<p>Confronted by the dual challenges of carbon emission reduction and financial constraints, power enterprises require innovative financing mechanisms. This study develops two such models using a Stackelberg game approach and KKT conditions. Through comparative and sensitivity analysis, the following key conclusions are obtained. (1) When the generator faces financial constraints, a lenient total carbon allowance regulation can lower electricity prices and reduce overall carbon emissions while simultaneously increasing investment in renewable energy, boosting electricity demand, and enhancing corporate profits. This approach benefits consumers, the environment, and enterprises alike. Conversely, if the government does not implement a lenient total carbon allowance regulation, adopting a unit carbon allowance regulation can yield comparable outcomes. (2) When the generator is not financially constrained, the unit carbon allowance regulation, in comparison to the total carbon allowance regulation, results in greater renewable energy investment, higher electricity demand, and increased corporate profits, alongside reduced overall carbon emissions and lower electricity prices. This approach delivers mutual benefits to consumers, the environment, and enterprises. (3) Under financial constraints, increases in both unit and total carbon allowances exert identical influences on equilibrium outcomes; they are inversely related to electricity prices and overall carbon emissions, yet positively correlated with renewable energy investments, electricity demands, and corporate profits. In the absence of financial constraints, however, the effects of these two types of regulations diverge significantly.</p>