Hola Chicos,
I think that I am going to be nailed here. Your CLXs power consumption is only less than 5 Watts from the wall socket or from your AC power conditioner. There is no current drain. I have a good power cables. I use Transparent brand on most of them. But these cables are connected to my power amps and preamps. Are connected to the devices that drain current. Here, I have noticed big changes when I did use thicker cables to power these devices. Also, my Signature Plus 3.5 BPT Balanced Power Conditioner, has a very heavy gauge power cord connected to the Mains AC socket wall.
I did hear an improved, with much dynamics and clear, transparent, with much quality sound, with no compression, full of nuances and much resolution. The bass improved substantially. The mid range opened up, with a truly sense of wide stage with a truly sense of 3D. The power cables should be connected to the devices that drain current. The power cables for the CLS, or the CLXs where only the current drain is less than 5 Watts, these cables do not need to be thick or special.
Think of this: The electrostatic speakers need a bias voltage circa 2KV. When the audio signal is applied to the speaker, there is a special circuit that detects this, and turns on the bias voltage circuit. This operation last only 1 second to charge completely the energy that it is needed for full operation. The voltage represents the water in a swimming pool. It is just quantity voltage, it is steady charge. No drain. The current is when you start to empty the pool, and this is not the case when powering the CLXs.
This is simple physics, it is wise to have a good power source and good contact from the wall or Power Conditioner. A simple rule is to touch the cable's plug after 15 to 20 minutes of operation. When you touch the connector, and it is a little warm, this cable should be change for a thicker gauge cable. All connectors should be cold. A little warm or hot, is telling that you should change them.
I wish that I could speak more fluent English, so I could express better myself, so please, excuse me!
Happy listening!