Here are three funding opportunities for off-grid companies and/or projects with deadline in June 2016:

Toyota Foundation — International Grant Program 2016
The themes for 2016 are multi-generational and multi-cultural Inclusion in communities. There is also an "open field" for additional subjects (for example, the Foundation has previously funded grants on sustainable energy). 
Eligible countries: Brunei, Cambodia, China (including Hong Kong and Macau), Indonesia, Japan, Laos, Malaysia, Mongolia, Myanmar, Philippines, Singapore, South Korea, Taiwan, Thailand, Timor Leste, and Vietnam. 
Application deadline: 10 June 2016. 
Read more (https://www.toyotafound.or.jp/english/program/asian_neighbors.html)

U.S. Department of State — Womens’ Entrepreneurship in Renewable Energy (wPOWER)
wPOWER aims to empower women as entrepreneurs for technologies in clean energy at the grassroots level in poor and rural communities.
Eligible countries: East Africa, Nigeria, and India. The program is open to nonprofit NGOs and educational institutions in the U.S. and internationally, and to public international organizations. 
Application deadline: 10 June 2016. 
Read more (http://www.grants.gov/web/grants/search-grants.html?keywords=wpower)

Climate Technology Initiative (CTI PFAN) — Clean Energy in Asia
The Asia Forum for Clean Energy Financing invites entrepreneurs, start-up and existing companies, project teams, and consortia with environmentally beneficial business to submit business plans for the development of clean energy and related technologies for South and Southeast Asia. 
Eligible countries: Bangladesh, Cambodia, India, Indonesia, Laos, Malaysia, Maldives, Mongolia, Myanmar, Nepal, Philippines, Sri Lanka, Thailand, and Vietnam. Short-listed projects will receive coaching from professional experts to improve the business plans in preparation for a financing forum. 
Application deadline: 20 June 2016.
Read more (http://cti-pfan.net/event/call-for-proposal-afcef-7/)