DC Generator Formulas and Equations

Here, we have listed all the important DC Generator Formulas and Equations, DC generator EMF equation, power equation etc.

E = \frac{P \times \Phi \times Z \times N}{60 \times A}

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 (I_a)	I_a = I_L + I_f	I_a = Armature current (A), I_L = Load current (A), I_f = Shunt field current (A)
Shunt Field Current (I_f)	$I_f = \frac{V}{R_f}$	I_f = Shunt field current (A), V = Terminal voltage (volts), R_f = Shunt field resistance (Ω)
Power Developed (P_gen)	$P_{\text{gen}} = E \times I_a$	P_gen= Generated power (W), E = Generated EMF (volts), I_a= Armature current (A)
Power Output (P_out)	$P_{\text{out}} = V \times I_L$	P_out = Output power (W), V = Terminal voltage (volts), I_L = Load current (A)
Efficiency (η)	$\eta = \frac{P_{\text{out}}}{P_{\text{gen}}}$	$\eta$ = Efficiency, P_out = 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), I_a = Armature current (A), R_a=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), I_f = Shunt field current (A), R_f = 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), I_a = Armature current (A), R_a = Armature resistance (Ω), I_f = Shunt field current (A), R_f = Shunt field resistance (Ω)
Condition for Self-Excitation	$R_f < R_{\text{critical}}$	R_f = Shunt field resistance (Ω), R_critical = Critical resistance

DC Series Generator:

Parameter	Formula	Where
Current	I_f= I_a = I_L	I_L = Load current (A) I_a= Armature Current (A) I_f= Field Current (A)
Terminal Voltage (V)	$V = E - I_a \cdot (R_a + R_{se})$	R_se =Series field resistance R_a = Armature resistance
Power Developed (P_g)	$P_g = E \cdot I_a$	E = Generated EMF (V), I_a= Armature current (A)
Power Delivered (P_o)	$P_o = V \cdot I_L$	V = Terminal voltage (V), I_L = Load current (A)
Copper Loss (P_cu)	$P_{cu} = I_a^2 \cdot (R_a + R_{se})$	I_a= Armature current (A) R_a = Armature resistance R_se =Series field resistance
Efficiency (η)	$\eta = \frac{P_o}{P_g} \times 100$	P_gen= Generated power P_o= Power Delivered
Magnetic Flux (Φ)	$\Phi \propto I_f$	I_f= 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 (I_se)	I_se = I_L	I_L = Load current (A)
Armature Current (I_a)	$I_a = I_{L} + I_{sh}$	I_L = Load current (A), I_sh = Shunt field current (A)
Shunt Field Current (I_sh)	$I_{sh} = \frac{V+I_{se} R_{se}}{R_{sh}}$	V = Terminal voltage (V), R_sh =Shunt field resistance R_se =Series field resistance
Terminal Voltage (V)	$V = E - I_a \cdot (R_a + R_{se})$	E = Generated EMF (V) I_a= Armature current (A) R_a = Armature resistance R_se =Series field resistance
Power Developed (P_g)	$P_g = E \cdot I_a$	E = Generated EMF (V), I_a = Armature current (A)
Power Delivered (P_o)	$P_o = V \cdot I_L$	V = Terminal voltage (V), I_L= 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.

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