# A physical analogy for ac electrical power

## Electricity cannot be seen physically; only its effects can be seen or felt. At times, some aspects of electricity can be difficult to understand. One such phenomenon is the presence of different types of power in ac electrical systems. This article presents a physical analogy of electrical power as a refresher to help you understand these concepts further.

12/10/2003

 Key Concepts Current and voltage are in phase for resistive loads. Inductive reactance causes current to lag supplied voltage. Capacitive reactance causes current to lead the supplied voltage, thereby correcting phase angles when applied to inductive circuits. Sections: Electrical power basics Power triangle Why compensate reactive power? Power analogy Conclusion More Info: Sidebars: Sources of leading reactive power Power factor (pf): How much improvement is desirable?

Electricity cannot be seen physically; only its effects can be seen or felt. At times, some aspects of electricity can be difficult to understand. One such phenomenon is the presence of different types of power in ac electrical systems. This article presents a physical analogy of electrical power as a refresher to help you understand these concepts further.

## Electrical power basics

For a purely resistive load, such as a resistance heater, both the supplied ac voltage and the load current waveforms are in phase; they cross the neutral line concurrently.

But loads such as motors that work on the magnetic induction principle, offset, or shift, the current waveform with respect to the supply voltage waveform such that they do not cross the neutral horizontal line at the same time. This is mainly due to the inductive effect caused by the magnetic flux necessary for the operation of the motorized equipment. The inductive reactance, along with the resistive component of the load, causes the current waveform to lag behind the voltage waveform by an angle that varies from one load to another, depending on the magnitude of the inductive reactance.

Capacitance is another parameter besides resistance and inductance that affects electrical systems. Capacitance is present in all electrical systems in the form of line charging or is introduced purposely in the form of capacitor banks. Converse to the inductive effect of loads, the capacitor draws a current that leads the ac supply voltage.

Considering ac circuits, the current through a pure inductance lags the applied voltage by 90 deg, whereas the current through a pure capacitance leads the supply voltage by 90 deg. Thus they behave like enemies, opposing each other in their characteristics.

Most industrial ac electrical loads fall under two categories — purely resistive loads and inductive loads with associated resistance. In an electrical power system, capacitors are used to compensate for the ill effects of inductive loads. A synchronous machine can perform the same function (see sidebar on "Sources of leading reactive power").

## Power triangle

For an inductive load with a resistive component — due to the phase lag of the current with reference to the ac voltage — the electrical power drawn from the supply system has three components:

• Active power — Current in phase with voltage, which is the power that performs actual work

• Reactive power — Current lagging voltage by 90 deg (in quadrature), which does not perform work

• Apparent power — The vectorial sum of the two.

• These three components of power can be visualized by the power triangle illustrated in Fig. 1. Angle Φ in the right triangle represents the angle by which the load current lags the supply voltage. These power components relate to the root-mean-square (RMS) values of voltage and current and the phase angle ( Φ ) between the two.

The following equations are for single-phase power. In the case of 3-phase power, these equations (1, 2, and 3) must include a multiplication factor√3 to obtain the total power in all three phases, V being the line-to-line voltage and I the current in amperes.

Equation 1

Active Power

P=VICosΦ in kW

P is the power used by the resistive elements of the device or circuit.

Equation 2

Reactive Power

Q=VISinΦ in reactive kVAR

Q is the power discharged in the inductive elements of the device or circuit.

Equation 3

Apparent Power

S= √( P in kVA

S is the vectorial sum of the active power and reactive power.

Equation 4

Power factor

pf=CosΦ=P/S

pf is a unitless number between 0 and 1

## Why compensate reactive power?

Power factor ( pf ) is a ratio of the actual ac power, as measured by a wattmeter, to the apparent power, as indicated by an ammeter and voltmeter. It is also a ratio of resistance to impedance resulting from reactance, which provides a measure of the loss of a reactive component. Mathematically, pf is expressed as the cosine of the phase angle between the voltage applied to a load and the current passing through it. Sometimes pf is multiplied by 100 and expressed as a percentage.

In layman's terms, pf is a measure of power system efficiency. It determines how much work-producing energy P and nonwork-producing energy Q are required to power a load. Apparent power S is the total system capacity needed to perform a certain amount of useful work. For the same work producing power P , if Q can be reduced, S will automatically be reduced, requiring less system capacity (Fig. 1).

Pf correction causes angle Φ to decrease, which obviously causes pf ( cosΦ ) to eventually increase. The simplest approach to improve pf is to introduce capacitance, which is also a reactive component, to compensate for the lagging reactive component of the load. Since the current through a capacitive reactance leads its applied voltage, it brings angle Φ closer to a resistive model — a condition where current and voltage are in phase. This change modifies the power triangle (Fig. 2). The leading kVAR, which is compensation reactive power ( Q c ), subtracts from the lagging kVAR ( Q 1 ). The process is also known as reactive power compensation.

As illustrated in Figure 2, a lag angle reduction from Φ 1 to Φ 2 helps to:

• Increase the system pf from cosΦ 1 to cosΦ 2

• Reduce the unusable reactive power from Q 1 to Q 2

• Decrease the apparent power from S 1 to S 2 , releasing the system capacity by ( S 1 %%MDASSML%%S 2 ) for the same active power P .

• The saving of apparent power ( S%%MDASSML%%S 2 ) is a great benefit of compensating the lagging reactive power because apparent power is the power demanded by the system for the connected loads. Electrical utility companies charge the users on the basis of this power, metered as maximum demand (kVA) computed over a time period. Therefore, reduced apparent power means lower energy bills. Due to reduced kVA demand S 2 , the current drawn after compensation (S 2 /V) would be less than the current before compensation (S 1 /V) . Hence, further savings in energy bills result through reduced energy loss ( kWh = I ), as users must pay for kWh also in a two-part tariff of utility companies. Other benefits are smaller feeder cable size and a smaller supply transformer, for the same active (useful) power requirement.

For a resistive load, the power triangle is reduced to a horizontal line, as angle Φ equals zero because the voltage and current are in phase. Substituting angle Φ = 0 in Equations 1, 2, and 4, we see that:

Active power P = apparent power S = VI ; reactive power Q = 0 and load power factor = 1.

## Power analogy

Assume that a heavy object on a desk must be pushed by hand to move it from position A to position B. The object can be pushed by positioning the hand in line with the desk surface or at any angle from 0 to 90 deg with respect to the desk line, but not at exactly 90 deg. These situations are illustrated in Figures 3, 4, and 5.

For the inline position in Figure 3, the effort required to push the object is the least (to overcome the object weight and resistance of the desk surface) and 100% of the force is doing useful work. This is similar to a purely resistive electrical load, with no reactive power ( pf=1 ) like a resistance heater. As the hand position increases, angle Φ also increases and the reactive force comes into the picture (Fig. 4).

In this case, the horizontal component is the same useful work effort P as before, and the vertical component is the nonwork producing force Q (but pressing down on the desk). The desk must react with an equal force Q . However, the total opposing force to be offered by the desk is not only Q but the vectorial sum of the reactive force Q and the useful working force P which is the hypotenuse S , called the apparent effort S . This is analogous to an electrical load comprising resistance and inductance with the power triangle as in Fig. 1. When the hand reaches the position perpendicular to the desk line ( Φ =90 deg), the whole applied effort is wasted as reactive, just pressing down on the desk, and no useful work is done to move the object (the object cannot move). In this case, the desk counteracts only against the reactive force of the hand Q (with object weight) (Fig. 5). This is similar to a pure inductance load ( pf = 0), like a reactor (with negligible resistance).

We encounter the above analogy situations in our day-to-day life, when we need to move some object by pushing with our hand. All the hand positions and their effect on the movement of an object are easily understood.

Now let us review how strong the desk should be in each case. Depending upon how the object is pushed, the desk strength would vary. For the inline push case (Fig. 3), a lightly designed desk, just to withstand the weight of the object and friction force between the desk and object, would be enough. For angular positions of hand (Fig. 4), the reactive force also comes into the picture. The desk strength would be the vectorial sum of the friction force (of course, with weight) and the reactive force caused by the angular position of the applied effort. At the 90 deg position, the desk must be strong enough to withstand the force, which is all reactive, offered by the hand (Fig. 5). Obviously, the desk strength is analogous to the electrical system capacity (kVA).

To demonstrate leading reactive power compensation and its benefits, assume that another person applies a force down vertically on the hand of the first person when he is pushing the object at an angular position (Fig. 6).

Assume that the force helps to bring the first hand position closer to desk line, decreasing the load angle from Φ 1 to Φ 2 . The benefit of doing this is that the first hand can now push the object with reduced effort from the new position, compared to the previous position. The apparent effort exerted by the first hand has now come down from S 1 to S 2 , and hence the desk loading is also brought down to S 2 . Thus the desk loading (capacity) is released by ( S%%MDASSML%%S 2 ). This explains the analogy of pf improvement by reactive power compensation per Fig. 2.

If the force applied by the second hand brings down the first hand below the desk line, the object tends to lift off the desk while moving forward and becomes unstable. This is analogous to overcorrection when the leading (compensating) kVAR Q c exceeds the lagging load kVAR, causing overvoltage and unstable conditions harmful to the connected equipment. The pf in this case would be leading, which is undesirable.

## Conclusion

The analogy discussed in this article applies to linear electrical loads as well as nonlinear loads that draw a nonsinusoidal current (causing distortion of the sinusoidal supply voltage itself), except that the harmonic currents generated by nonlinear loads have some effect on pf .

The author is available to answer questions about this article. He can be reached at shanmuga.pandian@aramco.com . For more information on this topic, visit our website at plantengineering.com . Article edited by Jack Smith, Senior Editor, 630-288-8783.

## Capacitors

A capacitor is an electrical energy storage device. It draws a current that leads the supply voltage. The power produced by the capacitor is the leading VAR (volt-amperes reactive) that helps to compensate the lagging VAR drawn by the loads. Hence a capacitor is known as a VAR generator. For reactive power compensation, a capacitor is connected in parallel (shunt) with the loads to be compensated. A capacitor is a static device with no moving parts. Hence systems using capacitors for power factor ( pf ) improvement are known as static VAR compensators (SVC) or shunt compensation systems.

## Synchronous machines

A synchronous machine can be operated to deliver leading VAR when the field is overexcited. Synchronous machines are either used exclusively for pf improvement or operated as motors to drive mechanical loads while improving pf at the same time.

## Power factor (pf): How much improvement is desirable?

Low pf can be a result of:

Equipment design — Loads such as motors, arc welders, and fluorescent lamp ballasts have poor pf

Equipment operating conditions — A lightly loaded induction motor has very low pf in the range 0.3 to 0.5. The average uncorrected pf of industrial loads is around 0.8. Normally reactive power compensation systems are designed to correct pf to be around 0.95. Though it would be ideal to have unity pf ( pf = 1), it is not attempted for fear of the overcorrection that may occur due to changes in system parameters, such as fluctuating load reactive power demand or supply voltage variation. Overcompensation leads to harmful overvoltage and unstable conditions.

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