BASIC ELECTRICAL POWER SYSTEM

7/29/2019 BASIC ELECTRICAL POWER SYSTEM

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BASIC ELECTRICAL POWER SYSTEM: AN OVERVIEW

1. Generation

2. Transmission3. Distribution

It is difficult to step up and step down D.C. currentand hence difficult to distribute.I proportional to P/V ; if more power is transmitted,voltage is to be more in order to minimise current. Ifcurrent increases, more cross sectional area isrequired and results in high material cost.POWER GENERATIONTypes of generation:1. Thermal (70%)2. Hydel (25%)3. Nuclear (3%)4. Non-conventional (2%)

Power generation capacity of india=150GW (approx)


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Energy equivalent of coal: 6*10^6 kg=1GW

Companies:

1. Generation Company(GENCO)- NTPC, NEEPCO,DVC etc2. Transmission Company(TRANSCO)- Power Grid etc3. Distribution Company(DISCO)-ASEB, Reliance etc

General transmission voltages: 220KV, 400KV, 765KV


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General distribution voltage: 1-phase: 220V, 2-phase: 415V.Some countries like japan, US have 60Hz supplywhereas others have 50Hz to restrict technology

outsource.

basic notations:Voltage - v/VCurrent - i/IResistor - r/RInductor - LCapacitor - C

ciRCUIT ELEMENTS:1A. Active elements: Elements which can providepower. eg:voltage & current source, amplifier2A. Passive elements: Elements which can absorbpower. eg: resistor, capacitor, inductor etc1B. Unilateral Elements: Magnitude of current fromboth sides on application of similar voltage isn'tsame. eg: diode, transistor etc

2B. Bilateral Elements: Magnitude of current fromsides on application of similar voltage is same. eg:resistor, inductor, capacitor etc1C. Linear Elements: f(g(t))=g(f(t)); f(g(t)+h(t))=f(g(t))+f(h(t))


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2C. Non-linear elements:

Node: Junction where two or more elements areconnected. eg: a,b,c,dBranch: Current carrying elements between twonodes. eg: a-b, b-c, a-c etcLoop: Closed path. eg: a-b-c-a, a-d-c-a, b-d-c-b etcMesh: Loop within which their is no other loop. eg: a-


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d-b-a, a-b-c-a etcGround: Voltage is zero at that pointKIRCHHOFF'S LAWS:1. KCL: Summation of currents in a node is zero.

2. KVL: Summation of all voltage drop in a loop iszero.Voltage divider:

Current divider:

Voltage Source:

current source:


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conversion of sourceVoltage source to current source:

If current is flowing from lower to higher potential

inside a source, its is discharging i.e. releasingenergy.

MESH LOOP ANALYSIS


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1. Draw the circuit (avoid crossover)2. Identify all loop and nodes.3. Apply KVL

node voltage method

1.Draw the circuit avoiding crossover.2. Identify all the nodes.3. Identification of reference node. (here 'd' is refnode)4. Apply KCL at each node except reference node.

star delta conversion


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delta--->starRc+Ra=Rac(Rab+Rbc)/(Rac+Rab+Rbc)Ra+Rb=Rab(Rac+Rbc)/(Rac+Rab+Rbc)

Rb+Rc=Rbc(Rab+Rac)/(Rac+Rab+Rbc)=>Rac+Rab+Rbc=(RabRbc+RbcRca+RcaRab)/(Rac+Rab+Rbc)Ra=(Rab)(Rca/(Rac+Rab+Rbc)Rb=(Rbc)(Rab)/(Rac+Rab+Rbc)Rc=(Rbc)(Rca)/(Rac+Rab+Rbc)

star--->delta

(Va-Vn)/Ra+(Vb-Vn)/Rb+(Vc-Vn)/Rc=0=>Vn=(Va/Ra+Vb/Rb+Vc/Rc)/(1/Ra+1/Rb+1/Rc)current through A-C(Va-Vn)/Ra=Vac/Rac+Vab/Rab=>Rab=Ra+Rb+RaRb/Rc (substituting value ofVn)similarly Rbc=Rb+Rc+RbRc/Ra;Rca=Rc+Ra+RcRa/Rb

superposition principleFor a linear bilateral network having two or morecurrent or voltage source; voltage and current at aparticular branch is the resultant voltage and currentdue to each source acting alone while other sources


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are replaced by respective internal resistance.Current source act as open circuit while voltagesource acts as close circuit.Steps:

1.Identify different voltage and current sources inthe circuit.2. Take one source at a time and find voltage andcurrent at particular branch.3. Resultant voltage or current at a particular branchis summation of the voltage or curent determined ineach source.

thevenin's theoremReplacement of a complex circuit by a voltagesource and resistance.

Norton's theorem

Maximum power theoremPl=RlIl^2=Rl{Vth/(Rth+Rl)}2

for maximum power-


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derivative(Pl/Rl)=0=>Rth=Rl(Pl)max=Vth2/4Rl

Graphical method for determination of V,I across anon-linear element:

D.C. transientInductance: It is the property of an element by virtueof which it can resist the rate of change of power.Faraday's law: E=-nd /dt`=-Ldi/dt; L=nd /di

Inductive circuit(L):


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Time constant: Measurement of response of a circuiton voltage change.It is the time required to obtain 63.2% of steadystate value of current for rise of current and timerequired to obtain 36.8% of steady state value ofcurrent for fall of current.T for inductive circuit=L/RHigher time constant=>Slower ResponseLower time constant=>Faster Response

Power consumption in R-L circuit:P=iv=iLdi/dt =>Pdt=iLdiintegrating t from 0 to t and i from o to iEnergy(E)=0.5Li^2

Capacitor:


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Capacitive circuit(C):

Power consumption of R-C circuit

P=iv=vCdv/dt => Pdt=CvdvE=0.5Cv^2

single phase ac circuit

Vavg=2Vm/Vrms=Vm/(2^0.5)Form factor=Vrms/Vavg=/2^(3/2)Concept of phasor diagram:


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In AC circuit,Impedence,Z=v/i=R+jXReal part of Z=R------resistanceImaginary part of Z=X------reactance

Phase angle==tan-1(X/R)

Resistive circuit:

Inductive circuit:


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Capacitive circuit:

R-L circuit

t:

After trignometric simplification: Im=Vm/(R2+w2L2)1/2 tan=wL/R


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Z=R+jwL

R-C circuit:

After trignometric simplification: Im=Vm/

(R2

+1/w2

C2

)1/2

tan

=1/wCRZ=R-j(1/wC)

L-C circuit:

R-L-C circuit (series):


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Im=Vm/{R2+(wL-1/wC)2)1/2 tan=(wL-1/wC)/RZ=R+j(wL-1/wC)The value of may be +ve or -ve and accordingly iwill lead or lag v

R-L-C circuit (parallel):

Im=Vm{(1/R2+(wc-1/wL)2}1/2 tan=(1/wL-wC)RZ={1/R-j(1/wL-wC)}/{1/R2+(wc-1/wL)}2}The value of may be +ve or -ve and accordingly iwill lead or lag v.

Reactance of inductor,Xl=wL

Reactance of capacitor,Xc=-1/wCAdmittance,Y=i/v=1/Z=G+jBReal(Y)=G----------------conductanceImaginary(Y)=B--------------susceptanceunit of admittance is siemens or mho1siemens=1mho


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Complex power,S=v.i* i* is complexconjugate of i

=ImVmcos+jImVmsin is

the angle between i and vReal(S)=P=ImVmcos-------active power unit--wattImaginary(S)=Q=ImVmsin-----reactive powerunit--volt ampere reactiveApparent power, mod(S)=(P2+Q2)1/2 unit--voltampereInductor consumes reactive power but capacitorreleases reactive power.

Power factor,P.F.=active power/apparentpower=cos=P/mod(S)For R-L-C circuit, cos=R/Zpower factor is zero for completely inductive andcapacitive circuit.

3-phase ac systemTypes of 3-phase AC circuit:

Line quantities: Quantities leaving the circuit.Phase quantities: Quantities inside the circuit.

Line voltage: Voltage between two lines. (Vl)


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Phase voltage: Voltage across a particular elementinside the box. (Vp)Line current: Current between two lines. (Il)Phase current: Current across a particular element

inside a box. (Ip)

For star: Vl=31/2Vp, Il=IpFor delta: Vl=Vp, Il=31/2Ip

In case of balanced load, the voltage in each phasewill be same for its maximum value and they will be120degree phase appart from each other.

For star:

For delta:

Magnetic circuit


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MMF:Magneto Motive ForceMMF=iN, where i is exciting current and N is number

of turns.Unit of MMF: ampere turnFlux( ) is generated in the magnetic circuit due to MMF.Reluctance(R):Reisitance of magnetic circuit to thefluxMMF=R

Comparision of DC electric circuit and magneticcircuit:1.EMF MMF2.Current(i) Flux()3.Resistance(R) Reluctance(R)4.Conductance(1/R) Permeance(1/R)

Representation of magnetic circuit:Magnetic field strength(H)=MMF/l=Ni/l i.e.MMF per unit lengthFlux density(B)=/A where A is cross sectionalareaB=H=0rH where 0=permeability of free

space=4*10-7 henry/metre


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r=relative permeability

Reluctance,R=MMF/=iN/=Hl/BA=l/0rA

B-H characteristics:

The curve should be linear as B=H, but as dipoleallign themselves with the increasing flux, after acertain time no more dipole is to be alligned and fluxbecomes constant.

A better ferromagnetic material shows more linearcharacteristics.

Series circuit:

can travel through air gapR=Rc+Ra


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Parallel circuit:

R=Rc+Rs/2

Types of flux:1.Main flux2.Leakage fluxLeakage flux is very less than main flux as the Ra>Rc

The bending of flux lines at the air gap is termed as

fringing effect. Its affect is low as more fringingimplies more air distance.

Multiple exciting current:Depending on the direction flux, net MMF issummation or difference of the individual MMFs.Direction of flux is decided by Biot-Savart law.

Biot=Savart law: B=

Ampere's circuital law:

B-H loop:


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Retentivity(b): Ability of ferromagnetic material toretain certain amount of residual magnetic flux whenmagnetic field is removed after achieving saturation.Residual flux density: The flux density that remainsin a material when the magnetic field is zero afterattaining saturation.Coercivity(c): Intensity of the applied magnetic field

required to reduce the magnetisation of the materialto zero after magnetization of the material is drivento saturation.Structure of loop vary from material to material.Strong materials have wide loop whereas weakmaterial have narrow loop.

Core losses:

1. Hysterisis loss:theoritical e=Nd/dt =>ei=Nid/dt=HlAdB/dt

Ph=VHdB/dt where V

is volumepractical Ph=KhBmxf where


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Kh :

constant of hysterisis lossBm : peak

value of flux densityx :

Steinmetz's constant (1.5-2.5)2. Core loss: Eddy current loss

Eddy current comes into existence to resistthe change of flux according to Lenz law.

Pe=KeBm2f2 where Ke is constant which

depends on material of core,resistivity of core,thickness of core.

Mesures to resist loss due to core loss:1. High resistivity material2. Lamination: Separation of core into large numberof parts to decrease cross sectional area.

transformerIt is a static electromagnetic device which convertselectrical power from one voltage level to anotherwith a constant frequency.


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Ideal transformer:=maxsin(wt)

e1= -T1dm/dt= -wT1maxcos(wt)= wT1maxsin(wt-/2)= e1 maxsin(wt-/2)

e1avg=20.5fT1max= 4.44fmaxT1e2=4.44fmaxT2

e.m.f. per turn=e1/T1=e2/T2Conditions of ideal transformer:1. Winding resistance is zero2. No leakage flux (r=infinity)

3. No leakage flux


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Practical Transformer(no load condition)

V1=-E1+I1R1+I1X1


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Magnitude of E1 and E2 depends on the number of

turns on each side.

Practical Transformer(on load condition):


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d.c. machines1. DC motor2. DC generatorparticle properties of waves

if


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Advantages of DC motor:1. Speed Control2. Initial High Torque3. Reversing of movement direction easily

Classification of DC machine (Mechanical Function):1. Stator2. RotorClassification of DC machine (Electrical Functions):1. Field (placed in stator)2. Armature (placed in rotor)

DC generator


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Types of DC generator:1.Seperately excited generator

If :current through field winding

where Eg: Voltage Generated

Z: Total Number of conductors in the armatureP: Number of poles of the DC generatorN: Speed of DC generator on rpmA: Number of parallel path in armature winding

Voltage Characteristics (open load condition):


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Eg=kN where k is a constant

Eg is proportional to

; and

& If shows propertiesas in B-H loop.Residual magnetism results in non-zero value of Eg at

If=0

For constant; Eg is proportional to N.


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BASIC ELECTRICAL POWER SYSTEM

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