Here, we have listed all the important DC Generator Formulas and Equations, DC generator EMF equation, power equation etc.
| Parameter | Formula | Where |
|---|---|---|
| EMF Equation | \( E = \frac{P \times \Phi \times Z \times N}{60 \times A} \) | E = Generated EMF (volts), P = Number of poles, \(\Phi\) = Flux per pole (Wb), Z = Total armature conductors, N = Armature speed (RPM), A = Number of parallel paths |
| DC Shunt Generator: | ||
| Terminal Voltage (V) | \( V = E – I_a R_a \) | V = Terminal voltage (volts), E = Generated EMF (volts), \( I_a \) = Armature current (A), \(R_a\) = Armature resistance (Ω) |
| Armature Current (Ia) | Ia = IL + If | Ia = Armature current (A), IL = Load current (A), If = Shunt field current (A) |
| Shunt Field Current (If) | \(I_f = \frac{V}{R_f}\) | If = Shunt field current (A), V = Terminal voltage (volts), Rf = Shunt field resistance (Ω) |
| Power Developed (Pgen) | \(P_{\text{gen}} = E \times I_a \) | Pgen= Generated power (W), E = Generated EMF (volts), Ia = Armature current (A) |
| Power Output (Pout) | \(P_{\text{out}} = V \times I_L \) | Pout = Output power (W), V = Terminal voltage (volts), IL = Load current (A) |
| Efficiency (η) | \(\eta = \frac{P_{\text{out}}}{P_{\text{gen}}} \) | \(\eta \) = Efficiency, Pout = Output power (W), \(P_{\text{gen}}\) =Generated power |
| Armature Copper Loss | \( P_{\text{cu,a}} = I_a^2 R_a \) | \(P_{\text{cu,a}}\)= Armature copper loss (W), Ia = Armature current (A), Ra=Armature resistance (Ω) |
| Shunt Field Copper Loss | \( P_{\text{cu,f}} = I_f^2 R_f \) | \(P_{\text{cu,f}}\) = Shunt field copper loss (W), If = Shunt field current (A), Rf = Shunt field resistance (Ω) |
| Total Copper Loss | \( P_{\text{cu}} = I_a^2 R_a + I_f^2 R_f \) | \(P_{\text{cu}}\)= Total copper loss (W), Ia = Armature current (A), Ra = Armature resistance (Ω), If = Shunt field current (A), Rf = Shunt field resistance (Ω) |
| Condition for Self-Excitation | \( R_f < R_{\text{critical}} \) | Rf = Shunt field resistance (Ω), Rcritical = Critical resistance |
DC Series Generator:
| Parameter | Formula | Where |
|---|---|---|
| Current | If = Ia = IL | IL = Load current (A) Ia= Armature Current (A) If= Field Current (A) |
| Terminal Voltage (V) | \(V = E – I_a \cdot (R_a + R_{se}) \) | Rse =Series field resistance Ra = Armature resistance |
| Power Developed (Pg) | \(P_g = E \cdot I_a \) | E = Generated EMF (V), Ia = Armature current (A) |
| Power Delivered (Po) | \(P_o = V \cdot I_L \) | V = Terminal voltage (V), IL = Load current (A) |
| Copper Loss (Pcu) | \(P_{cu} = I_a^2 \cdot (R_a + R_{se}) \) | Ia = Armature current (A) Ra = Armature resistance Rse =Series field resistance |
| Efficiency (η) | \(\eta = \frac{P_o}{P_g} \times 100 \) | Pgen= Generated power Po= Power Delivered |
| Magnetic Flux (Φ) | \(\Phi \propto I_f \) | If= Field Current (A) |
DC Compound Generator:
Here is the table with key formulas for a DC compound generator, classified separately for Short Shunt and Long Shunt configurations.
SHORT Shunt Compound Generator
In a short shunt compound generator, the shunt field winding is connected in parallel with the armature winding, while the series field winding is connected in series with the load.
| Parameter | Formula | Where |
|---|---|---|
| Series Field Current (Ise) | Ise = IL | IL = Load current (A) |
| Armature Current (Ia) | \(I_a = I_{L} + I_{sh}\) | IL = Load current (A), Ish = Shunt field current (A) |
| Shunt Field Current (Ish) | \(I_{sh} = \frac{V+I_{se} R_{se}}{R_{sh}} \) | V = Terminal voltage (V), Rsh =Shunt field resistance Rse =Series field resistance |
| Terminal Voltage (V) | \(V = E – I_a \cdot (R_a + R_{se})\) | E = Generated EMF (V) Ia = Armature current (A) Ra = Armature resistance Rse =Series field resistance |
| Power Developed (Pg) | \(P_g = E \cdot I_a\) | E = Generated EMF (V), Ia = Armature current (A) |
| Power Delivered (Po) | \(P_o = V \cdot I_L\) | V = Terminal voltage (V), IL= Load current (A) |
Long Shunt Compound Generator
In a long shunt compound generator, the shunt field winding is connected in parallel with both the armature and the series field winding.
| Parameter | Formula | Where |
|---|---|---|
| Series Field Current (Ise) | Ise = Ia | Ia = Load current (A) |
| Armature Current (Ia) | \(I_a = I_{L} + I_{sh}\) | IL = Load current (A), Ish =Shunt field current (A) |
| Shunt Field Current (Ish) | \(I_{sh} = \frac{V}{R_{sh}} \) | V = Terminal voltage (V), Rsh= Shunt field resistance |
| Terminal Voltage (V) | \(V = E – I_a \cdot R_a – I_{se} \cdot R_{se} \) | E = Generated EMF (V) Ia = Armature current (A) Ra = Armature resistance Rse =Series field resistance |
| Power Developed (Pg) | \(P_g = E \cdot I_a \) | E = Generated EMF (V), Ia = Armature current (A) |
| Power Delivered (Po) | \(P_o = V \cdot I_L \) | V = Terminal voltage (V), IL = Load current (A) |