The migration of professional audio systems towards Ethernet-based networking allows optimisation software to maximise key performance indicators (KPIs) such as the power required for particular applications. In this study, we focus on minimising peak power requirements by the use of supercapacitors (SCs) for demand smoothing with Class D audio amplification of at least 600 W root mean square (rms) output. Depending on the content, a 600 W maximum r.m.s output music programme is shown to draw just 60 W (10% of peak rms) on average. Our studies used music programme statistical analysis and probability theory, which enabled the minimum value of SC for a predetermined voltage drop to be found exactly and hence minimise costs/size requirements. The use of energy storage in audio (and other contexts) is not new of course, but we believe the probabilistic calculation and use of unprecedented SC reservoir capacitance values is original. This power averaging technique then allows Power-over-Ethernet (PoE) to be used, particularly the IEEE802.3 bt type 4 variant and AES67 Ethernet over powerline. As commercial PoE systems are now available for this standard, we have constructed a complete 600 W r.m.s class D sound system which has type 4 PoE as its sole power input. Again, PoE sound systems are not new but the extension to very high powers has not been reported to the best of our knowledge. In the powerline context, we describe a first-of-its-kind, outdoor venue, 5000 W peak rms, Class D audio system with > 1 km of standard 5 A mains cable, AES67 audio transport over powerline and lithium-ion energy storage at the amplifier location. An added benefit is that solar assistance can be used.