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ECEg439:-Electrical Machine II 2.5. Armature Generated Voltage and Electromagnetic Torque By Sintayehu Challa DC Generator Equivalent Circuit By Sintayehu Challa ECEg439:Electrical Machine II 2 DC Generator Equivalent circuit • The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated. • This induced voltage is represented by a voltage source. • The stator coil has resistance (R A), which is connected in series. • The pole flux is produced by the DC excitation/field current, which is magnetically coupled to the rotor • The field circuit has resistance(RF) and a source (VF) • The voltage drop on the brushes represented by a battery By Sintayehu Challa ECEg439:Electrical Machine II 3 DC Generator Equivalent circuit Rf Vf Vbrush ? max If Eag Mechanical power in Ra Load Iag Vdc Electrical power out • Figure Equivalent circuit of a separately excited dc generator. By Sintayehu Challa ECEg439:Electrical Machine II 4 DC Generator Equivalent circuit • The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated. • The dc field current of the poles generates a magnetic flux • The flux is proportional with the field current if the iron core is not saturated: ? ag ? K1 I f By Sintayehu Challa ECEg439:Electrical Machine II 5 DC Generator Equivalent circuit • The rotor conductors cut the field lines that generate voltage in the coils. E ag ? 2 N r B ? g v • The motor speed and flux equations are : v?? r?? ? ag Dg 2 ? BA ? B? g? ? B ? g D g By Sintayehu Challa ECEg439:Electrical Machine II 6 DC Generator Equivalent circuit • The combination of the three equation results the induced voltage equation: E ag ? Dg ? ? ? N r ?B ? g D g ?? ? N r ? ? 2 N r B ? g v ? 2 N r B ? g ??? ? ? 2 ? ag ? • The equation is simplified. Eag ? N r ? ag ? ? N r K1 I f ? ? K e I f ? By Sintayehu Challa ECEg439:Electrical Machine II 7 DC Generator Equivalent circuit • The generated voltage per conductor equals E ? flux per pole x No.of poles x rev per sec C ? 2 p? N volts 60 • The number of conductors connected in series per parallel path or circuit Z/2a,where is the number of path pairs and Z is the total conductor. The generated voltage becomes N Z pZ )x ? ( )? N 60 2 a 60 a ? Ke ? N E g ? (2 p? Where K e ? pZ 60 a By Sintayehu Challa ECEg439:Electrical Machine II 8 DC Generator Equivalent circuit • When the generator is loaded, the load current produces a voltage drop on the rotor winding resistance. • In addition, there is a more or less constant 1–3 V voltage drop on the brushes. • These two voltage drops reduce the terminal voltage of the generator. The terminal voltage is; E ag ? Vdc ? I ag Ra ? Vbrush By Sintayehu Challa ECEg439:Electrical Machine II 9 DC Generator Equivalent circuit • Assume the load is connected to the machine so that a current Ia flows in the armature, the generated power becomes Generated Power ? Pg ? E g I a ? K e? N I a • The input Prime Mover torque becomes ? 2? N ? Pg ? K e? N I a ? Torque x ? ? Tx? ? ? 60 ? ? 60 ? Torque ? T ? ? K e ?? I a ? K M ? I a ? 2? ? By Sintayehu Challa ECEg439:Electrical Machine II 10 DC Motor Equivalent Circuit By Sintayehu Challa ECEg439:Electrical Machine II 11 DC Motor Equivalent circuit Rf Vbrush ? Ra Electrical power in max Vf If Eam Iam Vdc DC Power supply Mechanical power out • Figure above Equivalent circuit of a separately excited dc motor • Equivalent circuit is similar to the generator only the current directions are different By Sintayehu Challa ECEg439:Electrical Machine II 12 DC Motor Equivalent circuit • The operation equations are: • Armature voltage equation Vdc ? E am ? I am Ra ? Vbrush The induced voltage Eam ? K e ? N By Ignoring the Brush Voltage Drop, The Speed of the motor becomes Vdc ? I a Ra N? K e? By Sintayehu Challa ECEg439:Electrical Machine II 13 DC Motor Equivalent circuit • The operation equations are: • The combination of the equations results in K e? N ? Eam ? Vdc ? I am Rm The current is calculated from this equation. The output power and torque are: Pout ? E am I am Pout T? ? Km ? Ia ? One of the most important properties of DC Motor is the fact that it has starting torque which can be calculated from torque equation. By Sintayehu Challa ECEg439:Electrical Machine II 14