Separately excited FIELD CONNECTION π£π = πΌπ (π π + +π ) Rf = field winding resistance (high value) R= field rheostat resistance (R=0 if not stated) Vf= DC field supply voltage If = field excitation current DC ARMATURE CIRCUIT πΈπ = ππ + πΌπ (π π + π ππ ) Rbc = brush contact resistance Rbc= 0 if not given Ra = armature winding conductor resistance Rbc+Ra = Combine armature and brush contact resistance Eg = dynamically induced emf in the armature conductor (open circuit or no load) Vt = bus bar voltage/ terminal load voltage / nameplate voltage/ rated voltage Il= load current/ ouput current Ia = armature current Il = Ia ππ = ππ‘ πΌπ ππ = ππ‘ 2 π πΏ ππ = πΌπΏ 2 π πΏ Po = output power of the generator =power delivered to the load RL = load resistance OHMS LAW πΈπ πΌπΏ = πΌπ΄ = π π + π ππ + π πΏ πΈπ − ππ‘ π π = πΌ MAXIMUM POWER πΈπ 2 πππππ₯ = 4π π GENERAL VOLTAGE EQUALTION FOR DC GENERATOR (Dynamically induced emf) π∅ππ × 10−8 πΈπ = π΄ × 60 P = no. of poles N= speed of rotation (rpm) ∅ = flux per pole (Maxwell or lune of force) Z = total number of armature conductor in series A = no. of parallel paths z/a = no of conductor in series per parallel path 60 = conversion factor minutes to seconds EXTERNAL FACTOR THAT DIRECTLY AFFECTS/ VARIES / CHANGES THE GENERATOR VOLTAGE ∅ = πΎ1 πΌπ If = field current ∅= flux per pole πΈπ = π∅π ; πΈπ = π (π1πΌπ )π πΈπ = π2 πΌπ π LAP WINDING π =π×π M = multiplicity P =no of poles WAVE WINDING π =2×π RATIO πΈπ2 πΈπ1 = πΌπ2π2 πΌπ1π1 SELF- EXCITED SHUNT N= rpm ππ‘ π π β Rsh = shunt field winding resistance Ish = If= shunt field excitation current πΌπ β = πΌπ = ∅ = πΎ1πΌπ ∅ = πΎ1πΌπ β by KCL πΌπ = πΌπ β + πΌπ By KVL πΈπ = ππ‘ + πΌπ(π π + π ππ ) πΈπ = ππ‘ + πΌππ π + πππ ; πππ = πΌππ ππ SERIES WOUND BY KCL πΌπ = πΌπ = πΌπ (Excitation current) BY KVL πΈπ = ππ‘ + πΌπ(π π + π ππ + π π ) πΈπ = ππ‘ + πΌπ(π π + π π ) + πππ Rs = Series field resistance ππ = πΌππ π VL =potential difference ππ‘ π π + π π Power generated in the armature ππ = πΈππΌπ πΌπ = COMPOUND WOUND Cumulative compound Under compounded Vnl > Vfl %VR =Percent voltage regulation πππ − πππ %ππ = π₯ 100% π£ππ Flat Compounded Vnl = Vfl %VR=0 Over compounded Vnl<Vfl %VR= NEGATIVE DIFFERENTIAL COMPOUND Long shunt By KCL πΌπ = πΌπ + πΌπ β ππ‘ πΌπ β = π π β πΈπ = ππ‘ + πΌπ(π π + π ππ + π π) πΈπ = ππ‘ + πΌπ(π π + π π) + πππ Rd = diverter resistance ππ‘ πΌπ β = π π β Sending erd ππ‘ = πΌππ π ; πππ = πΌπ π ππ At a particular load conduction ππππ β πΌπ β = ππ β SHORT SHUNT By KCL πΌπ = πΌπ + πΌπ β By KVL ππ β = ππ‘ + πΌππ π ππ β πΌπ β = π π β πΈπ = ππ β + πΌπ(π π + π ππ ) πΈπ = ππ β + πΌππ π + πππ ; πππ = πΌπ π ππ GENERATOR EFFICIENCY Electrical loss (EL) πΈπΏ = πππ’ = ∑(πΌ2 π ) a. Constant loss ππ β = (πΌπ β)2 π π β ππ β = ππ βπΌπ β ππ β2 ππ β = π π β b. Variable loss (VL) 1. SERIES FIELD WINDING LOSS (Ps) ππ = πΌπ2 π π series generator or long shunt ππ = πΌπΏ2 π π short shunt 2. ARMATURE WINDING LOSS (Pa) ππ = πΌπ 2 π π 3. BRUSH CONTACT RESISTANCE (Pbc) πππ = πΌπ 2 π ππ πππ = πππ πΌπ 4. DIVERTER RESISTANCE LOSS (Pd) ππ = πΌπ· 2 π π· 5. COMPENSATING FIELD WINDING LOSS (Pc) ππ = πΌπ 2 π π 6. INTERPOLES FIELD WINDING (Pi) ππ = πΌπ 2 π π -------------------------------------------------------------By KCL πΌπ = πΌπ + πΌπ β By KVL ππ β = ππ‘ + πΌππ π ππ β πΌπ β = π π β πΈπ = ππ β + πΌπ(π π + π ππ + π π ) πΈπ = ππ β + πΌππ π + πππ ; πππ = πΌπ π ππ -----------------------------------------------------------EFFIECIENCT OF DC GENERATORS π€ππ‘π‘π ππ’π‘ππ’π‘ πππππππ‘ ππππππππππ¦ = π₯ 100 π€ππ‘π‘π ππππ’π‘ Since, watts input= watts output + watts losses πππππππ‘ ππππππππππ¦ = π€ππ‘π‘π ππ’π‘ππ’π‘ π₯ 100 watts output + watts losses π€ππ‘π‘π πππ π ππ πππππππ‘ ππππππππππ¦ = (1 − )π₯ 100 watts output + watts losses Shunt copper loss= πΌππ» π π ππ» Series copper loss= πΌππΈ π π ππΈ Hysteresis loss ππ = ππ΅1.6 πππ₯ π π πππ‘π‘π Eddy current loss ππ = ππ΅2 πππ₯ π 2 π‘ 2 π πππ‘π‘π POWER STAGES AND EFFICIENCIES STRAY POWER LOSS (SPL) Friction and windage losses (rotational or mechanical loss) - Constant loss Core loss (CL) or Iron loss - Constant loss unless there Is change in flux and speed πΆπΏ = ππ + ππ ππ = hysteresis loss Special formulas ππ = Eddy current loss under Steinmetz law STRAY LOAD LOSS (SLL) – NORMALLY 1% OUTPUT, DUE TO ARMATURE REACTION Energy conversion: Mechanical Portion (torque and rotation speed) πππ = 2πππππ πΆπΉ πππ = Mechanical power input to the armature from the prime mover πππ = torque input (pulley driver) ππ(π) = 2ππππ πΆπΉ ππ(π) = Mechanical power generated to the armature ππ = torque developed / generated ππ = πππ − ππΏ ππΏ = torque loss πππ = ππ(π) + πππΏ πππΏ = πππ − ππ Nm = MECHANICAL EFFICIENCY ππ(π) ππ = π₯ 100 πππ ELECTRICAL PORTION (voltage and current) ππ(π) = πΈπ πΌπ = ππ ππ = ππ + πΈπΏ ππ = ππ πΌπΏ Ne = ELECTRICAL EFFICIENCY ππ ππ = π₯ 100 ππ(π) π = CONVENTIONAL EFFICIENCY = OVER-ALL EFFICIENCY = COMBINED EFFICIENCY = COMMERCIAL EFFICIENCY πππ = ππ + ππΏ ππΏ = torque loss ππΏ = πΈπΏ + πππΏ π = ππ ππ ππ π= π₯ 100 πππ NOTE: Assume that there are 2 brushes of it is not mentioned how many brushes but said each brushes In long shunt: πππ» = ππ Pin = ____bHP x 746= ans Series Generator: πΌπ = πΌπ = πΌπΏ MAXIMUM EFFICIENCY FOR DC GENRATOR (Maxima and minima) Series Generator πΌπ = πΌπΏ Constant losses =(πΉ + π ) + (πΆπΏ) = πππΏ Variable losses = Electrical losses (EL) = ππ + πππ + ππ = πΌπ 2 (π π + π ππ + π π ) 1ST CONDITION: (full load condition) πΌπ1 = ππ1 ππ 2ND CONDITION: (maximum efficiency) πΌπ′ = πΌπ1 √ ′ πΈπΏ′ Where EL’=SPL πΈπΏ1 πΌπ = πΌπ1 √ πππΏ πΈπΏ1 Therefore 2 ππ ′ πΈπΏ = πΈπΏ1 ( ) ππ1 ′ πΌπ′ = armature current at maximum efficiency condition ππ ′ = output power at max efficiency condition πΈπΏ′ = electrical loss at maximum efficiency condition πΈπΏ′ = πΌπ′2 (π π + π ππ + π π ) AT MAXIMUM EFFICIENCY CONDITION: ππΏ = 2 π πππΏ Where EL’=SPL ππ ′ ππππ₯ = π₯ 100 πππ′ ππ ′ ππππ₯ = ′ π₯ 100 ππ + ππΏ Variable Losses (ππΏ′ ) = ππππ π‘πππ‘ πππ π ππ ππΏ′ = ππ′ + πππ ′ = πΌπ′2 (π π + π ππ) Constant losses = SPL +Psh