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Single phase induction motors as the most used electric machines has recently been researched more strictly due to the intelligence of their variable speed drives into home application. The recent emphasis on energy conservation demands an improvement of the efficiency of SPIM. So an efficient control system can improve power consumption even more. After carrying out a detailed motor efficiency analysis, the concept of efficiency control is to keep the windings currents phase difference on its optimum value at various frequencies. A novel method for maximize motor efficiency by combining efficiency control with speed control is proposed and to be implemented. This method is independent of the motor operating conditions. Instead for mechanical relay to measure the speed, it is very convenient to utilize a simple and low cost electrical sensor. Both efficiency and speed control is achieved by sensing electrical variable that relates frequency and motor slip. Simulation results of the implemented system validate the proposed method.
Index Terms-- efficiency optimization, energy saving, motor drives, single-phase induction motor (SPIMs), speed control.
ingle-phase induction motors are widely used in many domestic appliances and light-duty industrial applications where three-phase power is not readily available. An SPIM is provided with two stator windings (i.e., main and auxiliary winding) and a squirrel cage rotor. The two windings, which are in space quadrature, usually have different impedances and are fed from a common single phase source. The recent rising of oil prices and environmental crises caused the efficient energy consumption and energy saving practices in all applications including SPIM. A number of works have reported the improvement of SPIMs efficiency so far. A rather old method is well-known stator voltage control . It has limited energy saving capability in a small speed range. Since it does not enjoy the potential of variable frequency. Also, it produces considerable harmonic distortion and provides a low power factor.
Cost reduction of VSDs during 1990's their utilization for driving SPIMs gradually increases . Some references
have presented various power converter topologies for variable speed SPIM drives. Also, the use of mechanical relays in drive structure has improved the SPIMs drive efficiency over the motor operating range. But VSDs make the motor often work in non rated conditions in which the motor power loss increases . Combining an efficiency control function in a VSD can improve power consumption in two ways: energy saving with VSD and efficient consumption with motor efficiency maximization under different operating conditions. This has not been reported for SPIM drives so far.
In this paper, after carrying out a thorough motor efficiency analysis, a method for senorless motor efficiency maximization control is presented . A SPIM drive is implemented based on the control method. Simulation results of the implemented system validate the proposed efficiency maximization control.
II. MAXIMUM EFFICIENCY OPERATION
A. Maximum Efficiency Conditions
According to the single phase induction motor model shown in figure 1, the motor voltage equation are obtained as
Using (1) and (2)
Using (4) and (5) in (1) and (2) and simplifying the result, a ratio of windings currents is obtained as
The right-hand side (RHS) side of (6) includes only impedance that is related to supply frequency and motor slip. Therefore, the ratio of windings currents is a function
of frequency and slip
Also, according to (4) and (5), the current ratios and are functions of frequency and slip
Fig. 1 Equivalent circuit of split capacitor SPIMs
Using previous equations, it can be shown that the input impedance of the machine is also a function of frequency and slip
Electromagnetic torque of an SPIM is represented by
According to (7)-(9), the ratios of the currents used in (12) are obtained as
Where . Equation (12) can also be represented by
So, electromagnetic torque can be written as
and electrical power loss is obtained as 
According to (20), under a specific load at each frequency, the motor electrical loss depends on motor slip. Therefore there may be an optimum slip in which the electrical power loss is a minimum. This slip can be found as follows:
As seen in (22), under a specific load, the root of is the optimum motor slip that is a function of frequency only, i.e.
According to (22), we have to solve (25) to find the optimal motor slip in terms of the supply frequency, as shown (24) and (25).
Almost all parameters and variables in (25) are functions of frequency and slip, which make the equation cumbersome to be solved analytically. Therefore, the optimum slip for each supply frequency is found through numerical solution of (25) or alternatively by experimental tests. We can maximize the motor efficiency by controlling the motor slip on its optimum value. But slip control requires a speed sensor that is too expensive to be used in an SPIM control system.
B. Appropriate Control Variable
It is very convenient to utilize a simple and low-cost electrical sensor, instead of a mechanical one, to avoid cost increase. Therefore, we should identify an appropriate electrical variable that removes the need for speed measurement. According to (23), we should find an electrical variable that depends on frequency and motor slip only to relate these two variables through that electrical variable.
Fortunately, an easily sensible electrical variable that depends on frequency and motor slip, i.e., the ratio of windings currents, can be seen in (7), which is repeated here both the amplitude and the angle of the ratio can be used as a medium variable to relate frequency to optimum motor slip.
Fig. 2 Electrical loss in terms of amplitude ratio of windings currents at various frequencies
The angle is, in fact, the phase difference of windings currents figs. 2 and 3 shows the motor electrical power loss under a constant 2 N-m torque at various frequencies in terms of amplitude of windings currents ratio and phase of windings currents ratio.
Fig. 3 Electrical loss in terms of phase difference of windings currents at various frequencies
It is seen that the slope of electrical loss, as seen in fig. 2, is sharp, while the range of variation of the amplitude ratio of windings currents is wide especially at low frequencies, but the slope of electrical loss is not sharp, as seen in fig. 3, because of short range of windings currents phase difference variation. It means that the disturbances can influence the sensing of amplitude ratio mare than the sensing of windings currents phase difference.
Therefore, it is preferred to sense and utilize the windings currents phase difference having
Where the winding current is phase difference and is that amount of in which electrical loss is minimum .
It is seen that, at each frequency, the minimum electrical loss is dissipated in a ï¬xed motor slip, as it was explained before. Therefore, according to (29), the minimum electrical loss at each frequency also takes place in a ï¬xed windings currents phase difference. Fig. 4 shows electrical loss in terms of windings currents phase difference and supply frequency under a ï¬xed 2 N m load, at different frequencies. A minimum loss curve is also shown in Fig. 4 over which the SPIM has minimum electrical loss. The optimum amount of currents phase difference and the minimum electrical loss at each frequency can be obtained from this curve over total range of motor load, because the optimum phase difference of windings currents does not depend on motor load and is a function of frequency only.
Fig. 4 Motor electrical loss in terms of phase difference of windings currents and frequency at different frequencies under constant load
A minimum electrical loss at a speciï¬c operating point results in a maximum efficiency. The motor efficiency in terms of windings currents phase difference and supply frequency under aï¬xed2N m load at different frequencies is shown in Fig. 5.Also, a maximum efficiency curve is depicted in Fig. 5. This curve gives the optimum amount of currents phase difference over the total range of motor load, and illustrates the relation between the optimum windings currents phase difference and frequency. This curve is a graphical representation of (29), and shows that the currents phase difference can be used as a practical and effective control variable in an efficiency optimization control system.
Fig. 5 Motor efficiency in terms of phase difference of windings currents and frequency at different frequencies under constant load
III. CONTROL SYATEM
A. Concept Exploration of Control
According to the aforementioned discussions, the concept of efficiency control is to keep the windings currents phase difference on its optimum value at various frequencies. In other terms, one should adjust the windings currents phase difference on the maximum efficiency curve to maximize motor efï¬ciency.
In a motor drive system, speed control is a prime concern. Therefore, in addition to efficiency optimization control, the motor speed control must be sought. Fortunately, the motor speed can be Controlled at each supply frequency by controlling the motor slip. Considering the relation between slip and currents phase difference, the motor speed can be controlled by controlling the motor slip through the currents phase difference at each supply frequency. Therefore, two controls, i.e., an efficiency optimization control and a speed control, can be designed by using the newly introduced control variable of currents phase difference, as will be presented in the next section.
B. Control System Design
A block diagram of the control system is shown in Fig. 6. It composed of two interrelated control subsystems: a variable frequency open-loop speed control subsystem and a variable speed motor efficiency control subsystem.
The efficiency control subsystem controls windings currents phase difference to its optimum value, considering the relation of Fig. 5 by a proportional-integral (PI) controller. The auxiliary and main windings currents are measured by sensing voltage drops across two installed resistors in series with motor windings as A1 and A2, respectively. As it can be seen in Fig. 6, a phase difference detector block measures the windings currents phase difference. The optimum value of currents phase difference is obtained from the motor frequency through an electronically implemented block, mapping the maximum efficiency curve. It is seen at the left top corner of the efficiency control subsystem in Fig. 6.
The efficiency control is a steady-state type of control and may not control the motor transient behavior well. It may even deteriorate the motor performance during transient states. Therefore, a transient state detection and compensation are considered as a part of the efficiency control subsystem, as seen in Fig. 6. This part neutralizes the effect of PI controller by adding a desired signal to the PI control output in transient states. In fact, a sudden variation of the main winding current indicates a transient state of the motor when an appropriate action must be provided to avoid system instability. This is done by detecting a sudden increase of the main winding current and producing an appropriate signal to be added to the PI output. The signal is provided through a proportional-derivative (PD) controller for quick action and a low-pass
Fig. 6 Block diagram of the proposed control system
ï¬lter (LPF) to eliminate noise. But in simulation low-pass filter is not needed. These are represented by LPF&PD block in Fig. 6. The function of the PD is to transform the sudden rise of the main winding current to additional motor voltage. Therefore, the setting of its derivative gain is so that the product of derivative gain and main winding current rising rate provides a rise of supply voltage up to that causes the motor ï¬‚ux level to rise to its rated value. The proportional gain is a small value to bias the PD to its linear operating range. An appropriate set of parameters of the controllers for normalized signals is for the PI controller and for PD controller.The speed control subsystem works like a constant control system. However, its voltage value is complemented by the efficiency control subsystem output. According to (29), by keeping the currents phase difference on a determined value, the relation between motor slip and frequency can be deï¬ned. Therefore, an appropriate supply frequency for any desired motor speed is obtained. This is done by performing system simulation, and the results are stored in a lookup table as the one shown by a block located in the top left corner of the speed control subsystem in Fig. 6. The block gives the required supply frequency in response to any commanded speed. The frequency is used both in speed control subsystem and efficiency control subsystem, as seen in Fig. 6.
IV. EXPERIMENTAL IMPLEMENTATION IN MATLAB SIMULINK
An Experimental Implementation is developed to evaluate the proposed efficiency and speed controls under variable frequency, speed, and load. A diagram of both v/f and efficiency control in MATLAB is shown in fig. 8 and 9.
The model includes an insulated gate bipolar transistor (IGBT) based single phase ac-dc-ac supply to provide a variable frequency-variable voltage to the motor. It also contains a control system to control the motor speed and efficiency, as explained in the previous section. The motor loading is provided by a step block in MATLAB capable of applying any value of load torque to the motor. The control system receives a speed reference and control the motor speed on its reference whereas maximizes the motor efficiency under wide range of load. To make control scheme attractive and affordable to the local industry, the control system is implemented with simple blocks. Designed using sim power system block sets in MATLAB 7.9.
Setting the initial load torque as 2 Nm and varying the torque to 1 Nm at 1 sec with speed reference as constant of 1500 rpm. Then the above motor variables responses to time are came from simulation. From fig. 7, after sudden variation of load the speed changes to around 1500 rpm, both input and output power reduced, but the output power decrease more compare to input power as a result the efficiency decrease from 60 to 50 percent. The stator current also varied according to the load.
Fig. 7 Motor variable in response to load disturbances under the constant V/f control method
By having the same varying load with constant speed reference for efficient controller, the motor variables are as shown above. After the sudden decrease of load torque to 1Nm, input power decrease with decrease of output power as a result the efficiency maintained constant throughout the load variation in efficient control method as around 70 percent. In this method also there will be a current variation. In speed command, initially 1500 rpm is varied to 1200 rpm in 0.5 sec
Fig. 8 Motor variable in response to load disturbances under the proposed control method
with constant load torque of 1Nm. From the graph after varying speed the input power is varied according to speed by v/f control method followed by output power, as a result efficiency is almost maintained constant as 49 to 45 percent. The current in stator side is maintained almost constant.
Fig. 9 Motor variables in response to speed command under the constant v/f control method
From fig. 10, after the speed reduced from 1500 rpm to 1200 rpm in 0.5 sec the following motor variables responses are observed. At initially efficiency as 66 percent, then varying the speed to 1200 rpm input power reduced to low value compare to output in pervious section so the efficiency is reduced to 60 percent, but this method is better to previous v/f control method. The current to motor is maintained constant as shown above.From fig. 11, In this case both load as well as reference speed is set at 2Nm and 1500 rpm in initial then it is changed to 1Nm at 0.8 sec and 1200 rpm at 0.5 sec. After 0.5 sec the speed reduced to 1150 rpm with efficiency as 66 percent then at 0.8 sec the load torque has reduced to 1Nm this increase the speed of the motor to 1350 rpm with efficiency as almost same as 66 percent .the stator current is maintained constant throughout the simulation.
Fig. 10 Motor variables in response to speed command under the proposed control method
Fig. 11 Motor variables in response to both load disturbance and speed command under the proposed control method
In this paper, the problem of maximum efficiency conditions for SPIM is achieved thorough analytical investigation. The suggested control method to maximize the motor efficiency under different operating conditions was proposed. The proposed method is independent of the motor operating conditions. By using windings currents phase difference as an appropriate electrical control variable, instead of motor slip, so the control method does not need any mechanical sensor. The motor slip is controlled indirectly under the proposed method by controlling windings currents phase difference. Therefore, a VSD with ability of speed control and efficiency maximization in different operating points is designed. Simulation results evaluated the proposed control method and confirm its superiority over the constant v/f control method by showing efficiency improvement of over 17%. So from, by using this efficient control in VSD for SPIMs makes cost effective and energy saving.
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