V. Ramakrishnan 1, and S.K. Srivatsa 2 1

Transcription

1 International Journal of Power Unbalance Elecronics and and Induction Technology Machines January-June 2011, Volume 1, Number 1, pp V. Ramakrishnan 1, and S.K. Srivatsa 2 1 Department of EEE, Bharath University, Chennai , India. 2 Department of ICE, St. Joseph's College of Engineering, Chennai , India ABSTRACT: An unbalance in a three-phase system can be seen as the presence of a negative sequence. In induction machines (IM s), even a small negative voltage will cause a large amount of negative sequence current. The negative sequence will cause a synchronous frequency second harmonic pulsation and unbalanced currents in the system. In induction machine, unbalanced 3-phase stator voltages cause a number of problems such as over heating, over current and thrust on the mechanical component from torque pulsation. Therefore, the machine torque, flux, and reactive power will have a 100 Hz pulsation. Unbalance condition appear that using active crowbar protection and direct torque control. The control strategy is validated by means of simulation. Induction Generator (IG) connected in the power system under balanced and unbalanced load, symmetrical and unsymmetrical components of voltages and currents are described. The definition of unbalance factor, harmonic content and synchronous frame unbalance theory are also analyzed. Experimental results under balanced condition are presented. Keywords: Balance and unbalance IM s, negative and positive and neutral sequence. 1. INTRODUCTION Wind power is one of the most promising renewable energy sources after the progress undergone during the last decade. However, its integration into power systems has a number of technical challenges concerning security of supply, in-term of reliability, availability and power quality. An unbalance of voltage may occur on long distance power transmission lines as shown in figure 1[1]. It occurs not infrequently in the case of generating stations supplying mixed 61

2 International Journal of Power Elecronics and Technology polyphase and single phase loads. The predetermination of the performance of three-phase induction motors under such conditions is a matter of importance that there is a reduction in the maximum load which an induction motor is capable of carrying safely when supplied with unbalanced voltages, but the extent of this reduction has not received the attention which it merits. It is carried out experiments on the performance of induction machines on unbalanced votages, but they have assumed that the load limit of the motor is reached when the current in one phase reaches its full load value, and hence their experiments underrate the performance of the motor [2]. It is treated the matter analytically and derived certain simple formulae to predetermine the output, but his results have not received conclusive experimental verification. The various conditions of symmetrical components, unsymmetrical components, balance and unbalance conditions, positive, negative, zero sequence and harmonic pulsations, voltage unbalance theory and factor have been discussed. The output of the simulation result has been verified by experimental calculation. Graphical method of resolving an unsymmetrical voltage system into two symmetrical systems is also described. igure 1: Physical Connection in the Power System 2. INDUCTION GENERATOR CONNECTED IN THE POWER SYSTEM UNDER UNBALANCED LOAD The unbalancing of the balanced voltages of the alternator was effected in two ways: (1) by injecting into one of the phases of the alternator an opposing e.m.f. derived from the secondary of a 62

3 transformer whose primary was connected across the alternator phase itself, this condition corresponding to pure unbalance of the star voltages with no phase shift; (2) by injecting into one of the phases a quadrature e.m.f. obtained from the secondary of a transformer whose primary was connected across the other two phases, as shown in igure 2.2 igure 2: Diagram Connections, UTr, Connecting Transformers, AA, AB, AC, Line Ammeters, VAB, VBC, VCA, Line Voltmeter, WA, WB, WC, Wattmeter s, VA, VB, VC, Star Voltmeters Measures were made of the star voltages, the line voltages, the line currents, and the power in each phase and the output. The method of procedure was to maintain a constant unbalance and load the motor gradually, taking all the readings until the currents far exceeded the normal value. While the unbalanced-phase voltage is small, large negative-sequence currents can result due to low negative sequence impedance of an induction generator. These large currents eventually can cause unbalanced heating (hot spots) in the machine windings, which can potentially lead to failure. Unbalanced-voltage operation will also create a pulsating torque which produces speed pulsation, mechanical vibration, and consequently, acoustic noise. The tests were repeated for various degrees of unbalance. The practical experimental calculations are given in Experimental Results chapter. As is well known, an unbalanced three-phase system may be resolved into two balanced component systems, one of which 63

4 International Journal of Power Elecronics and Technology has the same phase sequence or phase rotation as the unbalanced system, while the other has the opposite phase sequence. or the sake of brevity, we shall in what follows speak of the first balanced component as the direct phase or direct rotational system, and of the second as the reverse phase or counter-rotational system. The unbalance factor of a system is defined to be the ratio of the reverse phase voltage (or current) to the direct phase voltage (or current) and is frequently expressed as a percentage. The graphical method of relations connecting output and percentage unbalance is shown in igure 3. igure 3: The Graphical Method of Relations Connecting Output and Percentage Unbalance (A) When local losses equal to full load losses (B) When current in an one phase reaches full load value 64

5 3. TURBINE SPEED CLASSIIED IN TWO TYPES The wind turbine technology can mainly be classified into two sections. ixed speed wind turbine Variable speed wind turbine In 2003, 46% of the wind turbines installed were variable speed wind turbines with double fed induction generator and its market share is going to increase. It has several advantages over the other types. Now days Doubly ed Induction Generator (DIG) stator of such wound rotor machines is directly connected to the electrical grid and therefore, it is extremely sensitive to voltage disturbances due to voltage sags [3]. When unbalanced sags occur, the main problem is that very high current, torque, power oscillations appear at double the electrical frequency forcing a disconnection. Such oscillation is provoked by the negative sequence components injected by the unbalanced disturbance [4]. Unbalance condition appear that using active crowbar and direct torque control. A method based on a disturbance refection controller is proposed into compensate the 2*ω e ( ω e electrical angular velocity) oscillation produced by unbalances, by adding a feed forward component to the current controllers. A control strategy is proposed by choosing certain current reference values in the positive and negative sequences. So that torque and the DC voltage are kept stable during such unbalanced sequences. Both rotor and grid side converter are considered; detailing the control scheme of each converter which considering the effect of the crowbar protection. The control strategy is validated by means of simulation. Unbalance load condition, to control the DIG, on separating the positive and negative components of all the current and voltages for DC /AC converter both the grid side and rotor side[5]. But grid side converter control is not considered, to keep the DC bus stable is proposed, based on compensating the rotor power delivered by the rotor side converter in the grid side converter. 65

6 International Journal of Power Elecronics and Technology 4. (A) SYMMETRICAL COMPONENTS ortes cue method of symmetrical components is used in calculation in this paper. X 0 X + X XA a a X B a a X C Where X A, X B, X C are the phasors of unbalanced phasor system. X 0, X + and X_ are phasors of symmetrical components (zero, positive ands negative sequence respectively and q 1 < 120º is unit complex operator. The level of unbalance is described by current unbalance factor (more precisely known as sequence current unbalance factor), ρ i, which is given as the modulus of ratio of negative to positive sequence currents (same as for negative sequence voltage unbalance factor, ρ v ) as shown in igure 4. (1) igure 4: One Single-Phase Load Connected to Low Voltage Moreover, in non-counterweighted systems the zero sequence current (voltage) unbalance factor ε i (ε v ) is defined as the modulus of ratio of zero to positive sequence currents (voltages). Io Vo ε i 100, ε υ 100 (2) I V

7 The analysis of a three-phase circuit in which phase voltages and currents are balanced (of equal magnitude in the three phase and displaced 120º from each other) and in which all circuit elements in each phases are balanced and symmetrical is relatively single. Since the treatment of a single phase leads directly to the three phase solution positive, negative and zero sequence system of three successive application of a will rotate through 360º as shown in igure 5 [5]. igure 5: Symmetrical Components Positive and negative sequence impedance of a transformer one equal and zero sequence is also equal to the positive sequence impedance provided these are a through circuit for the earth currents and the compensating currents can flow: otherwise the impedance is infinite. (B) Unsymmetrical Components Unsymmetrical faults which occur as single line to ground faults, line to line faults or double to ground fault cause unbalanced currents to flow in the systems. The absence of a grounded neutral at the generator does not affect the fault current. It the generator neutral 67

8 International Journal of Power Elecronics and Technology is not grounded zero sequence impedance is infinite and zero sequence voltage is indeterminate, but line to line voltages may be found since they contains no zero sequence components as shown in igure 6. igure 6: Unbalanced Current Can be Resolved into under Balanced Condition (C) Under Balanced Condition The DIG is attached to the wind turbine by means of a gearbox. Stator windings are directly connected to the grid, which the rotor windings are controlled to a back-to-back converter. The converter is composed of the grid side converter connected to the grid and the rotor side converter connected to the wound rotor windings. The converter set points are established by the so called high level controller. It user the knowledge of the wind speed and the grid active and reactive power requirements to determine the optimum turbine pitch angle and the torque and reactive power set points referenced to the converter. The rotor side converter controls the torque and reactive power, which the grid side converter controls the DC voltage and grid side reactive power. The rotor side back-to-back converter can control both reactive power injected by the stator by controlling the rotor currents and the reactive power injected directly. To the grid with grid side converter, reactive power to deliver through the stator which keeping a low or null reactive power set point in the grid side converter. 68

9 (D) 5Under Unbalanced Condition Unbalanced sags imply negative sequence components in all the relevant quantities. Therefore, important oscillations appear in torque, active and reactive power. Such oscillations have a pulsation of 2*ω e. In order to mitigate such oscillations, an approach taking into account the negative sequence quantities is required that approach has been applied to the rotor side converter of a DIG. igure 7: Asymmetrical Components Unbalanced Condition of Voltage Vector Analyzes of a whole back-to-back converter taking into account both the positive and negative sequence components and proposes a technique to control optimally both the DC bus voltage and torque when unbalanced voltage sags occur [6]. igure 8: Asymmetrical Components Unbalanced Condition of Current Vector 69

10 International Journal of Power Elecronics and Technology The positive and negative sequence components calculation is done by using the Clarke transformation, rotating either e jωet or e jωet, and finally applying a notes-filter of 2*ω e to eliminate the opposite sequence. PI controller is used, tuned according to internal mode control. or a time constant T, the parameters obtained yield K p L / T; K i R/T. for the rotor side voltages are limited according to the rotor side voltages can be applied using standard space vector pulse with modulation technique. 5. PROBLEMS CAUSED BY VOLTAGE UNBALANCE Three-phase utility unbalance can be a problem in rural areas, where induction wind generators are likely to be located. In induction machines, unbalanced three-phase stator voltages cause a number of problems, such as overheating, over-current, and stress on the mechanical components from torque pulsations. Therefore, beyond a certain amount of unbalance, induction machines must be derated or removed from the network. In the case of a grid connected induction generator, this can exacerbate the grid balance. In addition, any time generation is removed, it means less money for the generation company. In this chapter, quantification of unbalance and how to analyze unbalanced induction machines is presented. 6. PER PHASE EQUIVALENT CIRCUIT UNBALANCES THEORY Using symmetrical component theory [7], a three-phase system can be represented as the sum of zero, positive and negative sequence circuits. When the three-phase system is perfectly balanced, only the positive sequence is present. When the system is unbalanced, one or both of the zero and negative sequence will be present. or a star connected machine without a neutral connection, no zero sequence current will flow. Therefore, for the purpose of performance analysis of a star connected machine without a neutral connection, the zero sequence can be ignored. Induction machines are very susceptible to a stator voltage unbalance. This can be easily understood by using the per phase equivalent circuit of a cage-type induction generator for the positive 70

11 and negative sequences, as shown in igure 9. With any induction machine, the larger the slip speed between the rotor conductors and the air-gap flux, the greater voltage and current impressed on the rotor. This is easily seen in igure 9(a), as the equivalent rotor resistance decreases with increasing slip. igure 9: Induction Machine Per Phase Circuit for (a) Positive Sequence; (b) Negative Sequence The negative sequence voltage is rotating in the opposite direction of the positive sequence. This gives rise to a flux component rotating in the negative direction. This negative sequence flux is rotating counter to the rotor, which appears as a very large slip. Therefore, the equivalent rotor resistance for the negative sequence is much smaller than the equivalent rotor resistance for the positive sequence, shown in igure 9 (b). Even a small amount of negative sequence voltage will give rise to a large amount of negative sequence current. This extra negative sequence current can cause over-heating, and it unbalances the stator currents. 71

12 International Journal of Power Elecronics and Technology In addition to the unbalanced currents, there will also be a periodic pulsation in the torque and reactive power. This pulsation will occur at twice the synchronous frequency. This can be understood better using more advanced tools: space vectors and dq theory. 7. DEINITION O UNBALANCE ACTOR There are many standards for defining the amount of unbalance for a three-phase system. Some methods focus on ease of calculation in the field (usually ignoring phase shift), others are more mathematically rigorous. The National Electrical Manufacturers Association (NEMA), defines line voltage unbalance (LVUR) [8] as ( Vab VLavg Vbc VLavg Vca VLavg ) max,, V Lavg Vab + Vbc Vca where, V Lavg 3 This method has the advantage of being easily calculated in the field, as it depends only on phase-phase voltage magnitudes. However, it does not account phase shift. In this research, the amount of unbalanced for a three-phase system is defined as the magnitude of the negative sequence over the magnitude of positive sequence. This is called the unbalance factor 2 and for voltage is denoted as voltage unbalance factor( VU) and for current as current unbalance factor( IU) Referring to igure 9: (3) (4) VU V V s2 s1 (5) The advantage of this definition of unbalanced is that it accounts for both a magnitude unbalance (where one of three-phases is off nominal in magnitude) and a phase unbalance (where one of the phases is not 120 degrees separated). It should be noted that not all unbalances are created equal. A 5 % VU for one system with an off-nominal voltage (like a voltage sag in one phase) and a five 72

13 percent VU for another system with a phase-shifted phase can affect a machine quite differently. However, the definition of is chosen as the best overall method of quantifying unbalance. As an interesting side note, for a system with perfect 120 phase delay between phases, and in the case where there is an over or under-voltage condition in a single phase, then LVUR is approximately twice VU. 8. SYNCHRONOUS RAME UNBALANCE THEORY A three-phase unbalance will add a double synchronous frequency harmonic to synchronous frame quantities. or example, a voltage unbalance (either by magnitude, phase, or in combination) in a 50 Hz system will add a 100 Hz harmonic to all the synchronous frame voltages and currents. This in turn adds a 100 Hz harmonics to the machine torque and power. A space vector is defined as V s (t) V a (t) + V b (t)e j120 + Vc(t)e j240 (6) These variables are shown as a function of time to emphasize that they are instantaneous values. Each phase quantity can be said to be equivalent to the sum of a zero, positive, and negative sequence component, represented by the subscripts 0, 1 and 2 respectively. V a (t) V s0 cos (ω syn t + θ 0 ) + V s1 cos (ω syn t + θ 1 ) + V s2 cos (ω syn t + θ 2 ) (7) V b (t) V s0 cos (ω syn t + θ 0 ) + V s1 cos (ω syn t + θ 1 ) + V s2 cos(ω syn t + θ ) (8) V c (t) V s0 cos(ω syn t + θ 0 ) V s1 cos (ω syn t + θ 1 ) + V s2 cos(ω syn t + θ 2 120) (9) Substituting (7) through (9) in to (6), we get () 3 ()() 1 2 Vs t ( ˆ j ω synt+θ ˆ j ω synt+θ Vs 1e + Vs 2e ) (10) 2 73

14 International Journal of Power Elecronics and Technology Here then it is seen that a space vector can be represented as a sum, of two synchronously rotating vector: one proportional to the positive sequence component, rotating in the positive direction, and another proportional to the negative sequence component, rotating in the negative direction. These two vectors will add constructively and destructively twice per revolution, thus causing the double frequency harmonic in torque and power. The d and q components of the vs space vector are defined as the scaled reflections of the space vector on to the dq reference frame (see igure 7) V sdq V + jv 2/3( V + V e j120 sd sq a b Substituting (7) through (9) into (10): V sdq j240 j d ) + Vc e e θ j() ω synt+θ1 sd + sq 3/2( s1 V jv V e ) + V e j() ω synt+θ2 jθd s2 e (11) (12) or a dq frame synchronized to the stator voltage space vector ( grid flux oriented, see Chapter 4, θ d simply the angle of v s. j()() ω synt+θ1 2 ( ˆ j ω synt+θ img V 1 s1e + Vs 2e ) Θ d tan ()() 1 2 ( ˆ j ω synt+θ ˆ j ω synt+θ real Vs 1e + Vs 2e ) Θ d tan ˆ ˆ ˆ V cos() ω t + cos() θ + Vˆ ω t + θ V 1 s1 sin() ω synt + sin() θ1 Vs 2 ω synt + θ 2 s1 syn 1 s2 syn 2 (13) (14) This equation becomes quite complex to analyze when there is an unbalance (i.e., v s2 0). Because the dq axes are aligned to analyze with the stator voltage space vector, at all times. The d-axis voltage is V sd V + V + (2V V 2/3 Vs 3/2 cos(2)) ω t + θ + θ 2 2 s1 s2 s1 s2 syn 1 2 (15) 74

15 It is interesting to note here that contains mostly a DC and second harmonic component, but due to the non-linearity of (13), there will be higher order harmonics as well. igure 10 shows vsd for a system with a 0.05 stator voltage balance factor (VU), and a 50 Hz synchronous frequency. igure 11 shows the harmonic content. Clearly, it can be seen that while there are higher order harmonics, the second harmonic (at twice the synchronous frequency, 100 Hz) is dominant. Similar results are shown for the rotational speed?d as shown in igure 12. and 13. igure 10: V sd for 0.05 Stator Voltage VU igure 11: V sd Harmonic Content 75

16 International Journal of Power Elecronics and Technology Looking at igure 10 through igure 12, it is then easy to see how this second harmonic propagates through the entire circuit, causing second harmonic pulsations in the reactive power and torque (active power). igure 12: for 0.05 Stator Voltage VU d igure 13: Harmonic Content d It s shown then that higher order harmonics resulting from instantaneous alignment can likely be safely neglected. Also, it may be that the positive sequence alignment strategy may result in less 76

17 of the second harmonic disturbance, since it does not add any noise through ω d. However, this may be offset by the fact positive sequence alignment has a second harmonic in v sq. All things considered, the instantaneous alignment is effective and simpler to implement. or more discussion on unbalance for positive sequence alignment, see [9] and [10] 9. EXPERIMENTAL RESULTS The test consisted in determining how far the induction motor is capable of correcting the unbalance in the supply voltage. Induction motor on unbalanced supply through Lab Experimental IM s values is given below. A three phase star connected 440 Volt (line to line), 10 HP 50 Hz six pole induction motor has the following constants in ohms per phase. R Ω/phase, R Ω/phase, R m 120 Ω/phase, X 1 X Ω/phase, X m 13.2 Ω/phase. or a slip s (operation as a motor), compute I, V A, I m, I 2, speed in r/min, Total output torque and power, power factor, Total three-phase losses and efficiency. The applied voltage to neutral is V o Voltage V/Phase; 3 3 As per U.S.A Standard value adopted in calculation, Line to Line Voltage 220V, Phase Voltage value º V / phase 3 R 0.14 Z 2 2 jx2 j0.35 S j º Ω Z m jrmxm j(120)(13.2) º Ω R + jx j13.2 m m 77

18 International Journal of Power Elecronics and Technology Z in I 1 Z Z R m jx 1 + Z Z m + 2 ( º )( º ) j º º º Ω V o 1 o Z in V A V 1 I 1 (R 1 + jx 1 ) º A 127 0º ( º )( j0.35 ) º V I m º º A º V º I 2 A º A Z º The speed (ns) r/m The Total Torque T m 90[ I ] R πn S s 2 90(20.83)(0.14) π(1200)(0.025) Total Mechanical Power N-m/red 2πTm P m ω n * Tm 2π(1170)(58.01) Watts Hoarse Power HP

19 Power actor (p.f) cos θ; where, θ V I rad, X C 1 ωc Q V R 2 2 sin θ var, Watts, V I P VI I R 2 2 V Q VI I X var X (θ) Lead indicates that θ is negative i.e., p.f. 0.8 lead Complex Power S P + jq + S θ VA Z R + jx; X C 1 ; X L L ωc π ω π Total losses in the motor P Loss 3 V R A m I R + 3 I R Watts Efficiency 3 ( )2 +3 (24.01) 2 (0.30) + 3(20.83) 2 (0.14) watts Watts η Pm 7107 m P + P m Loss 0.872, 87.2% (Induction motor) The efficiency of the 3-phase induction motor has been determined under balanced conditions. If any fault occurs in one of the phases, unbalance condition arises and hence the efficiency can be determined only after bringing to balance condition. It was considered desirable to observe experimentally what the resulting balance voltage is when the unbalanced supply is corrected by means of a reverse phase series booster, and how far this value agrees with the direct phase component as obtained from the vector analysis of the unbalanced voltages. 79

20 International Journal of Power Elecronics and Technology 10. CONCLUSION Thus, a controller of doubly fed induction generator used in wind turbine has to withstand disturbances, have capabilities discussed earlier, and keep turbine operational. It is also desirable to have controller, which can guarantee to perform despite known variations in system parameters and wind. DIG Unbalance Compensation Control Design presents the modifications to the basic control that are designed to handle the unbalanced voltage. An unbalance in a 3-phase system can be seen as the presence of a negative sequence. In induction machines, even a small negative sequence voltage will cause a large amount of negative sequence current. The negative sequence will cause a synchronous frequency second harmonic pulsation in the system and cause unbalance current. The amount of torque pulsation and reactive power pulsation are almost linear function of voltage unbalance factor. This is another advantage of using VU to quantify unbalance but it was observed that it is important for both reactive power and active power to be compensated. If only one at the loop is compensated, the stator current will become very much distorted. Also it was observed that the compensation loops tend to decrease the total harmonic distortion slightly. It may be worth further investigation. irst and foremost would be the grid side rotor converter. It may be advantageous to implement a special control on this converter to deal with the extra harmonics that will be active on the DC link. Also, it may be possible to unbalance the current drawn from the converter to complement the unbalance stator current to effectively completely balance the current into the system though this may again impact the DC link voltage. It is an area worth investigating. In addition, it should be possible to extend the compensation control to dq control used in power systems, such as three-phase synchronous rectifiers. The induction motor is tested & verified at laboratory as per USA standard and it gives the result as follows: Total Torque N-m/radian, Total Mechanical Power 9.53 HP, Pf 0.8 lead, Total Losses in the Motor Watts, Efficiency of the Motor %. 80

21 presents and explains the problems caused in induction machines when connected to an unbalanced supply. The mathematical impact of unbalance is explained, tested in the lab, and the amount of unbalance is quantified. REERENCES [1] S. D. Rubira and M. D. McCulloch, Control Method Comparison of DWG Connected to the Grid by Asymmetrical Transmission Lines, IEEE Transactions on Industry Applications, 36, No. 4, July/August [2] A. Von Jouanne and B. Banerjee, Assessment of Voltage Unbalance, IEEE Transactions on Power Delivery, 16, No. 4, October [3] YiZhou, Paul Bauer, Jan A. erreira, and Jan Pierik, Operation of Grid- Connected DIG Under Unbalanced Grid Voltage Condition, IEEE Transactions on Energy Conversion, 24. No: 1, 2009, pp [4] Oriol Gomis-Bellmunt,Adria Junyent-erre,Andreas Sumper and Joan Bergas- Jane, Ride-Through Control of a DIG under Unbalanced Voltage Sags, IEEE Transactions on Energy Conversion, 23. No. 4, 2008, pp [5] Jaime. A. Peralta, ranciso de Leon, and Jean Mahserdjian, Unbalanced Multi Phase Load-low Using a Positive-Sequence Load low Program, IEEE Transactions on Power Systems, Vol. 23. No: 2, 2008, pp [6] Jesus Lopez, Eugenio Gubie, Pablo Sanchis, Xavier Roboam and Luis Marroyo, Wind Turbines Based on DIG under Asymmetrical Voltage Dips, IEEE Transaction on Energy Conversion, 23. No. 1, 2008, pp [7] B. Wollenberg, A. J. Wood, Power Generation Operation and Control, John Wiley & Son s, New York [8] C. Y. Lee, Effects of Unbalance Voltage on the Operation Performance of a three Phase Induction Motor, IEEE Transaction on Energy Conversion, 14. No: 2, June [9] H. S. Song, K. H. Nam (1999), Dual Current Control Scheme for PWM Converter Under Unbalanced Input Voltage Conditions, IEEE Transactions on Industrial Electronics, 46, No: 5, October1999. [10] H. S. Song, K. H. Nam, Instantaneous Phase-Angle Estimation Algorithm under Unbalanced Voltage-Sag Conditions, Generation, Transmission and Distribution, IEE Proceedings 147, Issue 6,, Nov , Page(s);