complex power in power system
lagging VAR to magnetize its core and transfer the power through mutual induction.
The receiving end reactive power is given by,
Where, θ is the power angle which is kept very low due to stability reasons, Xl is the reactance of the transmission line, Vs is the sending end voltage and Vr is the receiving end voltage.
So, Qr becomes,
Now equation is formed as,
Solving we get,
Mathematically, the expression given for the reactive power
Note: We did not take negative sign as then Vr will become zero when Qr is zero which is not possible.
Let Q1 be the reactive power demanded by the load at the receiving end and Q2 be the reactive power supply from the generating or sending end. Then Qr is (Q1 - Q2).
Case - 1 When supply Q2 is equal to demand Q1 then Vs = Vr, the receiving end voltage will be equal to sending end voltage, which is desirable.
Case - 2 When demand is more and supply is less, Qr becomes negative. And so the receiving end voltage becomes less than sending end voltage.
Case - 3 When demand is less, supply is high, Qr becomes positive. Thus, the receiving end voltage becomes greater than sending end voltage which is very dangerous. In this way, we saw how voltage (and its level management) which is very basic requirement of any electrical load; depends on reactive power. During the daytime, the demand for reactive power increases, therefore voltage dip occurs. On the other hand, during morning time, demand for reactive power is less, so rise in voltage level occurs. To maintain the voltage level we need to make Q1 = Q2.
For low electrical power factor loads, the reactive power demand is very high. Therefore, we need to increase the power factor using capacitor bank. This reduces the var demand by supplying the appropriate amount of reactive power to the load. Other methods include use of shunt capacitor, synchronous phase modifiers, on-load tap changing transformer and shunt reactor. An overexcited synchronous motor is used in shunt with the load. It serves as a capacitor and is also called synchronous condenser. A shunt reactor is used for the reduction of electrical power factor. In the on-load tap changing transformers, turns ratio is adjusted accordingly to maintain the desirable voltage level as the voltage differencebetween the sending and receiving end determines the reactive power. Mathematically, the expression given for the reactive power(Q) needed to increase the electrical power factor from cosθ1 to cosθ2 is given as,
Where, P is real power demand of the load (in watts).
In case the electrical power factor is to be decreased from cosθ2 to cosθ1, the reactive power which must be absorbed by the shunt reactor at the load end is given by,
The values of capacitance or inductor thus required can be calculated by using,
Reactive Power in Transmission Lines
In an electrical power transmission line, the flow of reactive power in the line decides the receiving end voltage. Managing voltage level at the receiving end is very important, as higher voltage can damage the consumer's equipment and there will be a great loss. In many cases, we see sudden voltage rise or fall due to lightning or due to any fault on the healthy phases and in any case damage to the equipment occurs. Let us see how voltage depends on reactive power.The receiving end reactive power is given by,
Where, θ is the power angle which is kept very low due to stability reasons, Xl is the reactance of the transmission line, Vs is the sending end voltage and Vr is the receiving end voltage.So, Qr becomes,
Now equation is formed as,Solving we get,Mathematically, the expression given for the reactive powerLet Q1 be the reactive power demanded by the load at the receiving end and Q2 be the reactive power supply from the generating or sending end. Then Qr is (Q1 - Q2).
Case - 1 When supply Q2 is equal to demand Q1 then Vs = Vr, the receiving end voltage will be equal to sending end voltage, which is desirable.
Case - 2 When demand is more and supply is less, Qr becomes negative. And so the receiving end voltage becomes less than sending end voltage.
Case - 3 When demand is less, supply is high, Qr becomes positive. Thus, the receiving end voltage becomes greater than sending end voltage which is very dangerous. In this way, we saw how voltage (and its level management) which is very basic requirement of any electrical load; depends on reactive power. During the daytime, the demand for reactive power increases, therefore voltage dip occurs. On the other hand, during morning time, demand for reactive power is less, so rise in voltage level occurs. To maintain the voltage level we need to make Q1 = Q2.
Reactive Power Compensation
As already discussed excess of reactive power as well as its scarcity should be monitored. For this purpose, compensation is done by using various devices. Here the reactor absorbs excess reactive power whereas the capacitor supplies for makeup of reactive power in cases of high demand.For low electrical power factor loads, the reactive power demand is very high. Therefore, we need to increase the power factor using capacitor bank. This reduces the var demand by supplying the appropriate amount of reactive power to the load. Other methods include use of shunt capacitor, synchronous phase modifiers, on-load tap changing transformer and shunt reactor. An overexcited synchronous motor is used in shunt with the load. It serves as a capacitor and is also called synchronous condenser. A shunt reactor is used for the reduction of electrical power factor. In the on-load tap changing transformers, turns ratio is adjusted accordingly to maintain the desirable voltage level as the voltage differencebetween the sending and receiving end determines the reactive power. Mathematically, the expression given for the reactive power(Q) needed to increase the electrical power factor from cosθ1 to cosθ2 is given as,
Where, P is real power demand of the load (in watts).In case the electrical power factor is to be decreased from cosθ2 to cosθ1, the reactive power which must be absorbed by the shunt reactor at the load end is given by,
The values of capacitance or inductor thus required can be calculated by using,
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