carb cycling is easily defined as having a high carb day, then low carb day and then a no carb day.
high carb days are just that, any amount until you feel satisfied. low carb days are 1g carbs/lb bodyweight. no carb days are well, no carbs except for fiberous veggies in 3 meals(out of 6). protein stays consistent (1.5g/lb bodyweight) and added healthy fat sources in 2 meals(out of 6) while also supplementing with 10g fish oil caps daily.
do a search for Twin Peaks carb cycling diet.
as for planned refeeds, when one drops calories and carbs low, not only do energy levels suffer, but metabolism begins to slow, thyroid output decreases, leptin levels fall, glycogen stores are depleted and hormones can become unbalanced. all this resulting in a slow down of fat loss and risk of loosing muscle. on a refeed we increase all of the above and reset the body back to norm, this upshift gets things running back in high gear so when you return to the diet your burning even more fat at a quicker rate. planned refeeds depend on your current bf%, the leaner that you are the more often that you need to refeed, the higher Bf% the less. refeeds could vary in length from 8 hours to 36 hours(usually on a keto type diet tho). they consist of many high glycemic foods, limited fructose, very little fat(has no connection with leptin levels) and protein drops to 1g/lb bodyweight.
If youd like more info then I can post links to some very good articles.