## 2 Materials and Methods  
The main electromechanical ratios of the EOS three-engine system can be determined through a \(T\)-shaped equivalent circuit. The angular mismatches of the rotors of differently loaded motors are denoted by \(\varphi_{1}\), \(\varphi_{2}\), and \(\varphi_{3}\) relative to some imaginary axis rotating in coordination with the motor rotors. According to the theory of the electric shaft, mechanical angles of rotation can be considered in electrical degrees relative to the applied voltages along the stator circuits by multiplying the voltages by \(e^{i\varphi_{1}},e^{i\varphi_{2}},\) and \(e^{i\varphi_{3}}\). The phase shifts of all motor currents are taken into account by multiplying using the same multipliers. This approach is necessary to make the formulas more symmetrical. Further calculations are carried out according to the principle of the overlay method [10]. When the supply voltage of individual motors changes, we accept the following generally accepted assumptions for the multi-motor electric drive with electrical communication through rotary circuits:  
* The parameters of the system engines are identical;
* The magnetic field along the circumference of the air gap of each engine is distributed evenly, and only the main harmonic field is taken into account;
* Losses in the steel of the stator and rotor are not taken into account, and the magnetic circuits of the motors are unsaturated;
* Voltage is applied to the stator windings (symmetrical three-phase process);
* The superposition principle is used to determine currents and torques;
* The resistance of the connecting cables is not taken into account;
* When studying stability, deviations \"in the small\" are taken into account. To determine the currents and moments of the MAED synchronous rotation (SR) system with electrical communication through common rotor circuits, which includes three asynchronous motors, we use a \(T\)-shaped equivalent circuit, which is shown in Figure 1. The variables are as follows (Figure 1):\(U_{1}\), \(U_{2}\), and \(U_{3}\) are the main voltages for each motor; \(I_{11}\), \(I_{12}\), \(I_{13}\), \(I_{21}\), \(I_{22}\), and \(I_{23}\) are the stator and rotor currents of the machines; \(r_{11}\), \(r_{12}\), and \(r_{13}\) and \(x_{11}\), \(x_{12}\), and \(x_{13}\) are the active and inductive resistances of the stator windings for the corresponding motors of the system with electrical connections through rotor circuits; \(r_{21}\), \(r_{22}\), and \(r_{23}\) and \(x_{21}\), \(x_{22}\), and \(x_{23}\) are the active and inductive resistances of the rotor windings; \(x_{01}\), \(x_{02}\), and \(x_{03}\) are the inductive resistances of the magnetization circuits; \(Ra\) is the additional resistance in the rotor circuit; \(S\) is the slip; and \(\rho_{1}\), \(\rho_{2}\), and \(\rho_{3}\) are the angular shifts of the rotors in electrical degrees relative to the accepted reference axis. Denoting the complex resistances of the stators and rotors while sliding \(S\) through \(Z_{1}\) and \(Z_{2}\), and taking into account the identity of the motor parameters and reduction in rotor resistances, we obtain the following:  
\[Z_{1}=r_{1}+j(x_{0}+x_{1}) \tag{1}\]  
\[Z_{2}=\frac{r^{\prime}_{2}}{S}+j\big{(}x_{0}+x^{\prime}_{2}\big{)} \tag{2}\]  
where \(\frac{r^{\prime}_{2}}{S}\), \(x^{\prime}_{2}\), and \(\frac{R^{\prime}}{S}\) are, respectively, the active resistance, inductive resistance, and resistance (\(Ra\)) of the general rotor circuit reduced to the stators of the motors. Then, the voltage equations for the stator and rotor circuits are as follows [11]:  
\[\dot{U}=I_{1n}Z_{1}-I_{2 nj}X_{0} \tag{3}\]  
\[(I_{1n}jx_{0}-I_{2n}Z_{2})e^{i\phi_{n}}=\frac{R^{\prime}}{S}{\sum_{L=1}}^{n} I_{2n}e^{i\phi_{n}}. \tag{4}\]  
Figure 1: \(T\)-shaped equivalent circuit for three asynchronous motors with electrical connection through rotary circuits.