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Tiny Calculator

Frequently used

Wire Length

$$\class{X04}{L}=\frac{\class{X03}{A}\cdot\class{X06}{\Delta{U}}}{\class{X02}{\rho}\cdot \class{X05}{I}}$$

Loss in the wire

$$\class{X09}{P_{L}}=\class{X06}{\Delta{U}}\cdot \class{X05}{I}$$

Component Sizing

Slip

$$\class{X05}{s}=\bigg(1-\frac{{\class{X02}{V}-\class{X04}{N_p}}}{4\cdot\pi\cdot \class{X03}{F_{nom}}}\bigg)$$

Electric Output Power

$$\class{X14}{P_E}=\class{X02}{V}\cdot \class{X08}{T_M}\cdot(1-\class{X05}{s})$$

Efficiency

$$\class{X18}{\eta}=\frac{\class{X08}{T_M}\cdot(1-\class{X05}{s})}{\class{X08}{T_M}+\class{X07}{T_F}}$$

Component Sizing

Electric Output Power

$$\class{X15}{P_E}=(\class{X08}{T_S}-\class{X09}{T_F})\cdot \class{X01}{\omega} - \class{X13}{P_L}$$

Efficiency (%)

$$\class{X20}{\eta}=\frac{\class{X10}{T_M}\cdot\class{X01}{\omega}-\class{X13}{P_L}}{\class{X08}{T_S}\cdot\class{X01}{\omega}}$$

Output Voltage

$$\class{X19}{U}=\class{X18}{R}\cdot \left({\class{X16}{I_A}+\class{X17}{I_F}}\right)$$

Armature Current

$$\class{X16}{I_A}=\sqrt{\frac{\class{X15}{P_E}\cdot \left[{\class{X05}{R_{FP}}-\class{X07}{K}\cdot \class{X01}{\omega}\cdot \left({\class{X06}{L_{FP}}+\class{X04}{L_{FS}}}\right)}\right]}{{\class{X07}{K}\cdot \class{X01}{\omega}\cdot \left[{\class{X02}{R_A}\cdot \class{X06}{L_{FP}}+\class{X02}{R_A}\cdot \left({\class{X04}{L_{FS}}+\class{X04}{L_{FS}}\cdot \class{X05}{R_{FP}}}\right)}\right]}}}$$

Parallel Field Current

$$\class{X17}{I_F}=\frac{{\class{X15}{P_E}-\class{X07}{K}\cdot \class{X04}{L_{FS}}\cdot {{\class{X16}{I_A}}^2}\cdot \class{X01}{\omega}}}{{\class{X07}{K}\cdot \class{X16}{I_A}\cdot \class{X01}{\omega}\cdot\left({\class{X06}{L_{FP}}+\class{X04}{L_{FS}}}\right)}}$$

Component Sizing

Capacitance

$$\class{X01}{C}=\frac{\class{X02}{P}\cdot[tan(\class{X03}{PF_{actual}})-tan(\class{X04}{PF_{desired}})]}{{\class{X05}{U}}^{2}\cdot 2\cdot\pi\cdot\class{X06}{f}}$$

Reactive Power

$$\class{X09}{Q_c}=\class{X01}{C}\cdot \class{X05}{U}^{2}\cdot 2\cdot\pi\cdot \class{X06}{f}$$

Component Sizing

Capacitance (Star Connection)

$$\class{X01}{C}=\frac{\class{X02}{P}[tan(arccos(\class{X03}{PF_{actual}}))-tan(arccos(\class{X04}{PF_{desired}}))]}{{\class{X05}{U}}^{2}\cdot 2\cdot\pi\cdot \class{X06}{f}}$$

Reactive Power (Star Connection)

$$\class{X09}{Q_c}=\class{X01}{C}\cdot \class{X05}{U}^{2}\cdot 2\cdot\pi\cdot \class{X06}{f}$$

Capacitance (Delta Connection)

$$\class{X01}{C}=\frac{\class{X02}{P}[tan(arccos(\class{X03}{PF_{actual}}))-tan(arccos(\class{X04}{PF_{desired}}))]}{3\cdot {\class{X05}{U}}^{2}\cdot 2\cdot \pi\cdot\class{X06}{f}}$$

Reactive Power (Delta Connection)

$$\class{X09}{Q_c}=3\cdot \class{X01}{C}\cdot \class{X05}{U}^{2}\cdot 2\cdot\pi\cdot \class{X06}{f}$$

Component Sizing

Capacitance

$$\class{X01}{C}=\frac{\class{X05}{Q_c}}{{\class{X02}{U}^{2}\cdot 2\cdot\pi\cdot \class{X03}{f}}}$$

Current

$$\class{X11}{I}=\frac{\class{X04}{U}\cdot \sqrt{{\class{X05}{R}}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}{{\class{X05}{R}\cdot \class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}}$$

Power Factor

$$\class{X08}{cos(\varphi)}=\frac{\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}{\sqrt{{\class{X05}{R}^{2}+\left({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}\right)^{2}}}}$$

Active Power

$$\class{X02}{P}=\frac{\class{X04}{U}^{2}}{\class{X05}{R}}$$

Apparent Power

$$\class{X01}{S}={\class{X04}{U}}^{2}\cdot \sqrt{\frac{1}{{\class{X05}{R}}^{2}}+\frac{1}{({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Phase difference (Current-Voltage)

$$\class{X12}{\varphi}=\arccos{\bigg(\frac{\sqrt{\class{X01}{S}^2-\class{X03}{Q}^2}}{\class{X01}{S}}\bigg)}$$

Impedance (Resistance connected in parallel with the inductance)

$$\class{X10}{Z}=\frac{{\class{X05}{R}\cdot \class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}}{{\sqrt{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}}$$

Inductance

$$\class{X06}{L}=\frac{\class{X04}{U}^2}{\class{X03}{Q}\cdot 2\cdot\pi\cdot \class{X09}{f}}$$

Resistance

$$\class{X05}{R}=\frac{\class{X04}{U}^2}{\sqrt{\class{X01}{S}^2-\class{X03}{Q}^2}}$$

Component Sizing

Current (Resistance connected in series with the inductance)

$$\class{X11}{I}=\frac{\class{X04}{U}}{{\sqrt{{\class{X05}{R}}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}}$$

Power factor (Resistance connected in series with the inductance)

$$\class{X08}{cos(\varphi)}=\frac{\class{X05}{R}}{{\sqrt{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}}$$

Apparent Power (Resistance and Inductance connected in series)

$$\class{X01}{S}=\frac{\class{X04}{U}^{2}}{\sqrt{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Reactive Power

$$\class{X03}{Q}=\frac{\class{X04}{U}^{2}\cdot \class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}$$

Angle

$$\class{X12}{\varphi}=\arccos{\bigg(\frac{\sqrt{\class{X01}{S}^2-\class{X03}{Q}^2}}{\class{X01}{S}}\bigg)}$$

Impedance (Resistance connected in series with the inductance)

$$\class{X10}{Z}=\sqrt{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}$$

Active Power

$$\class{X02}{P}=\frac{\class{X04}{U}^{2}\cdot \class{X05}{R}}{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}$$

Inductance

$$\class{X06}{L}=\frac{\class{X03}{Q}\cdot \class{X04}{U}^2}{2\cdot\pi\cdot \class{X09}{f} \cdot \class{X01}{S}^2}$$

Component Sizing

Power Factor

$$\class{X08}{cos(\varphi)}=\frac{\class{X02}{P}}{\class{X01}{S}}$$

Active Power (Star connection)

$$\class{X02}{P}=\frac{{\class{X04}{U}^{2}\cdot \class{X05}{R}}}{{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Apparent Power

$$\class{X01}{S}=\sqrt{\class{X02}{P}^{2}+\class{X03}{Q}^{2}}$$

Reactive power (Star connection)

$$\class{X03}{Q}=\frac{{\class{X04}{U}^{2}\cdot \class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}}{{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Component Sizing

Power Factor

$$\class{X08}{cos(\varphi)}=\frac{\class{X02}{P}}{\class{X01}{S}}$$

Active Power (Star connection)

$$\class{X02}{P}=\frac{{\class{X04}{U}^{2}\cdot \class{X05}{R}}}{{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Apparent Power

$$\class{X01}{S}=\sqrt{\class{X02}{P}^{2}+\class{X03}{Q}^{2}}$$

Reactive power (Star connection)

$$\class{X03}{Q}=\frac{{\class{X04}{U}^{2}\cdot \class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}}{{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Active Power (Delta connection)

$$\class{X02}{P}=\frac{{3\cdot \class{X04}{U}^{2}\cdot \class{X05}{R}}}{{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Reactive Power (Delta Connection)

$$\class{X03}{Q}=\frac{{3\cdot \class{X04}{U}^{2}\cdot {\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}}}}{{\class{X05}{R}^{2}+({\class{X06}{L}\cdot 2\cdot\pi\cdot \class{X09}{f}})^{2}}}$$

Component Sizing

Rated Power

$$\class{X04}{P}=\class{X01}{U}\cdot \class{X03}{I}$$

Rated Voltage

$$\class{X01}{U}=\class{X02}{R}\cdot \class{X03}{I}$$

Component Sizing

Resistance

$$\class{X02}{R}=\frac{\class{X01}{U}^2}{\class{X04}{P}}$$

Resistance, Star connected

$$\class{X02}{R}=\frac{\class{X01}{U}^2}{\class{X04}{P}}$$

Resistance, Delta connected

$$\class{X02}{R}=\frac{3\cdot \class{X01}{U}^2}{\class{X04}{P}}$$

Component Sizing

Resistance

$$\class{X02}{R}=\frac{\class{X01}{U}^2}{\class{X04}{P}}$$

Inductors

$$\class{X03}{\%_1}\class{X04}{\%_2}\class{X17}{\%_3}\class{X01}{L_{total}}$$

Resistances

$$\class{X03}{\%_1}\class{X04}{\%_2}\class{X17}{\%_3}\class{X02}{R_{total}}$$

Transconductance Parameter

$$\class{X02}{K}=\frac{{\sqrt{2\cdot \mid \class{X03}{I_{d1}}\mid }-\sqrt{2\cdot \mid \class{X04}{I_{d2}}\mid }}}{\left({\class{X05}{V_{gs1}}-\class{X06}{V_{gs2}}}\right)^{2}}$$

Threshold Voltage

$$\class{X01}{V_{th}}=\frac{{\class{X05}{V_{gs1}}\cdot \sqrt{\mid \class{X04}{I_{d2}}\mid }-\class{X06}{V_{gs2}}\cdot \sqrt{\mid \class{X03}{I_{d1}}\mid }}}{{\sqrt{\mid \class{X04}{I_{d2}}\mid }-\sqrt{\mid \class{X03}{I_{d1}}\mid }}}$$

Component Sizing

Channel Length Modulation Parameter

$$\class{X02}{\lambda}=\frac{{\class{X03}{I_{d1}}\cdot {\class{X01}{V_{th}}}^{2}-\class{X07}{I_{dss}}\cdot \left({\class{X05}{V_{gs1}}-\class{X01}{V_{th}}}\right)^{2}}}{{\class{X07}{I_{dss}}\cdot \class{X08}{V_{ds}}\cdot \left({\class{X05}{V_{gs1}}-\class{X01}{V_{th}}}\right)^{2}}}$$

Threshold Voltage

$$\class{X01}{V_{th}}=\frac{{\class{X05}{V_{gs1}}\cdot \sqrt{\class{X04}{I_{d2}}}-\class{X06}{V_{gs2}}\cdot \sqrt{\class{X03}{I_{d1}}}}}{{\sqrt{\class{X04}{I_{d2}}}-\sqrt{\class{X03}{I_{d1}}}}}$$

Component Sizing

Channel Length Modulation Parameter

$$\class{X02}{\lambda}=\frac{{\class{X03}{I_{d1}}\cdot {\class{X01}{V_{th}}}^{2}-\class{X07}{I_{dss}}\cdot \left({\class{X05}{V_{gs1}}-\class{X01}{V_{th}}}\right)^{2}}}{{\class{X07}{I_{dss}}\cdot \mid \class{X08}{V_{ds}}\mid \cdot \left({\class{X05}{V_{gs1}}-\class{X01}{V_{th}}}\right)^{2}}}$$

Threshold Voltage

$$\class{X01}{V_{th}}=\frac{{\class{X05}{V_{gs1}}\cdot \sqrt{\mid\class{X04}{I_{d2}}\mid}-\class{X06}{V_{gs2}}\cdot \sqrt{\mid\class{X03}{I_{d1}}\mid}}}{{\sqrt{\mid\class{X04}{I_{d2}}\mid}-\sqrt{\mid\class{X03}{I_{d1}}\mid}}}$$

Component Sizing

Early Voltage

$$\class{X02}{V_{a}}=\frac{\class{X03}{I_{c}}}{\class{X04}{h_{OE}}}$$

Base Current

$$\class{X05}{I_{b}}=\frac{\class{X03}{I_{c}}}{\class{X01}{\beta}}$$

Saturation Current of the Emitter Junction

$$\class{X06}{I_{ES}}=\frac{\class{X12}{I_{s}}}{\class{X08}{\alpha_{F}}}$$

Saturation Current of the Collector Junction

$$\class{X07}{I_{CS}}=\frac{\class{X12}{I_{s}}}{\class{X09}{\alpha_{R}}}$$

Forward Gain

$$\class{X08}{\alpha_{F}}=\frac{\class{X03}{I_{c}}}{{\class{X10}{h_{FE}}+\class{X03}{I_{c}}}}$$

Reverse Gain

$$\class{X09}{\alpha_{R}}=\frac{{\class{X03}{I_{c}}-\class{X11}{h_{RE}}}}{\class{X03}{I_{c}}}$$

Component Sizing

Capacitance

$$\class{X01}{C}=\frac{\class{X02}{q}}{\class{X03}{U_{c}}}$$

Current

$$\class{X08}{I_{c}}=\class{X01}{C}\cdot {\frac{\class{X04}{\Delta U_c}}{\class{X05}{\Delta t}}}$$

Design of the Smoothing Capacitor

$$\class{X01}{C}=\frac{\class{X08}{I_{c}}}{{\class{X16}{\Delta U}\cdot \class{X17}{f}}}$$

Energy

$$\class{X06}{E}=\frac{1}{2}\cdot \class{X01}{C}\cdot {\class{X03}{U_{c}}}^{2}$$

Angle: Low-Pass Filter

$$\class{X13}{\theta}=-\arctan{(\class{X15}{R}\cdot \class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f})}$$

Cut-off Frequency

$$\class{X14}{f_{c}}=\frac{1}{{2\cdot \pi\cdot \class{X15}{R}\cdot \class{X01}{C}}}$$

Gain: Low-Pass Filter

$$\class{X12}{G}=20\cdot \log{\bigg(\frac{1}{\sqrt{1+\left({\class{X15}{R}\cdot \class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}}\right)^{2}}}\bigg)}$$

Angle: High-Pass Filter

$$\class{X13}{\theta}=\arctan{\bigg(\frac{1}{{\class{X15}{R}\cdot \class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}}}\bigg)}$$

Gain: High-Pass Filter

$$\class{X12}{G}=20\cdot \log{\bigg(\frac{\class{X15}{R}\cdot \class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f} }{{\sqrt{1+\left({\class{X15}{R}\cdot \class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f} }\right)^{2}}}}\bigg)}$$

Phase Difference: Real Model

$$\class{X13}{\theta}=\arctan{\bigg(\frac{{-\class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}\cdot {\class{X10}{R_{p}}}^{2}}}{{\class{X10}{R_{p}}+\class{X09}{R_{s}}+\left({\class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}}\right)^{2}\cdot {\class{X10}{R_{p}}}^{2}\cdot \class{X09}{R_{s}}}}\bigg)}$$

Impedance: Real Model

$$\class{X11}{Z_{c}}=\sqrt{\frac{{{\left({\class{X10}{R_{p}}+\class{X09}{R_{s}}}\right)^{2}+\left({\class{X09}{R_{s}}\cdot \class{X10}{R_{p}}\cdot \class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}}\right)^{2}}}}{{1+\left({\class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}\cdot \class{X10}{R_{p}}}\right)^{2}}}}$$

Reactive Power

$$\class{X07}{Q}=\class{X01}{C}\cdot 2\cdot\pi\cdot \class{X17}{f}\cdot {\class{X03}{U_{c}}}^{2}$$

Component Sizing

Emission Constant

$$\class{X09}{n}=\frac{{\class{X03}{V_{f}}-\class{X13}{V}}}{{\frac{{\class{X11}{k}\cdot \class{X05}{T}}}{\class{X12}{q}}\cdot \ln{\bigg(\frac{{\class{X04}{I_{f}}+\class{X08}{I_{0}}}}{{\class{X14}{I}+\class{X08}{I_{0}}}}\bigg)}}}$$

Saturation Current

$$\class{X08}{I_{0}}=\frac{\class{X04}{I_{f}}}{{ {e}^\class{custom-exp-e}{{\frac{{\class{X03}{V_{f}}\cdot \class{X12}{q}}}{{\class{X05}{T}\cdot \class{X11}{k}\cdot \class{X09}{n}}}}}-1}}$$

Component Sizing

Energy

$$\class{X17}{E}=\frac{1}{2}\cdot \class{X05}{L}\cdot {\class{X09}{I_L}}^{2}$$

B Field

$$\class{X08}{B}=\class{X01}{\mu_{0}}\cdot \class{X02}{\mu_{r}}\cdot \class{X07}{H}$$

H Field

$$\class{X07}{H}=\frac{{\class{X04}{N}\cdot \class{X09}{I_L}}}{\class{X06}{l}}$$

Magnetic Flux Calculation (inductance)

$$\class{X11}{\Phi}=\frac{{\class{X05}{L}\cdot \class{X09}{I_L}}}{\class{X04}{N}}$$

High low filter : Angle

$$\class{X21}{\theta}=-\arctan{\bigg(\frac{{\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}}}{\class{X24}{R}}\bigg)}$$

Cut-off frequency

$$\class{X23}{f_{c}}=\frac{\class{X24}{R}}{{\class{X05}{L}\cdot 2\cdot \pi}}$$

Low pass filter : Gain

$$\class{X22}{G}=20\cdot \log{\bigg(\frac{\class{X24}{R}}{\sqrt{\class{X24}{R}^{2}+\left({\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}}\right)^{2}}}\bigg)}$$

High pass filter : Gain

$$\class{X22}{G}=20\cdot \log{\bigg(\frac{\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}}{{\sqrt{\class{X24}{R}^{2}+\left({\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}}\right)^{2}}}}\bigg)}$$

Angle

$$\class{X21}{\theta}=\arctan{\bigg(\frac{\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}}{\class{X18}{r}}\bigg)}$$

Impedance

$$\class{X20}{Z}=\sqrt{(\class{X18}{r})^{2}+({\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}})^{2}}$$

Inductance

$$\class{X05}{L}=\frac{{\class{X01}{\mu_{0}}\cdot \class{X02}{\mu_{r}}\cdot \class{X04}{N}^{2}\cdot \class{X03}{A}}}{\class{X06}{l}}$$

High pass filter : Phase Difference

$$\class{X21}{\theta}=\frac{\pi}{2}-\arctan{\bigg(\frac{\class{X05}{L}\cdot 2\cdot\pi\cdot \class{X19}{f}}{\class{X24}{R}}\bigg)}$$

Component Sizing

Dissipated power

$$\class{X04}{P}=\class{X01}{R}\cdot {\class{X03}{I}}^2$$

Current

$$\class{X03}{I}=\frac{\class{X02}{U}}{\class{X01}{R}}$$

Component Sizing

Resistance between terminal 1 and terminal 2

$$\class{X01}{R_{1-2}}=\class{X02}{P}\cdot \class{X03}{R}$$

Resistance between terminal 1 and terminal 2

$$\class{X01}{R_{1-2}}=\class{X02}{P}\cdot \class{X03}{R}$$

Resistance between terminal 1 and terminal 2

$$\class{X01}{R_{1-2}}=\class{X02}{P}\cdot \class{X03}{R}$$

Mechanical Power

$$\class{X06}{P_{mec}}=\class{X07}{T_m}\cdot \class{X04}{N_m}$$

Electrical Power

$$\class{X08}{P_{elec}}=\class{SmallSquareRoot}{\sqrt{3}}\cdot \class{X09}{U}\cdot \class{X10}{I}\cdot \class{X11}{cos\varphi}$$

Full-Load Efficiency

$$\class{X12}{\eta}=\frac{\class{X06}{P_{mec}}}{\class{X08}{P_{elec}}}$$

Synchronous Speed

$$\class{X01}{N_s}=\frac{\class{X03}{f}}{\class{X02}{p}}\cdot 2\cdot \pi$$

Starting Time Calculation

$$\class{X35}{t_s}=\frac{{(\class{X34}{J_m}+\class{X45}{J_{l}})}\cdot \class{X36}{\Omega_f}}{\frac{\class{X44}{T_{n}}\cdot {\frac{\class{X32}{T_s}}{\class{X44}{T_{n}}}+2}}{3}-\class{X33}{T_l}}$$

Stator Resistance calculation in Star connection

$$\class{X13}{R_S}=\frac{\class{X37}{U_{DC}}}{{2\cdot \class{X38}{I_{DC}}}}$$

Core Losses Resistance calculation

$$\class{X18}{R_c}=\frac{3\cdot {\class{X17}{U_{NL}}}^{2}}{\class{X41}{P_{CORE}}}$$

Rotor Resistance Calculation

$$\class{X22}{R_R}=\frac{\class{X42}{P_{JR}}}{{3\cdot {\class{X21}{I_{LR}}}^{2}}}$$

Rotor Inductances calculation

$$\class{X26}{L_R}=\frac{\class{X43}{Q_{LR}}}{{2\cdot \pi\cdot \class{X03}{f}} \cdot 3 \cdot {\class{X21}{I_{LR}}}^2}$$

Stator Inductances calculation

$$\class{X27}{L_S}=\frac{2\cdot\pi\cdot \class{X03}{f}\cdot \class{X43}{Q_{LR}}}{{3\cdot {\class{X21}{I_{LR}}}^2 \cdot \class{X25}{x}}}$$

Magnetic Inductances calculation

$$\class{X28}{L_m}=\frac{3\cdot {\class{X17}{U_{NL}}}^2}{{2\cdot \pi\cdot \class{X03}{f}\cdot \class{X29}{Q_{NL}}}}$$

Component Sizing

Shaft Mechanical Output Power

$$\class{X10}{P_S}=\class{X15}{P_E}\cdot(1-\class{X06}{s})-\class{X03}{V}\cdot \class{X08}{T_f}$$

Slip (%)

$$\class{X06}{s}=\frac{{\frac{{4\cdot \pi\cdot \class{X04}{F_{nom}}}}{\class{X05}{N_p}}-\class{X03}{V}}}{\frac{{4\cdot \pi\cdot \class{X04}{F_{nom}}}}{\class{X05}{N_p}}}$$

Efficiency (%)

$$\class{X17}{\eta}=1-\frac{{\class{X06}{s}\cdot \class{X15}{P_E}+\class{X03}{V}\cdot \class{X08}{T_F}}}{\class{X15}{P_E}}$$

Component Sizing

Turns Ratio

$$\class{X05}{a}=\frac{\class{X03}{N_{P}}}{\class{X04}{N_{S}}}$$

Primary Power

$$\class{X06}{P_{P}}=\frac{{\class{X01}{V_{P}}}^2}{\class{X05}{a}^2\cdot \class{X10}{R}}+\class{X11}{P_{L}}$$

Secondary Power

$$\class{X08}{P_{S}}=\frac{{\class{X01}{V_{P}}}^2}{\class{X05}{a}^2\cdot \class{X10}{R}}$$

Efficiency (%)

$$\class{X12}{\eta}=1-{\frac{\class{X11}{P_{L}}}{\frac{{\class{X01}{V_{P}}}^2}{\class{X05}{a}^2\cdot \class{X10}{R}}+\class{X11}{P_{L}}}}$$

Component Sizing

Primary to Secondary Turns Ratio

$$\class{X07}{a_{A}}=\frac{\class{X04}{N_{P}}}{\class{X05}{N_{SA}}}$$

Primary to Tertiary Turns Ratio

$$\class{X08}{a_{B}}=\frac{\class{X04}{N_{P}}}{\class{X06}{N_{SB}}}$$

Secondary A Power

$$\class{X11}{P_{SA}}=\frac{\class{X01}{{V_{p}}}^2}{{\class{X07}{a_{A}}}^2\cdot \class{X15}{R_{A}}}$$

Secondary B Power

$$\class{X12}{P_{SB}}=\frac{\class{X01}{{V_{p}}}^2}{{\class{X08}{a_{B}}}^2\cdot \class{X16}{R_{B}}}$$

Primary Power

$$\class{X09}{P_{P}}=\class{X11}{P_{SA}}+\class{X12}{P_{SB}}+\class{X17}{P_{L}}$$

Efficiency (%)

$$\class{X18}{\eta}=1-\left(\frac{\class{X17}{P_{L}}}{\class{X09}{P_{P}}}\right)$$

Component Sizing

Turns Ratio

$$\class{X05}{a}=\frac{\class{X03}{N_P}}{\class{X04}{N_S}}$$

Primary Power

$$\class{X06}{P_{P}}=\frac{{\class{X01}{V_{p}}}^2}{\class{X05}{a}^2\cdot \class{X10}{R}}+\class{X11}{P_L}$$

Secondary Power

$$\class{X08}{P_{S}}=\frac{{\class{X01}{V_{p}}}^2}{\class{X05}{a}^2\cdot \class{X10}{R}}$$

Efficiency (%)

$$\class{X12}{\eta}=1-{\frac{\class{X11}{P_{L}}}{\frac{{\class{X01}{V_{p}}}^2}{\class{X05}{a}^2\cdot \class{X10}{R}}+\class{X11}{P_L}}}$$

Component Sizing

Turns Ratio Between Primary and Secondary A

$$\class{X07}{a_A}=\frac{\class{X04}{N_P}}{\class{X05}{N_{SA}}}$$

Turns Ratio Between Primary and Secondary B

$$\class{X08}{a_B}=\frac{\class{X04}{N_P}}{\class{X06}{N_{SB}}}$$

Secondary A Power

$$\class{X11}{P_{SA}}=\frac{{\class{X01}{V_P}}^2}{3\cdot {\class{X07}{a_A}}^2\cdot \class{X15}{R_A}}$$

Secondary B Power

$$\class{X12}{P_{SB}}=\frac{{\class{X01}{V_P}}^2}{3\cdot {\class{X08}{a_B}}^2\cdot \class{X16}{R_B}}$$

Primary Power

$$\class{X09}{P_P}=\class{X11}{P_{SA}}+\class{X12}{P_{SB}}+\class{X17}{P_L} $$

Efficiency (%)

$$\class{X18}{\eta}=1-\frac{\class{X17}{P_L}}{\class{X09}{P_P}}$$

Component Sizing

Turns Ratio

$$\class{X05}{a}=\frac{\class{X03}{N_P}}{\class{X04}{N_S}}$$

Primary Power

$$\class{X06}{P_P}=\frac{{\class{X01}{V_P}}^2}{3\cdot {\class{X05}{a}}^2 \cdot \class{X10}{R}}+\class{X11}{P_L}$$

Secondary Power

$$\class{X08}{P_S}=\frac{{\class{X01}{V_P}}^2}{3\cdot {\class{X05}{a}}^2 \cdot \class{X10}{R}}$$

Efficiency

$$\class{X12}{\eta}=1-\frac{\class{X11}{P_L}}{\frac{{\class{X01}{V_P}}^2}{3\cdot {\class{X05}{a}}^2 \cdot \class{X10}{R}}+\class{X11}{P_L}}$$

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$$\class{X04}{A_p}=\pi\cdot\left(\frac{\class{X01}{d_p}}{2}\right)^2$$

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Step 2 : Sizing - {0}

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