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A five leg inverter (FLI) control is incorporated to drive two independent rated permanent magnet synchronous motors (PMSMs) for automotive applications. Literature evidences many attempts of employing the FLI for controlling two general purpose/special motors, where variety of modulation techniques has been practiced for performance enhancement. Also in these cases one leg of inverter is common to both the motors. The expanded two arm modulation (ETAM) has been generally engaged in FLI. In ETAM the percentage voltage utilization factor (VUF) is calculated based on “
α_{max}
”, where “
α_{max}
” is the maximum modulation index and equal to
and hence it restricts the VUF to 50%. This makes the FLI drives to use the dc link in inefficient way, which is due to the fact that conventional ETAM works with voltage reference. This paper modifies the ETAM in an ingenious way to improve the VUF further through current reference. In addition, the developed current reference expanded two arm modulation (CRETAM) minimizes the current harmonics and torque ripple as well. A detailed comparison of the CRETAM with the conventional ETAM and the competent digital counterpart, space vector pulse width modulation (SVPWM), is also presented. The enhancement in VUF, torque ripple minimization and current total harmonic distortion (THD) reduction are found in the MATLAB based simulation results.

With the increasing demand for environmentally friendlier and higher fuel economy, the vehicle automotive industries have started to focus on electric vehicles, hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs) and fuel cell vehicles. In electric vehicles, the challenge is to achieve high efficiency, ruggedness, small sizes and also low cost power converters and electric machines as well as in associated electronics [

Traditionally, two separate drives, each employing a separate three phase voltage source inverter (VSI), are being used to gain independent control as shown in

A multiple current-regulated pulse width modulated VSI (PWM-VSI) based dual two phase PWM inverter (B4 topology) has been proposed [

en-phase indirect rotor flux oriented control (RFOC) has been developed and discussed with the examination of speed and torque modes [

Various PWM techniques have been reported in the literature, they are dual voltage modulation (DVM), modulation block method (MBM), inversion table method (IVM) and double zero-sequence injection method (DZM) [

More recently, the closed loop integrated dual ac drive is used to control two PM motors, which has the merit of neglecting extra copper loss in the main motor caused by the auxiliary motor current, has been proposed [

Though the earlier schemes of FLI driven two motors control targeted the performance enhancements such as VUF, switch count, overall losses and magnitude of dc link current, these schemes need to be further improved in terms of THD, torque ripple minimization, VUF etc. This paper presents a current reference expanded two arm modulation (CRETAM) technique to control the two differently rated PMSMs. The performance of the proposed CRETAM is compared with the SVPWM and ETAM schemes.

The power circuit of FLI which consists of five legs, each leg consists of pair of power switching device (MOSFET) with anti-parallel diode, is shown in

The switching function and the restriction condition can be described by the following equation.

Switch on: S_{ma} = 1

Switch off: S_{ma} = 0

Restricted Function = S_{m}_{1} + S_{m}_{2} = 1

where, m ε {1, 2, 3, 4, and 5} is the number of legs and a ε {1, 2} is the number of arms.

It is worth noting that even though the FLI is an integrated drive for double PMSM arrangement, it is always possible to control the motors independently with different set points, speed control schemes, dynamic performance requirements, frames of control schemer etc. The drive can be operated in various conditions such as,

・ Reference speed commands of main and auxiliary PMSM drives are different.

・ Loads torque commands of main and auxiliary PMSM drive are different.

・ Rated specification and parameters of two motors are different etc.

Usually when two motors are driven with two individual three-leg inverters, there are twelve power switching devices are needed. A two motor drive supplied using the FLI topology offers a saving of two switches. The size, gate drive requirement and control complexity of the inverter are therefore reduced. All of these features lead to a potential reduction in capital cost when compared with standard dual three phase inverter approach. Driving two motors independently, the amplitude of the peak current flow in common leg can be up to twice of others, hence its design must be taken care of appropriate rating. This makes the drive to lose its modularity in terms leg interchangeability.

The conventional PWM techniques applicable to the three phase VSI cannot be used for the FLI in the independent drive mode. The state-of-the-art PWM techniques of the FLI, applicable when two motors are controlled, are as follows.

1) ETAM.

2) Voltage reference based Space Vector Approach.

It is possible to independently control the two PMSMs (which are the main traction motor and the auxiliary compressor motor) by providing different commands to each motor with the help of ETAM. ETAM is basically a natural sampled sine PWM (SPWM) logically extended for FLI. This extension inherits two important features viz. synchronization of reference functions and decoupling between two sets of reference functions. The decoupling between the references function of main drive and auxiliary drive legs make them to work independently.

The foremost step in ETAM is synthesizing the reference functions which are ingenious/decoupled combination of phase voltages. Each drive manipulates two reference voltages by assuming the third phase as common as indicated in _{cmin} is added. To keep the inter-relations among the reference functions, this V_{cmin} is added with all the reference functions.

The voltage commands (reference functions) of individual leg are calculated as follows.

where, V_{LLm} is the voltage command of m^{th} leg. m = {1, 2, 3, 4, 5}; V_{A}, V_{B}, V_{C}, V_{A}_{1}, V_{B}_{1}, and V_{C}_{1} are the phase voltage commands (references involved in two VSI based drive system). The common rule in the natural sampled PWM scheme is the expected (terminal) voltage must be the reference function or at least it must be the function expected voltage. The reference functions described in (1) to (5) are just functions derived from fictions dual three-phase supply system. Those reference functions can always be related with the output voltage command as follows.

Equations (6) to (11) are for just validation purpose while the functional references are obtained by adding V_{cmin} with them.

The references from (12) to (16) can be used with regular carrier for generating the gating pulses.

The digital PWM approach called, SVPWM, is extended to FLI as well. The idea is involving two three phase SVPWM modulators to control two PMSMs independently. Using space vector principle, the decoupled reference functions can be obtained for each PMSM in synchronously rotating frame, the d-q axis. For any arbitrary position of the reference vector, apposite two active vectors are chosen from the six vector group. The generated output from SV modulators are restructured to obtain the duty cycle δ over the total switching period. Adopting both modulators in the standard manner to operate for application under equally shared total timing between zero vectors 000 and 111, and each reference vector will be realized on average over the switching period by means of two adjacent active vectors.

In a similar way as in case of ETAM, a simple summing of the duty cycles (δ) generated from each modulator can be used to determine the culminating (five) duty cycles for the FLI.

The first three relations of equation of (17), duty cycle, δ_{c}_{2} is added to all the three duty cycles of modulator 1, while δ_{c}_{1} is added to outcomes of modulator 2.

In case of two three phase VSIs,

Thus the individual SVPWM signals are generated for each PMSM drive and the modulator is able to satisfy the needs of both main and auxiliary PMSMs simultaneously.

An ingenious PWM technique for FLI to command each motor is suggested in this section. The proposed current reference expanded two arm modulation (CRETAM), is similar to hysteresis control, and requires actual current and reference current signals to generate the pulse pattern. The crux of the CRETAM is schemed in

In the CRETAM, current references are given by the equations.

where, i_{a}, i_{b} and i_{c} are the actual currents of motor1. i_{a}_{r}, i_{br}, and i_{cr} are the reference currents of motor 1. Similarly, i_{a}_{1}, i_{b}_{1} and i_{c}_{1} are the actual currents of motor 2 and i_{ar}_{1}, i_{br}_{1} and i_{cr}_{1} are the reference currents of motor 2.

I_{ea}, I_{eb} and I_{ec} are the current errors of motor1 and I_{ea}_{1}, I_{eb}_{1} and I_{ec}_{1} are the current errors of motor2. I_{L}_{1}, I_{L}_{2}, I_{L}_{3}, I_{L}_{4} and I_{L}_{5} are the current references which are compared with triangular carrier signals to generate the pulses of

FLI. The CRETAM paves to reduction in both torque ripple and THD, and enhancement in VUF.

The dynamic model of the PMSM is derived in synchronously rotating frame (dq axes). The stator dq axes’ voltage equations of the PMSM in the rotor reference frame are

where, λ_{q} = L_{q}i_{q} and λ_{d} = L_{d}i_{d} + λ_{af}; V_{d} and V_{q} are the dq axis voltages; i_{d} and i_{q} are the dq axes stator currents; L_{d} and L_{q} are the dq axes inductances; λ_{d} and λ_{q} are the dq axes stator flux linkages; R and ω_{s} are the stator resistance and synchronous (angular) frequency. λ_{af} is the stator flux linkage due to the rotor magnets.

The electromagnetic torque is given by

And the equation for the motor dynamics is

“p” is the number of pole pairs; T_{L} is the load torque; B is the damping coefficient; ω_{r} is the rotor speed and J is the moment of inertia.

For dynamic simulation, the equation of the PMSM presented in (29)-(33) must be expressed instate space form as shown between (34) and (38).

The dq variables are obtained from a, b, c variables through the park transform defined below:

The a, b, c variables are obtained from the d, q variables through the inverse park transform defined below:

The configuration of independent vector control scheme of an integrated dual PMSM under CRETAM technique is shown in _{ds} = 0, which keeps linearity between motor torque and current. The main traction motor and auxiliary compressor motor share the common fifth leg. Two speed controllers are employed both of which are PI types. The speed controller generates torque producing current component i_{qs}, which in turn is transformed into a, b, c frame, for the purpose of reference current generation.

It is seen from the above figure that both main and auxiliary PMSMs generate independent reference current signal. For CRETAM, current control current error is necessary, which is the difference of reference and sensed current. The current error which is generated by the difference of reference and sensed current is compared with triangular waveform and necessary switch in the leg is made to be turned on or off. By properly selecting hysteresis band, the hysteresis control can also be employed in the above scheme. At the driving two motors independently, the amplitude of the peak current flow in common leg is up to twice as others, so it is necessary to equip the power switching devices of common leg to double the capacity compared to others.

The configuration of independent vector control scheme of an integrated dual PMSM under SVPWM technique is shown in _{1} and B_{1} supply phases A and B of the second machine while phases C are paralleled to the inverter leg C. Thus the individual SV references of each machine are complementary and the modulator is able to simultaneously satisfy the needs of both motors.

It is also visible that in the remaining instants the individual SV references of each machine are conflicting and so the needs of one machine are met, whereas the second machine receives zero SV (111 or 000). It means

that all 2^{5} = 32 switching states of a FLI are utilized and there are no restrictions regarding the use of any of them. The resulting PWM pattern is symmetrical with two commutations per inverter leg. It is seen that both main and auxiliary motors’ have separate control signals which lead to an independent vector control.

The configuration of independent vector control of main PMSM and auxiliary PMSM are simulated using the Matlab/Simulink/Sim Power system environment. The simulation is carried out such that parameter of main PMSM (PMSM_01) and auxiliary PMSM (PMSM_02) is same as shown in

The dynamic response of PMSM_01 and PMSM_02 under SVPWM technique running independently with different speed commands and load torques is shown from Figures 15-18. Exactly similar operating points and the perturbations are induced like CRETAM. Figures 19(a)-(d) shows the line to line voltages and phase voltages of integrated PMSM drive in FLI while adopting SVPWM technique.

In adopting CRETAM method, there is a considerable decrease in torque ripple compared to SVPWM method as shown in

is considerable reduction in torque ripple (0.07 Nm) at same load. The main reason for reduction in torque ripple in CRETAM approach is mainly due to improved THD in comparison with SVPWM. As an illustration from Figures 20(c)-(h) the harmonic current spectrum at two different modulation techniques CRETAM and SVPWM are shown, i.e. THD is 9.89% for SVPWM and THD is 4.05% for CRETAM. The harmonic spectra of line to line voltage are also shown.

There is a considerable increase in DC bus voltage utilization in CRETAM in comparison with SVPWM.

Parameters | PMSM_01 | PMSM_02 |
---|---|---|

Rated output power (kW) | 0.25 | 1.65 |

Rated speed (rpm) | 3000 | 2000 |

Back EMF constant (V_{L-L peak}/krpm) | 62.2859 | 62.28 |

No of Poles | 4 | 8 |

Rated Torque (Nm) | 0.8 | 8 |

Stator Resistance (Ω) | 18.7 | 0.9585 |

Stator d and q axis inductance (H) | 0.02682 | 0.00525 |

Inertia (Kg∙m^{2}) | 2.26e−5 | 0.0006329 |

Friction Factor (Nm∙s) | 1.349e−5 | 0.0003035 |

Flux Linkage | 0.171 | 0.1827 |

PWM Techniques | CRETAM | SVPWM | ||
---|---|---|---|---|

Modulation Index | V_{line}_RMS (V) | V_{phase}_RMS (V) | V_{line}_RMS (V) | V_{phase}_RMS (V) |

1 | 168.3 | 97.39 | 171.5 | 100.53 |

0.8 | 152.3 | 87.86 | 157 | 90.58 |

0.6 | 133.3 | 76.96 | 138.1 | 79.66 |

0.4 | 111.5 | 64.47 | 115.8 | 66.51 |

0.2 | 84.56 | 48.54 | 87.19 | 50.35 |

Input Voltage | PMSM1 | PMSM2 |
---|---|---|

Current THD (%) | Current THD (%) | |

150 | 24.77 | 19.16 |

200 | 31.19 | 9.23 |

250 | 41.23 | 10.34 |

300 | 43.03 | 12.78 |

350 | 48.28 | 12.41 |

A novel independent vector control of an integrated PMSM drive is proposed which can be extended to automotive application to control main traction PMSM and auxiliary HVAC compressor PMSM. The control algorithm for driving two Three-phase-PMSMs is achieved. A modified PWM method for FLI i.e. CRETAM technique has been adopted and tested in MATLAB/simulink. The simulation result reveals that, main and auxiliary PMSM motors can be independently controlled with different speed and torque commands even though the parameters for main and traction motor are different and it also clarifies the adopting of ETAM technique for independent control of traction and HVAC drive suffers from poor voltage utilization, increased THD and objectionable torque ripple.

V. Krishnakumar,V. Kamaraj,C. Adrien Perianayagam, (2016) An Integrated Drive for Two PMSMs Involved Automotive Applications and Development of Current Reference Expanded Two Arm Modulation Technique. Circuits and Systems,07,1794-1815. doi: 10.4236/cs.2016.78155