Electricity-Access is a growing concern in developing countries of Sub-Saharan Africa where approximately 563million people (8% of the global population) lack electricity. Many use fossil-fuel generators and/or solar-home-systems (SHSs) with storage. Given the observed excess and unutilized electricity generated from these SHSs, a novel community peer-To-peer (P2P) electricity-market using automated negotiations is presented as a solution to improve access to electricity. Software agents representing World Bank Tiers 1-4 electricity-Access households bilaterally negotiate electricity price and quantities applying five different negotiations heuristics. Simulation results show 65-100% trade of the excess generation; with Tiers 1-2 (low-income households) negotiating sufficient electricity (1-1.1kWh/day) at the least market-price of £0.35/kWh to move to Tier 3. Likewise, the Tier 3 household agent negotiated 1.5kWh/day sufficient to meet its needs. This novel electricitymarket model can help drive the United Nations goal of affordable, sustainable and modern energy for all by 2030.