Electric Machines I DC Machines - DC Generators Dr. Firas Obeidat 1 Working of Simple Loop Generator The current which is obtained from such a simple generator reverses its direction after every half revolution, this current is known as alternating current. To make the flow of current unidirectional in the external circuit, the slip rings are replaced by split rings. In the first half revolution segment a is connected to brush 1 and segment b is connected to brush 2, while in the second half revolution segment b is connected to brush 1 and segment a is connected to brush 2. In this case the current will flow in the resistor from M to L in the two halves of revolution. The resulting current is unidirectional but not continuous like pure direct current. 6 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Types of DC Generators Generators are usually classified according to the way in which their fields are excited A. Separately Excited Generators: are those whose field magnets are energized from an independent external source of DC current. B. Self Excited Generators: are those whose field magnets are energized by current produced by the generators themselves. There are three types of self excited generators named according to the manner in which their field coils are connected to the armature. i. Shunt Wound: the field windings are connected across or in parallel with the armature conductors and have the full voltage of the generator applied across them. ii. Series Wound: the field windings are joined in series with the armature conductors iii. Compound Wound: it is a combination of a few series and a few shunt windings and can be either short-shunt or long-shunt. In compound generator, the shunt field is stronger than the series field. When series field aids the shunt field, generator is said to be commutativelycompound. In series field oppose the shunt field, the generator is said to be differentially compounded. 7 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Types of DC Generators Separately Excited Generators Short Shunt Generators Shunt Wound Generators Series Wound Generators Long Shunt Generators 8 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Types of DC Generators 9 Dr. Firas Obeidat Faculty of Engineering Philadelphia University The Terminal Characteristic of a Separately Excited DC Generator For Separately Excited DC Generator πΌπ΄ = πΌπΏ IF + ππ = πΈπ΄ − πΌπ΄ π π΄ VF ππΉ = πΌπΉ π πΉ - πΈπ΄ = πΟππ The terminal voltage can be controlled by: 1. Change the speed of rotation: If π increases, then πΈπ΄=π ππ increases, so ππ = πΈπ΄ − πΌπ΄ π π΄ increases as well. 2. Change the field current. If RF is decreased. then the field current increases (ππΉ = πΌπΉ π πΉ ). Therefore, the flux in the machine increases. As the flux rises, πΈπ΄=π ππ must rise too, so ππ = πΈπ΄ − πΌπ΄ π π΄ increases. IA RF LF IL + + RA VT EA - Where IA: is the armature current IL: is the load current EA: is the internal generated voltage VT: is the terminal voltage IF: is the field current VF: is the field voltage RA: is the armature winding resistance RF: is the field winding resistance : is the flux πm: is the rotor angular speed 10 Dr. Firas Obeidat Faculty of Engineering Philadelphia University The Terminal Characteristic of a Self Excited Shunt DC Generator For Self Excited Shunt DC Generator πΌπ΄ = πΌπΉ + πΌπΏ IA + RA RF IF EA LF - ππ = πΈπ΄ − πΌπ΄ π π΄ ππ = πΌπΉ π πΉ IL + VT - πΈπ΄ = πΟππ The terminal voltage can be controlled by: 1. Change the speed of rotation: If π increases, then πΈπ΄=π ππ increases, so ππ = πΈπ΄ − πΌπ΄ π π΄ increases as well. 2. Change the field current. If RF is decreased. then the field current increases (ππΉ = πΌπΉ π πΉ ). Therefore, the flux in the machine increases. As the flux rises, πΈπ΄=π ππ must rise too, so ππ = πΈπ΄ − πΌπ΄ π π΄ increases. 11 Dr. Firas Obeidat Faculty of Engineering Philadelphia University The Terminal Characteristic of a Self Excited Series DC Generator For Self Excited Series DC Generator πΌπ΄ = πΌπ = πΌπΏ IA + RA EA - ππ = πΈπ΄ − πΌπ΄ (π π΄ +π π ) πΈπ΄ = πΟππ Is Rs IL Ls + VT - At no load, there is no field current, so VT is reduced to a small level given by the residual flux in the machine. As the load increases, the field current rises, so EA rises rapidly The IA(RA+ Rs) drop goes up too, but at first the increase in EA goes up more rapidly than the IA(RA+ Rs) drop rises, so VT increases. After a while, the machine approaches saturation, and EA becomes almost constant. At that point, the resistive drop is the predominant effect, and VT starts to fall. 12 Dr. Firas Obeidat Faculty of Engineering Philadelphia University The Terminal Characteristic of Cumulatively Compound DC Generator For Long Shunt Cumulatively Compound DC Generator IA πΌπ΄ = πΌπΉ + πΌπΏ + RA EA - ππ = πΈπ΄ − πΌπ΄ (π π΄ +π π ) ππ = πΌπΉ π πΉ πΈπ΄ = πΟππ IL Rs Ls + RF IF LF VT - For Short Shunt Cumulatively Compound DC Generator πΌπ΄ = πΌπΉ + πΌπΏ IA ππ = πΈπ΄ − πΌπ΄ π π΄ −πΌπΏ π π + RA RF IF EA LF - πΈπ΄ = πΟππ IL Rs Ls + VT - The terminal voltage Cumulatively Compound DC Generator can be controlled by: 1. Change the speed of rotation: If π increases, then πΈπ΄=π ππ increases, so ππ = πΈπ΄ − πΌπ΄ π π΄ increases as well. 2. Change the field current. If RF is decreased. then the field current increases (ππΉ = πΌπΉ π πΉ ). Therefore, the flux in the machine increases. As the flux rises, πΈπ΄=π ππ must rise too, so ππ = πΈπ΄ − πΌπ΄ π π΄ increases. 13 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Examples Example: A shunt DC generator delivers 450A at 230V and the resistance of the shunt field and armature are 50 and 0.3 respectively. Calculate emf. IA πΌπ΄ = πΌπΉ + πΌπΏ = 4.6 + 450 = 454.6π΄ πΈπ΄ = ππ + πΌπ΄ π π΄ = 230 + 454.6 × 0.3 = 243.6V + RA RF IF EA LF - IL=450A + - VT=230V 230 πΌπ = = 4.6π΄ 50 VT=500V Example: A long shunt compound DC generator delivers a load current of 50A at 500V and has armature, series field and shunt field resistances of 0.05 , 0.03 and 250 respectively. Calculate the generated voltage and the armature current. Allow 1V per brush for contact drop. 500 πΌπΉ = = 2π΄ 250 IA IL=50A + πΌπ΄ = πΌπΉ + πΌπΏ = 2 + 50 = 52π΄ + RA Rs Ls RF IF Voltage drop across series winding=πΌAπ s=52×0.03=1.56V EA LF Armature voltage drop=πΌAπ A=52×0.05=2.6V Drop at brushes=2 1=2V πΈπ΄ = ππ + πΌπ΄ π π΄ + π πππππ ππππ + πππ’π βππ ππππ = 500 + 2.6 + 1.56 + 2 = 506.16V 14 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Examples Example: A short shunt compound DC generator delivers a load current of 30A at 220V and has armature, series field and shunt field resistances of 0.05 , 0.3 and 200 respectively. Calculate the induced emf and the armature current. Allow 1V per brush for contact drop. Voltage drop across series winding=πΌLπ s =30 ×0.3=9V Voltage across shunt winding=220 + 9=229V IA πΌπ΄ π π΄ = 31.145 × 0.05 = 1.56V Drop at brushes=2 1=2V + RA RF IF EA LF - Rs IL=30A + Ls - VT=220V 229 πΌπΉ = = 1.145π΄ 200 πΈπ΄ = ππ + πΌπ΄ π π΄ + π πππππ ππππ + πππ’π βππ ππππ = 220 + 9 + 1.56 + 2 = 232.56V 15 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Examples VT=230V Example: A long shunt compound DC generator delivers a load current of 150A at 230V and has armature, series field and shunt field resistances of 0.032 , 0.015 and 92 respectively. Calculate (i) induced emf (ii) total power generated and (iii) distribution of this power. IA IL=150A 230 (i ) πΌ = + = 2.5π΄ πΉ L R R R s A s F 92 + IF EA πΌπ΄ = πΌπΉ + πΌπΏ = 2.5 + 150 = 152.5π΄ LF Voltage drop across series winding= πΌAπ s=152.5 ×0.015=2.2875V Armature voltage drop=πΌAπ A=152.5 ×0.032=4.88V πΈπ΄ = ππ + πΌπ΄ π π΄ + πΌ π = 230 + 2.2875 + 4.88 = 237.1675V (ii) Total power generated by the armature=πΈπ΄ πΌπ΄ =237.1675 152.5=36168.04375W (iii) Power lost in armature=πΌπ΄ 2 π π΄ =152.52 0.032=744.2W Power dissipated in shunt winding=ππ πΌπΉ =230 2.5=575W Power dissipated in series winding=πΌπ΄ 2 π π =152.52 0.015=348.84375W Power delivered to the load=ππ πΌπΏ =230 150=34500W Total power generated by the armature=744.2 + 575 + 348.843 + 34500=36168.04375W 16 Dr. Firas Obeidat Faculty of Engineering Philadelphia University E.M.F. Equation of DC Generator Let : flux/pole in weber. Z: total number of armature conductors Z=number of slots × number of conductors/slot A: number of parallel paths in armature N: armature rotation in rpm E: emf induced in any parallel path in armature Generated emf EA=emf generated in any one of the parallel paths Average emf generated/conductor=d /dt volt Flux cut/conductor in one revolution d = P Wb Number of revolutions /second=N/60 Time for one revolution dt=60/N second E.M.F. generated/conductor= d /dt= PN/60 volt 17 Dr. Firas Obeidat Faculty of Engineering Philadelphia University E.M.F. Equation of DC Generator For simplex wave-wound generator Number of parallel paths=2 Number of conductors (in series) in one path=Z/2 πππ π ππππ × = π£πππ‘ 60 2 120 For simplex lap-wound generator πΈ. π. πΉ. πππππππ‘ππ/πππ‘β(πΈπ΄ ) = Number of parallel paths=P Number of conductors (in series) in one path=Z/P πππ π πππ πΈ. π. πΉ. πππππππ‘ππ/πππ‘β(πΈπ΄ ) = × = π£πππ‘ 60 π 60 In general where πππ π A=2 for simplex wave-winding πΈπ΄ = × π£πππ‘ 60 π΄ A=P for simplex lap-winding 1 2ππ π ππ 2ππ Where ππ = 60 πΈπ΄ = × × ππ × = πππ π£πππ‘ 2π 60 π΄ 2ππ΄ For a given DC machine Z,P and A are constant ππ Where π = 2ππ΄ πΈπ΄ = ππππ π£πππ‘ 18 Dr. Firas Obeidat Faculty of Engineering Philadelphia University E.M.F. Equation of DC Generator Example: A four pole generator, having wave wound armature winding has 51 slots, each slot containing 20 conductor. What will be the voltage generated in the machine when driven at 1500 rpm assuming the flux per pole to be 7mWb? πππ π 7 × 10−3 × 51 × 20 × 1500 4 πΈπ΄ = × = × = 357π£πππ‘ 60 π΄ 60 2 Example: An 8 pole Dc generator has 500 armature conductors, and a useful flux of 0.05Wb per pole. what will be the emf generated if it is lap-connected and runs at 1200 rpm? What must be the speed at which it is to be driven produce the same emf if it is wave-wound? With lap-wound, P=A=8 πππ π 0.05 × 500 × 1200 8 πΈπ΄ = × = × = 500π£πππ‘ 60 π΄ 60 8 With wave-wound, P=8, A=2 πππ π 0.05 × 500 × π 8 πΈπ΄ = × = × = 500 60 π΄ 60 2 → π = 300πππ 19 Dr. Firas Obeidat Faculty of Engineering Philadelphia University E.M.F. Equation of DC Generator Example: A four pole lap-connected armature of a DC shunt generator is required to supply the loads connected in parallel: (a) 5kW Geyser at 250 V and (b) 2.5kW lighting load also at 250V. The generator has an armature resistance 0.2 and a field resistance of 250 . The armature has 120 conductors in the slots and runs at 1000 rpm. Allowing 1V per brush for contact drops, find (1) Flux per pole, (2) armature current per parallel path (1) IA With lap-wound, P=A=4 RF=250Ω IF LF - 5kW Geyser 2.5kW lighting + EA - IL + VT=250V 5000 + 2500 = 30π΄ 250 250 πΌπΉ = = 1π΄ 250 πΌπΏ = RA=0.2Ω πΌπ΄ = πΌπΏ + πΌπΉ = 30 + 1 = 31π΄ πΈπ΄ = ππ + πΌπ΄ π π΄ + πππ’π βππ ππππ = 250 + 31 × 0.2 + 2 × 1 = 258.2V πΈπ΄ = πππ π π × 120 × 1000 4 × = × = 258.2π£πππ‘ 60 π΄ 60 4 → π = 129.1πππ (2) Armature current per parallel path=31/4=7.75A 20 Dr. Firas Obeidat Faculty of Engineering Philadelphia University E.M.F. Equation of DC Generator Example: A separately excited DC generator, when running at 1000 rpm supplied 200A at 125V. What will be the load current when the speed drops to 800 rpm if IF is unchanged? Given that the armature resistance 0.04 and brush drop 2V. πΈπ΄1 = ππ1 + πΌπ΄ π π΄ + πππ’π βππ ππππ = 125 + 200 × 0.04 + 2 = 135V ππ΄1 = 1000πππ ππ΄2 800 = πΈπ΄1 = 135 = 108π ππ΄1 1000 π ππππ 125 = = 0.625Ω 200 + RF VF LF + EA1 - RA - πΈπ΄2 = ππ2 + πΌπ΄2 π π΄ + πππ’π βππ ππππ 108 = πΌπ΄2 × 0.625 + πΌπ΄2 × 0.04 + 2 108 − 2 πΌπ΄2 = = 159.4A 0.625 + 0.04 ππ2 = πΌπ΄2 π ππππ = 159.4 × 0.625 = 99.6π IL=159.4A VF - RF LF + EA2 - RA + VT2=99.6V ππ2 = πΌπ΄2 π ππππ IF + + VT1=125V πΈπ΄2 IL=200A IF - 21 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Total Loss in a DC Generator (A) Copper Losses (i) Armature copper losses=Ia2Ra This loss is about 30-40% of full load losses. (ii) Field copper loss: In case of shunt generator, field copper losses=IF2RF In case of shunt generator, field copper losses=IL2Rs This loss is about 20-30% of full load losses. (iii) The loss due to brush contact resistance. (B) Magnetic (Iron or Core) Losses (i) Hysteresis Loss, πΎπ ∝ π©πππ π.π π (ii) Eddy Current Loss, πΎπ ∝ π©πππ π ππ These losses are practically constant for shunt and compound wound generators, because in their case, field current is approximately constant. This loss is about 20-30% of full load losses. (C) Mechanical Losses (i) Friction Loss at bearing and commutator. (ii) Air Friction or Windage Loss of rotating armature This loss is about 10-20% of full load losses. 22 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Total Loss in a DC Generator Armature Cu Loss Total Losses Copper Losses Shunt Cu Loss Series Cu Loss Hysteresis Loss Iron Losses Eddy Current Loss Friction Loss Mechanical Losses Air Friction or Windage Loss Stray Losses Iron and mechanical losses are collectively known as Stray (Rotational) losses. Constant or Standing Losses Field Cu losses is constant for shunt and compound generators. Stray losses and shunt Cu loss are constant in their case. These losses are together known as Constant or Standing Losses (Wc). 23 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Power Stages and Efficiency Mechanical Efficiency ππ = πππ‘ππ π€ππ‘π‘π πππππππ‘ππ ππ πππππ‘π’ππ πΈπ΄ πΌπ΄ × 100% = × 100% πππβππππππ πππ€ππ π π’ππππππ ππ’π‘ππ’π‘ ππ ππππ£πππ ππππππ Electrical Efficiency ππ = πππ‘π‘π ππ£πππππππ ππ ππππ ππππ’ππ‘ ππΌπΏ × 100% = × 100% πππ‘ππ π€ππ‘π‘π πππππππ‘ππ ππ πππππ‘π’ππ πΈπ΄ πΌπ΄ Overall or Commercial Efficiency ππ = π π × ππ = πππ‘π‘π ππ£πππππππ ππ ππππ ππππ’ππ‘ ππΌπΏ × 100% = × 100% πππβππππππ πππ€ππ π π’ππππππ ππ’π‘ππ’π‘ ππ ππππ£πππ ππππππ 24 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Power Stages and Efficiency Example: A shunt generator delivers 195A at terminal voltage of 250V. The armature resistance and shunt field resistance are 0.02 and 50 respectively. The iron and friction losses equal 950W. Find (a) emf generated (b) Cu losses (c) output of the prime motor (d) commercial, mechanical and electrical efficiencies. (a) 250 πΌπ = = 5π΄ 50 πΌπ΄ = πΌπΉ + πΌπΏ = 5 + 195 = 200π΄ πΈπ΄ = ππ + πΌπ΄ π π΄ = 250 + 200 × 0.02 = 254V (b) π΄ππππ‘π’ππ πΆπ’ πππ π = πΌπ΄ 2 π π΄ = 2002 × 0.02 = 800π πβπ’ππ‘ πΆπ’ πππ π = πΌπ 2 π π = 52 × 50 = 1250π πππ‘ππ πΆπ’ πππ π = 800 + 1250 = 2050π (c) Stray losses=950W Total losses=950+2050=3000W πΊππππππ‘ππ ππ’π‘ππ’π‘ = ππΌπΏ = 250 × 195 = 48750π ππ’π‘ππ’π‘ ππ π‘βπ πππππ πππ‘ππ = πΊππππππ‘ππ ππππ’π‘ 25 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Power Stages and Efficiency πΊππππππ‘ππ ππππ’π‘ = πΊππππππ‘ππ ππ’π‘ππ’π‘ + π‘ππ‘ππ πππ π ππ = 48750 + 3000 = 51750π ππ’π‘ππ’π‘ ππ π‘βπ πππππ πππ‘ππ = 51750π (c) πΊππππππ‘ππ πππππ‘πππππ πππ€ππ(πΈπ΄ πΌπ΄ ) = πΊππππππ‘ππ ππππ’π‘ − π π‘πππ¦ πππ π πΊππππππ‘ππ πππππ‘πππππ πππ€ππ(πΈπ΄ πΌπ΄ ) = 51750 − 950 = 50800π πΈπ΄ πΌπ΄ 50800 × 100% = × 100% = 98.2% ππ’π‘ππ’π‘ ππ ππππ£πππ ππππππ 51750 ππ = ππΌπΏ 48750 ππ = = × 100% = 95.9% πΈπ΄ πΌπ΄ 50800 ππ = ππΌπΏ 48750 × 100% = × 100% = 94.2% ππ’π‘ππ’π‘ ππ ππππ£πππ ππππππ 51750 26 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Power Stages and Efficiency Example: A shunt generator has a full load current of 196 A at 220V. The stray lassos are 720W and the shunt field coil resistance is 55 . If it has full load efficiency of 88%, find the armature resistance. πΊππππππ‘ππ ππ’π‘ππ’π‘ = ππΌπΏ = 220 × 196 = 43120π ππΌπΏ ππ = × 100% = 88% → πΈπ΄ πΌπ΄ = 43120 ÷ 0.88 = 49000π πΈπ΄ πΌπ΄ πππ‘ππ πππ π ππ = 49000 − 43120 = 5880π πΌπ = 220 ÷ 55 = 4π΄ πβπ’ππ‘ πΆπ’ πππ π = πΌπ π = 4 × 220 = 880π Constant losses=Shunt Cu losses+stray losses=880+720=1600W Total losses=Armature losses + Constant losses=πΌπ΄ 2 π π΄ +1600=5880 πΌπ΄ 2 π π΄ = 5880 − 1600 = 4280π πΌπ΄ = πΌπΏ + πΌπ = 195 + 4 = 199π΄ π π΄ = 4280 ÷ 1992 = 0.108Ω 27 Dr. Firas Obeidat Faculty of Engineering Philadelphia University Voltage Regulation The voltage regulation (VR) is defined as the difference between the no-load terminal voltage (VNL) to full load terminal voltage (VFL) and is expressed as a percentage of full load terminal voltage. It is therefore can be expressed as, ππππ‘πππ π πππ’πππ‘πππ ππ = πππΏ − ππΉπΏ πΈπ΄ − ππΉπΏ × 100% = × 100% ππΉπΏ ππΉπΏ Example: A 4-pole shunt DC generator is delivering 20A to a load of 10 . If the armature resistance is 0.5 and the shunt field resistance is 50 , calculate the induced emf and the efficiency of the machine. Allow a drop of 1V per brush. ππππππππ ππππ‘πππ = πΌπΏ π = 20 × 10 = 200π πΌπ = 200 ÷ 50 = 4π΄ πΌπ΄ = πΌπΏ + πΌπ = 20 + 4 = 24π΄ πΌπ΄ π π΄ = 24 × 0.5 = 12π πΈπ΄ = πΌπ΄ π π΄ + π + πππ’π β ππππ = 12 + 200 + 2 = 214π ππΌπΏ 200 × 20 × 100% = × 100% = 77.9% πΈπ΄ πΌπ΄ 214 × 24 πΈπ΄ − ππΉπΏ 214 − 200 ππ = × 100% = × 100% = 7% ππΉπΏ 200 ππ = Dr. Firas Obeidat Faculty of Engineering Philadelphia University 28 Uses of DC Generators Shunt Generators Shunt generators with field regulators are used for ordinary lighting and power supply purposes. They are also used for charging batteries because their terminal voltages are almost constant. Series Generators Series generators are used as boosters in a certain types of distribution systems particularly in railway service. Compound Generators The cumulatively compound generator is the most used DC generator because its external characteristics can be adjusted for compensating the voltage drop in the line resistance. Cumulatively compound generators are used for motor driving which require DC supply at constant voltage, for lamp loads and for heavy power service such as electric railways. The differential compound DC generator has an external characteristic similar to that of shunt generator but with large demagnetization armature reaction. Differential compound DC generators re widely used in arc welding where larger voltage drop is desirable with increase in current. 29 Dr. Firas Obeidat Faculty of Engineering Philadelphia University 30