Active, Reactive & Apparent Power

AC System is used at ship due to its flexibility in application i.e. easily converted into DC, voltage variation as required, smaller & compact machinery for particular power rating etc.

Major electrical Services at ship are Motor, Lighting & Heating. These services are also called as load for power generator (Generator). These loads draw electrical power through resistor, inductor and capacitor. These are passive electrical components because of their energy acceptor character. Actually these components store or maintain energy in the form of voltage or current.

Electrical power (Electrical power is nothing but the flow of electrical energy) of AC system has 2 components: Active Power & Reactive Power

Passive Components of Electrical Power

  • Resistor: It consumes Real power.
  • Inductor: It consumes Reactive power.
  • Capacitor: It consumes Reactive power.

Note: Inductor and Capacitor are energy storage components.

Active power

  • Assume a simple circuit with a resistor, V (voltage) supply and I (current) flow. The waveforms of voltage and current are in phase i.e. current and voltage are in same phase. And its power waveform (V × I) is always positive i.e. power flow is always positive. It means power is taken from the supply (source) and converted into a power output by resistor. This power is nothing but Active Power.
  • It is the loss of power across resistance. This is actual power which is supplied to the load.
  • Active power flows only in one direction and represents power output.
  • This power is also called as Real Power, Actual Power, True Power, Useful Power & Watt-full Power.
  • Its symbol is (P) and unit is (kW). (1000 W = 1 kW)

Reactive power

  • Assume an inductor in a circuit with V (voltage) supply and I (current) flow. Here the waveforms of voltage and current are 90° each other i.e. current and voltage are not in a same phase like active power flow. Its power waveform is positive as well as negative. This power is nothing but Reactive Power.
  • It is the loss of power across reactance (Reactance = Inductance + Capacitance). This power continuously move in to-and-fro (i.e. flow between load and source).
  • Reactive power reverses its direction in every 1/4th cycle and it doesn’t represent power output.
  • During starting every 1/4th cycle, electric current is transferred from source to load (energy storage component) as current increases and energy is stored in magnetic field/electric field of load. And in the next 1/4th cycle, current falls to zero and magnetic field/electric field of load with its stored energy disappears. This stored energy is supplied back to the source. Again in next 1/4th cycle, current increases and supplies to the load and process is repeated.
  • Here, power is alternately positive and negative as energy is stored and discharged. So the power waveform is first positive and then negative.
  • This power is also called as Useless Power & Watt-less Power.
  • Its symbol is (Q) and unit is (kVAr). (1000 VAr = 1 kVAr)

Total power

  • This is a resultant power of active power and reactive power.
  • Total Power = Active Power + Reactive Power
  • This power is also called as Apparent Power.
  • Its symbol is (S) and unit is (kVA). (1000 VA = 1 kVA)

Electrical Power in Single Phase & Three Phase System: (for 3-phase system, power equations are multiplied by √3 with power equations of single phase system)

Now, we can understand the relationship between active power, reactive power & apparent power by power triangle.
Power Triangle

Relationship of active power, reactive power & apparent power can be represented trigonometrically (i.e. by using right angle triangle) and this representation is named as power triangle.
For graphical representation, assume Active power = Base (Horizontal), Reactive power = Height (Vertical) and Apparent power = Hypotenuse, then according to Pythagoras theorem: (Apparent Power)² = (Active Power)² + (Reactive Power)².
Power Factor = (Active Power)/(Apparent Power) i.e. Cos ϕ = kW/kVA

For more practical understanding, we are considering two famous analogies: Beer analogy & Chips packet analogy
Beer Analogy

Let’s assume that you are in a restaurant for beer and now observe the glass of beer and relate with these electrical power:
Actual quantity of beer = Active power, Quantity of foam = Reactive power & Total quantity of beer is nothing but (actual quantity of beer + quantity of foam) and it’s same as Apparent power.
Here, only actual quantity of beer fulfils our demand or thirst not foam. In the same way, only active power fulfils the demand of power not reactive power and that’s why it’s called as useful power.

Apparent power is summation of active power and reactive power. If you want to increase the active power (kW) then you have to decrease the reactive power (kVAr) for a particular machinery. kVA = kW ↑ + kVAr ↓, It means for constant power rating (kVA), as active power increases, reactive power decreases.

Chips Packet Analogy

Consider a chips packet and relate as: Actual chips present = Active power, Air (empty) present = Reactive power and total capacity (size) of packet is nothing but the Apparent (total) power.
Here, only actual quantity of chips is useful not air (empty space) and in the same way in ac system, only active power is useful not reactive.

Concept of Power Factor

  • It is nothing but the share of active power in total power. For example: If power factor is 0.8 then it means there is 80% active power in total power (100%).
  • It measures the conversion efficiency of total power into power output (active power).
  • It is a cosine of angle between current and voltage i.e. angle of lag of current. It means range of cos is the range of power factor i.e. -1 ≤ Power Factor (cos ϕ) ≤ 1 
  • Cos ϕ = kW/kVA, Cos ϕ = P/VI, Cos ϕ = Resistance/Impedance, Cos ϕ = True power/Apparent power
  • At ship, power factor is preferred 0.8 but it’s not necessary. There are always some inductive loads in the electrical system that’s why we can’t ignore reactive power completely.

We want power factor as close as possible to 1. It means active power should tend to be apparent power, because higher power factor (i.e. higher active power) indicates less loss, good voltage regulation, high efficiency, reduced size of machinery etc.

Low power factor

P = VI Cos ϕ, I = P/(V Cos ϕ) and thus power factor is inversely proportional to current.
If power factor decreases then current will increase. And due to high current following possibilities are possible:

  • Losses will be high & efficiency will be low.
  • For high current, bigger size of conductor is required and that’s why it is costly.
  • Lower power factor implies higher Kva rating, larger size of machinery and thus higher cost.
  • Lower power factor implies higher current and it leads to higher voltage drop. There will be imbalance in voltage regulation.

Improvements of power factor

Generally, all loads consume both active as well as reactive power. But ideally, they should consume active power. So there should be system for increasing the active power and reducing the reactive power. And this is done by improving the power factor. Improvement of power factor means improvement in sharing of active power in apparent (total) power. For improving the power factor, we need to increase active power or to decrease reactive power and this is done by following methods:

  • By using capacitor: It decreases the inductive load i.e. reactive power and minimizes the phase difference between current and voltage.
  • By using synchronous condenser: It acts like a capacitor and increases power factor. It is costly to use.
  • By using phase advancer: It is used for motors to excite the ampere-turns for improving the power factor. Phase advancer is just an exciter.

Note: In DC system, there is no power factor i.e. Cos ϕ = 0 because there is only active power and its unit is kW.

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