Archive for February, 2010

Bitter Harvest

February 28, 2010

I read this article Bitter Harvest by Radha Rajadhyaksha, in Time of India dated 28th Feb 2010. It is about ‘Nero’s Guests’, Deepa Bhatia’s award-winning documentary film centering around farmers’ suicides, in rural India. I am quite moved by this article and I hope to see the DVD also. I give below a few excerpts from this article for your quick view.

Says P. Sainath, a Magsaysay Award winner and a chronicler of the unending human tragedy that’s unfolding in rural India, “There are 311 billionaires in India, a survey says this is the fourth happiest country in the world, and we had not one but two fashion meets this year.’’ The scathing sarcasm is laced with anger: “It’s very clear who the government exists for. When the sensex fell a few years ago, it took two hours for the then finance minister to come to Bombay by a special flight to hold the hands of weeping billionaires. It took ten years for the prime minister to visit farm households in a state where over 40,000 farmers have committed suicide since 1995 according to government data.’’

Now to visuals of a hungry child asking his mother for food, now to cattle patiently ploughing the soil:

Mute calves from Warhad are we

Watching the plunder of mother’s milk

Drenching the earth drop by drop

With our sweat yielding pearls

Yet our babies in hunger fret.

(Warhad is a village in Maharashtra)

 
There’s a clip of Sainath’s address to Parliament where he talks of how farmers were forced to kill themselves because they couldn’t get 8,000 rupees at a decent rate of interest. “And after covering such cases, I come back to my house and get a letter from my bank offering me a loan for a Mercedes at six per cent interest, no collateral required. What kind of justice is there in such a society? What kind of justice is this?’’ he demands agitatedly as Rahul Gandhi and Mani Shankar Aiyer look visibly uncomfortable. 

Deepa closes her film by cutting back to the question raised at the beginning: Who were Nero’s guests? Sainath then relates the true story of Nero, the notorious Roman emperor who, faced with a paucity of lighting at a grand party, provided it by emptying his prisons and burning undertrials at the stake. “The guests at the party were the elite of Rome, and to the best of our knowledge, nobody protested,’’ Sainath says. “I always wonder what sort of mindset it would require to pop one more grape as another human being bursts into flames.’’ Parallel drawn, he pauses for a second, and then continues: “We can differ on how to solve this problem, on even our analysis of the problem. But maybe we can make one starting point: we can all agree that we will not be Nero’s guests.’’

You can revisit your conscience by logging on to http://www.nerosguests.com. You may by the DVD and Part of the proceeds will go to farmers’ families in distress.

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Active Power, Reactive Power and Power Factor

February 19, 2010

1.0   Introduction

Many practicing electrical engineers, some even in the utility, do not have a clear  understanding of the concepts of Active and Reactive Powers and the Lagging and Leading Power Factors in electrical supply lines. Many do have an implicit knowledge of them, adequate under any normal circumstances. In this note an attempt is made to derive these concepts from basic principles of Ohm’s law and I2R power. This will also lead to a better understanding of quality issues of electrical power as supplied to customers.

2.0   Basics

Power in an electrical circuit is commonly understood as the product I2R of resistance and current-squared. By Ohms law, it is also expressed as VI or V2/R where I, V and R are the usual representations for Current, Voltage and Resistance. The above expressions remain largely true as long as we consider direct current (DC) circuits. When you consider alternating currents, the input voltage is alternating between a positive and a negative voltage, as a sine wave, (normally) at a frequency of 50 or 60 cycles per second. In this dynamic situation, two other major elements of the circuitry gain importance, namely, the Inductance (L) and the Capacitance (C). They are together called as Reactance (X) and they, along with the Resistance (R), affect the flow of current in a circuit profoundly. When a voltage is applied to a circuit with reactance (X), it takes some time for the current to get established to a steady state condition, due to induced voltage across the inductance and due to charging up of the capacitance. Even in the case of AC voltage input, the resulting alternating current reaches a steady state condition, but due to the effects of induced voltage and capacitance charging, there is a displacement between the current and voltage waveforms. This displacement is known as phase angle between the AC-voltage and the current. Coming back to our discussion on electrical power, V*I is still the power, but in this case, it is an alternating power. Initially let us consider an AC circuit only with a resistive load. As before I2R is the power consumed in the circuit. As the current is alternating the power also will be ‘alternating’. So the average power in the circuit will be R multiplied by the average of I2 over a cycle of the alternating current. This average of I2 over a cycle is knows as the Mean Square value. The square root of this current is known as the Root Mean Square value or IRMS . Same way, we can define a VRMS for the voltage wave form. Without going into rigours of mathematics, Power in a AC circuit with a resistive load, can be expressed as:

Power, P = IRMS2.R =   VRMS2/R =  VRMS * IRMS .

For a pure sinusoidal waveform, RMS value = Peak Value/ √2

3.0   Complex Power

Now let us consider an AC circuit with Resistance (R) and Reactance (X). To represent resistance and reactance together, we have a term known as Impedance (Z). As discussed earlier, power can be expressed as I2Z or V2/Z. To enable AC circuit analysis, all these parameters are expressed as vectors or complex numbers, as below:

Voltage V= V e jo= V + j0  —- (Reference)     

Current C = I e – jØ   =  Ia – jIr

Impedance Z = Z e jØ = R + jX

Total Power = V* C*  = V * I e jØ = P + jQ

[where Ø = arctan(X/R)]

The Total Power as mentioned in the above expression is normally known as Apparent Power, S, expressed in units of Volt-Ampere (VA). In Z, if reactance X is zero, then Ir will be zero, hence Ir is known as reactive current. Same way if R is zero, Ia will be zero, hence it is known as resistive current, or more commonly known as active current.

Now we have, from above,

S = V*(I cos Ø + j I sin Ø) = P + jQ = V*Ia + jV*Ir

This angle Ø is immediately recognised as the phase displacement between voltage and current waveforms introduced by the presence of reactance X in the circuit. At the instant, when ‘V’ achieves its peak value of the sine wave from, ‘I’ will lag behind and will have a value of only I cosØ. Active power, P, is the actual Active Power in the circuit, whereas Q is the imaginary power generated by the induced emf in the inductance (and the charging emf in the capacitance), as a reaction to the (sinusoidally) varying applied voltage. Hence Q is termed as Reactive Power, expressed in units of Volta-Ampere-Reactive (VAR). 

Now we are ready to write the full expressions for Power in the AC circuit with resistance and reactance as,

The Magnitude of Apparent Power |S| =  VRMS . IRMS       (VA)    

Active Power       P  =  VRMS . IRMS cos Ø,     (Watt)

Reactive Power    Q = VRMS . IRMS sin Ø        (VAR)

 The term ‘cos Ø’ is known as the Power Factor.

4.0   Effects of Frequency and Distortion

Another important factor is that the value of reactance X is frequency dependant.  The inductive reactance XL increases directly as frequency whereas capacitive reactance XC decreases inversely as frequency. The modern power systems have consumers whose loads include many more dynamic elements in addition to L and C in the form of rectifiers, non linear loads and switched mode power supplies for electronics circuitry, etc. These loads tend to distort the current and voltage wave forms away from a pure sinusoid. To analyse such circuits, the current and voltage forms are considered to have several harmonics components superimposed over the basic sine wave of 50 or 60Hz. The power calculations get further complicated if these harmonics are considerably high. Even in DC circuits the so-called ripples create similar ill-effects on power calculations.

5.0   3-Phase Power

So far we have confined our discussions to single phase AC circuits. Now let us move on to 3-Ph AC.

From now on, V and I mean only RMS values unless otherwise specified.

Trivially we may write for 3-ph AC,

P = 3 (V I) cosØ

However we should specify that both V and I are per-phase values. In a normal situation voltage between phases (known as line voltage) is more important than voltage of each phase, (Phase Voltages). In a 3-phase system,

V = V(line) = √3 * V(Phase), and hence,

P = √3 (V I) cosØ, and Q = √3 (V I) sinØ

6.0   Lagging and Leading Phase Angle

Ø is already recognised as the angular displacement between the voltage and current sinusoids of the circuit. This displacement is the result of the presence of inductance and/or capacitance in the circuit. The induced voltage across the inductance makes the current to lag behind voltage by a phase angle Ø, whereas the delay in charging up the capacitance  makes the current to lead the voltage by a  phase angle Ø. Accordingly the phase angle Ø will be (+) positive  or (-) negative. The active power P remains positive in either case, whereas the reactive power Q changes sign as per the inductance or capacitance in the circuit. It may be observed that the lagging reactive power Q is rendered as positive in the earlier expressions for complex power. Lagging Q is considered as consumption of lagging reactive power. The leading reactive power is negative and is sometimes considered as generation of lagging reactive power.

7.0   Active and Reactive Power.  

Active power is the real power resulting in actual work done. Reactive power is a necessary nuisance. The inductive load requires a higher current for the same amount of power and thus the power source also needs to supply this increased current. As this increased current does not result in any actual work done, it is termed as reactive current, Ir. The current I in the circuit is resolved into two components: one component Ia is in phase with Voltage and another component, Ir, with a phase angle of 90 degrees lag with the Voltage. This lagging reactive power requires to be compensated by the source, by ‘generating’ this reactive power. This is done dynamically by the following process: with active power remaining same (say), if reactive load increases, it results, (a) in a demand for higher current, (b) which drops the voltage all along, (c) voltage regulator at the generator end senses this, (d) generator terminal voltage gets picked up automatically or manually (for essentially the same output power), (e) phase angle between voltage and current increases, resulting in higher generation of reactive power as required by the system. But generators in the system have capacity limitations on reactive power generation and total volt-ampere generation. These may ultimately result in lower voltages all through the system, when the system reactive power requirement exceeds the total reactive capacity of generators in the system. Generation of reactive power is comparatively cost free. But to generate the same at the generator end and then to transmit it to the load end where it is required, is costing the power utility in terms of higher transmission losses. Hence the reactive power compensation is more effectively done at the load end, by using shunt capacitor banks. We know that capacitors act as leading-reactive loads. But in this context, we use them as lagging-reactive source. In general, in a utility power system, – just like we balance the active power requirement by active power generation by using frequency as our index -, reactive power requirement is balanced by reactive power generation by using system voltage as the index. In this process, in addition to generators, the shunt capacitors also contribute as lagging reactive sources. For voltage/reactive control of power systems, utilities also use a device known as Synchronous Condensers, loosely described as AC generators-without-a-prime-mover, which can generate only reactive power, both leading and lagging.

8.0   Direction of flow of Active and Reactive Power

Even though the AC current flows alternatively in both the directions, the direction of AC current is always rendered positive in the direction of power flow. In power balance calculations at any node in the power system, by a convention adopted by most of the utilities, the outgoing power from the node is taken as positive and incoming power as negative. For a detailed discussion on directions of active and reactive power flow please refer to the link below

Direction of flow of Active and Reactive Power 

The link also includes a drawing showing the quadrant principle of power factor.

9.0   Power Factor Monitoring

The power factor has already been defined earlier as cosine of phase angle between voltage and current wave forms in an AC electrical circuit. This is an important parameter that affects the quality of power supply and also the performance of the power system. Hence power factor requires to be monitored at all the important nodes in a power system and also at all bulk power supply points. But what is a power factor? It is just a measure of reactive power requirement as demanded by the various types of connected loads. In a three phase AC power utility system, the power factor is rather an ambiguous measurement for the following reasons – the phase angle between current and voltage wave forms is very likely to differ significantly among the three phases – both current and voltage waveforms may not remain strictly sinusoidal due to the presence of harmonics thus affecting the phase angle and power factor. In a way to solve some of these ambiguities in the power factor as defined (called some times as displacement power factor), another term, true power factor is defined as the ratio of total active power to total apparent power. Utility penalties and other decisions to improve performance of the power system are based on this true power factor.

In addition there are problems in online monitoring of the power factor. Power factor varies in the range of 0 to 1. The value as such does not say whether it is lagging or leading.  Some utilities use a range of ‘-1 to 0 to +1’ for power factor to go from lagging to leading PF ! In this representation the middle range of, say, -0.5 to +0.5, is a non acceptable range. The ends of this range, -1 and +1, are essentially same representing unity PF with no phase lag or lead. Such a representation for power factor as a mesurment appears ridiculous. (even the limits for LOLO, LO, HI and HIHI conditions cannot be defined for this parameter).

Some energy meter manufacturers use a range of 0 to 100 to 200 for pf; 0 to 100 representing ‘lagging pf 0 to 1’ and 100 to 200 representing ‘leading pf 1 to 0’. Many utility engineers are not comfortable with this usage. The author of this note has solved this problem in an Indian utility by defining two pfs, namely ‘Leading pf’ varying from 0 to 1 and ‘Lagging pf’ varying from 0 to 1. Both were derived as calculated points from the actual measurement of pf.

Furthermore, pf is a not an easily measurable parameter and it is a highly fluctuating parameter.  For all the above reasons, the author of this note feels pf may not serve well as a parameter to monitor and we may think of other ways to achieve monitoring of reactive power requirement in a system. May be tan Ø, instead of cos Ø, will serve this function better. Tan Ø varies from -(infinity)  to 0 to +(infinity) , as Ø varies from -90 to 0 to +90. It gives the ratio of reactive power to active power and hence may be termed as ‘Reactive Factor’. Utility penalties and other decisions to improve performance of the power system can be based on this reactive factor. This reactive factor can be easily monitored. This is only a suggestion for further consideration by power system operators and experts.

10.0   Conclusion

An attempt has been made in the above note to resolve some of the ambiguities as felt by many practicing utility and industrial electrical engineers in understanding the concepts of Reactive Power and Power Factor. The effect of high reactive requirement on the utility system and the need to penalise low pf consumers are also explained. I will be glad to receive suggestions and comments.