| Parameter | Symbol / Formula | Where |
|---|---|---|
| Primary EMF Equation of Single Phase Transformer (Ep) | \(E_p = 4.44 \cdot f \cdot N_p \cdot \Phi \) | f= frequency Np =Number of primary turns \(\Phi\) = maximum flux |
| Secondary EMF Equation (Es) | \(E_s = 4.44 \cdot f \cdot N_s \cdot \Phi \) | f= frequency Ns =Number of secondary turns \(\Phi\) = maximum flux |
| Transformation ratio (K) | \({\frac{N_s}{N_p} = \frac{V_s}{V_p}=\frac{I_p}{I_s}=K}\) | Ns =Number of secondary turns Np =Number of primary turns Vp =Primary voltage Vs =Secondary voltage |
| Turn Ratio | \(\frac{N_p}{N_s} = \frac{V_p}{V_s}\) | Ns =Number of secondary turns Np =Number of primary turns Vp =Primary voltage Vs =Secondary voltage |
| No load Primary Current (I0) | \(I_0=\sqrt{I_m^2+I_w^2}\) | Im= Magnetising Component Iw=Active or Working or Iron loss component |
| Active or Working or Iron loss component (Iw) | \(I_w=I_0\cos{\phi_0}\) | \({\phi_0}\)= Angle between Vp and I0 |
| Magnetising Component (Im) | \(I_m=I_0\sin{\phi_0}\) | \({\phi_0}\)= Angle between Vp and I0 |
| Impedance Ratio | \(\frac{Z_1}{Z_2}=K^2 \) \(\frac{R_2}{R_1}=K^2 \) \(\frac{X_2}{X_1}=K^2 \) | Z2= Secondary Impedance Z1 = Primary Impedance |
Shifting in a Transformer (Referred to Primary) | \(R_{01} = R_1 + R_2′ = R_1 + \frac{R_2}{K^2}\) \(X_{01} = X_1 + X_2′ = X_1 + \frac{X_2}{K^2}\) \(Z_{01} = \sqrt{R_{01}^2 + X_{01}^2}\) \(V_2’=\frac{V_2}{K}\) \(I_2’={I_2}{K}\) | R01= Equivalent resistance referred to primary X01= Equivalent reactance referred to primary Z01=Equivalent impedance referred to primary R2‘=Secondary resistance referred to primary X2‘=Secondary reactance referred to primary V2‘= Secondary voltage referred to primary I2‘= Secondary current referred to primary |
Shifting in a Transformer (Referred to Secondary) | \(R_{02} = R_2+ R_1′ = R_2 + {R_1}{K^2}\) \(X_{02} = X_2 + X_1′ = X_2 + {X_1}{K^2}\) \(Z_{02} = \sqrt{R_{02}^2 + X_{02}^2}\) \(V_1’={V_1}{K}\) \(I_1’=\frac{I_1}{K}\) | R02= Equivalent resistance referred to secondary X02= Equivalent reactance referred to secondary Z02=Equivalent impedance referred to secondary R1‘=Primary resistance referred to secondary X1‘=Primary reactance referred to secondary V1‘= Primary voltage referred to secondary I1‘= Primary current referred to secondary |
| Percentage Voltage Regulation | 1) \(\%Reg_{down} = \frac{V_{nl} – V_{fl}}{V_{nl}} \times 100\%\) 2) \(\%Reg_{up} = \frac{V_{nl} – V_{fl}}{V_{fl}} \times 100\%\) ***** (1) No. equation is generally used | Vnl= No load secondary voltage Vfl= Full load secondary voltage ****** Voltage regulation-down (Regdown): This happens when the secondary transformer terminal’s voltage output decreases due to a load attached to it. Voltage regulation-up (Regup): This occurs when the secondary terminal of the transformer experiences an increase in voltage upon removal of the load. |
| Voltage Regulation for lagging and leading | For lagging p.f Vnl – Vfl = I2R02cosφ2 + I2X02cosφ2 For lagging p.f Vnl – Vfl= I2R02cosφ2 -I2X02cosφ2 | R02= Equivalent resistance referred to secondary X02= Equivalent reactance referred to secondary |
| Power (Ideal Transformer) | \( P_p = P_s \) or \( V_p \cdot I_p = V_s \cdot I_s \) | ( P_p ) and ( P_s ) are the primary and secondary powers, ( V_p, V_s ) are the voltages, ( I_p, I_s ) are the currents. |
| Copper Loss (PCu) | \(P_{Cu} = I_p^2 R_p + I_s^2 R_s \) | Ip ,Is are the currents, Rp, Rs are the resistances of primary and secondary windings |
| Core Loss or Iron loss | \(P_i = P_{h} + P_{e} \) | Pi = Total core loss Ph = Hysteresis loss Pe =eddy current loss |
| Total losses in Transformer | Total losses = Pi +PCu = Constant Loss + Variable Loss | Pi = Total core loss or Constant loss PCu= Copper loss or Variable loss |
| Hysteresis loss (in watts) (Ph) | \( P_h = \eta B_{\text{max}}^{x} f V\) | η = Steinmetz hysteresis coefficient (depends on the material) Bmax = Maximum flux density in the core f= Frequency of the magnetic field (in hertz) v= Volume of the core (in cubic meters) |
| Eddy current loss (in watts) (Pe) | \(P_e=k_e\ B_{\max}^2f^2t^2v\) | ke = Constant that depends on the material’s resistivity and geometry Bmax = Maximum magnetic flux density (in teslas) f = Frequency of the magnetic field t = Thickness of the core laminations (in meters) v = Volume of the core (in cubic meters) |
| Efficiency (η) | \(\eta = \frac{P_{out}}{P_{in}} \times 100\% \) \(\eta=\frac{P_{out}}{P_{out}+\ Losses}\times 100\% \) | Pout = Output power, Pin = Input power. |