英雄联盟删除的英雄:第六章 电力系统稳定性

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----------------------- Page 1-----------------------                       第六章 电力系统稳定性 本章重点内容: 1.  不同形式的转子运动方程,功角的概念; 2. 凸极和隐极发电机以各种电势表示的输出功率与功角关系——功角特性; 3. 电力系统静态稳定的基本概念,静态稳定判据,静态稳定储备系数; 4. 静态稳定性分析的小干扰法; 5.  提高电力系统静态稳定性的具体措施; 6. 电力系统暂态稳定的基本概念,等面积定则; 7.  提高电力系统暂态稳定性的具体措施。 一、稳态运行状态     稳态运行状态:系统中并列运行得发电机都保持相同得角速度运转,系统中
的状态变量保持不变。
     电力系统的稳定,电力系统受到大的或微小的扰动之后,系统能否恢复到原
来的运行状态或过渡到新的运行状态。
     暂态稳定-系统受到大的扰动,能否恢复到原来的运行状态或过渡到新的运
行状态。短路或大的发电机组突然退出运行,状态量发生比较大的偏移,强非线
性问题,不能用线性话方法解决。
   静态稳定-电力系统受到一个微小的扰动后,能否恢复到原来的运行状态,
或者过渡到一个新的运行状态,如负荷波动,状态偏移比较小,可以用线性话方
法解决。            
状态方程:A         AX  ?BU 二、 转子运动方程                               d? 1
                                      (P  ?P  )
                               dt   T   T    E
                                     j     T  -当转子受到额定转矩作用,转子的转速由0 加到额定转速所用的时间。
     j     d?
         (???1)?
              0           0
    dt 三、 电磁功率                                                        U                                                I ----------------------- Page 2-----------------------如上所示,单机无穷大系统                                                      
                                                
                                       P     Re  UI I
                                         E       ? ?
                                                
                                       U    Ud  ?jU q                                        I    I d ?jI q                                        P     U  I   ?U  I
                                         E     d  d     q  q 隐极机相量图如下: 159 页                            x      x   ?x   ?x      x    ?x    ?x   ?x
                            d ?     d    T     L     ad    ?     T     L                                    
                           Eq    U ?jx d I                                                  
                           UG    U ?j (x T  ?xL )I                                       
                           E    U ?jxd I                            P     U  I   ?U  I
                            E      d  d     q q                            U     E   ?I   x
                             q     q     d d ?                            U     I  x
                             d     q d ?                                  E  U
                           P       q   sin?
                            E
                                 x
                                   d ?                                              2
                              E  U          U    x   ?x?
用暂态电抗表示:P ?= q                      sin??  d ?           d ?sin 2?
                         E
                          q
                              x ?            2    x   x?
                                d ?                 d ? d ? 对如下简单系统:                                                                              S                                                E  U
                                        P        q   sin?
                                          E
                                               x
                                                 d ? 如下图简单系统的功率特性 176 页                                 dP
                                   E
简单电力系统静态判据:  ?0
                                 d? ----------------------- Page 3-----------------------静态稳定储备系数:                                   P   ?P
                             k     M     0 ?100%
                              m      P
                                      0                                    E U
                             P      q
                              M
                                   x
                                    d ? P 初始功率
 0 潮流越大,静态稳定性越差。 P      传输功率极限 (静态稳定)
 M 四、 小干扰法分析电力系统静态稳定性 小干扰法――在系统初始运行条件下对系统进行线性化处理,得出系统的状态方
程,求线性系统的稳定性。       d?
    
           (??1)?
                  0
      dt
    
    
      d? 1
             (P  ?P  )
                T    E
       dt   T
            j
    
     
       0
    
     
       0
     d??
          
      dt         0      d (1???)    d?? 1  ?  E       U            ?
                           P  ? q    sin(????)
                          T             0       ?
         dt       dt    Tj ?  xd ?              ?
          E U               E  U          dP         1 d 2 P
           q                  q             E              E        2
     P         sin(????)         sin ??(      )    ? (      )    ????
      E            0                  0        ??            ??
                                                 0        2     0
          x                  x            d?        2   d?
           d ?                d ?        E U          dP
     q   sin??(     E )   ?? P    ??P
                0        ??        0    E
       x            d? 0
        d ? 所以:                             d??
                          
                                  
                           dt           0
                          
                          
                            d??  1         dP
                                  (      E  )
                           dt       Tj     d?
                                              
                                                  0 上式写成矩阵形式:                                 0          ??
                                               0
                          
                                              
                                              
                                              
                                 1  dP
                          (         E )    0  ? ?
                                           
                                        0      ? ?
                        T        d?
                                j              ?
                                               它的一般形式为: ----------------------- Page 4-----------------------                                   
                                  X   A?X
求得A 的特征值?为:                                      dP
                               0       (  E  )
                              1, 2    T    d?
                                       j
                                               
                                                0         dP
     当(   E  )? ?0 ,系统不稳定;
        d? 0         dP
     当(   E  )? ?0 时,系统将作等幅振荡,若系统中存在着正的阻尼因素,则??
        d? 0 和??作衰减振荡,即系统受到小干扰后经过衰减振荡,最后恢复同步。
     发电机的阻尼绕组可提供阻尼功率
阻尼绕组对系统静态稳定性的影响                             d?
                                  (??1)?
                                         0
                             dt
                           
                          
                             d? 1
                                    (P  ?P  ?P  )
                                       T   E    D
                             dt   T
                                  j
                                      0          ??
                         0
     
                        
                        
                         
得          ?1  dP      ?1
     (        E  )      ? ?
                      
                  0      ? ?
   T       d?      T
          j             j ?
                               D     1     2         dP
               D  ?4?T  (    E  )
 1,2  2Tj   2Tj          0 j d??                                   0 1)D ?0,系统不稳定                  dP                    dP
2)D ?0 时,若(         E  )? ?0 稳定;若(       E )? ?0  不稳定;
                  d? 0                 d? 0 五、提高电力系统稳定性的措施 1, 采用自动励磁装置
2, 减小元件电抗
    1) 分裂导线;
    2) 串联电容器;
3, 提高电压等级
4, 采用并联补偿或改变网络结构 六、电力系统暂态稳定性      物理过程分析:图8-1  (a)所示为一简单系统,正常运行时发电机经变压
器和双回线路向无限大系统送电。
205 页 ----------------------- Page 5-----------------------                 E  U
           P       q  sin?
            
                 x
故障前:              d??
                              x
                                L
           x       x  ?x    ? ?x
             d??    d     T 1        T 2
                               2 故障期间在故障处叠加一个电抗x?                               E  U
                        P       q   sin ?
                         
                              x
                                d???                                                                     x
                                                        (xd ?x T1 )( L ?xT2 )
                                            xL                      2
                        x       x  ?x    ? ?x         ?
                          d??    d     T1          T2
                                            2                     x? 故障后:                                            E  U
                                    P        q   sin ?
                                    
                                          x
                                            d????                                     x       x   ?x    ?x   ?x
                                     d????    d    T1    L     T2 等面积定则                                d?
                                    
                                            0
                               dt
                               d? d?? 1
                                                 (P  ?P   )
                               dt      dt     T    T     E
                                               j                                     
                                      C
                              A        (P   ?P   )d?
                                1   ?T         E
                                    
                                      0                                  d??
                              T           P  ?P
                                j  dt      T    E                                  d??                         d?
                              T        ???? (P         ?P   )
                                j             0      T    E
                                   dt                         dt                                                    
                                                       C
                                   T ????d??             (P  ?P  )d?
                              j            0        ?T          E
                                                   
                                 0                     0                                         2       2
                                     
                              T ?  c            0      C (P ?P  )d?
                                j  0                ?T          ??
                                                    
                                          2           0                                     
                                      C
                              A         (P  ?P  )d?
                                2   ?T          E
                                    
                                      0                                        1       ??
                                Tj? (??)         e
                                     0         ??
                                       2         c                                        1       2
                                Tj? (???)
                                     0         c
                                       2  A1    A2  ,面积相等 能量转化与守恒
求极限切除角 ----------------------- Page 6-----------------------                                               
                        cr                       ?
                          (P  ?P    sin ?)d?  h    (P    sin??P  )d?
                       T        M??           ? M???             T
                                              
                        0                        cr                                 P  (???) ?P        cos??P       cos?
                       cos?  T       h    0     M???    h    M??     0
                            cr                P    ?P
                                               M???   M?? 多机电力系统暂态分析
      1、.数值仿真法
     2  、能量函数法
提高系统暂态稳定性的措施
      1、快速切除故障
     2、自动重合闸成功,有利于稳定性;不成功,恶化系统稳定性。
      3、强行励磁
     4、电气制动,注意电阻大小与时间的配合。
      5、变压器中性点经小电阻接地。
      6、减小机械功率。