standard methods pq calculation.pdf
TRANSCRIPT
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Signal Processing and PQ
Z.Leonowicz, PhD
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Stationarity
• Normal operation• Steady-state operation• Stationary signal• Statistical properties
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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)
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Voltage Magnitude
• IEC 61000-4-30 – 10 (12) cycles
• RMS
• Max. Amplitudes
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RMS
• Noise , Frequency Errors
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Three-phase measurements
• Mean
• RMS
• Instantaneous RMS
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Frequency
• Counting of zero-crossings• PLL• Advanced methods
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Waveform Distortion
• IEC 61000-4-7 IEC 61000-4-30• Measurement setup
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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
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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 [-
]
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Example
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Example
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Inter/Harmonic & sub/groups
200 ms window
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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
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Harmonic Subgroup
• Harmonic plus adjacent components
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Interharmonic group
• All harmonic components between harmonic of order n
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Interharmonic subgroup
• Frequency components between the harmonic groups
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Example (arc furnace)
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Example (normal)
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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
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Three-phase Unbalance
• Negative-sequence voltage
• IEC 61000-4-30
+
−
=UUUunbalance
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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
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Example 2% neg-seq. voltage
2
1,3,4
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Example 2% neg-seq.+1,5% zero-seq.
2
1
4
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Calculation of Unbalance
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Unbalance
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Unbalance
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Positive and negative seq. voltages
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Unbalance
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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
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Formulas
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Formulas
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Other indices
• Crest factor• Transformers K-factor• THD cap – Capacitor banks• THD mach – Rotating machines• Telephone Interference
factor
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3-phase aggregation
• Balanced THD
• Unbalanced THD
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Example
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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
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Budeanu powers
• Budeanu Powers-1927• Reactive
• Distortion
222BBV DQPS ++=
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Problems
• No PF is correct !• Effective voltage & current
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PF
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Frequency Domain Analysis
• Signal is decomposed into harmonics• Discrete Fourier Transform• Window Functions
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Window Size
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Interpolation
• Zero-padding• Does not increase frequency resolution• Generates interpolated spectrum• Frequency resolution
tNΔ≈Δ
πω 289.0
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Synchronization
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Examples
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Examples
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Examples
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Examples