Result
The following video shows a demonstration of the program:
Introduction
Imagine you have an induction motor and only the information from its nameplate or datasheet is available. Now, what happens if you want to use this motor in an application different from the one it was originally designed for? Maybe you need to operate it at higher power, at a higher altitude, in a warmer environment, with a different voltage or frequency, or even with a different connection configuration. How do these changes affect the starting curves, current, and winding temperature?
This tool was created precisely to assist in such situations: to provide an approximate estimate of the behavior of an existing asynchronous motor when certain operating conditions are modified. Based on the basic data, it is possible – using certain simplifications and linear approximations – to predict how key motor parameters might change under new circumstances.
Although the operation of an asynchronous motor is complex, there are known relationships between some variables that, under moderate changes, allow for reasonably useful calculations. It is important to note that since the results are based on linearizations, they are valid only for relatively small deviations from the original operating point. The greater the change, the less accurate the estimate will be.
Starting Curves
The behavior of an asynchronous motor during startup is described using two fundamental curves: the torque vs. speed curve (M–n) and the current vs. speed curve (I–n). The following image shows an example of the starting curves of an asynchronous motor:
As shown in the image, the current drawn by the motor during startup is significantly higher than the current consumed under nominal operating conditions. As the motor gains speed, the current decreases until it reaches the rated value. Torque, on the other hand, starts at a low value at the beginning of startup – sometimes even below the rated torque. As the motor accelerates, the torque increases until it reaches a maximum and then drops again to the nominal point. The torque development during startup can be estimated using the Kloss formula, based on the maximum torque (\(T_{max}\)) and the slip at maximum torque (\(s_{max}\)):
\[ T(s) = \frac{ 2 \cdot T_{max} }{ \frac{ s }{ s_{max} } + \frac{ s_{max} }{ s } } \]
Usually, the slip at the point of maximum torque is not included on the nameplate or in the datasheet. Therefore, it was estimated based on the starting point \( [s=1, T(1)] \) and the maximum torque (\(T_{max}\)).
Calculation of Rated Current and Torque
The rated torque can be calculated from the rated power \( P_n \) in kW and the rated speed \( n \) in revolutions per minute, both of which are typically available on the motor’s nameplate. The formula used is:
\[ T_n = \frac{P_n \cdot 1000}{2\pi \cdot \left(\frac{n}{60}\right)} \]
For a three-phase motor, the rated current is calculated based on the rated power \( P_n \) (in kW), rated voltage \( U_n \), efficiency \( \eta \), and power factor \( \cos\varphi \) using the following formula:
\[ I_n = \frac{P_n \cdot 1000}{\sqrt{3} \cdot U_n \cdot \eta \cdot \cos\varphi} \]
Variation of Frequency and Voltage
The magnetic flux in an induction motor is directly related to the operating frequency and voltage. The starting current is approximately proportional to the magnetic flux:
\[ I_{st} \propto \phi \propto \frac{U}{f} \]
The torque, on the other hand, is proportional to the square of the magnetic flux:
\[ T_{st}, T_{max} \propto \phi^2 \propto ( \frac{U}{f} )^2 \]
Based on this relationship, three main cases are considered:
| \(U\) increases or decreases \( f = const.\) | \(U = const. \) \( f \) increases or decreases | \(U\) and \(f\) increase or decrease \( U/f = const.\) |
| \( \phi \propto U^2 \) | \( \phi \propto 1/f^2 \) | \( \phi = const. \) |
| \( T_{st}, T_{max} \propto U^2 \) | \( T_{st}, T_{max} \propto 1/f^2 \) | \( T_{st}, T_{max} = const. \) |
| \( I_{st} \propto U \) | \( I_{st} \propto 1/f \) | \( I_{st} = const. \) |
A variation in supply frequency also affects the synchronous and rated speed of the motor. Frequency \( f \) and synchronous speed \( n_s \) are related based on the number of poles \(p\) as follows:
\[ n_s = \frac{120 \cdot f}{p} \]
Star or Delta Connection
There are two possible winding connections in a three-phase motor: star (Y) and delta (Δ). A star connection allows operation at a higher voltage with a lower current compared to the same motor connected in delta. When changing the motor’s connection type, the applicable voltage and current vary according to the following relationship:
\[ U_Δ = \frac{U_Y}{\sqrt{3}}, \quad I_Δ = \sqrt{3} \cdot I_Y \]
Temperature Rise
There are mainly four types of losses in an induction motor: ohmic losses, magnetic losses, mechanical losses, and additional losses. Typically, ohmic losses tend to predominate. They are directly related to the current:
\[ P_{cu} = I^2 \cdot R \]
In our calculations, we assume that these losses are the primary source of heat generation in the motor, and therefore the main contributors to temperature rise. This allows us to establish a direct relationship between the nominal current and the temperature increase in the windings, assuming that the other losses (magnetic, mechanical, and additional) remain constant or are relatively minor in comparison. It’s important to note that this simplification becomes less accurate as magnetic flux variation increases.
The IEC60034-1 standard describes the relationship between ambient temperature and the motor’s temperature rise. According to IEC60034-1, it is generally possible to assume that the ambient temperature \(T\) and the temperature rise \(\Delta T\) are related in the following way:
\[ \Delta T_{new} = \Delta T_{old} + (T_{new} – T_{old}) \]
As the altitude above sea level at which the motor is operated increases, the density of the cooling air decreases. This negatively impacts the motor’s cooling capacity. The IEC60034-1 standard defines the following relationship between altitude \(H\) and the temperature rise \(\Delta T\):
\[ \Delta T_{op} = \frac{ \Delta T_{test} }{ 1 + \frac{H_{test} – H_{op}}{10000 \text{ m}} } \]
If the operating altitude \(H_{op}\) or the test altitude \(H_{test}\) is below 1000 m, their value is replaced by 1000 m.
Rotor Current and Voltage
If the motor in question is a slip ring motor, it is important to know the rotor current and voltage. In our calculations, we assume that the rotor voltage and stator voltage are directly proportional:
\[ U_{Rotor} \propto U_{Stator} \]
The rotor current is estimated using the following relation:
\[ I_{Rotor} = \frac{ 1,1 \cdot P_n }{ U_{Rotor}\cdot \sqrt{3} } \]