^{1}

^{2}

^{1}

^{2}

New hybrid model for efficiency optimization of induction motor drives (IMD) is presented in this paper. It combines two strategies for efficiency optimization: loss model control and search control. Search control technique is used in a steady state of drive and loss model during transient processes. As a result, power and energy losses are reduced, especially when load torque is significant less related to its rated value. Also, this hybrid method gives fast convergence to operating point of minimal power losses and shows negligible sensitivity to motor parameter changes regarding other published optimization strategies. This model is implemented in vector control induction motor drive. Simulations and experimental tests are performed. Results are presented in this paper.

Induction motor is a widely used electrical motor and a great energy consumer. The vast majority of induction motor drives are used for heating, ventilation, and air conditioning (HVAC). These applications require only low dynamic performance, and in most cases only voltage source inverter is inserted between grid and induction motor as cheapest solution. The classical way to control these drives is constant V/f ratio, and simple methods for efficiency optimization can be applied [

One interesting algorithm which can be applied in a drive controller is algorithm for efficiency optimization.

In a conventional setting, the field excitation is kept constant at rated value throughout its entire load range. If machine is underloaded, this would result in overexcitation and unnecessary copper losses. Thus in cases where a motor drive has to operate in wider load range, the minimization of losses has great significance. It is known that efficiency improvement of IMD can be implemented via motor flux level and this method has been proven to be particularly effective at light loads and in a steady state of drive. Also flux reduction at light loads gives less acoustic noise derived from both converter and machine. From the other side low flux makes motor more sensitive to load disturbances and degrades dynamic performances [

Drive loss model is used for optimal drive control in loss model control (LMC) [

Search strategy methods have an important advantage compared to other strategies [

For electrical drives that work in periodic cycles, it is possible to calculate the optimal trajectory of magnetization flux, using optimal control theory, so that power losses in one working cycle are minimal [

Hybrid method combines good characteristics of two optimization strategies SC and LMC [

The process of energy conversion within motor drive converter and motor leads to the power losses in the motor windings and magnetic circuit as well as conduction and commutation losses in the inverter [

The losses in the motor consist of hysteresis losses and eddy current losses in a magnetic circuit (iron losses), losses in the stator and rotor windings (copper loss), and stray losses. In nominal operating conditions the iron losses are typically 2-3 times smaller than the copper losses, but at low loads, these losses are dominant. These losses consist of hysteresis and eddy current losses. Eddy current losses are proportional to the square of supply frequency, and hysteresis losses are proportional to supply frequency. Both components of iron losses are dependent of stator flux level, so next expression is suitable to represent these losses:

Copper losses are appeared as a result of the passing the electric current through the stator and rotor windings. These losses are proportional to the square of current through stator and rotor windings, and they are given by

The total additional losses typically do not exceed 5% when the drive works with light loads. This case is the most important for the power loss minimization algorithms, so stray losses are not considered as a separate loss component.

Losses in the drive converter consist of the losses in the rectifier and the conductive and switching losses in the inverter. The losses in the rectifier are independent of the magnetizing flux and not specifically taken into account. Only conductive losses in the inverter are dependent on the magnetizing flux, and these can be presented in the next form:

Based on the previous considerations, the losses in the induction motor drive, dependent on the magnetizing flux, can be expressed as follows:

Take into account expression for output power:

expression for input power can be written in the next form:

Two typical cases are differed:

linear dependence of magnetizing flux from the magnetizing current,

nonlinear dependence of magnetizing flux from the magnetizing current.

In the algorithms for loss minimization, magnetizing flux is less than or equal to the nominal value, so it is used in the linear part of magnetization characteristics.

Starting from the expressions (

Slip angular speed can be defined as follows:

Based on expression (

Putting

Parameter

First and second derivations of

Value

Based on the specified optimal value of

This procedure of parameter identification is a mainly based on the procedures described in [

The proposed procedure of parameter identification is shown in Figure

A method for determining the parameters

Values

Vector

That is

The choice of

Electrical drive with block for efficiency optimization is shown in Figure

Overall proposed block diagram of efficiency optimization controller in IMD.

Hybrid model for efficiency optimization consists from 3 blocks,

On the basis of speed reference and measured speed, SSC block defines its output and controls switches (Figure

Optimal control calculation in LMC for a given operational conditions is described in Section

Expressions for

This method is sensitive to parameter changes due to temperature changes and magnetic circuit saturation, what consequently leads to error in a current references calculation. So, algorithm for parameter identification is always active, and parameters in the loss model are continuously updated (Figure

Search algorithm is used in steady state, which is detected in the SSC block. Error that exists between the current reference

For two successive values

When the two values of magnetization current

In this way, there are no oscillations of

Hybrid method for efficiency optimization of

Speed reference and load torque are shown in Figure

Speed reference and load torque [p.u.].

Graphs of

Graphs of power loss for nominal flux and hybrid method are given in Figure

Graph of power loss for nominal flux and applied hybrid method.

The experimental tests have been performed on the setup which consists of the following:

induction motor (3 phases,

incremental encoder connected with the motor shaft,

three-phase drive converter (DC/AC converter and DC link),

PC and dSPACE1102 controller board with TMS320C31 floating point processor and peripherals,

interface between controller board and drive converter.

Parameters of used induction motor are given in the appendix of the paper.

The algorithm observed in this paper used the MATLAB-Simulink software, dSPACE real-time interface, and C language. Handling real-time applications is done in ControlDesk.

All experimental tests and simulations have been done in the same operating conditions of the drive, and some comparisons between algorithms for efficiency optimization are made through the experimental tests. Graphs of power losses for nominal flux and when the hybrid method is applied are shown in Figures

Power losses for nominal magnetization flux and operational conditions shown in Figure

Power losses when the hybrid method is applied and operational conditions shown in Figure

Magnetization current

Speed response when the hybrid method is applied and operational conditions shown in Figure

Based on graph in Figure

Algorithms for efficiency optimization of induction motor drive are briefly described. Detailed theoretical analysis of power losses in induction motor is presented. Algorithm for parameter identification in the loss model based on Moore-Penrose pseudoinversion is presented. Also, hybrid algorithm for efficiency optimization has been applied. According to the theoretical analysis, performed simulations, and experimental tests we have arrived to the following conclusions.

If load torque has a value close to nominal or higher, magnetizing flux is also nominal regardless of whether an algorithm for efficiency optimization is applied or not.

For a light load, hybrid method for efficiency optimization gives significant power loss reduction (Figures

There is no oscillation of magnetization flux which is characteristic of the search algorithms (Figures

Also, this hybrid method shows good dynamic performances and no sensitivity to parameter changes (Figure

Implementation of presented algorithm is simple, and it can be universally applied to any electrical motor. Changes are only related to different models of power losses.

Parameters of used induction motor

3 phase

3,7/2,12 A (nominal stator current)

0.75 kW (nominal mechanical power)

1410 r/min (nominal mechanical speed)

^{2} (inertia moment)

Resistance of stator and rotor winding

Self-inductance of stator and rotor

Magnetizing inductance

Leakage factor

Stator transient inductance

Number of pole pairs

Rotor flux angle and angular speed

Rotor angle and angular speed

slip speed

Elektromagnetic torque

Magnetizing flux