Управление качеством переходных процессов в многосвязных системах. Задание на курсовое проектирование, страница 8

В (2.34) исключим I_d с помощью (2.26)

       U₀cosd₀     E_q                                                                                             I_d = ———– – —–                                                                             (2.36)                     X_d          X_d

       E_qU₀                U₀(X_d–X_q)sind₀*U₀*cosd₀                                                    P = ––––– sind₀+ ———————————— –                                                                 X_q                                  X_qX_d

   U₀(X_d–X_q)sind₀*E_q                                                                                         – ————————–                                                                       (2.37)                      X_qX_d

Таким образом:

     E_qU₀               U₀²(X_d–X_q)                                                                            P= ––––– sind₀+ —————– sin2d₀                                                (2.38)                       X_q                    2X_qX_d

В уравнении (2.38) U₀ = const, то есть DU₀ = 0. Поэтому линеаризованное уравнение принимает вид:

        ¶P            ¶P              E_qUo                U₀²(X_d–X_q)                                     DP = –— Dd+ —— DE_q=  ——– cosd₀ + —————— cos2d₀ Dd +          

                  ¶d           ¶E_q                X_d                       X_qX_d

   U₀sind₀                                                                                                  

        + ———— DE_q                                                                                  (2.39)                X_d

Исключим из (2.28) DI_d, используя (2.26):

      U₀cosd₀     E_q                                                                                             I_d = —–—— – —–                                                                              (2.40)                     X_d         X_d

           U₀sind₀           DE_q                                                                                  DI_d = – ———– Dd – —––                                                                  (2.41)                         X_d                X_d

                            X_d – X'_d                       X_d – X'_d                                             (X_d – X'_d)DI_d = – ———— U₀sind₀Dd – ———— DE_q                      (2.42)                                           X_d                                 X_d

Тогда уравнение (2.28) примет вид: