Reactive power – Practical relevance
Even though the reactive power does not ‘consume’ any energy, it does affect the efficiency of power system operation. In practice, the oscillatory power flow cannot be avoided since power system devices such as motors and transformers need a magnetic field for their operation. Hence, power system engineers need to live (and let live) with oscillatory power flows.
The effects of oscillatory power flow in power systems are as given below:
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- Reactive power flow does require current flow. Such additional current flow uses up the capacity of generators, transformers, transmission lines etc. Hence, their full capacity or rating is not available for supplying the useful or productive loads.
- The current flow due to reactive power results in substantial power loss (I2R loss) in transmission and distribution system. So, the reactive power flow indirectly causes power losses in the system.
- The current flow due to reactive power results in an additional voltage drop in transmission and distribution system. The voltage drop due to reactive power flow is much more severe than the voltage drop due to useful (resistive) power flow. In fact, the voltage drops in practical power systems are mostly due to reactive power flows!
An important objective of power system design and operation is to maintain reactive power flows to minimum feasible values. Fortunately, it is possible to reduce reactive power flows in power systems by providing capacitive compensation as close to inductive loads as possible.
Reactive power measurement
We now know that the ‘oscillatory’ part of the power flow is called the ‘reactive’ power and it is denoted by the letter ‘Q’.
The question is, how to quantify the magnitude of the reactive power?
The ‘average’ value of the oscillatory power is not relevant as it is always zero.
The magnitude of reactive power is defined as below:
Q = E I sin(φ) vars … (4)
It should be noted that the value of ‘Q’ is a defined quantity. It has no relation to the area under the ‘p’ curve. It might look arbitrary at first, but it is a cleverly chosen value. Our main objective is to minimise the oscillatory power flow. The ‘defined’ value of ‘Q’ is a convenient and sufficient measure for our purposes.
In Equation 4, we have not only defined the ‘magnitude’ of the oscillatory power flow, but we have also given it a unit a measurement, namely ‘var’. The term ‘var’ is an abbreviation of the term ‘volt-ampere-reactive’. The instruments designed to measure reactive power are called ‘var’ meters!
As we have noticed before, most SI units are named after their inventors or those who have contributed substantially to the topic. It will be interesting to see when and how the unit ‘var’ will be renamed. I used to tell my students that if they contributed enough on the topic of reactive power, it could be named after them!
Example 2
A power system load is operating at a ‘rms’ voltage (E) of 240 V and a ‘rms’ current (I) of 5 A. Calculate the useful (active!) and reactive power flows for the following cases:
(a) Pure resistive load
(b) Pure inductive load
(c) Induction motor load with current lagging the voltage by 30o
(a) For a pure resistive load, we have the phase angle difference φ = 0o
P = E I cos(φ) = 240 x 5 x cos(0o) = 1,200 watts
Q = E I sin(φ) = 240 x 5 x sin(0o) = 0 vars
We have,
P = 1,200 watts – maximum possible ‘useful’ power transfer
Q = 0 vars – there is no reactive (oscillatory) power flow
(b) For a pure inductive load, we have the phase angle difference φ = 90o
P = E I cos(φ) = 240 x 5 x cos(90o) = 0 watts
Q = E I sin(φ) = 240 x 5 x sin(90o) = 1,200 vars
We have,
P = 0 watts – there is no ‘useful’ power transfer
Q = 1,200 vars – maximum possible reactive (oscillatory) power flow
(c) For an induction motor load operating with a phase angle difference φ = 30o
P = E I cos(φ) = 240 x 5 x cos(30o) = 1,039 watts
Q = E I sin(φ) = 240 x 5 x sin(30o) = 600 vars
The useful power flow is 1,039 watts out of the possible maximum value of 1,200 watts. The ratio of useful power to maximum possible power is called the ‘power factor’ in power system terminology.
Hence, the ‘power factor’ for this example is (1039/1200)*100 = 86.6%.
We can improve the power factor to 100% by installing a 600 var capacitor. This reduces the reactive (oscillatory) power flow in the generation and transmission system to zero. Note that installing a capacitor greater than 600 vars will result in reactive (oscillatory) power flow due to the capacitor. In practical power systems, switchable (switched!) capacitors are used in the case of variable load conditions.
Power factor improvement is an important topic in power systems. We shall deal with it in more detail in a future blog.
Equation for power in AC
It is now obvious that the equation P = E I cos(φ) is not sufficient to represent the power flow in AC systems.
The complete AC power flow equation must include the reactive power flow equation Q = E I cos(φ) as well.
The derivation of a versatile equation for power flow in AC systems requires a detailed presentation of additional concepts. This is the topic for the next blog!
Conclusions
Many power system engineers find the term ‘reactive power’ confusing. This is understandable since this term does not clearly convey concepts. I prefer the term ‘oscillatory power’. It may not be the ideal term, but it is better than the term ‘reactive power’ to explain the power flow concepts in AC systems.
Practical power systems are primarily established to transfer ‘useful’ power for energy conversion purposes. Reactive power flows in AC systems are a waste of resources. Hence, every effort must be made to keep the reactive power flows to a minimum. Since most power system loads are inductive, it is feasible to reduce the reactive power flows by installation of suitably rated capacitors.
The main objective of this blog is to provide a clear understanding of the term ‘reactive power’ in power systems. The forthcoming blogs will provide a more detailed exposure to AC power flow equations, practical examples, and case studies in power factor correction.
