Power Notes 5

Power Notes 5 - .SZPW ry "235 “Lon-oil Unit 04 Power...

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Unformatted text preview: .SZPW ry "235 “Lon-oil Unit 04 Power Factor When a RL load is supplied with a sinusoidal voltage, Figure '1. RL load with supply source ***** u(t)= ‘5 UcosaJt then the supply current can be decomposed into a component that is in-phase with the voltage and a component shifted by 90 degrees i(t) = x5 Icos(a)t— w) = = filcosp cosmt + filsingo sinaJt = = 13.10) + i(t) The in—phase components is equal to ia(t) =fi1acoswt, Ia=Icos¢=§, and it is called the active current. The component shifted by 90 degrees = 1r: Ism¢=EQ]_. is called the reactive current. These two currents are shifted mutually by 90°, thus the supply current RMS value is equal to I = JI§+13 = ./(§>2+(—g—)2. When the load has the active power P = U 1 cos qr, then the supply has to provide the voltage of the RMS value U and the current of the RMS value I. It means, that the source could be loadad with the active power U I, but due to the current phase shift, (0, the active power of the load is equal to P = U 1 cos w. Therefore, the ratio _ P _ W is referred to as the power factor (PF). It is a measure of the supply utilization. It can be expressed as [a P A = =‘an====, :lPZ + Q2 J]: + Ir2 The presence of the reactive power, Q, with associated reactive current, 1}, increases the supply current and its RMS value. Consequently, the power factor, A, declines from unity value. There are three main harmful effects of low PF, i.e., the increased supply current RMS value in circuits as shown in ) Figure 1 . These are: 1. Enhanced voltage drop, Au, on the supply source impedance. 2. = cosw, 2. Enhanced active power loss, AP, on the supply source resistance. 3. Enhanced required power ratings of the supply equipment or its reduced capability to supply customers. These three affects of the low power factor make energy delivery more expensive. More expensive equipment might be required and more fuel is needed because of the active power loss in the supply. These three affects of the low power factor make energy delivery more expensive. More expensive equipment might be required and more fuel is needed because of the active power loss in the supply. The difference in the voltage drop in a circuit that at the same active power, P, and the same load voltage RMS value, U, operates at low PF, 2. = 0.5 or at high PF, 2. = 0.95, is shown in the diagram of complex RMS (CRMS) values in Figure 2. Figure 2. Diagrams of CRMS values (a) at low PF and (b) at high PF ***** Observe that the internal voltage RMS value, E, of the source that supplies the load with low power factor has to be higher than the internal voltage of the source that SUpplies the load with high power factor. To balance the voltage loss, the intemal voltage RMS value, E, of the supply has to be enhanced. There are some operational cost related to the load voltage control by an increase in the distribution voltage. All components of the increased cost of energy delivery at low power factor are on the side of energy supplier. Thus, low power factor reduces the supplier’s revenue. Therefore, power utilities are concerned with the low power factor and have various policies to enhance it. Power Factor Improvement. Power factor at supply : 'S’upélyséotitée‘ ' Figure 3. Circuit with capacitive compensator ***** terminals can be enhanced by retrofitting the load equipment with equipment that has an enhanced power factor or by reactive power compensators. Over-exited synchronous motors can serve in three-phase systems as such compensators. In single-phase systems with RL loads only shunt capacitor banks, connected as shown in Figure. 3, can by used for such a purpose. The shunt capacitor, C, loads the supply with a reactive current of the opposite sign than the reactive current of the RL load, thus it reduces the reactive component of the supply current. This reduces the phase-shift of the supply current and its RMS value as shown in Figure 4. Figure 4. Diagram of CRMS values for compensated load ***** To improve the PF from ,1 = cosq) to zl’= cosqo', the capacitor should change the reactive current of the supply by the value IC= mCU=Isingo—Isin(o’. If the load has the active power P = U I A, then the compensator should have capacitance equal to P U21 [sin(cos'1/1) - sin(cos'1/1,)] . a) C: In particular, to improve the power factor to unity, the capacitance should be equal to — P L wU2/1 wUZ' Benefits of a higher power factor have to be paid by the investment cost of the compensator. Therefore, a trade off these benefits and the compensator cost is needed and consequently, compensators usually have capacitance lower than C0. Its choice is based on investigation of the active power and voltage loss in the distribution system versus compensator capacitance C. The dependence of the active power loss and the voltage loss in the distribution system on capacitance C is illustrated in Figure 5. C0 sin(cos'1/1) = Figure 5 show the change of the PF, ,1, power loss and voltage loss versus capacitance C for a normalized load that at voltage U = 100V has the active power P = 10 kW at power factor ,1 = 0.5. The load is supplied from a sinusoidal voltage source that has the short circuit power 40 times higher than the load active power P and the reactance to resistance ratio, Xs/R, = 3. With such parameters and the frequency normalized to ah = 1 rd/s, the capacitance needed for total compensation, Co = 1.7 F. Voltage loss in Figure 5 is defined as the difference of internal voltage, e, and load voltage, u, RMS values, i.e., E - U. The voltage loss in the supply declines with the compensating capacitance at an almost constant rate. For over-compensated loads this voltage loss could even be negative. One could notice, however, that the voltage loss, E— U, in the supply source has different meaning than the voltage drop, E-U, on the supply source impedance, since, AU: E—U ¢ E—U=ZSI’. In particular, the voltage drop, Zs I ’, cannot be negative. our! to “AFR/k3le ‘ 0.9 0.3 --- Power Factor 0.7 0.5 -- Voltage Loss 05 DA 03 Q2 Max. Pow. Loss = 316 W 0.1 Max. Volt. Loss = 4.9 V a C u 0.5 1 1.5 2 F Figure 5. Plot of power factor, voltage loss and power loss versus compensator capacitance C $$$$$ D Figure 5 shows that the active power loss can be reduced more than three times by improving the power factor to unity, although in the capacitance range around Co the power loss reduclion is not significant. Therefore, to reduce the cost of the compensator, a capacitance, C, below the value of C0 is usually selected. ...
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This note was uploaded on 02/06/2012 for the course EE 3410 taught by Professor Staff during the Fall '08 term at LSU.

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Power Notes 5 - .SZPW ry "235 “Lon-oil Unit 04 Power...

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