Ohm's Law and kirchoff's law

Ohms law:

•v(t) = i(t) R  - or -  V = I R

•p(t) = i2(t) R = v2(t)/R  [+ (absorbing)]

Kirchoffs law:

•Kirchhoff’s Current Law (KCL)

–sum of all currents entering a node is zero

–sum of currents entering node is equal to sum of currents leaving node

•Kirchhoff’s Voltage Law (KVL)

–sum of voltages around any loop in a circuit is zero

Kirchoffs Current Law :

The sum of currents entering the node is zero:

Analogy: mass flow at pipe junction

KVL Polarity

•A loop is any closed path through a circuit in which no node is encountered more than once

•Voltage Polarity Convention

–A voltage encountered + to - is positive

–A voltage encountered - to + is negative

Electrical Analogies (Physical)

Basic Electrical Quantities

•Basic quantities: current, voltage and power

–Current: time rate of change of electric charge

  I = dq/dt 

1 Amp = 1 Coulomb/sec

–Voltage:  electromotive force or potential, V 

1 Volt = 1 Joule/Coulomb = 1 N·m/coulomb

–Power:  P = I V 

1 Watt = 1 Volt·Amp = 1 Joule/sec

•Active elements can generate energy

–Batteries

–Voltage and current sources

•Passive elements cannot generate energy

–Resistors

–Capacitors and Inductors (but CAN store energy)

An independent source (voltage or current) may be DC (constant) or time-varying, but does not depend on other voltages or currents in the circuit.

The dependent source magnitude is a function of another voltage or current in the circuit.

A motor problem

Q) A 25 HP 6 Pole 50 Hz 3 phase 960 rpm at full load. I 2 = 35 A, Allowing 250 W as Cu loss in SC gear . 1000 W = Mech losses.
How much is r2?
Ans)

Q) 440 V , 50 Hz, 6P, 3 phase, 

Ans) F2 = 100/60 

RL circuit on a AC source.

In the previous post we had seen RL circuit on DC source. Now lets see it on AC source

Transients in power system

Transients in simple circuit

DC Sources:

• Resistance only
• Inductance only
• Capacitance only
• 
  
• RC Circuit
• 
  
• RLC Circuit:

How to control voltage in power system

We have seen total grid collapsing twice recently. How voltage is controlled? Lets see in the above diagram


Sources and sink of Reactive power

• Transmission line
• Cables

• Synch. Machines
• Shunt capacitors and reactors
• Series capacitors

Insulated Cables

Capacitance of three core cables

Grounding

Advantages of neutral grounding:

• Voltage of phases are limited to phase to ground voltage.
• High voltages due to arcing grounds or transient line-ground faults are eliminated.
• Sensitive protective relays against LG faults can be used.
• Overvoltages due to lightening are discharged to ground.

Advantages of isolated neutral

• It is possible to maintain supply with fault on line.
• Interference with communication lines is reduced because of no Z sequence current.

Effective grounding systems:

X0 / X1 < 3

Least Expensive is = maxm Vphase= 0.8 V line

Series or Shunt Capacitor

Voltage Boost:

Shunt Capacitor: Evenly distributed over transmission line.

Series Capacitor: -----------------------I  I-------------------------
                                                   V1            V2
                                     Sudden change of voltage

• Shunt Capacitor improves power factor of the load whereas Series capacitor has little effect on pf.
• For long transmission line, where total reactance is high, series capacitors are effective for improvement of system stability.