The children, aged seven and eight, died after touching a Western Power aerial attachment when trying to retrieve a frisbee from the roof of their house.
Western Australia's electricity and gas regulator Energy Safety has alleged the attachment was not maintained in a safe condition.
It is believed the children had been trying to when they touched the aerial attachment.
The prosecution is one of six charges brought by WA electricity and gas regulator Energy Safety against Western Power for alleged failures to ensure electrical equipment between power poles and individual buildings was installed and maintained safely.
Other offences included three instances in which Western Power workers allegedly did not connect the service cable neutral conductor following work and two instances of workers allegedly transposing the neutral and active conductors after reconnecting an installation.
People at the premises later received electric shocks, according to Energy Safety.
Western Power could also still face charges over the deaths of two women in a fire near the small town of Tenterden, 350km south-east of Perth in December 2003.
A report by Energy Safety concluded the fire was caused by a fault on Western Power powerlines that prompted molten globules to ignite dry stubble.