Jab,

A little knowledge for you.  The newer LiPo batteries come with built-in Battery Management Systems (BMS) that communicate over the positive connection to other batteries in parallel in a bank.  The built-in BMS usually accepts charge rates up to 10% of Ah capacity (C/10) from any type of charger, adjusted for each individual cell's temperature and age.  The BMS also limits discharge too, max 10 x C.  LiPo cells can be discharged at 10 times their capacity, but it is wise to reduce this.  Don't mix old and new batteries and definately don't mix battery chemistries.

Under high loads lead acid will start output ~13V and rapidly drop towards 11V; LiPo starts around 15V and drops slowly to ~13V where the BMS will cut them off.  Lead acid can only deliver all its charge at 5% or less of capacity discharge rate (C/20), any higher rate results in lots of losses and a shortened cycle life, LiPo can be discharged at 1,000% of capacity (C x 10), again with a loss of capacity, but virtually no change to the number of recharge cycles thanks to the BMS cutting them off before damage occurs.  For best capacity the LiPo discharge rate should not exceed 2 x Ah capacity.  Calculations following are made using a 'nominal' 12V, then variations explained.

For a 120Ah battery a 3000W inverter (with 85% efficiency) supplying a 2000W kettle needs 12V at 200A for nearly 3 minutes to boil 2L of water (from 20°C), using 200A x 3/60minutes = 200 x 3 / 60 = 10Ah, at typical discharge rate of 200Aout/120Acapacity = 1.67C.  This is fine for LiPo (less than 2 x C) but is terrible for Lead acid at greater than C/20 = 120 / 20 = 6A max.  For lead acid 2 batteries in parallel will be needed, allowing 12A max draw for long life.  A kettle is a purely resistive load, but tv power supplies and electric motors, etc add inductive energy (stored as a magnetc field in a wire coil) and these have a startup surge to buildup the store of reserve power.  A compressor fridge that uses 2A while running will often be advertized as 1A per hour because it cycles On and Off, only running for half the time.  But that is a lie, each time the motor starts it draws 8-10A for a while until the compressor is running at its design speed; if your battery bank can't supply this 10A on top of other, standing loads it will struggle to start (or not start at all).  Hence the example includes 50% 'headroom' for the inverter which relies on large inductive coils to be able to convert DC to AC.

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