40 CHAPTER 3 IMPROVEMENT OF LOAD POWER FACTOR USING FACTS CONTROLLERS 3.1 INTRODUCTION The low power factor effects on transmission line, switchgear, transformers etc. It is observed that if the power plant works on low power factor, the capital cost of plant in generation, transmission and distribution systems is increased. Higher the capital charges means, higher the annual fixed charges, which will increase the cost per unit or the effect of all headed over the consumer who has to pay more. Thus it is always an advantage for both the consumers and the suppliers to work at higher power factors. Usually the suppliers encourage the people to work at improved power factors by adopting a two part tariff, charging the consumer on his maximum demand in kva and the number of units consumed by him. The maximum demand of the consumer is measured with a maximum demand meter, installed at consumer s premises; the reading of meter is taken annually. If the consumers will try to work at low power factor, for the same power from the mains, he will draw more current or his kva demand is increased for which he has to pay extra. This is how the consumer is discouraged to have low power factors. The power factor is the ratio of active power component (kw) & apparent power component (kva) of any A.C. system. B kvar o kw kva Fig 3.1 Power Triangle
41 Referring Fig 3.1 Power triangle OAB, OA-represents active or real component of power (kw). OB- represents reactive or wattless components of power (kvar) & AB-represents the apparent power component (kva). Basically power factor is defined as the cosine of power triangle which must be right angled triangle. Therefore: from Fig 3.1 kw = kva cos Φ (3.1) kvar= kva.sin Φ (3.2) kvar = kw tan Φ (3.3) kva= (kw) (3.4) cosφ The power factor will be of leading nature, if the current is leading the voltage, it will be of lagging nature, if current is lagging the voltage and unity if current and voltage are in phase with each other.[28] 3.2 FACTORS AFFECTING LOW POWER FACTOR a) As most of the electrical applications are with induction motors, they work, on lagging power factor of the power supplied. b) The transformers at power stations, sub-station etc draw the magnetizing current which causes the total current of the line to be lagging the line voltage c) The industrial heating furnaces particularly induction heating will have very low lagging power factor consuming system. d) Arc lamps, fluorescent lamps, mercury vapour lamps etc. operate at lagging power factor. e) Transmission and distribution lines & feeders will also have more inductive effect, hence main power flow through both the systems will be at low power factor.
42 3.3 EFFECT OF LOW POWER FACTOR ON POWER FLOW & POWER CONSUMPTION Let us consider an alternator delivering 1000 A at 500 V. (single phase). Then its Rating = VI/1000 = 1000x500/ 100 = 500kVA (3.5) If the alternator is loaded at unity power factor, then the load supplied: kva x p.f = 500 x 1= 500 kw (3.6) If the load p.f is 0.6 lagging, then the power supplied by alternator is: Load supplied = kva x p.f = 500 x 0.6 = 300 kw At 0.6 p.f lagging (3.7) By the above computation, it is observed that alternator is developing its maximum current and voltage even at 0.6 p.f lagging and supplying only 60% of its total capacity therefore in order to supply its actual power say (500 kw) the alternator is to be over leaded and the conductors connected between alternator and load must be provided with maximum cross-sectional area to withstand the overload current. Hence for the given amount of power generation or transmission, the size of alternator is bigger and large conductors are to be used for the power transmission. In other words, greater will be the cost of generation and transmission. That is the reason that the suppliers always stress the consumers to increase the power factor with their utilities[28]. 3.4 EFFECTS OF LOW POWER FACTOR ON TRANSMISSION LINES Effect on generators: The generated kva and kw capacities will have low power factor. Because of this, the power supplied by the exciters is increased, copper losses in the generator winding are increased, and so, the efficiency of generator is decreased.
43 Effect on transmission lines : For the transmission of power, more current has to be sent at low power factor. As the line has to carry more current, its cross sectional area should have to be increased, which increases the capital cost of the transmission line. Also increased current increases the line losses and decreases the line efficiency. The line drop is also increased. Effect on transformers: The transformers which are connected with transmission lines and with distribution feeders will have the effect of decrease in kw capacity with the decrease in power factor also increase in line voltage Effect on switchgear and bus bar The cross-sectional area of bus bars, and the contact bars enlarged for the same amount of power to be delivered at low power factors. Effects on prime movers The generator will develop more reactive (kvar) or wattles power with low power factor, but certain amount of energy is needed to develop this power, which is being supplied by the prime mover. This energy supplied by the prime mover is idle and represents as dead investment. Working on low power factor decreases the efficiency of prime mover. [29] 3.5 BENEFITS OF POWER FACTOR IMPROVEMENT The following are the benefits, listed with improved power factor. i) The kw capacity of transformers and the lines is increased ii) The efficiency of generating plant is increased iii) The overall consuming cost per unit is decreased iv) The regulation of transmission lines and distribution feeder is improved
44 v) The kw capacity of alternator is increased. vi) The energy of the prime mover is better utilized. 3.6 METHOD OF IMPROVING POWER FACTOR By the use of static capacitors The static capacitors are connected in parallel with the supply mains, which draw the current, leading the voltage by 90 0 and neutralize the reactive lagging current component of the load current, hence to improve the power factor nearest to unity. By the help of synchronous condenser The synchronous condenser is also called as synchronous motor. This motor draws the current from the mains at leading power factor, there by neutralizing lagging reactive component of the load current. It also develops the mechanical power Phase advancer These are the special commutator machines, which improve the power factor of induction motors. FACTS controller These are the powerful power electronics devices which are used to improve the power factor of bulk or small quantity of power transmission and distribution lines [30] Reactive Current for the improvement of p.f Considering an a.c. circuit with inductive load as shown in Fig. 3.2 and its vector diagram as in Fig 3.3 I K Ir (Iµ) 230V150 HZ a.c. supply Ic c r Load L Fig 3.2 Circuit diagrams with inductive load
45 A Reactive components IsinΦ Active components IcosΦ V Fig 3.3 vector diagram to represent current components I Let the current supplied to the circuit is I Amp. and let this current is lagging the voltage by an angle of Φ 0. The current supplied to this circuit can be resolved into two components one along the voltage vector and the other is in quadrature. The component along the voltage vector is known as in phase vector or active component of current which is I.cos Φ and the other is known as reactive component of current which is -I sin Φ. They are shown in Fig 3.3 In order to improve the power factor, angle Φ should be decreased to zero for unity power factor as cos Φ= cos.0 =1 In order to decrease the angle Φ the reactive component of current, I sin Φ is to be decreased. This is obtained by introducing leading current, Ic through capacitor of magnitude equal to the reactive component (I ) in the circuit as in Fig 3.2 observed in Fig 3.3. This leading current, I c will lead the voltage exactly by 90 0 and will be in phase opposition to I the reactive inductive component of current. Now I c = +I sin Φ & I = -I sin Φ will neutralize each other leaving supply current (I) in phase with V. Theory gives the power factor is unity. Thus the required leading reactive current to compensate the existing lagging reactive current is given as I c = I [ 1-(p.f) 2 ] [ 31] (3.8)
46 3.7 POWER FACTOR IMPROVEMENT By the method of introducing leading components of current in common component of current is commonly employed. It is obtained by connecting a number of capacitors in parallel across the main supply at the end. The value of the total capacitance required for improving the power factor nearest to unity for a given power P, in the network at a frequency f and voltage V is determined as follows P= VI (p.f) (3.9) I = P (3.10) V(p.f) C = P.tan Φ (3.11) 2 v 2 It is observed from equation (3.11) that the capacitance required for improving the power factor is inversely proportional to frequency f this shows that the static capacitors are best suited for high frequencies also it is seen that the capacitance required is inversely proportional to the square of the operating voltage. Thus the total value of the capacitance required per phase in three phase system depends upon the nature of connections, whether star connected or delta connected. In practice it is observed that the delta connection is preferable. A calculation of capacitance of a capacitor to improve the power factor from 0.73 lagging to 0.93 lagging is done. 3-ph supply 3-ph I.M Star connected Capacitor bank delta connected Fig 3.4 Delta connected static capacitors bank
47 Motor & elements parameters Out put of I.M =400 hp Voltage (L-L) = 2000V Frequency of supply = 50 Hz Working p.f = 0.73 lagging Improved p.f = 0.93 lagging Capacitance of each capacitor = 57.47 µf Total number of capacitor in series = 4 Each capacitor voltage = 500 V Frequency of supply = 50 Hz. Efficiency of motor = 85% Motor line current with working p.f = I L1 = 142.8A (3.12) Ip 1 = 99.96-J 101.98 (3.13) Motor line current with required improved p.f = 0.93 I L2 = 107.43 A (3.14) Phase current (I p2 ) =I p2 = 99.91- J39.48 (3.15) Reactive current to be neutralized = I µ = I µ1 - I µ2 = 62.56A (3.16) The bank of capacitors used to improve the power factor is connected in delta, therefore phase voltage (V ph ) = 2000V, but each unit of capacitors connected in series is as shown in Fig 3.4.The reactive current in each phase of the bank is I µp = 62.56 = 36.12 A (3.17) 3 Let Xc be the capacitive reactance of each capacitor X c = 500 = 13.846 (3.18) 36.12
48 C = 229.95µF (3.19) Thus the capacitance of each capacitor of the bank is [C =229.95 = 57.48µF] (3.20) 4 Hence the capacitor bank of each capacitor must have 57.48µF capacitance to improve the p.f from 0.73 lagging to 0.93 lagging. [32] 3.7.1 Improvement of p.f by FACTS Controller approach 98.1 kva 62.89 D A ph Is I d 98.1 kva L d 20.10 kvar 58.5mH S C V ph =115v 229.95 F B N Booster converter Single phase diode bridge rectifier Fig 3.5 FACTS Controller Circuit Diagram Supply current (I s ) = kva = 98.1 x 1000 = 84.93A (3.21) V p 1155 Thus Rating of rectifier = V p I p /1000=S = 98.1 kva. (3.22) Diode or Inductor current (I d ) =Rectifier Rating = I d = 62.89A (3.23) 1.35x Vp Peak current (I pk ) = Form factor x I d = I pk = 69.81A (3.24) Voltage across diode & inductor (V d ) = V ph = V d = 816.71V (3.25) 2 Inductance of inductor (L d ) = V d = 58.5mH (3.26) 4 f I pk Switching rating = rectifier rating = 98.1 kva. (3.27) Capacitor rating Data I n 2 = (38.11) 2, ω n = 2π50 = 314.16 rad/sec (3.28) Where I n = 1.55x kvar/v d = 38.11A
49 C = 229.95 µf (3.29) Therefore capacitor rating = I n 2 = Q = 20.10 kvar (3.30) 2 fc B Q=20.1 kvar S=98.1 kva o A P Fig 3.6 Power Triangle for FACTS sin Ф = kvar = 20.10 = 0.20 (3.31) kvr 98.10 Ф = sin -1 (0.20) = 11.53 0 (3.32) p.f = cos Ф = cos (11.53 0 ) = 0.98 [33] (3.33)
50 3.8 SIMULATION RESULTS continuous power current 1 model Voltage measurement V PQ I current 2 current Active & Reactive power Fig 3.7 Simulation diagram for improvement of Power Factor 0.6283 1 V 2 I magnitude signal angle V_fundamental magnitude signal angle I_fundamental X k- cos Deg->Rad sin X X Display I/2 Gain 1 PQ Fig 3.8 Circuit Diagram with Inductive load
51 Fig 3.9 Input current waveform for Inductive Load (Time on x-axis, Current on y-axis) Fig 3.10 Real and Reactive power waveforms (Yellow colour line = Q, Purple colour line=p) (Time on x-axis, P-Q on y-axis) 0.7333 1 V 2 I Magnitude Signal angle V_fundamental Magnitude Signal angle I_fundamental X + - K- cos Deg->Rad sin X X Display I/2 Gain -0.6799 Display 1 1 PQ
52 Fig 3.11 Simulated diagram of Delta connected static capacitors bank Fig 3.12 Waveform of Improved active & reactive power quality response (Yellow colour line = Q, Purple colour line=p) (Time on x-axis, P-Q on y-axis) 120V 60Hz T 100VA 120V/24V D1 D2 100mH D3 D6 D4 D5 Vo 200µF D2&D4; Circuit Current measurement V d1 V d2 V PQ I Active & Reactive power Scope1 Scope2 Max Fig 3.13 Simulated diagram of FACTS (UPFC)-Single phase rectifier
53 [1.1 4e+007] Display 1 V abc 2 I abc X P 1 PQ + - 1.16 4e+007 + - Display1 + - X 1/sqrt(3) Fig 3.14 Simulated diagram of FACTS Controller Approach (RP/AP= tan Ф) The Fig 3.14 computes the 3-ph instantaneous real power and reactive power using the following equations: 1) P=Va 1 la+vb 1 lb+vc 1 lc 2) Q=1/sqrt(3) (Vbc 1 la+vca 1 lb+vab 1 lc) Note: Equation-2 is valid only for a balanced & harmonics-free system.
54 Fig 3.15 Real & Reactive power waveform of UPFC with Max. p.f (Yellow colour line = Q, Purple colour line=p) (Time on x-axis, P-Q on y-axis) Fig 3.16 Output waveform of diode rectifier voltage with FACTS controllers (Time on x-axis, V dc on y-axis) 3.9 CONCLUSION In this work the power factor is computed by static capacitors approach and FACTS controllers approach theoretically & verified the results by simulation. The simulation results are noted. In comparison, it is found that the FACTS controller approach is better than the static capacitor approach for power factor correction. Hence the FACTS controllers methods can be implemented for the power factor improvement in both transmission & distribution lines effectively. The comparative evaluated results of power factor are tabulated in Table 3.1 Table 3.1 Evaluation of Power factor
55 S.No Name of the circuit Power factor 1 Inductive load 0.73 2 Induction motor with C- bank 0.93 3 Using FACTS (UPFC controller) 0.98