It's not your math but your assumptions - Power is used to describe the size of the generator. Energy (Kw-hr) is indicator of the throughput of the machine.
20GW installed capacity was at the end of the year, at the beginning it was half of that. Also Solar plants only run 8-10 hrs a day (may be you were trying to say this) so they produce lot less than a nuclear/thermal plant that can run 24 hours. This means you need 3-4 solar plants to generate as much as a coal plant of the same size. This has been an uphill battle for solar energy for last several decades, it had to produce cost competitive energy with a handicap of 3-4x. They have now reached/crossed the line by reducing the capital and operating cost. Once energy storage devices become more affordable they would become more comprehensive/reliable power providers. But the question of what if it rains for a week would remain and that means coal/gas/nuclear would have a lions share in the mix for foreseeable future
But again it does not matter to consumer how you generate your power, if the cost is comparable and falling it's going to fly! It does not matter to developer either, if he can make profit by selling his power to consumer.
For Dec 2017 solar energy generated was:
2226.17 MU = 2,226,170,000 KWHr = 8.015e15 Joules
December has 31 days = 744 Hr = 2,678,400 seconds
Actual power generated = 2.993 GW
Installed capacity as of 31.12.17 = 17.052 GW (Revised) http://www.cea.nic.in/reports/monthly/installedcapacity/2017/installed_capacity-12.pdf
Actual/installed = 17.55%
This is certainly better, but we need to wait for the end of year report in May with latest actual and installed capacity. As far as actual/installed power saying it doesn't matter; it does when you put it on the grid for utility scale. You have limited time, land allocation, and capital expenditure which is true not just in India, but everywhere. The recurring cost of fuel for thermal will come from the state electricity board operating budgets. The 2022 goal of 100 GW installed capacity of solar in India will most likely be 2/3 rooftop solar and 1/3 utility solar parks. Utility scale storage devices will make the capital expenditure too expensive for solar. It may happen for roof top applications.
The total installed capacity in India as of 31.12.17 = 333.55 GW
There is the need for more power, but the small gain from utility solar can easily be reached with just a few nuclear power plants.