This comes after 43-year-old David Ngwenya appeared at the Springs Magistrates' court on Monday morning charged with the premeditated murder of Yende.
Ngwenya was denied bail and is expected back in court on Friday. He was arrested in Carletonville last week.
Yende's decomposing body was discovered last month locked inside one of the Eskom substation offices in Springs in Ekurhuleni. She had been reported missing for several days before her body was found.
Thirty-year-old Yende had been last seen when she went to her workplace in Springs on May 17. A post-mortem confirmed that she had been strangled.
Yende's family has been holding intermittent pickets outside the substation in the hopes that their questions to the utility about her mysterious death would be answered.
Numsa's acting spokesperson, Phakamile Hlubi, said the union hoped that this latest development would be the first step in helping the Yende family to achieve a sense of justice over her murder.
"We hope that the investigation will result in a successful prosecution of the alleged perpetrator and that the courts will hand down a stiff sentence for this heinous crime," Hlubi said.
"Numsa remains committed to supporting the family through this terrible ordeal and will continue to offer them whatever assistance that they require."
There were allegations that Ngwenya was a senior supervisor with Eskom management, but police said he was not an employee of the power utility.
Hlubi said if these allegations were true, Eskom has no choice but to take full responsibility for Yende's death.
"We will continue to keep up the pressure on Eskom to improve safety conditions for our members particularly those who are forced to work in isolated places," Hlubi said.