Thanks for the invitation to join this discussion.
I want to address each of the three questions:

1) What does energy poverty mean for the welfare, income-generation, and empowerment of women and girls in Africa?

Amongst other things, I propose that energy poverty means minimal ability to respond to shocks. Shocks keep or push households back into poverty. Shocks can include many things such as death or illness but also climate induced shocks through sever weather events (short or prolonged) and long term change in climate. Thus energy poverty is related to ability to adapt and demonstrate resilience. This hypothesis is quite critical because if we can make a link between energy poverty and adaptation it means that we can finance programs that reduce energy poverty using the concept of adaptation rather than mitigation.

I believe this is significant because the concept of mitigation finance worked (to a degree) under the Kyoto Protocol but it does not work well under the Paris Agreement. The idea that developed countries will buy significant amounts of mitigation from developing countries faces a number of critical challenges under the Paris Agreement, most notably due to the moral hazard created by the PA's voluntary nature (ie a selling country can lower its level of ambition in order to sell more), but there are also many other challenges which are elaborated elsewhere (see AfDB blogs for CoP22, but they are not posted yet).

However, funding these projects on the basis of adaptation is much more promising. Connecting a house to (an affordable) supply of electricity is probably the greatest single adaptation benefit we can provide - largely because it frees up women and children's time to do better things - income generating opportunities, safer food prep and storage, studying, more time at school, less time collecting firewood and lower indoor air pollution (though this assumes that households use electricity for cooking or at least move up the cooking energy ladder) etc.

2) How can these realities be integrated into the Bank’s interventions and projects to improve energy security within the Light Up and Power Africa initiative?

We have proposed the creation of an Adaptation Benefit Mechanism (ABM) as a financing instrument under the Paris Agreement. AfDB has submitted this in response to the call for inputs on Art 6.8 of the Paris Agreement and you should be able to read it here: http://unfccc.int/documentation/submissions_from_non-party_stakeholders/... under Article 6.8 (currently 3rd box down) but our submission is not yet uploaded.
The ABM is a results based payment mechanism where donors, impact investors and CSR buyers would pay for the delivery of verified adaptation benefit units over the lifetime of a project. It is very similar to the Clean Development Mechanism which stimulated massive private sector investment in mitigation under the Kyoto Protocol. The differences are that there is no compliance mechanism, the units are not fungible (exchangeable), which means they can be measured in different ways (households using a clean cooking stove for a year, households connected to a (mini-)grid etc.) and the buyer buys the story behind the unit - these differences go a long way towards addressing some of the shortfalls of the Kyoto Protocol and the CDM.
But critically, they preserve the financial instrument - an Adaptation Benefit Offtake Agreement (instead of an Emission Reduction Purchase Agreement under the CDM). This contract, signed with a AAA rated offtaker, can be used to borrow money to build the project.

Our hope is that the Parties to the UNFCCC could adopt this as a formal mechanism but even if they do not, AfDB and other Development Finance Institutions could develop it as a voluntary mechanism and use it to encourage private sector engagement in adaptation.

3) How have other organizations tackled this challenge? What can we learn from these experiences?
In my opinion, and looking from a climate finance perspective, we have tried to tackle energy poverty through mitigation. It worked to a degree but with the collapse of the Kyoto Protocol, the demand disappeared. The Paris Agreement will enter into force on 4th Nov and it has no sunset clause. Adaptation is a much more powerful lever to attract climate finance for many reasons and I think we can learn from the successes and failures of the CDM and create a new financing mechanism that would efficiently and transparently transfer funds to households and communities that are most in need of them.

We are now appointing consultants to draft the modalities and procedures and I am seeking an off-taker (donor, Corporate Social Responsibility buyer or an impact iunvestor who is willing to sign the first Adaptation Benefit Off-take Agreement to demonstrate that this new financial mechanism can work.
- If you are interested, let me know g.phillips@afdb.org