In this paper, an overview of the magnetohydrodynamic instabilities induced by energetic electrons on HL-2A is given and some new phenomena with high-power electron cyclotron resonance heating (ECRH) are presented. A toroidal Alfvén eigenmode with frequency from 200 to 350 kHz is identified during powerful ECRH. In the lower frequency range from 10 to 35 kHz, which is in the beta-induced Alfvén eigenmode frequency range, the coexistence of multi-mode is found during the high-power ECRH for the first time. The spectra become wide when the power is sufficiently high. The frequencies of the modes increase with and are much lower than the Alfvén frequency. The relationship between the mode frequency and (7/4 + Te/Ti)1/2 (Ti)1/2 can be obtained by statistical data analysis. Between the two previous frequency ranges, a group of new modes with frequencies from 50 to 180 kHz is observed with high-power ECRH and neutral beam injection heating together. The modes have clear frequency chirping within several milliseconds or several tens of milliseconds, which are identified as energetic particle mode like instabilities. The new features of the fishbone instability excited by energetic electrons are identified. It is interesting to find the frequency jump phenomena in the high-power ECRH. The difference between the low and high frequencies increases with ECRH power. The frequency jumps between 8 and 15 kHz within about 25 ms periodically, when the power is 1.2 MW.