With the increase of renewable energy penetration, the shortage of flexibility resources in power systems has become more prominent due to large-scale renewable integration. A bi-level optimization model incorporating flexible regulation services is constructed based on the concept of full cost of electricity. The lower-level model is transformed into constraints of the upper-level model using the KKT (Karush-Kuhn-Tucher) condition, and the problem is linearized by applying the big-M method. The impacts of the traditional clearing model and the model accounting for flexible regulation services on the revenue of power generators are compared, and it is found that introducing flexible regulation services can reduce the total cost for system operators, enhance power system security, and improve the economy of system operation. In addition, a sensitivity analysis of the flexible regulation service prices and the carbon emission prices shows that both operator cost and generator revenue are positively correlated with carbon emission prices. Moreover, when the price of flexible regulation services exceeds the unit cost of interrupted load, the electricity market clearing mechanism fails.