Synchronous motor model in numerical simulation of machine network transient process Dai Jiayu (Shenzhen Energy Group Co., Ltd., Shenzhen 518054, Guangdong Province) Really undamped winding synchronous motor model, by using the first solution and then using the trapezoid method to find the product Differentiating the voltage equations of the synchronous motor successfully eliminates the coupling between the direct-axis voltage equation of the synchronous motor and the cross-axis voltage equation caused by the rotating potential, and derives the mutually decoupled direct and orthogonal axes. Transient equivalent circuit. The simulation results of the model and the E T P model are compared by an example. It is proved that the new model is correct and its simulation algorithm is more accurate and stable than the E TP algorithm.
1 Introduction In the numerical simulation of the transient process of the power system network, for synchronous motors, the dqo coordinate system is used to describe almost without exception. However, the rotational potential in the voltage equations expressed by the differential equation in the dqo coordinate system makes the coupling between the direct-axis voltage equation and the cross-axis voltage equation. How to deal with the rotating potential is the key to the numerical simulation of synchronous motors. So far, there are two main methods for numerical simulation of synchronous motors. It is a differential method with coupling, which uses the implicit trapezoidal method to directly differentiate the voltage equations of synchronous motors and solve them simultaneously with the flux equations. At this time, there is coupling between the direct-axis component and the cross-axis component. One synchronous motor is described by 12 simultaneous differential and algebraic equations, and the formation of the coefficient matrix is â€‹â€‹not regular, and it is not easy to program. Decoupling calculations cannot be implemented, so practical applications are few. The second simulation method is an estimated equivalent circuit method model, which uses an implicit trapezoidal method to differentiate parts other than the rotating potential in the voltage equations to obtain a transient equivalent circuit, and uses the former obtained in the simulation process. The values â€‹â€‹of the direct axis and the cross-link flux of the two time steps are extrapolated to estimate the value of the rotational potential of the current simulation step, and the estimated value of the rotational potential is added to the equivalent circuit. This synchronous motor model is used in the well-known E T P program. The literature  pointed out that because the prediction method is used to calculate the rotating potential, when the simulation step size is large, the algorithm will be unstable and the simulation accuracy will be reduced.
The synchronous motor model and its transient equivalent circuit proposed in this paper differentiate the voltage equations of the undamped winding synchronous motor by using the first-complex solution and the trapezoidal method, which successfully eliminates the rotational potential. The coupling between the straight-axis voltage equation of the synchronous motor and the cross-axis voltage equation is realized, which realizes the decoupling calculation of the direct axis and the intersecting axis, and avoids the simulation algorithm caused by the prediction of the rotating potential. Stability, while retaining the basic structure of the E TP transient equivalent circuit for ease of programming and use. The example shows that the new model has better stability and has higher calculation accuracy than the model in the same simulation step.
2 Differentialization of voltage equations It is well known that in the practical positive direction, the dynamic behavior of a non-damped winding synchronous motor can be described by the following voltage equations and flux equations: grid technology writes the voltage equation (1) into the following matrix form: strictly speaking, In the transient process of the machine network, the mechanical angular velocity k is a variable that changes with time. However, in a small simulation time step [ ( tÎ”t ), t ], the rate of change is much smaller than the rate of change of electromagnetic variables such as flux linkage, current and voltage, so it can be approximated that in time step [ ( Within t Î”t ),t ], k is a constant. Thus, the equation (3) is similar in form to the voltage equation of the three-phase inductive component in the dqo coordinate system in , which is modeled after the derivation in , using the first solution and then the trapezoidal method. The method of product (Note: the literature  only introduces this specific difference format, and does not name the difference format), you can get the following difference format for the voltage equation of the undamped winding synchronous motor: in the past, the implicit method is directly adopted. The trapezoidal method differentiates the voltage equation (1) of the synchronous motor, and the coupling between the straight-axis voltage difference equation and the cross-axis voltage difference equation is unavoidable. Now the first step is to solve the voltage equation (1) of the synchronous motor by the trapezoidal method. In the difference format shown in equation (4), since the sum is O, the simulation is performed. The voltage and flux linkage at time step (t Î”t ) is a known quantity determined by equation (6). Therefore, the direct-axis flux linkage j (t ) at time t is only simultaneously with the straight-axis voltage u (t ) Regarding, regardless of the quadrature axis voltage u (t ) at that time, the quadrature flux linkage j at the time t is only related to the simultaneous intersection axis voltage, and is independent of the direct axis voltage u. That is to say, the direct-axis voltage difference equation is decoupled from the cross-axis voltage difference equation.
3 The direct-axis and cross-axis transient equivalent circuit rewrites the flux linkage equation of the linear winding in equation (2) into the following form: the leakage inductance of the stator equivalent straight-axis winding, the leakage inductance of the excitation winding, and Equivalent to the straight-axis armature reaction inductance. From the equations (4)(5) and (7), the straight-axis transient equivalent circuit of the undamped winding synchronous motor expressed by the equivalent resistance and the equivalent voltage source can be obtained, as shown by the source, as shown in Fig. 2.
From the equation of the flux linkage of equation (2) and the equations (4) and (5), the quadrature transient equivalent circuit can be directly obtained. However, for the symmetry of the transient equivalent circuit with the direct axis, I suggest The inductance of the stator equivalent cross-winding winding is split into two parts, corresponding to the leakage inductance of the equivalent cross-winding winding (the value can be taken as equal to the leakage inductance of the straight-axis winding) and the equivalent cross-axis armature reaction inductance. In this way, the flux linkage equation for the quadrilateral winding in equation (2) can be rewritten as follows: Undamped by equivalent resistance and equivalent voltage source can be obtained from equations (4)(5) and (10) The quadrature transient equivalent circuit of the winding synchronous motor is shown in Figure 3 (a). The equivalent circuit can also be represented by an equivalent conductance and an equivalent current source, as shown in Figure 3 (b).
The equivalent current source has a basic structure similar to the transient equivalent circuit of a synchronous motor in E T P . However, in the direct axis and quadrature axis equivalent circuits of E TP, there are respectively connected to the rotating potential E (t ). When performing the simulation calculation at time t, they are all unknown, and need to be based on the results of the first two simulation calculations. It is estimated that when the simulation step size Î”t is large, the simulation error will increase and the simulation algorithm will be unstable. In the new synchronous motor model and its equivalent circuit, there is no electromagnetic variable that needs to be estimated. Therefore, the simulation calculation of the transient process is performed according to the above transient equivalent circuit, even if the simulation step size is slightly larger, There is also no problem with algorithm instability.
4 The example shows that the parameters of the undamped winding synchronous generator represented by the standard value are as follows = 5. 0 s, the rated power factor is 0.85, and the adjustment of the excitation system and the mechanical system during the transient process is negligible, ie It is assumed that the excitation voltage and the angular frequency of the generator remain the pre-fault values â€‹â€‹during the transient process. The synchronous motor model described in this paper is used to simulate the transient processes of the following three faults. The simulation steps are all 0. 25s: Fault 1: When the no-load operation occurs, a sudden three-phase short-circuit fault occurs on the machine side. 2: A sudden three-phase short-circuit fault occurs at the machine end during full load operation. 3: When the load is full, the machine end is x = 0. Phase short circuit.
It is assumed above that when a short circuit occurs, the rotor just runs to a position where its axis coincides with the axis of the stator a phase winding. The results of the simulation calculations on the stator phase current and rotor current are shown in Tables 1 and 2. In order to verify the correctness of the synchronous motor transient model, the theoretical values â€‹â€‹of the fault currents obtained by the analytical method under three faults are also given in the table  for comparison. In addition, for fault 1, the results of the simulation calculation using the E TP model according to different simulation steps are also given in Table 1 for comparison.
It can be seen from the simulation calculation results that according to the above-mentioned simulation calculation of the transient equivalent circuit model of the synchronous motor, the result is stable regardless of the type of fault, and the calculation accuracy is also high, when the simulation step is taken 0. 25s, the overall calculation error does not exceed 0.1, can meet the actual needs of the project. When using the E TP model for simulation calculation, the simulation result changes with the simulation step size. If the step size is taken as 0.25s, when the simulation is over 300s, the calculation result has seriously deviated from its theoretical value, and the simulation error More than 5. The duration of the transient process required to be considered in the project is more than a few seconds. As the simulation calculation continues, this error rapidly expands. If you want to control the simulation error of the E TP model to be at the same level as the model described in this paper, you need to reduce the simulation grid technology step size to 0. 10 to 0. 05s, which will increase the simulation calculation multiple times. Quantity and calculation time.
Simulation result of rotor current i ( t) stator current i rotor current i theoretical value simulation result E TP method simulation result theoretical value simulation result E TP method simulation result ( t) and rotor current i fault 2 fault 3 stator current i Rotor current i Stator current i Rotor current i Theoretical value Simulation value Theoretical value Simulation value Theoretical value Simulation value Theoretical value Simulation value 5 Conclusion (1) The synchronous motor model introduced in this paper can realize the decoupling calculation of the direct axis and the intersecting axis. Thereby achieving the purpose of facilitating programming and reducing the amount of simulation calculation of the transient process.
(2) Compared with the conventional synchronous motor model, the model introduced in this paper does not need to estimate the rotating potential, the program is simpler, the algorithm is more stable, and the calculation result is more accurate.
Computational Theory [ ]. Beijing: Water Power Press, 1991.
He Yangzan, Wen Zengyin, Wang Yuying, and so on. Power System Analysis [ ]. Wuhan: Huazhong Institute of Technology Press, 1984.
Dai Jiaxuan (1964), male, master, senior engineer, engaged in power system automation research.

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