# Flexible Simulation Platform for Generating Realistic Waveforms with Voltage Notches
## 5 Comparison of Simulations with Field Measurements
### Quantitative Validation  
A more comprehensive comparison of field measurements with simulations is proposed through an approach for generating a similar set of synthetic waveforms. To facilitate quantitative characterization and subsequent comparison, a set of features is introduced to characterize voltage and current waveforms. The selection of these features is based on their relevance to the behavior of voltage notches and their alignment with standard definitions and practices in power quality analysis [5]. The proposed features include the following:  
* Voltage features:
* Maximum relative depth of notches in a cycle of phase _a:_\(d_{\mathit{cont}}\) (%): This feature represents the severity of voltage notches, as deeper notches can have more significant impacts on equipment performance. * Maximum width of notches in a cycle of phase _a:_\(\Delta t_{\mathit{com}}\) (us): The width of the notch indicates the duration of the disturbance, which affects the potential for interference with sensitive equipment. * POW of the first notch in a cycle of phase _a:_\(POW_{\mathit{com}}\) (\({}^{\circ}\)): The POW provides insight into the timing of the notch occurrence within the voltage cycle, which is important for synchronization and timing-sensitive applications. * Current features:
* The magnitude of the fundamental component of current in a cycle of phase _a:_\(I_{1}\) (A): The fundamental current magnitude is a key parameter in assessing the loading conditions and the power drawn by the rectifier. * Phase of the fundamental component of current in a cycle of phase _a:_ angle (\(\underline{l}_{1}\)) (\({}^{\circ}\)): The phase angle of the current fundamental component relative to the voltage provides information on the displacement power factor, which is critical for power system operation and efficiency. * The magnitude of the fifth harmonic of current in a cycle of phase _a:_\(I_{5}\) (A): The fifth harmonic is typically the most significant harmonic component in systems with six-pulse rectifiers [4], and it contributes to the overall distortion in the current waveform. The selection of these features focuses on time-domain characteristics of voltage notches and the most significant frequency-domain component, aligning with standard practices for power quality assessment. Other harmonic orders, e.g., 7 th, 11 th, 13 th, were considered for inclusion; however, preliminary analyses indicated that their additional contribution to the validation process was marginal, given that similar magnitudes of harmonic orders do not necessarily mean similarity in time-domain waveforms. Therefore,the features selected provide a comprehensive yet efficient set of indices for comparing the essential characteristics of voltage notches in both the simulated and measured data. This set of six features was extracted from 164 field measurement records. The resulting histograms are illustrated in Figure 18. The histograms derived from the field measurements show limited variability in certain features, reflecting the relatively constant operating point of the rectifier in the installation. This contrasts with the simulations, where a broader range of parameter variations was explored. Despite this, the simulations successfully captured the essential characteristics of the voltage notches and their dependencies on key parameters. To obtain a comparable set of simulations, parameters are varied as follows:  
* Short-circuit power \(S_{Sc}\): varied from 3.7 MVA to 4.3 MVA with uniform distribution. * Firing angle \(\alpha\): varied from 78\({}^{\circ}\) to 84.5\({}^{\circ}\). * Rectifier's rated apparent power \(S_{F}\): varied from 72 kVA to 197 kVA. * Linear load parameters: \(S_{ll}\) is randomly varied with a normal distribution (\(\mu\) = 25 kVA, \(\sigma\) = 2 kVA), and \(PF_{ll}\) is randomly varied with a normal distribution (\(\mu\) = 0.87, \(\sigma\) = 0.034). * RC-snubber: A fixed RC-snubber is designed with optimal values.