Take a look at contact , their good nights plan. We are only on the low user plan in Auckland which is 90 cents per day, and 30 cents per kWh, and manage to get around 30% of our monthly usage into the free off-peak time period (every night 9pm-midnight).

They also offer fibre broadband, and if you join for a year they currently offer a $300 account credit. 

Taking into account the account credit on offer, it could be worthwhile joining for a year, then explore your options again.

These days it makes no sense to stay loyal to one provider, as there tends to be sign up bonuses for new customers, which makes it well worth while to change yearly.