Hello and welcome to Just Answer. My name is ***** ***** I will be happy to assist you with your electrical question.
1) If the home has a total PV output of 5kW, then the inverter needs to be rated at a minimum of 5kW and not 4kW. Not safe nor reliable since the inverter can overload.
2) The rule of thumb is that the inverter should always be rated higher in wattage than the total PV system wattage.
3) In addition to having a smaller wattage rated inverter than the total PV system wattage, you are not fully benefiting from the total available PV wattage. 1kW of watts is being wasted. You either need to de-install some panels to get the total PV system wattage below 4kW or you need to increase the inverter size.
Hope this helps………If you have any additional questions, let me know and I’ll be glad to answer them for you.
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The next time you have an electrical question, you can also request for me at: http://www.justanswer.com/home-improvement/expert-your-electrician ……….Thanks…………..Kevin!