Modeling and simulation of all-electric propulsion system with three-closed loop control

Abstract

Marine electric propulsion system is a complex power chain of ship-engine-propeller composed by inverter, propulsion motor and propeller. Ship power system is an independent power grid, its propulsion motor and propeller are easily affected by complex and variable sea environment and working conditions, which can easily cause shafting vibration or even malfunction and then affecting the power supply system. Its modeling is difficult. Simulation time is long. Torque fluctuations are frequent and so on. To solve these problems, a set of mathematical model of marine electric propulsion system including inverter, permanent magnet synchronous motor (PMSM), propeller and hull is established firstly. Based on the two-closed loop control of field-oriented control (FOC), a third closed-loop control, that is torque closed loop, is added to relieve torque fluctuations and the PI parameters are discussed of the controller. The anti-jamming and dynamic-static performance of the system under sudden changes by additional constant load, random fluctuating load and changing reference speed are analyzed. The experimental results show that the model can simulate the all-electric propulsion system very well. Three-closed loop control reduces the vibration of the motor shaft and makes the propulsion system to follow the reference speed quickly and keep the torque stable than the two-closed loop control when the propeller torque and the reference speed is changing.

Keywords

Electric propulsion system ship-engine-propeller model PMSM three-closed loop control all-electric-ship

1. Introduction

With the development of ship modernization, electric propulsion has gradually become the main propulsion mode of ships [1]. Especially with the continuous development of shipboard weapons, offshore drilling, container shipping and other applications [2], the role of electric propulsion in ships is becoming more and more important. Ship electric propulsion system is a way to drive the ship forward by rotating of the propeller which is driven by the motor. Compared with the traditional mechanical propulsion ship driven by diesel engine, the electric propulsion has the advantages of superior economy, good maneuverability, convenient integration, low noise, safe driving, etc. [3, 5]. In the electric propulsion system, the selection of propulsion motor type and its control mode is one of the key technologies. At present, the main types of propulsion motors are DC motor, AC asynchronous motor, AC synchronous motor and permanent magnet synchronous motor (PMSM). The synchronous motor has strong ability to withstand disturbance, wide speed range and can be directly connected with the propeller. Therefore, most modern marine electric propulsion systems adopt synchronous motor [6]. The PMSM has higher power density and power factor, larger torque density, smaller electromagnetic torque ripple coefficient, lower noise, higher efficiency, better maintenance and less pollution than conventional synchronous motor [7, 8], so it is the direction of future. The FOC is one of control technology mainly of PMSM using physical variables such as current and flux to the decoupling calculation of the motor. It has the advantages of high control accuracy, less harmonics and approximate circle flux linkage. The combination with space vector PWM control (SVPWM) can better play the characteristics for PMSM. The research of propulsion system combining PMSM and its control mode with propeller is an important part of all-electric ship research. How to improve the stability, reduce noise and provide the whole network simulation system is a key research content.

In this paper, according to the characteristics of PMSM with its control system and propeller load characteristics, a three-closed loop control system including current closed-loop control, torque closed-loop control and speed closed-loop control is designed and the presetting problem of PI controller parameters is analyzed. Finally, a complete integrated digital simulation model of electric propulsion including ship, engine and propeller is established and simulated on MATLAB/Simulink platform. Experiments show that the simulation model can reduce the running time of system simulation to provide convenience for researchers to engage in related research. It can reduce the torque fluctuation and low the mechanical fatigue or failure caused by motor shaft torque vibration and prolong the service life of the motor. It can provide a digital simulation experimental platform to simulate the ship-propeller characteristics for the study of ship’s dynamic and static characteristics and anti-jamming capability.

The remaining of the paper is organized as follows. Section 2 introduces the structure of ship propulsion system. In the Section 3, the mathematical model of each device in the power chain of the ship propulsion system is described. Subsequently, in Section 4, the chain of ship propulsion system is constructed, the three-closed loop control is designed and the presetting method of PI parameters for three-closed loop of is deducted. In Section 5, a complete ship-engine-propeller model on Matlab/Simulink is established and the system simulation is carried out. A brief conclusion of the study is presented in Section 6.

2. Structure of electric propulsion system

A lot of literatures have studied on marine electric propulsion system. Some literatures focus on the analysis of the performance and control optimization of the propulsion motor. However, there is a certain deviation between the static performance and the actual electric propulsion system for using the simple constant torque input to simulate the propeller load without considering the characteristics matching between the propeller and the motor caused by the influence of different sea conditions [9]. Some focus on the analysis of propeller load characteristics and the simulation of propeller motion under different working conditions, but they lack of consideration of propeller load driven by marine propulsion motor [10, 11]. Some people specialize in the matching research of propeller, but the model is too complex to realize [12]. In addition, the propeller rotating in water produces forward thrust, but the harsh sea and wind environment and frequent manual start and stop operation bring great impact to the propeller. Through the action of propeller shaft and thrust bearing on the hull, the load torque of the propeller will be changed and finally the characteristics of the propulsion motor will be changed, which will cause the vibration of the motor shaft and even the hull. Those reduce the stability of the ship and often lead to the failure of the propulsion system and even unexpected shutdown [13, 15]. Therefore, it is very important to model and simulate the whole electric propulsion system including ship-engine-propeller and to study the necessary characteristics for further control and fault diagnosis.

Ship power system is usually a branch structure. Take the power system of an all-electric ship as an example [9], as shown in Fig. 1. Particularly, redundancy of generators and propulsion motors are shown for the optional operation mode. Overall structure of all electric ship system consists of two sets of main generator with rated capacity of 11 MW and two sets of auxiliary generator with rated capacity of 6 MW. Two 12 MW permanent magnet synchronous motors are marine thrusters with one redundancy each. Two 2.2 MW cargo pump motors, and a total capacity of 1.5 MVA full-time consumption of domestic electricity load. In the virtual box is the electric propulsion system.

Figure 1.

Structural diagram of marine power system.

Figure 2.

Typical electric propulsion system structure.

The typical electric propulsion structure is introduced as shown in Fig. 2.

Considering the relationship between propeller and ship and the energy conversion of converter, propulsion motor and propeller, as well as the influence of sea wave and wind wave, a more detailed outline structure of electric propulsion system is show as Fig. 3.

Figure 3.

Ship-engine-propeller outline structure.

3. Electric propulsion system model

3.1 Permanent magnet synchronous motor model

The stator voltage equation of the PMSM in the synchronous rotating $d-q$ coordinate system is shown as follows [16].

$\displaystyle u_{d}=R_{s}i_{d}+p\varphi_{d}-n_{p}\omega_{r}\varphi_{q}$ (1) $\displaystyle u_{q}=R_{s}i_{q}+p\varphi_{q}+n_{p}\omega_{r}\varphi_{d}$ (2) $\displaystyle\varphi_{d}=L_{d}i_{d}+\varphi_{f}$ (3) $\displaystyle\varphi_{q}=L_{q}i_{q}$ (4) $\displaystyle\varphi_{f}=L_{md}i_{f}$ (5)

Where $\varphi_{d}$ , $\varphi_{q}$ , $L_{d}$ , $L_{q}$ , $i_{d}$ , $i_{q}$ , $u_{d}$ , $u_{q}$ are stator flux components, equivalent inductance of stator winding, stator current components, stator voltage components in d and q axes respectively. $\varphi_{f}$ is the permanent magnet flux linkage. $R_{s}$ is the stator wingding resistance. $p$ is the differential operator. $\omega_{r}$ is the rotor mechanical angular velocity. $n_{p}$ is the pair of poles.

The electromagnetic torque and its mechanical motion equations of the PMSM in d-q coordinate system is shown as Eqs (6) and (7).

$\displaystyle T_{e}=\frac{3}{2}n_{p}(\varphi_{d}i_{q}-\varphi_{q}i_{d})$ (6) $\displaystyle T_{e}-T_{l}=J\frac{d\omega_{r}}{dt}+B\omega_{r}$ (7)

where $T_{e}$ is electromagnetic torque. $T_{l}$ is load torque. $J$ is moment of inertia. $B$ is viscous friction coefficient.

Through Eqs (3), (4) and (6), the electromagnetic torque can be expressed as:

$\displaystyle T_{e}=\frac{3}{2}n_{p}(i_{d}i_{q}(L_{d}-L_{q})+\varphi_{f}i_{q})$ (8)

3.2 Propeller model

The model of propeller is introduced according to reference [16].

Advance ratio:

$\displaystyle J^{\prime}=\frac{v_{s}(1-w)}{\sqrt{v_{s}^{2}(1-w)^{2}+n^{2}D^{2}% }},J^{\prime}\in[-1,1]$ (9)

Propeller thrust:

$\displaystyle P=\frac{K_{P}^{\prime}\rho D^{2}v_{p}^{2}}{J^{\prime 2}}$ (10)

Propeller Torque:

$\displaystyle M=\frac{K_{M}^{\prime}\rho D^{2}v_{p}^{2}}{J^{\prime 2}}$ (11)

Thrust-deduction fraction:

$\displaystyle t_{h}=(P-P_{e})/P$ (12)

Propeller effective thrust:

$\displaystyle P_{e}=(1-t_{h})P$ (13)

Equation of motion of propeller:

$\displaystyle(m+\Delta m)\frac{dv_{s}}{dt}=P_{e}-R$ (14)

Total hull resistance:

$\displaystyle R=rv_{s}^{2}$ (15)

where $n$ is propeller rotate speed. $v_{p}$ is propeller velocity. $v_{s}$ is ship velocity. $w$ is wake factor. $D$ is propeller diameter. $P$ is propeller thrust and $P_{e}$ is propeller effective thrust. $M$ is propeller torque. $\rho$ is sea-water density. $m$ is ship weight. $\Delta m$ is attachment weight of sea water. $r$ is total drag coefficient of ship. $K_{M}^{\prime}$ is torque coefficient. $K_{p}^{\prime}$ is thrust coefficient, respectively.

In literature [16], the model does not give the coefficients of $r$ , $w$ , $t_{h}$ , $K_{M}^{\prime}$ , $K_{p}^{\prime}$ and the appropriate acquisition method. Based on these literatures [17, 19], a refined propeller characteristic model including the effects of wind, wave and current is established. $K_{M}^{\prime}$ and $K_{p}^{\prime}$ uses 8-order Chebyshev formula to fit, while parameters of $r$ , $w$ and $t_{h}$ are described as follows:

$\displaystyle t_{h}=\left\{\begin{array}[]{cc}0.33&n<-n_{e}\\ -0.33n/n_{e}&-n_{e}\leqslant n<0\\ 0.13n/n_{e}&0\leqslant n<n_{e}\\ 0.13&n\geqslant n_{e}\\ \end{array}\right.$ (16)

where $n_{e}$ is rated rotate speed of propeller, $r/s$ .

$\displaystyle w=\left\{\begin{array}[]{cc}0&v_{s}\leqslant 0\\ 0.22v_{s}/v_{se}&0\leqslant v_{s}<v_{se}\\ 0.22&v_{s}\leqslant v_{se}\\ \end{array}\right.$ (17)

where $v_{se}$ is the rated ship velocity, $m/s$ .

$\displaystyle r=R_{fr}+R_{wa}+R_{pv}+R_{wi}$ (18)

where $R_{fr}$ is frictional resistance, $R_{wa}$ is wave making resistance, $R_{pv}$ is viscous resistance of seawater, $R_{wi}$ is wind resistance.

4. Three-closed loop control of PMSM

4.1 Three-closed loop control based on FOC

FOC control is used commonly method for PMSM. FOC consists of outer speed control loop and inner current control loop. Combining with space vector control, it can form SVM-FOC (Space Vector Modula Field-Oriented Control), as shown in Fig. 4. But in electric propulsion system, because of the complex propulsion system model, large inertia and poor robustness, PI controllers are prone to large overshoot torque and long adjustment time, which lead to a long period of transition in the process of start-up and load sudden change. Furthermore, due to the strong coupling and non-linearity of the high-power converter and the huge capacity of motor and the three-phase stator current can’t reach the ideal waveform, which makes the output torque of the motor fluctuate greatly. The motor is usually connected with the propeller through the shafting, which causes vibration and affects the service life and overall performance of the propulsion system. Therefore, considering the stability of the torque, by introducing the torque closed-loop, this paper establishes the three-closed loop controller of the speed, torque and current for PMSM. The torque closed-loop controller is shown as the dotted line part in Fig. 4. According to this model, the dynamic performance of the PMSM can be optimized.

Figure 4.

Speed, torque and current closed loops control.

4.2 Presetting parameters design of PI controller

4.2.1 PI parameter design of current closed loop

When the dynamic terms $\omega\varphi_{f}$ and coupling terms $\omega L_{d}i_{d}$ of PMSM are neglected, Eq. (2) can be converted to:

$\displaystyle u_{q}=R_{s}i_{q}+L_{q}\frac{di_{q}}{dt}$ (19)

Then the transfer function of the motor can be expressed as:

$\displaystyle G_{p}(s)=\frac{i_{q}}{u_{q}}=\frac{1}{L_{q}s+R_{s}}$ (20)

when the delay of the inverter and the system be approximated to the first order small inertia link, the current control loop transfer function is shown in Fig. 5.

Figure 5.

Current closed loop transfer function.

where

$\displaystyle T_{ii}=\frac{L_{q}}{R_{s}}$ (21)

Because $f_{\textit{SVPWM}}$ is relatively large, it can be assumed that $t_{d}=T_{s}$ , $k_{\textit{SVPWM}}=$ 1, where $T_{s}$ is the system sampling time, then the part combined inverters and circuit delay inertia is expressed as follow:

$\displaystyle G_{\sum t}(s)\approx\frac{1}{1.5T_{s}s+1}$ (22)

Then, the current open-loop transfer function Eq. (23) can be deduced.

$\displaystyle G_{i}(s)_{\textit{open}}=G_{\textit{ipi}}(s)G_{\sum t}(s)G_{p}(s% )=\frac{2K_{ip}}{3L_{q}T_{s}}\cdot\frac{1}{s(s+\frac{2}{3T_{s}})}$ (23)

and the current closed-loop transfer function can be obtained:

$\displaystyle G_{i}(s)_{\textit{close}}=\frac{K_{g}}{s^{2}+\frac{2}{3T_{s}}s+K% _{g}}$ (24)

where $K_{g}=\frac{2K_{ip}}{3L_{q}T_{s}}$ .

Comparing to the standard of transfer functions of second order systems as Eq. (25),

$\displaystyle G(s)=\frac{\omega_{n}^{2}}{s^{2}+2\xi\omega_{n}s+\omega_{n}^{2}}$ (25)

The Eqs (26) and (27) can be deduced:

$\displaystyle\omega_{n}=\sqrt{K_{g}}$ (26) $\displaystyle\xi=\frac{1}{3T_{s}\sqrt{K_{g}}}=\frac{1}{\sqrt{6K_{ip}T_{s}/L_{q% }}}$ (27)

Then, Eq. (28) can be got:

$\displaystyle K_{ip}=\frac{L_{q}}{6\xi^{2}T_{s}}$ (28)

where $\xi=0.6\sim 0.8$ is damping coefficient. The PI parameters of the current loop can be determined by Eqs (21) and (28).

4.2.2 PI parameter design of torque closed loop

In the FOC, the $i_{d}$ is zero, so from the Eq. (8) , the following transfer function can be obtain:

$\displaystyle G(s)=\frac{3}{2}n_{p}\varphi_{f}$ (29)

when $\xi=$ 0.707, then current closed-loop transfer function Eq. (24) can be equivalent to first order system:

$\displaystyle G_{i}(s)_{\textit{close}}=\frac{1}{3T_{s}s+1}$ (30)

So the torque closed loop including speed PI controller, current closed loop, circuit delay and motor motion equation is considered as shown in Fig. 6.

Figure 6.

Torque closed loop transfer function.

In this paper, the sampling time of speed loop, torque loop and current loop is the same. so it can be obtained:

$\displaystyle G_{\sum{dt}}(s)=G_{i}(s)_{\textit{close}}\cdot\frac{1}{t_{d}s+1}% \approx\frac{1}{4T_{s}s+1}$ (31)

Then, the opened loop transfer function of torque in Fig. 5 can be expressed as follow:

$\displaystyle G_{T}(s)_{\textit{open}}=G_{Tpi}(s)G_{\sum dt}(s)G_{t}(s)=\frac{% 3}{2}n_{p}\varphi_{f}\cdot\frac{K_{Tp}(T_{Ti}s+1)}{T_{Ti}s(4T_{s}s+1)}$ (32)

Supposing that

$\displaystyle T_{Ti}=4T_{s}$ (33)

Then, the torque opened loop transfer function Eq. (32) can be simplified:

$\displaystyle G_{T}(s)_{\textit{open}}=G_{\textit{Tpi}}(s)G_{\sum dt}(s)G_{t}(% s)=\frac{3}{2}n_{p}\varphi_{f}K_{Tp}\cdot\frac{1}{T_{Ti}s}$ (34)

and the closed-loop transfer function of torque can be got:

$\displaystyle G_{T}(s)_{\textit{close}}=\frac{K_{h}}{s+K_{h}}$ (35)

where

$\displaystyle K_{h}=\frac{3n_{p}\varphi_{f}K_{Tp}}{2T_{Ti}}=\frac{3n_{p}% \varphi_{f}K_{Tp}}{8T_{s}}$ (36)

when $K_{h}=$ 1, then

$\displaystyle K_{Tp}=\frac{8T_{s}}{3n_{p}\varphi_{f}}$ (37) $\displaystyle G_{T}(s)_{\textit{close}}=\frac{1}{s+1}$ (38)

So, The PI parameters of the torque closed loop can be determined by Eqs (33) and (37).

4.2.3 PI parameter design of speed closed loop

The following transfer functions can be derived from Eqs (7) and (8):

$\displaystyle G_{1}(s)=\frac{30}{\pi}\cdot\frac{1}{Js}$ (39) $\displaystyle G_{2}(s)=\frac{3}{2}n_{p}\varphi_{f}$ (40)

Therefore, the speed closed loop including speed PI controller, torque closed loop, circuit delay and motor motion equation is shown in Fig. 7.

Figure 7.

Speed closed loop transfer function.

In this paper, torque loop and current loop on the sampling time of speed loop is the same. it can be obtained:

$\displaystyle G_{\sum{dt}}(s)=G_{T}(s)_{\textit{close}}\cdot\frac{1}{t_{d}s+1}% \approx\frac{1}{s+1}$ (41) $\displaystyle G_{N}(s)_{\textit{open}}=K_{k}\cdot\frac{1}{s+1}\cdot\frac{1}{s}$ (42)

where

$\displaystyle K_{k}=\frac{45K_{np}n_{p}\varphi_{f}}{\pi J}$ (43)

So, when the value of $T_{ni}$ is relatively large, the Eq. (44) is available.

$\displaystyle G_{N}(s)_{\textit{close}}=\frac{K_{k}}{s^{2}+s+K_{k}}$ (44)

Comparing to the standard of transfer functions of second order systems, the following formula can be obtained:

$\displaystyle K_{np}=\frac{\pi J}{180n_{p}\varphi_{f}\xi_{n}^{2}}$ (45)

The PI parameters of the speed loop can be determined by Eq. (45) with the condition of $T_{ni}>>K_{np}$ .

It should be point out that the PI parameters of speed, torque and current closed-loop are obtained by a certain degree of approximation and equivalence, so there is deviation. These calculated values can only be used as presetting values before fine tuning.

5. Simulation results and their analysis

According to the above mathematical deduction and analysis, the simulation model is established on the plant of MATLAB/Simulink as shown in Fig. 8 and the simulation experiments are carried out. Parameters of PMSM is shown in Table 1 and parameters of propeller is shown as Table 2.

Table 1
Parameters of PMSM

Parameter	Value
Stator resistance	$R_{s}=$ 2.875 e-1 ( $\Omega$ )
Direct axis inductance	$L_{d}=$ 0.0015 ( $H$ )
Quadrature axis inductance	$L_{q}=$ 0.0015( $H$ )
Pair of poles	$n_{p}=$ 4
Moment of inertia	$J=$ 0.008 ( ${\textit{kgm}}^{2}$ )
Permanent magnet flux linkage	$\varphi_{f}=$ 0.175 ( $w b$ )
Viscous friction coefficient	$B=0$

Table 2

Parameters of propeller

Parameter	Value
Propeller diameter	$D=$ 1 ( $m$ )
Sea-water density	$\rho=$ 1025 ( $\textit{kg/m}^{3}$ )
Rated velocity of ship	$V_{se}=$ 2.4 2 ( $m/s$ )
Rated rotate speed of propeller	$n_{e}=$ 10.8 (r/s)
Ship quality	$m=$ 16229000 ( $k g$ )
Adhesion quality of seawater	$\Delta m=$ 1298320 ( $k g$ )
Friction factor	$R_{fr}=$ 22300
Wave making resistance coefficient	$R_{wa}=$ 413553
Viscous drag coefficient	$R_{pv}=$ 3250
Wind drag coefficient	$R_{wi}=$ 2180

Figure 8.

All-electric propulsion system simulation model based on ship-engine-propeller.

5.1 Additional constant torque effect

It is quite common for ships to encounter suddenly increase of torque in water, when the blades of propeller is entangled by foreign bodies or the sudden encounter of continuous ocean currents, and so on. From Figs 9 to 11 simulating the case, the reference speed of the propeller is 150 r/min and the additional constant torque of 250 N $\cdot$ m is suddenly increased at 0.5 s.

Figure 9.

Electromagnetic torque change under additional constant torque.

Figure 10.

Speed variation under additional constant torque.

Figure 11.

Current variation under additional constant torque.

From these figures, it can be seen that the model well realizes the ship-engine-propeller model of all-electric ship propulsion system. At the same time, it also shows that the three-closed loop control has less overshoot and fluctuation than the two closed-loop control in this case.

5.2 Additional random torque effect

Because of the action of wave, wind and current, the propeller torque is random variable, which is a non-constant value, so the random torque in a certain range can best simulate the real environment. From Fig. 12 to Fig. 14 simulating the case, the ship propeller reference speed is 150 r/min and the simulation time is 2 s. The change period of random torque is 0.1 s from 0.2 s to 1 s and range of random torque is from $-$ 100 N $\cdot$ m m to $+$ 100 N $\cdot$ m em. After 1 s, the fluctuation disappears.

Figure 12.

Variation of speed under random torque.

Figure 13.

Electromagnetic torque change under random torque.

It can be seen from the Fig. 12 that the three-closed loop control is better than the two closed-loop control in speed tracking when the random torque changes. At point A, the start time, there is almost no overshoot in three-closed loop control, but the two closed-loop has very high overshoot. At point B, the three-closed loop control has the same overshoot with the two closed-loop control, but less fluctuation period than the latter. At point C, although the overshoot is larger than the two closed-loop control, but the three-closed loop control speed fluctuation period is less than the two closed-loop control.

Seeing from Fig. 13, there is basically no overshoot of the three-closed loop control at every change piont, but the two closed-loop control has overshoot in each process of torque conversion, specially at the start-up moment.

Figure 14.

Stator voltage trajectory under random torque.

From the stator voltage trajectory in Fig. 14, since the rotor frequency of the motor is the same as random torque (10 Hz i.e. 0.1 s), therefore, the figure reflects the stator voltage fluctuation caused by a periodic torque fluctuation in the place of the circle. It can be seen that the three-closed loop stator voltage trajectory has a clearer trajectory under different torques, which indicates that the three-closed loop control has a smaller fluctuation than the two closed-loop control.

5.3 Effect of speed change

Figure 15 simulates the electromagnetic torque and stator speed fluctuation of the motor when the reference speed changes from 150 r/min to 170 r/min at 0.5 s.

Figure 15.

Changes of rotational speed and electromagnetic torque with reference speed.

From the Fig. 5, it can be seen that the fluctuation of speed and electronic torque of three-closed loop control is smaller than that of two closed-loop control.

6. Conclusion

This paper presented a complete digital simulation model of all-electric propulsion system which is driven by PMSM. A speed-torque-current three-closed loop controller based on SVM-FOC is proposed supplying for it to reduce the fluctuation of the torque and the vibration of the transmission shaft. At the same time, the PI parameters of the three-closed loop control are analyzed in detail. The digital simulation including additional sudden constant torque change, sudden random torque fluctuation, suddenly speed increase show that the three-closed loop control enables the speed to respond quickly, the torque to be controlled smoothly and also has good dynamic response ability and anti-interference ability of the system model under these changes of external conditions. Because the torque keeps changing all the time while sailing, so this situation is a severe test for the motor, propeller and the shafting between them. Therefore, the three-closed loop control can reduce the vibra tion of the propulsion system, reduce the electrical fluctuation of the propulsion system, and reduce the failure rate of the propulsion system.

Footnotes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 61503240 and in part by the Project Funded by Postgraduate Innovation Fund of Shanghai Maritime University 2015ycx072. This is a Shanghai Science and Technology Program funded project, 20040501200.

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Modeling and simulation of all-electric propulsion system with three-closed loop control

Abstract

Keywords

1. Introduction

2. Structure of electric propulsion system

3.1 Permanent magnet synchronous motor model

4.1 Three-closed loop control based on FOC

4.2.1 PI parameter design of current closed loop

Table 1 Parameters of PMSM

Footnotes

Acknowledgments

References

Table 1
Parameters of PMSM