Lecture 10: Grid Faults and Disturbances

Transcription

1 / 2 Lecture : Grid Faults and Disturbances ELEC-E842 Control of Electric Drives and Power Converters (5 ECTS) Jarno Kukkola and Marko Hinkkanen Spring 27

2 2 / 2 Learning Outcomes After this lecture you will be able to: Explain modeling concepts for unbalanced 3-phase grid voltages Explain the relation between the positive- and negative-sequence grid-voltage components and symmetrical or asymmetrical grid faults Detailed knowledge of this lecture is not required in the exam

3 3 / 2 Outline Introduction Unbalanced Grid Conditions Grid Faults Grid-Voltage Harmonics

4 4 / 2 Introduction Ideally, the phase voltages at the point of common coupling (PCC) are Sinusoidal Symmetrical With constant frequency and amplitude In a real grid, a grid converter has to withstand Unbalanced phase voltages Voltage harmonics Grid faults Converters should provide reliable response under the faults and distorted conditions In renewable power generation, the grid converters are required to support the grid under the faulty operation conditions

5 5 / 2 Outline Introduction Unbalanced Grid Conditions Grid Faults Grid-Voltage Harmonics

6 6 / 2 Balanced Grid Conditions Symmetrical phase voltages u ga (t) = u g cos(ω g t) u gb (t) = u g cos(ω g t 2π/3) u gc (t) = u g cos(ω g t 4π/3) Corresponding space vector u s g (t) = u ge jϑg(t) = u gα (t) + ju gβ (t) rotates at the angular frequency of ω g = 2πf g Angle of the vector is ϑ g (t) = ω g t Amplitude is constant u s g (t) = u g Voltage (p.u.).5.5 u ga u gb u gc Imaginary part (p.u.).5.5 β.5.5 Real part (p.u.) > ϑ g u s g α

7 7 / 2 Unbalanced Phase Voltages Asymmetry in phase voltages, for example: u ga (t) =.25u g cos(ω g t) u gb (t) = u g cos(ω g t 2π/3) u gc (t) = u g cos(ω g t 4π/3) Voltage (p.u.).5.5 u ga u gb u gc β Corresponding space vector u s g (t) = u gα + ju gβ has elliptical locus Neither the amplitude u s g (t) nor the rotation speed is constant Imaginary part (p.u.).5.5 u s g >ϑg α.5.5 Real part (p.u.)

8 8 / 2 Oscillations in the Magnitude and Angle 8 Oscillations in u s g, u s g and d( us g )/dt under unbalanced conditions Frequencies of the oscillating components are multiples of 2ω g Voltage (p.u.) Magnitude (p.u.).5 Angle (deg).5 u ga gb u gc 9 8 u s g u s g Frequency (Hz) 9 5 d( u s g )/dt

9 9 / 2 Positive and Negative Sequences Unbalanced grid voltage can be expressed as a combination of positive and negative sequence components β u s g (t) = us g+ (t) + us g (t) Amplitudes = u g+ e jωgt + u g e j( ωgt+φ ) u s g+ (t) = u g+ and u s g (t) = u g Positive-sequence component rotates counterclockwise at ω g Negative-sequence component rotates clockwise at ω g Imaginary part (p.u.).5.5 u s g u s g u s g+ u s g u s g+ u s g.5.5 Real part (p.u.) α

10 / 2 Active and Reactive Power in Unbalanced Conditions Let the grid current and voltage contain positive and negative sequences Complex power is = 3 2 u s g = us g+ + us g = u g+e jωgt + u g e j( ωgt+φ ) i s g = i s g+ + i s g = i g+ e j(ωgt+φ ) + i g e j( ωgt+φ 2) s = 3 2 us g is* g = 3 2 (us g+ + us g )(is g+ + i s g ) [ u g+ i g+ e jφ + u g i g+ e j( 2ωgt+φ φ ) } {{ } constant } {{ } oscillating + u g+ i g e j(2ωgt φ 2) }{{} oscillating Active power is p = Re{s} and the reactive power is q = Im{s} Active and reactive powers may oscillate at 2ω g With proper control of i s g oscillations from p or q can be eliminated ] + u g i g e j(φ φ 2 ) }{{} constant

11 / 2 Voltage (p.u.) Power (p.u.) Current (p.u.) u ga u gb u gc i ga i gb i gc 2 p g q g

12 2 / 2 Consequences of Unbalanced Grid Conditions in Control Control is often synchronized with the grid-voltage vector Phase-locked loop (PLL) is used for tracking the vector PLL is designed to estimate positive and negative sequence components (instead of the oscillating magnitude, angle, and frequency) For controlling instantaneous active and reactive power, the converter should be able to inject and control positive- and negative-sequence currents

13 3 / 2 Outline Introduction Unbalanced Grid Conditions Grid Faults Grid-Voltage Harmonics

14 4 / 2 Faults and Variations in the Grid Symmetrical faults: 3-phase voltage dips and overvoltages Asymmetrical faults: -phase and 2-phase faults, line-to-ground, line-to-line, and 2-phase line-to-ground short circuits... Fault seen by the converter depends also on the impedances Z S and Z F Phase angle jumps may happen, if the X/R ratios of Z S and Z F are different Frequency variations (unbalance between load and generation) Source Z S PCC Z F Fault

15 5 / 2 Symmetrical Faults Depth and length of the dip can vary Phase angle jump is present in the figures on the right side Voltage (p.u.).5 Voltage (p.u.).5 u ga gb.5 u ga gb u gc u gc Imaginary part (p.u.).5.5 β.5.5 Real part (p.u.) u s g Pre-fault Under fault α Imaginary part (p.u.) β.5.5 Real part (p.u.) > u s g α Angle jump Pre-fault Under fault

16 6 / 2 Asymmetrical Faults -phase, 2-phase and asymmetrical 3-phase dips Depth and length of the dip can vary Positive and negative sequence components Phase angle jumps may appear Voltage (p.u.).5 Voltage (p.u.).5 u ga gb.5 u ga gb u gc u gc Imaginary part (p.u.).5.5 β u s g.5.5 Real part (p.u.) u s g+ u s g Pre-fault Under fault α Imaginary part (p.u.) β u s g u s g+ u s g Pre-fault Under fault.5.5 Real part (p.u.) α

17 7 / 2 Propagation of the Voltage Dips Voltage dips are propagated through transformers in electric power system Transformers between the fault and the converter may affect the voltage dip experienced by the converter (depends on the type of the transformer) PCC PCC2 Source Z S Z F Fault

18 8 / 2 Outline Introduction Unbalanced Grid Conditions Grid Faults Grid-Voltage Harmonics

19 Distorted Phase Voltages Phase voltages can have harmonics, e.g., u ga (t) = u g cos(ω g t).2u g cos( 5ω g t) +.u g cos(7ω g t) Voltages u gb and u gc are shifted in phase Corresponding space vector u s g (t) = u gα + ju gβ has non-circular locus Amplitude u s g (t) and rotation speed are pulsating Voltage (p.u.) Imaginary part (p.u.).5.5 u ga u gb u gc β > ϑ g u s g α.5.5 Real part (p.u.) 9 / 2

20 2 / 2 Positive and Negative Sequence Harmonics In distorted conditions, the voltage includes harmonic components u s g (t) = m Amplitudes u g,m u s g,m (t) = u g,me jϑg,m(t) Angles ϑ g,m (t) = mω g t + φ m Typical harmonics m = ±6n +, n =, 2,... Harmonic components rotate counterclockwise for m > and clockwise for m < m = ± fundamental frequencies Imaginary part (p.u.).5.5 β u s g,7 u s g,5 u s g.5.5 Real part (p.u.) u s g+ α

21 2 / 2 Consequences of Harmonics in Control PLLs are designed to estimate fundamental frequency components and to reject harmonic-frequency components Total Harmonic Distortion (THD) of the converter current is typically limited Impact of grid-voltage harmonics on THD is reduced by proper design of current (or power) control Harmonic components may cause oscillations in the active and reactive power