Before studying the Power Triangle concept, we have to understand AC circuit basics.

We have tried to explain this topic by using a simulation tool called MULTISIM so you can make a better practical understanding about AC circuits and Power Triangle.

In AC circuits, there are three types of loads called Resistance, Inductance, and Capacitance. Let us explain the concept of Voltage and current using MULTISIM in the above-said loads.

In the case of only Resistive Loading, Voltage and Currents are always in phase and there is no phase difference as shown in fig 2. Figure 1: Resistive Loading MULTISIM Figure 2: Voltage Current Relation Figure 3: Vector Diagram in case of Resistive Loading

In fig 1, a Resistor of value 50 Ω is connected with 120 V, 50 Hz AC supply. You can also see an Oscilloscope connected with the circuit to monitor the phase difference between Voltage and Current.

After simulating the circuit, Voltage-Current waveform relation has been achieved as shown in fig 2. It is clear from the waveform result that Voltage and current waveforms are in phase (Both values are zero, maximum, and minimum at the same time). Fig 3 is about the vector diagram of the Voltage and current of the circuit. This fig is also telling that voltage and current are in phase.

The angle between V and I is 0  in case of Resistive Loading and Active Power is also maximum as:

Active Power=P=VI Cos⁡(0°)

P=VI

Similarly, Reactive power should be zero as the load is of resistive nature. It can be proved by using the following equation:

Reactive Power=Q=VISin(0°)=VI×0

Q=0

So apparent power can be found using Pythagoras Theorem:

Apparent Power=S=sqrt(P^2+Q^2) S=P

In the case of a pure inductor (there is no pure inductor practically as it has some resistance value), fig 4 represents pure inductive loading connected with AC supply, and fig 4 is representing waveform result.  Figure 5: Voltage-Current Waveform in case of Inductive Loading Figure 6: Vector Diagram in case of Inductive Loading

Theoretically, it is said that there happens a 90-degree phase shift between voltage and current values. It also means that the current lags behind the voltage by 90 degree . This theoretical concept can be understood using fig 5 result. In fig 5, you can see that aqua colored bar represents the voltage waveform and the yellow bar to the current waveform. It is clear that when the voltage value is at the maximum positive value, the current is at zero position. It means that there is a phase difference of 90 .  Moreover fig 7 is depicting about vectors of voltage and current.

Power values in case of pure inductive loading are:

Active Power=P=VI Cos⁡(90°=0)

Reactive Power=Q=VISin90°=VI

Apparent Power=S=VI=Q

When the capacitor is attached with AC supply, current leads the voltage by 90 degree. This concept can be understood using MULTISIM as below shown in fig 7, 8, and 9.  Figure 8: Voltage Current Waveform in case of Capacitive Loading Figure 9: Vector Diagram in case of Capacitive Loading

In fig 8, it can be seen that the yellow bar of current is before the voltage bar and the current is leading by 90  as when the current is at 0°, the voltage is at-90°.  Fig 9 also represents the vector diagram in which the current is making 90° leading angle.

Power values in case of capacitive load are:

Active Power=P=VI Cos⁡(-90°)=0

Reactive Power=Q=VI Sin(-90°)=-VI

(-ve sign indicated that capacitor generate the reactive power)

Apparent Power=S=VI=-Q

Most of the loads are motor loads and they are actually RL (Resistive-Inductive Load). So it is very necessary to observe voltage and current behavior in case of RL loading.

Below is the section for understanding the V-I relation for RL load.

All the motors have high inductance and low resistance values so they exhibit RL loading condition. Fig 10 represents the circuit diagram when RL load is connected with the AC Supply. By simulating the circuit in MULTISIM, we get Voltage and Current sinusoidal waveforms as shown in fig 11.  Figure 11: Voltage Current Waveform in case of RL Loading Figure 12: Vector Diagram in case of RL Loading

Look at fig 8, you can see that “voltage’s zero position” as shown by “aqua-colored bar” is earlier than the “yellow-colored bar” of “current’s zero position”. It means that the current is lagging behind the voltage by an angle. But this lag angle is lower than

Power values in case of capacitive load are:

Active Power=P=VI Cos⁡θ

Reactive Power=Q=VISinθ

Apparent Power=S=VI

# Power Triangle

Power triangle is a triangle that shows Load consumption in Active, Reactive, and Apparent Powers.

## Power Triangle in case of RL Loading:

When RL load is connected with the AC supply as discussed in the previous section, Load’s Resistance consumes Active Power and Inductance consumes Reactive Power. The power Triangle is shown in fig 13. Figure 13: Power Triangle in case of RL Load

As the load’s inductance part absorbs the reactive Power, so vector is drawn upward at a 90˚ angle while the load’s Resistance part absorbs Active Power that has been shown horizontally at an angle of 0˚.

Why Happens So?

As discussed before, in the case of only Resistive load, Voltage and current were in phase or had 0˚ phase difference. So there were only Active Power and Reactive Power was zero. Moreover, in the case of pure Inductive Load, the phase difference was 90˚ and hence Active Power part became zero and the Reactive Part became maximum at 90˚.

But in the case of RL loading condition, both Resistance and Inductance are used, so both Active & Reactive Power are calculated. Apparent power is the vector sum of both these power and its magnitude can be calculated using Pythagoras theorem.