FLY by night over Uttar Pradesh in northern India, the country’s most populous state, and its cities appear as dazzling islands. In between, however, lies an inky sea. Perhaps two-thirds of Uttar Pradesh’s 200m people have no regular electricity. In India as a whole, 700m, or more than half of the population, suffer unreliable connections to the national grid, or none at all.

On paper, plans exist for linking the country’s northern and southern grids. That would help, yet nobody expects rural India to be properly plugged in for a long time yet. Meanwhile, villagers soldier on with paraffin lamps, which harm lungs and emit a dim light that is of little use for school homework. Darkness breeds danger, so women stay home after the sun goes down. A lack of electricity limits business, as markets and shops close early. Banks have been ordered to reach villages, but they need electricity. And though most Indians have mobile phones, many struggle to recharge them. Lots of India’s 400,000 mobile-phone towers are powered at least in part by diesel generators, which are noisy, dirty and costly. Power can account for two-fifths of a mobile-phone company’s operating costs.

Official figures boast that 90% of villages are electrified, but that means little. If just a tenth of a village is on the grid, plus a few homes of low-caste or minority families, officials count it as entirely electrified. It is also quite another matter how much electricity actually flows down the wires.

The lack of grid power grows more severe as rural incomes rise and feed demand. Diesel prices are up by a fifth since September because subsidies have been cut, pushing up the cost of running generators. What is more, the government has told mobile-phone firms to switch half of their rural towers, and a fifth of those in cities, to green energy by 2015. Around 150,000 will need a new power supply.

With the state incapable of providing electricity, the good news is that aid donors, “social entrepreneurs”, NGOs and investors are rushing to promote rural off-grid power. Arunabha Ghosh of CEEW, a Delhi consultancy, counts 250 companies in the field, mostly relative newcomers. A few try mini-power stations that use hydropower or burn rice husks or methane from cow dung. The vast majority, however, bet on solar energy using increasingly cheap equipment, often made in China.

One approach is to stick panels on a village roof and run wires to a few dozen nearby homes, allowing each seven hours of light a day plus a phone charger. Brian Shaad of Mera Gao Power, a firm in Uttar Pradesh, says even poor households can pay for this, by switching spending from paraffin. The firm has so far wired up some 9,000 homes. Mr Shaad says he sees “kids studying, coming from the dark homes to the light ones to do homework”. He also tells of a woman who, thanks to being able to work later under LED lights, has tripled her overnight production of the samosas she sells at market each morning.

Others work on a bigger scale. Omnigrid Micropower Company (OMC) has built ten solar plants that power phone towers and sell electricity to around 3,000 nearby households, as well as to businesses. It plans 4,000 more such plants in the next three years, mostly in Uttar Pradesh. They will light millions of households. It begins by renting out charged lanterns, fans and battery boxes, laying cables to households and businesses later.

The impact is striking. In one Uttar Pradesh village with a solar plant a shopkeeper claims his income soared once he opened late, while his wife and other women took to making bangles in the evening. A tailor in a mud house says longer stitching hours lifted his monthly income by nearly half, to 7,000 rupees ($120).

Last year in nearby Atrauli village, on the edge of mango woods, OMC opened a solar plant to power two phone towers. Once a local businessman, Pradeep Singh, got electricity to his petrol station, he opened it 24 hours a day. Next he rented a dozen lanterns for his bar. Sales rose and costs fell.

For Mr Singh, in neatly ironed shirt and white trainers, the sky is now the limit. On July 1st he opened a college for 550 undergraduates, built on a field behind the plant. Mr Singh claims he will outshine the competition. Electricity means not only light: “I offer fans to the students,” he says. “No other college will offer that.” Some 165 students have enrolled. Now Mr Singh plans a rural mall for 20 small businesses, such as a motorcycle repair shop, restaurants and a cinema. A Swiss firm is mulling a water-purification plant. A state bank is moving in. OMC hopes to develop solar-run irrigation for farmers, plus a scheme to rent villagers cheap tablet computers to serve as televisions. Village leaders hope that electricity and the economic growth it brings will help slow the rush of youngsters to Lucknow, the state capital, 50 kilometres (about 30 miles) away.

If anything, the government’s lack of interest has fed the boom. With cheap land and little regulation in rural areas, OMC can set up a solar plant for just $165,000, which it can then run for decades at little cost. Unlike with grid-supplied power in India, no one blocks or diverts off-grid electricity for the sake of bribes or some sort of electoral gain.

Such schemes are of little help to industry or other heavy users of electricity. Nor is solar power yet as cheap as the grid. For all that, the rapid arrival of electric light to Indian villages is long overdue. When the national grid suffers its next huge outage, as it did in July 2012 when hundreds of millions were left in the dark, look for specks of light in the villages.