# Parametric PSpice Circuit of Energy Saving Lamp Emulating Current Waveform
## Materials and Methods
### Test Rig  
The measurements of the amplitude and phase shift of the fundamental and harmonic currents have to be performed in order to obtain the components of the proposed PSpice circuit. For a given ESL, these measurements have to be performed by setting five voltage levels at the lamp terminals: 0.9 \(V_{nom}\), 0.95 \(V_{nom}\), \(V_{nom}\), 1.05 \(V_{nom}\), and 1.1 \(V_{nom}\). For each current harmonic, a polynomial function has to be obtained by measurements interpolation. Similarly, polynomial functions have to be obtained for, respectively, the active and reactive current. The coefficients of these polynomial functions have to be used to select the components of the PSpice circuit according the rules that are described in the next section. Moreover, the quantities related to these components are also related to these coefficients as described in the following. With this in mind, this section describes the test rig used to set the desired voltage levels across the lamp terminals and to perform the aforesaid measurements. Figures 2 and 3 depict the measurements of the fundamental current and the odd current harmonic amplitudes up to the 13 th for both a CFL and a LED light bulb. The measurements highlighted that a linear interpolation of the current harmonics turns out to be enough accurate:  
\[ \begin{array}{l}I_{P1}\stackrel{{\text{def}}}{{=}}I_{P1}(V_{1} )=a_{P1}+b_{P1}V_{1}\\ I_{Q1}\stackrel{{\text{def}}}{{=}}I_{Q1}(V_{1})=a_{Q1}+b_{Q1}V_{1} \\ I_{k}\stackrel{{\text{def}}}{{=}}I_{k}(V_{1})=a_{k}+b_{k}V_{1} \\ k=2,\;3,\;\ldots K\end{array}  \tag{14}\]  
with \(K\) the number of harmonics considered for emulating the waveform of the current drawn from the lamp. **Remark 1**. : \(I_{P1}\) _is always positive regardless its trend in Equation (14) because it is obtained by multiplying \(I_{1}\) with \(cos(\gamma_{1})\), where the former is positive by definition while the latter has been previously proved to be positive \(\left(\text{since }-\frac{\pi}{2}<\gamma_{1}<\frac{\pi}{2}\right)\). Similar considerations are valid for \(I_{k}\) as well as for the terms in the related interpolation functions. On the other hand, although \(I_{1}\) is positive by definition, \(I_{Q1}\) may be positive or negative, it depends on \(\gamma_{1}\)._  
**Remark 2**. : _Considering the previous remark and that \(V_{1}\) is positive by definition, at least one between \(a_{P1}\) and \(b_{P1}\) in the interpolation function have to be positive. Similar considerations are always valid for \(a_{k}\) and \(b_{k}\), while for \(a_{Q1}\) and \(b_{Q1}\) are valid only when \(I_{Q1}\) is positive. On the other hand, when \(I_{Q1}\) is negative, a dual behaviour occurs, that is at least one between \(a_{Q1}\) and \(b_{Q1}\) in the interpolation function have to be negative._  
Figure 2: Measured amplitude of the fundamental current and greatest harmonics for a CFL. The linear interpolation functions are reported on the right with the related current symbol. In the test rig (Figure 4), a transformer with continuous variable transform ratio (variac) is connected to the mains voltage with the aim of emulating the variable voltage on the mains. In other words, each time a measurement has to be performed at a given voltage level, the variac is properly tuned to emulate such a voltage level across the lamp terminals. The variac feeds the ESL through a power analyser used to measure the voltage across the lamp terminals as well as to measure the fundamental and harmonic currents (in terms of amplitude and phase shift) drawn. Moreover, to simultaneously observe the current harmonics amplitude and the waveforms of the voltage and current at ESL terminals, an oscilloscope is also used. More specifically, the current drawn from the ESL has been displayed through the oscilloscope. The power analyser has a 1 A shunt probe that offers a high resolution and accuracy for testing currents as low as 80 \(\upmu\)A. This enables the meter to measure standby power as low as 20 mW at 240 V. The maximum voltage peak can reach 2 kV, with an accuracy of 20 mV.