# PD-Free Design of Insulation Systems: An Application to Laminated Busbars
## 2 PD-Free Design Principles  
The first information to attain for insulation system design is the extent and type of stress. As regards the electrical field, stress depends on the voltage waveform and magnitude, type of insulating material and equivalent circuit of the test object (which include insulation thickness, electrodes, and defects). Electric stress is the cause of intrinsic aging, and the electric field drives the likelihood of PD inception. PD impacts on aging activation energy, reducing the damage activation energy, which can be taken into account by the slope of the electro-thermal lifeline [4]. A general expression for electrical aging, \(A\), is given by [3]  
\[A(p)=K(E)t, \tag{1}\]  
where \(p\) is a diagnostic property, \(K(E)\) is a reaction rate constant, \(E\) is the electric stress, and \(t\) is time. Assuming that the electric stress is constant in time, a simple inverse-power life model can be devised for \(K(E)^{-1}\)[2; 3]:  
\[L=h\;K(E)^{-1}=t_{\mathrm{R}}\;\left(\frac{E}{E_{\mathrm{R}}}\right)^{-n}\; \left(\frac{f_{0}}{f}\right), \tag{2}\]  
where \(L\) is the life or failure time, \(h\) is a proportionality constant, \(t_{\mathrm{R}}\) and \(E_{\mathrm{R}}\) are the reference time and electric field (stress), often referred to a very high value, and \(n\) is the voltage endurance coefficient. The larger the \(n\), the longer life referring to the point (\(E_{\mathrm{R}}\), \(t_{\mathrm{R}}\)). If only intrinsic aging is expected, typical values of \(n\) for insulating materials used in MV and HV applications are between 5 and 10, but if and when PDs incept, then the lifeline suffers an abrupt change in \(n\) (thus of slope) to values as large as 10 or 20. This results in significant life and reliability reduction, which means premature failure.  
Equation (2) can therefore work for both intrinsic and extrinsic aging, but the inception of extrinsic aging could be so random and unpredictable that PD-free design is the most convenient approach to fit to life and reliability specifications. In this way, (2) can refer to the voltage endurance coefficient estimated through accelerated life testing carried out on specimens of the materials used for the insulation system.  
It is noteworthy that (2) holds, in principle, for AC, DC, and AC-modulated waveforms (in DC terms, \(f_{0}/f\) is not present), referring to the peak value of the electric stress [1; 3]. This is an important aspect of the model, because in the case of electrical assets fed by power electronics, both AC-modulated and DC voltage can be supplied, and sometimes both can stress the same insulation system depending on the operation time and conditions (hybrid supply). The extent of aging depends, then, on the electric stress magnitude and frequency.  
As regards the evaluation of PD inception in a test object (generated inside bulk insulation defects or affecting the insulation surface), the correct procedure would be to test PD under the same voltage waveform applied to the insulation system in service. However, it is indicated in [1] that a sinusoidal AC voltage waveform can be used also for PWMsupply provided that reference is made to the peak voltage and modulation frequency (for multi-level inverters) or carried frequency (for two-level inverters). As a matter of fact, PWM PDIV can be investigated by sinusoidal wave as long as there is a relatively small slew rate (i.e., long rise times); otherwise, it would be more appropriate to use PWM waveforms [15]. However, PDIV does not seem too much different from sinusoidal to repetitive impulse voltage waveforms on simple tests of objects where the voltage rise time does not affect field distribution (as it would occur for low-inductance objects).