A New Four Quadrant Field Orientation-Controlled Three-Phase Induction Motor Drive Based on Hysteresis Current Comparison

A new four quadrant Field OrientationControlled (FOC) three-phase induction motor drive based on Hysteresis Current Comparison (HCC) has been developed. The direct relationship between current and torque in the Direct-Quadrature (dq) reference frames has been exploited to develop an HCC scheme that offers accurate tracking of current and torque based on the pulse width modulation technique. The parameters of the inner HCC and the outer ProportionalIntegral (PI) speed controllers have been optimised to obtain effective current and torque tracking. The complete closed loop system being speed-controlled, four quadrant operation has been obtained using step speed input while the suitability of the developed model has been tested under full load stress during steady state. The results obtained satisfy the four quadrant operation requirements of advanced drives where controlled starts and stops are essential in both forward and reverse directions. This is evident in the effectiveness of current and torque tracking and ease of speed transition from motoring to regeneration and vice versa. The developed model finds applications in advanced industrial drives as an energy-efficient and cost-effective alternative to eliminate the effects of supply voltage drops and mechanical load variations.


Introduction
The induction machine, particularly with squirrel cage, is the most commonly used machine in AC drives being very economical, rugged and reliable [1], [2], [3], [4], [5] and [6].Advances in power electronic devices and fast digital processors have provided the possibility of achieving high performance drives; even in four quadrants to satisfy the requirements of advanced drives [7] and [8].
Four quadrant drives offer the opportunity for the utilization of induction motor drives in high dynamic applications where controlled starts and stops are required.If a machine is required to be brought to rest from steady state, instead of abrupt supply interruption with its attendant hazards, the machine can be made to work as a generator thereby the stored kinetic energy can be effectively transferred to the source.This saves energy and brings the machine to rest rapidly and safely.To make a machine transit from motoring to generating mode, power flow is reversed from the machine to the power supply source.This is called regenerative braking.The braking is accomplished by regeneration implying that a negative torque is generated in the machine as opposed to positive motoring torque [9], [10], [11], [12], [13], [14], and [15].The Tab. 1 summarises the four quadrant operation modes where '+' and '−' represent positive and negative respectively.
Figure 1 illustrates the torque-speed profile in four quadrant drives.A mirror image of the torque speed characteristics of quadrant I is obtained in quadrant IV.The quadrant I and IV represent forward motoring and forward regenerating respectively in the forward direction.Some applications require operation in both forward and reverse directions.In such cases, quadrant III and quadrant II represent reverse motoring and reverse regenerating respectively.Due to the direct proportionality of current and torque, current control strategies are employed in adjustable speed drives (ASD) to ensure that stator currents track their respective reference values.Prominent among the current control strategies is the HCC due to ease of implementation, excellent transient response, attainment of maximum current limit and insensitiveness to load parameter variations [16], [17], [18], [19] and [20].The developed HCC is a three-phase Pulse Width Modulation technique and is suitable for a variety of industrial applications such as variable speed electric motor drives, uninterruptible power system, active power filters, and more recently, in renewable energy conversion systems and hybrid vehicles [21].
In this work, a new four-quadrant field orientation-control (FOC) of three-phase induction motor drive based on Hysteresis Current Comparison (HCC) is presented.The parameters of both the outer PI speed controller and the inner HCC of the complete closed loop speed-controlled system are optimised to obtain optimum performance using four-quadrant step speed input simultaneously with full load stress at designated points during steady state to determine the suitability of the developed speed-controlled system for four-quadrant operation.
The simulation environment is MATLAB/Simulink software 2014 version.

Model of Three-Phase Induction
Motor for Field Orientation Due to the direct proportionality of current and torque, current control strategies are employed in Adjustable Speed Drives (ASD) to ensure that stator currents track their respective reference values.Prominent among the current control strategies is the HCC due to ease of implementation, excellent transient response, attainment of maximum current limit and insensitiveness to load parameter variations [16], [17], [18], [19] and [20].The developed HCC is a three-phase Pulse Width Modulation technique and is suitable for a variety of industrial applications such as variable speed electric motor drives, uninterruptible power system, active power filters, and more recently, in renewable energy conversion systems and hybrid vehicles [21].
In this work, a new four-quadrant Field Orientation-Control (FOC) of three-phase induction motor drive based on Hysteresis Current Comparison (HCC) is presented.The parameters of both the outer PI speed controller and the inner HCC of the complete closed loop speed-controlled system are optimised to obtain optimum performance using four-quadrant step speed input simultaneously with full load stress at designated points during steady state to determine the suitability of the developed speed-controlled system for fourquadrant operation.The simulation environment is MATLAB/Simulink software 2014 version.

Model of Three-Phase Induction Motor for Field Orientation Control
The dynamic voltage equations of the squirrel cage induction motor in the synchronously rotating reference frame is shown in Eq. ( 1) [22] and [23].
The electromagnetic torque and rotor dynamic equations are shown in Eq. ( 2) and Eq. ( 3) respectively.
The FOC controls the stator current vector of the induction machine to achieve a precise and independent control of torque and flux as obtainable in the DC machines.The stator current vector contains the torque controlling component, i qs , and the flux controlling component, i ds as shown in the phasor diagram of Fig. 2.
From Fig. 2, field orientation is feasible because the entire rotor flux Ψ r is aligned to the d-axis thereby making the q-axis flux component Ψ qr zero since they are perpendicular to each other.Consequently, Eq. ( 2) reduces to Eq. (4) where T e ∞ i qs .Also, from the rotor flux orientation described above, Eq. ( 5) shows that the rotor flux Ψ r ∞ i ds .
Under this condition, the induction motor behaves exactly as the separately excited DC motor where the q-axis stator current i qs entirely controls the electromagnetic torque and the d-axis stator current i ds entirely controls rotor flux.

Complete Schematic of the Speed-Controlled Drives System
The induction motor in the scheme of figure 3 is fed by an HCC PWM inverter operating as a three-phase sinusoidal current source.
The rotor speed r ω is measured by the speed sensor and filtered by the 1st order low pass filter.The speed error between the actual rotor speed and its reference is processed through the proportional-integral (PI) speed controller to nullify the steady state error in speed.The output is restricted to an upper and a lower limit to produce The reference phase currents are computed using the inverse park's transform as:

Complete Schematic of the Speed-Controlled Drives System
The induction motor in the scheme of Fig. 3 is fed by an HCC PWM inverter operating as a three-phase sinusoidal current source.
The rotor speed ω r is measured by the speed sensor and filtered by the 1 st order low pass filter.The speed error between the actual rotor speed and its reference is processed through the Proportional-Integral (PI) speed controller to nullify the steady state error in speed.The output is restricted to an upper and a lower limit to produce a realistic reference torque T * e .The Fig. 4 shows the realisation of the reference phase currents as expressed from Eq. ( 6) to Eq. ( 16).All reference or command values are superscripted with * in the diagrams.
where τ r = Lr Rr is the rotor time constant. ) The reference phase currents are computed using the inverse park's transform as: The reference phase currents (i * a , i * b , and i * c ) and the corresponding actual phase currents (i a , i b , and i c ), obtained by feedback, are compared using the control logic shown below:

END
From the control logic shown above, it is seen that error signals are generated and used to generate the voltage gating signals for the switches of the Three-Phase (3φ) IGBT Voltage Source Inverter (VSI).The (Fig. 4) HCC action is made possible by ∆i * s , where ∆, which is between 0 and 1 (0 < ∆ < 1), is an adjustable hysteresis window which determines the effectiveness of current and torque tracking [24].

IM IGBT
Current control is achieved by the appropriate firing of the power semiconductor switches S 1 to S 6 of the three-phase inverter.The inverter is supplied by an adequately filtered DC source V dc .Each phase current to the motor is limited by the series RL branch (R =0.001 Ω and L = 5 mH).

Results and Discussions
The appendix A shows the parameters of the threephase induction motor under study.The complete drive system is simulated for a four-quadrant opera-tion from 500 rpm to 500 rpm to 500 rpm and the results presented and discussed.Best performance was obtained by the appropriate tuning of the controller variables as is the practice in industry.The optimal control variables are: Proportional gain = 5, Integral gain = 100, 1 st Order Low Pass Filter Time Constant = 1.6•10 −3 seconds, Torque Limiter Upper Lower = 75 Nm/−75 Nm, Hysteresis Band ∆ = 0.05.
The HCC property that determines the inverter switching is shown in Fig. 6 for time range 0.2936 to 0.2938 seconds using phase 'a' for illustration.Similar behaviours are obtained for phases 'b' and 'c'.The phase 'a' current i a tracts the upper boundary i * a +∆i * s (increases) when switch S 1 is conducting and tracts the lower boundary i * a − ∆i * s (decreases) when switch S 4 is conducting.The Hysteresis Current Control action, which makes i a to track its reference i * a , is seen as

Results and Discussions
The appendix A shows the parameters of the three-phase induction motor under study.The complete drive system is simulated for a four-quadrant operation from 500rpm to 500 rpm to 500 rpm and the results presented and discussed.Best performance was obtained by the appropriate tuning of the controller variables as is the practice in industry.The optimal control variables are: Proportional gain=5, Integral gain=100, 1st Order Low Pass Filter Time Constant= 1.6e-3 seconds, Torque Limiter Upper Lower= 75 Nm/-75Nm, Hysteresis Band ∆=0.05.
The HCC property that determines the inverter switching is shown in figure 6  hysteresis bands imply higher switching frequency and vice versa.This may constitute a practical limitation on the power device switching capability due to switching losses, which need to be mitigated.
On no load, a reference speed of 500rpm is applied until 0.4 seconds when a speed command of -500 rpm is made, followed by a step up to 500rpm at 0.8 seconds to complete a drive in four quadrants as shown in figure 7. The rotor position remained on the increase for as long as the motor speed is positive (Forward Motoring, FM and Forward Regeneration, FR).As soon as the rotor speed becomes negative, the rotor position reverses orientation (Reverse Motoring, RM and Reverse Regeneration, RR).At steady state during reverse motoring, full load step input is applied and removed at 0.65 seconds and 0.7 seconds respectively as shown in figure 8.It is also repeated during forward motoring at 1.05 seconds and 1.1 seconds respectively.The effect of sudden gain and loss of load is evident in the rotor speed and on the phase currents.
Comparing figures 9 and figure 10, the actual phase current accurately tracts the reference both during transient disturbances and steady state condition.The switching period, is seen from the current waveforms, to be the same both for positive speed of 500rpm and negative speed of -500rpm.moves between i * a + ∆i * s to i * a − ∆i * s as switches S 1 and S 4 conduct alternately.The narrower the hysteresis band δ, the more accurately the actual current i a tracts the reference current i a .Smaller hysteresis bands imply higher switching frequency and vice versa.This may constitute a practical limitation on the power device switching capability due to switching losses, which need to be mitigated.
On no load, a reference speed of 500 rpm is applied until 0.4 seconds when a speed command of −500 rpm is made, followed by a step up to 500 rpm at 0.8 seconds to complete a drive in four quadrants as shown in Fig. 7.The rotor position remained on the increase for as long as the motor speed is positive (Forward Motoring, FM and Forward Regeneration, FR).As soon as the rotor speed becomes negative, the rotor position reverses orientation (Reverse Motoring, RM and Reverse Regeneration, RR).
At steady state during reverse motoring, full load step input is applied and removed at 0.65 seconds and  Comparing Fig. 9 and Fig. 10, the actual phase current accurately tracts the reference both during transient disturbances and steady state condition.The switching period, is seen from the current waveforms, to be the same both for positive speed of 500 rpm and negative speed of −500 rpm.

Conclusion
A new four quadrant field orientation-controlled threephase induction motor drive based on Hysteresis Current Comparison (HCC) has been successfully realised.By applying step transition in speed and full stress step loading, motor operation in all the four possible quadrants of operation namely Forward Motoring (FM), Forward Regeneration (FR), Reverse Motoring (RM) and Reverse Regeneration (RR) was obtained.This is what obtains in numerous applications in industry where controlled starts and stops are required in both forward and reverse directions.Dynamic braking occasioned by regeneration in both the forward and reverse direction proves to be a better mean of stopping the motor rather than the usually hazardous option of supply interruption.The controller variables of the developed speed-controlled drives system were optimised to obtain optimal drives performance.The results presented show that the developed HCC algorithm offered excellent dynamic response and steady state performance necessary in advanced motor drives.
SECTION POLICIES VOLUME: XX | NUMBER: X | 2017 | MONTH © 2017 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 3 behaves exactly as the separately excited dc motor where the q-axis stator current qs i entirely controls the electromagnetic torque and the d-axis stator current ds i entirely controls rotor flux.

a
realistic reference torque * e T .The figure 4 shows the realisation of the reference phase currents as expressed from equation 6 to equation 13.All reference or command values are superscripted with * in the diagrams.

Fig. 3 :
Fig. 3: Complete schematic of the speed-controlled induction motor drive system.
for time range 0.2936 to 0.2938 seconds using phase 'a' for illustration.Similar behaviours are obtained for phases 'b' and 'c'.The phase 'a' current a i tracts the upper boundary * S4 conduct alternately.The narrower the hysteresis band ∆ , the more accurately the actual current a i tracts the reference current * a i .Smaller

Fig. 6 :
Fig. 6: Hysteresis current and gating signals for phase A.