{t_{}}}}{\varPsi _D} + {r_D}{i_D} \equiv 0\text{，}\\{u_Q} = \displaystyle\frac{{\rm d}}{{{\rm d}{t_{}}}}{\varPsi _Q} + {r_Q}{i_Q} \equiv {\rm{0}}\text{。}\end{array} \right.$ (2)

2）磁链方程

 $\begin{split}& \left[ {\begin{array}{*{20}{c}}{{\varPsi _{{\rm{ }}dq0}}}\\{{\varPsi _{fDQ}}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{\varPsi _d}}\\{{\varPsi _q}}\\{{\varPsi _0}}\\{{\varPsi _f}}\\{{\varPsi _D}}\\{{\varPsi _Q}}\end{array}} \right] = \\& \left[ {\begin{array}{*{20}{c}}{{X_d}}&0&0&{{X_{ad}}}&{{X_{ad}}}&0\\0&{{X_q}}&0&0&0&{{X_{aq}}}\\0&0&{{X_0}}&0&0&0\\{{X_{ad}}}&0&0&{{X_f}}&{{M_R}}&0\\{{X_{ad}}}&0&0&{{M_R}}&{{X_D}}&0\\0&{{X_{aq}}}&0&0&0&{{X_Q}}\end{array}} \right]\left[ {\begin{array}{*{20}{r}}{ - {i_d}}\\{ - {i_q}}\\{ - {i_0}}\\{{i_f}}\\{{i_D}}\\{{i_D}}\end{array}} \right]\text{。}\end{split}$ (3)

1）定子励磁电势

 ${{{E}}_{{f}}}{{ = }}{{{X}}_{{{ad}}}}\frac{{{{{u}}_{{f}}}}}{{{{{r}}_{{f}}}}}\text{，}$ (4)

2）电机q轴空载电动势

 ${E_q} = {X_{ad}}{i_f}\text{，}$ (5)

3）电机q轴瞬变电动势

 ${E_q}' = \frac{{{X_{ad}}}}{{{X_f}}}{\varPsi _f}\text{，}$ (6)

4）电机q轴超瞬变电动势

 ${E_q}'' = \frac{{{X_{ad}}}}{{{X_f}{X_D} - {X_{ad}}^2}}({X_{D1}}{\varPsi _f} + {X_{f1}}{\varPsi _D})\text{，}$ (7)

5）电机d轴超瞬变电动势

 ${E_d}'' = - {X_{ad}}{var\varPsi _Q}/{X_Q}\text{。}$ (8)

1）定子电压方程

 \begin{aligned}& {u_d} = \frac{{{\rm d}{\varPsi _d}}}{{{\rm d}t}} - \omega {\varPsi _q} - {r_a}{i_d}\text{，}\\& {u_q} = \frac{{{\rm d}{\varPsi _q}}}{{{\rm d}t}} + \omega {\varPsi _d} - {r_a}{i_q}\text{。}\end{aligned} (9)

 \begin{aligned}& {\varPsi _d} = {{E''}_q} - {{X''}_d}{i_d}\text{，}\\& {\varPsi _q} = - {{E''}_d} - {{X''}_q}{i_q}\text{。}\end{aligned} (10)

2）转子电压方程

f绕组 ：

 ${{{T'}}_{{{d0}}}}\frac{{{{\rm d}}{{{{E'}}}_{{q}}}}}{{{{{\rm d}t}}}}{{ = }}{{{E}}_{{f}}}{{ - }}\frac{{{{{X}}_{{d}}}{{ - }}{{{{X''}}}_{{d}}}}}{{{{{{X'}}}_{{d}}}{{ - }}{{{{X''}}}_{{d}}}}}{{{E'}}_{{q}}}{{ + }}\frac{{{{{X}}_{{d}}}{{ - }}{{{{X'}}}_{{d}}}}}{{{{{{X'}}}_{{d}}}{{ - }}{{{{X''}}}_{{d}}}}}{{{E''}}_{{q}}}\text{，}$ (11)

D绕组：

 ${T''_{d0}}\frac{{{\rm d}{{E''}_q}}}{{{\rm d}t}} = - {E''_q} + {E'_q} - \left( {{{X'}_d} - {{X''}_d}} \right){i_d}\text{，}$ (12)

Q绕组：

 ${T''_{q0}}\frac{{{\rm d}{{E''}_d}}}{{{\rm d}t}} = - {E''_d} + \left( {{X_q} - {{X''}_q}} \right){i_q}\text{。}$ (13)

3）转子运动方程

 $\left\{ \begin{array}{l}{T_J}\displaystyle\frac{{{\rm d}\omega }}{{{\rm d}t}} = {T_m} - {T_e} - D\left( {\omega - 1} \right)\text{，}\\\displaystyle\frac{{{\rm d}\delta }}{{{\rm d}t}} = \omega - 1\text{。}\end{array} \right.$ (14)

4）电磁转矩表达式

 ${T_e} = {E''_q}{i_q} + {E''_d}{i_d} - \left( {{{X''}_d} - {{X''}_q}} \right){i_q}{i_d}\text{。}$ (15)

2.2 柴油机及其调速系统数学模型

 $J\frac{{{\rm d}\Delta \omega }}{{{\rm d}t}} = \Delta {T_d} - \Delta {T_r}\text{。}$ (16)

 ${\left( {\frac{{\partial {T_d}}}{{\partial {f_i}}}} \right)_0} = \frac{{{T_{d0}}}}{{{f_{i0}}}}\text{，}$ (17)

 $J\frac{{{\rm d}\Delta \omega }}{{{\rm d}t}} + {C_1}\Delta \omega = \frac{{{T_{d0}}}}{{{f_{i0}}}}\Delta {f_i} - \Delta {T_r}\text{，}$ (18)

 $\Delta {f_i} = {k_p} \cdot \Delta \omega + {k_i} \cdot \int_0^h {\Delta \omega } {\rm d}t + {k_d} \cdot \frac{{{\rm d}\Delta \omega }}{{{\rm d}t}}\text{。}$ (19)

$\Delta {f_i}$ 可认为是调速器的输出量，即喷油量调整量，而调速器的输入为转速差信号 $\Delta \omega$ ，输出量是转速的比例项、积分项和微分项的线性组合。

2.3 励磁系统数学模型

 ${E_f} = {k_p} \cdot \Delta U + {k_i} \cdot \int_0^h {\Delta U} {\rm d}t + {k_d} \cdot \frac{{{\rm d}\Delta U}}{{{\rm d}t}}\text{。}$ (20)
3 基于隐式梯形积分法的仿真算例

 $\frac{{\rm d}y}{{{\rm d}t}} = f(y,z,t)\text{，}$ (21)

 ${y_{n + 1}} = {y_n} + \frac{h}{2}\left[ {f({y_n},{z_n},{t_n}) + f({y_{n + 1}},{z_{n + 1}},{t_{n + 1}})} \right]\text{，}$ (22)
 ${{g(}}{{{y}}_{{{n + 1}}}}{\rm{,}}{{{z}}_{{{n + 1}}}}{\rm{,}}{{{t}}_{{\rm{n + 1}}}}{\rm{) = 0}}\text{。}$ (23)

 图 2 C#求解流程图 Fig. 2 Solution flow chart of C#
4 大扰动下柴油发电机组动态仿真分析

4.1 船舶柴油发电机组仿真参数取值

4.2 仿真曲线分析

 图 3 突加负载时转速变化曲线 Fig. 3 Speed change curve under sudden load

 图 4 突加负载时电压变化曲线 Fig. 4 Voltage change curve under sudden load