# Effect of Harmonics on Ferroresonance in Low Voltage Power Factor Correction System--A Case Study
## 3 System Description
### Measurement Setup  
Voltage and current waveforms were recorded using the two DEWESOFT SIRIUS synchronized acquisition systems, which comply with the IEC 61000-4-30 class A standard. Currents were measured with Rogowski coils and current clamps via the high-speed low voltage input (HS-ACC), while voltages were measured directly via the high-speed high voltage input (HS-HV). The sampling frequency was 20 kHz. The general data are as follows:  
DEWESOFT SIRIUS: 4 xHS-HV, 4 xHS-ACC, ADC type: 16-bit SAR, sampling rate: up to 1 MS/s simultaneously  
SIRIUS HS-HV: range: \(\pm\)800 V, bandwidth: 2 MHz, accuracy up to 10 kHz: \(\pm\)0.1% of reading \(\pm\)0.05% of range  
SIRIUS HS-ACC: range: \(\pm\)1 V, bandwidth: 500 kHz, accuracy: \(\pm\)0.05% of reading \(\pm\)0.02% of range  
Rogowski coils: range: \(\pm\)30\(\backslash\)\(\pm\)3000 \(\backslash\)\(\pm\)3000 A, 100\(\backslash\)10\(\backslash\)1 mV/A, accuracy: \(\pm\)1% of range, 10 Hz-50 kHzDC/AC current clamps: range: \(\pm 140\,\pm 1400\) A, \(10\,\backslash 1\) mV/A, accuracy: \(\pm 1.5\%\) of reading, DC--10 kHz  
AC current clamps: range: \(\pm 5\) A, \(0.2\) V/A, accuracy: \(5\) mA-\(0.5\) A \(\pm 2\%\) of reading, \(0.5\) A-\(1\) A \(\pm 1\%\) of reading, \(1\)-\(12\) A \(\pm 0.5\%\) of reading, \(2\) Hz-\(10\) kHz  
Related to Figure 6, the secondary voltage \(U_{f}\) of transformer T1 and the capacitor voltage \(U_{C}\) were measured directly at the inputs HS-HV. The reactor voltage \(U_{L}\) for each phase was calculated in the data acquisition software DewesoftX as:  
\[u_{L}(t)=\left\{\begin{array}{ll}0,&\text{if capacitor stage is switched off}\\ u_{f}(t)-u_{C}(t),&\text{if capacitor stage is switched on}\end{array}\right. \tag{2}\]  
The medium voltage \(U_{fMV}\) was measured at the inputs HS-HV from the second secondary of the voltage instrument transformers installed on the MV busbar. The ratings of the voltage instrument transformers are \(10/\sqrt{3}//0.1/\sqrt{3}//0.1/3\), Yynd, \(0.5/3\)P, \(25\) VA, \(6\)P, \(25\) VA. The first secondary is normally used for operation and protection measurement, while the second is in open delta connection.  
The secondary current \(I_{f}\) of transformer T1 was measured at the inputs HS-ACC with AC current clamps and installed current transformer \(2000/1\) A, \(15\) VA. The medium voltage feeder current \(I_{fMV}\) was measured at the inputs HS-ACC with AC current clamps and installed double core current transformer \(400/1/1\) A, \(5\)P10, \(10\) VA, \(0.5\)Fs10, \(10\) VA. The stage current \(I_{S}\) was measured at the inputs HS-ACC with Rogowski coils and DC/AC current clamps.  
The reactor flux \(\phi_{L}\) for each phase was calculated in DewesoftX data acquisition software as an integral of the reactor voltage. A low-pass filter was used instead of the pure integrator to eliminate drift problems and the need for initial values [35]. The gain of the low-pass filter was adjusted to achieve the same behavior in the high-frequency region as the integrator. The transfer function in the continous time domain is given as:  
\[G_{LPF}(s)=\frac{\Psi_{L}(s)}{U_{L}(s)}=\frac{1}{s+\omega_{c}} \tag{3}\]  
where \(\omega_{c}\) is the cut-off frequency set at \(2\pi\) rad/s.