I think the terms you are looking for are ‘backward vertical integration’ and ‘horizontal integration’.
A company uses the process of backward vertical integration as it decides to independently carry out a previous production stage. It can also exhibit backward vertical integration when it controls subsidiaries that produce some of the inputs used in the production of its products.
By mentioning the construction of a mini power station, in order to provide the necessary power for the smelting process, you gave an example of backward vertical integration.
Another example is an automobile company that owns a tire company, a glass company, and a metal company. Control of these three subsidiaries is intended to create a stable supply of inputs and ensure a consistent quality in their final product. It was the main business approach of Ford and other car companies in the 1920s, who sought to minimize costs by integrating the production of cars and car parts as exemplified in the Ford River Rouge Complex.
Horizontal integration, however, is an economic term that indicates that a company integrates multiple activities at the same level in different production chains.
Regarding your example, starting to sell the electricity that the mini power plant generated, is an example of horizontal integration. The shutdown of the aluminum smelter, however, is a logical decision because in your case, selling the generated power is more lucrative than the original core business of the company.
A familiar example of horizontal integration is a fuel station that also sells grocery items. Music shops that nowadays also sell films and computer games are also a common phenomenon.
At production level, we can think of companies like Philips. They produce a large variety of products, ranging from consumer electronics to medical equipment.
The discovery of penicillin is attributed to Scottish scientist and Nobel laureate Alexander Fleming in 1928. He showed that, if Penicillium chrysogenum was grown in the appropriate substrate, it would exude a substance with antibiotic properties, which he dubbed penicillin. This serendipitous observation began the modern era of antibiotic discovery.
Last but not least, the beginning of another era, the era of the smartphones and tablets, is also linked to the vertical approach of integration: http://venturebeat.com/2010/05/06/vertical-vs-horizontal-silicon-apple-google
I hope this will help you