CONTROL OF VOLTAGE & REACTIVE POWER

1. Voltage times the current in a circuit
2. Voltage times the current times the cosine of the angle between the voltage & current
3. Voltage times current times the sine of the angle between the voltage & current

Ans.c

1. In a lightly loaded transmission line of such a length that the capacitive reactance is appreciable, the receiving end voltage

Voltage drop between two nodes1 and 2,at voltages V1 and V2 respectively, connected by a short transmission line of impedance R + j X is

= (RP2 +XP2)/V2

where P2, Q2 is the real and reactive power at node V2. For most power networks X>> R and the voltage drop determines Q.

If V1 is in phase advance of V2, then the power P flows from node1 to node2.

If V1 >V2, then reactive power is transferred from node1 to node 2.

If by varying the excitation of generators at nodes 1 & 2 V2 is made >V1, then the direction of Q will be reversed from node 2 to node1.

Hence P can be sent from node 1 to node2 or from node 2 to node1 by suitably adjusting the amount of steam (or water0 admitted to the turbine and Q can be sent in either direction by adjusting the voltage magnitudes. These two operations are approximately independent of each other if X>>R.

If a scalar voltage difference exists across a reactive link, the reactive power flows towards the node of lower voltage. Or, if there is a deficiency of Q at a point, this has to be supplied from the connecting lines and hence the voltage at that point falls. If there is a surplus of Q generated (lightly loaded cables absorb leading or negative vars and hence generate positive vars) then the voltage will rise.

Voltage can be controlled at a node by injecting into the node a Q of the correct sign. Other methods of controlling the voltage are the use of tap changing transformers and voltage boosters.

These can be used to generate or absorb Q. The ability of the generator to supply Q is determined by the short circuit ratio (S.C.R=1/Xs). In modern machines SCR is made low for economic reasons and hence the inherent ability of the machine to operate at leading power factors is not large. The Var capacity of the generator can be increased by the use of continuously acting voltage regulators. An overexcited machine generates reactive power. An underexcited machine absorbs (or generates negative or leading) Vars. The generator is the main source of supply to the system of both positive & negative Vars.

When fully loaded an overhead line absorbs Q (=I²X per phase). On light loads, the shunt capacitance of long lines may become predominant and the lines become Var generators

Transformers always absorb Q.

Vars absorbed by a transformer = (VA of load) ²* Xpu/Rated VA

where Xpu is the pu reactance of the transformer.

Underground cables are generators of Q owing to their high capacitance.

A load of 0.95 pf lagging implies a Q demand of 0.33 kVar per kW of power. In planning a network it is desirable to assess the Q requirements to ascertain whether the generators are able to operate at the required power factors for the extremes of load to be expected.

Three methods of injecting Q at the loads are:

1. Static shunt capacitors
2. Static series capacitors, and
3. Synchronous compensators

Shunt capacitors are used for lagging power factor circuits. Shunt capacitors are disposed along routes to minimize losses and voltage drops. On light loads, when the voltage is high, the capacitor output is large and the voltage tends to rise to excessive levels.

Shunt reactors are used for leading power factor circuits, as in lightly loaded cables.

The major drawback of series capacitors is: high overvoltages are produced when a short circuit current flows through the capacitor and special capacitive devices have to be incorporated (e.g. spark gaps)

1. If the load Var requirement is small, series capacitors are of little use.
2. If voltage drop is the limiting factor, series capacitors are effective. Voltage fluctuations due to arc furnaces are also evened out.
3. If the total line reactance is high, series capacitors are very effective and stability is improved.

Synchronous motors running without mechanical load can absorb or generate Q depending on the excitation. As the synchronous motor losses are considerable compared to static capacitors, the power factor is not zero. When used with a voltage regulator, the compensator can automatically run overexcited at times of high load and underexcited at light loads. The advantage of the synchronous compensator is its flexibility of operation for all load conditions.

An expression for determining the Q at the receiving end may be derived in terms of the receiving end power Pr, complex A, B parameters of the line such that the receiving end voltage, Vr is equal to or a specified ratio of the sending end voltage, Vs.

To determine the tap changing ratios required to completely compensate for the voltage drop in the line, the product of the transformer tap ratios ts and tr at the two ends f the line is made equal to unity. This ensures that the overall voltage level remains in the same order and the minimum range of taps in both transformers is used.