A method for operating a microgrid with both a renewable generation domain and a conventional generation domain, wherein the renewable generation domain comprises generators (DG1, DG2, DG3) comprising renewable energy sources which are inherently transient and wherein each generator comprises an L (series)-C(series)-C(shunt) filtered inverter or an L (series)-C(series)-C(shunt)-L(series) filtered inverter to couple the renewable energy source to the renewable generation domain of the microgrid, and wherein the conventional generation domain comprises at least one conventional generator; the method for operating the renewable generation domain comprising: using a grid-forming generator producing its reference voltage with a constant system frequency of either 50Hz or 60Hz or other fundamental frequency; and the grid-forming generator producing its output real power reference based on its terminal voltage's variation from its rated value or other predetermined voltage value or producing fixed real and reactive power references; and the grid-supporting generators taking the voltages at their respective coupling points with the microgrid as references; and the grid-supporting generators producing their respective real power references based on their respective terminal voltages' variation from their respective rated values or other pre-determined values, and each of the grid-supporting generators having its respective upper limit for output real power reference; and dynamic reactive power compensations or power factor corrections being adopted at different locations in the microgrid making the power factor close to one at each of major buses or at each of major loads or groups of loads or groups of equivalent loads; the method for operating the conventional generation domain comprising using conventional generators such as hydro-electric power generations and diesel-engine generations being adopted to power loads in that domain; and interconnecting each domain at its every joining point with other parts of the microgrid through back-to-back converters or through other AC power to AC power converters (110a, 110b, 110c), through which power is exchanged between each domain and other parts of the microgrid. and a conventional generation domain, wherein the renewable generation domain comprises generators (DG1, DG2, DG3) comprising renewable energy sources which are inherently transient and wherein each generator comprises an L (series)-C(series)-C(shunt) filtered inverter or an L (series)-C(series)-C(shunt)-L(series) filtered inverter to couple the renewable energy source to the renewable generation domain of the microgrid, and wherein the conventional generation domain comprises at least one conventional generator; the method for operating the renewable generation domain comprising: using a grid-forming generator producing its reference voltage with a constant system frequency of either 50Hz or 60Hz or other fundamental frequency; and the grid-forming generator producing its output real power reference based on its terminal voltage's variation from its rated value or other predetermined voltage value or producing fixed real and reactive power references; and the grid-supporting generators taking the voltages at their respective coupling points with the microgrid as references; and the grid-supporting generators producing their respective real power references based on their respective terminal voltages' variation from their respective rated values or other pre-determined values, and each of the grid-supporting generators having its respective upper limit for output real power reference; and dynamic reactive power compensations or power factor corrections being adopted at different locations in the microgrid making the power factor close to one at each of major buses or at each of major loads or groups of loads or groups of equivalent loads; using a grid-forming generator producing its reference voltage with a constant system frequency of either 50Hz or 60Hz or other fundamental frequency; and the grid-forming generator producing its output real power reference based on its terminal voltage's variation from its rated value or other predetermined voltage value or producing fixed real and reactive power references; and the grid-supporting generators taking the voltages at their respective coupling points with the microgrid as references; and the grid-supporting generators producing their respective real power references based on their respective terminal voltages' variation from their respective rated values or other pre-determined values, and each of the grid-supporting generators having its respective upper limit for output real power reference; and dynamic reactive power compensations or power factor corrections being adopted at different locations in the microgrid making the power factor close to one at each of major buses or at each of major loads or groups of loads or groups of equivalent loads; the method for operating the conventional generation domain comprising using conventional generators such as hydro-electric power generations and diesel-engine generations being adopted to power loads in that domain; and interconnecting each domain at its every joining point with other parts of the microgrid through back-to-back converters or through other AC power to AC power converters (110a, 110b, 110c), through which power is exchanged between each domain and other parts of the microgrid.