Having seen regulators approve in December an increase in Eversource Energy’s fixed-rate charge to its customers, some lawmakers are now proposing a cap on future increases.

Senate Bill 570 has been introduced by state Senate President Martin M. Looney and 10 other lawmakers. Although the language of the bill doesn’t mention a specific number, a few lawmakers talked about a cap of $10 per month, which is similar to one proposed in California.

Looney, D-New Haven, said in testimony before the legislature’s Energy and Technology Committee Tuesday that fixed-rate charges are “inherently regressive.”