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Signal Processing and PQ
Z.Leonowicz, PhD
Stationarity
• Normal operation• Steady-state operation• Stationary signal• Statistical properties
Parameters
• Magnitude – rms value• Frequency – counting of zero-crossings• Distortion – spectrum estimation• Unbalance – 3phase• Flicker severity – fast changes in
magnitude < 1s• Very Short Variations (3 s – 10 min)
Voltage Magnitude
• IEC 61000-4-30 – 10 (12) cycles
• RMS
• Max. Amplitudes
RMS
• Noise , Frequency Errors
Three-phase measurements
• Mean
• RMS
• Instantaneous RMS
Frequency
• Counting of zero-crossings• PLL• Advanced methods
Waveform Distortion
• IEC 61000-4-7 IEC 61000-4-30• Measurement setup
61000-4-30
• Harmonic current when emission compared to limits
• Fourier series 10 (12) cycles, rectangular window, synchronized with frequency
• 5 Hz spacing between components
Example, arc furnace current
T1
T2HV
L
-ia
ia,ref+regulator
firingcircuit
MV
-2000
0
2000
0 0.01 0.02 0.03 0.04 0.05
Cur
rent
[A]
Time [s]
200 400 6000
0.01
0.02
0.03
Frequency [Hz]
Am
plitu
de [-
]
Example
Example
Inter/Harmonic & sub/groups
200 ms window
Harmonic Group
• 9 frequency components between n and n+1 harmonic (11 for 60 Hz systems)
• Lowest four -> Group n• Highest four -> Group n+1• Middle one divided into two groups
Harmonic Subgroup
• Harmonic plus adjacent components
Interharmonic group
• All harmonic components between harmonic of order n
Interharmonic subgroup
• Frequency components between the harmonic groups
Example (arc furnace)
Example (normal)
Disturbances in range 2-9 kHz
• IEC 61000-4-7 annex• 100 ms window not synchronized to 50 Hz• Sampling frequency 30-50 kHz• Band pass filter• 10 Hz separation grouped into 200 Hz
bands• 2100, 2300,…,8700,8900 Hz
Three-phase Unbalance
• Negative-sequence voltage
• IEC 61000-4-30
+
−
=UUUunbalance
Problems with Unbalance
1. Maximum deviation from average phase voltage – IEEE 1159
2. Difference between highest and lowest rms voltage (ref. to averaged 3 voltages) – IEEE 936
3. Ratio of negative to positive sequence –IEEE 1159
4. Maximum deviation from average line voltage , ref. to average of line voltages
Example 2% neg-seq. voltage
2
1,3,4
Example 2% neg-seq.+1,5% zero-seq.
2
1
4
Calculation of Unbalance
Unbalance
Unbalance
Positive and negative seq. voltages
Unbalance
Power Quality Indices
• THD Total Harmonic Distortion• TWD Total Waveform Distrotion• TnHD Total Non-Harmonic Distortion
• THDe – Total Even Harmonic Distortion• THDo - ?• THDv THDI
• THDnom, THDrms
Formulas
Formulas
Other indices
• Crest factor• Transformers K-factor• THD cap – Capacitor banks• THD mach – Rotating machines• Telephone Interference
factor
3-phase aggregation
• Balanced THD
• Unbalanced THD
Example
Power and PF
• IEEE 1459• Uses 3 line voltages• Instantaneous power
p(t)=vaia+vbib+vcic• Arithmetic apparent power-sum of S• Vector apparent power – Budeanu def.• PF ratio of active power to apparent
power
Budeanu powers
• Budeanu Powers-1927• Reactive
• Distortion
222BBV DQPS ++=
Problems
• No PF is correct !• Effective voltage & current
PF
Frequency Domain Analysis
• Signal is decomposed into harmonics• Discrete Fourier Transform• Window Functions
Window Size
Interpolation
• Zero-padding• Does not increase frequency resolution• Generates interpolated spectrum• Frequency resolution
tNΔ≈Δ
πω 289.0
Synchronization
Examples
Examples
Examples
Examples