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Yes, you should be able to use any of the PlantEquipmentOperation:### objects with the PlantComponent:UserDefined object. The EMSUserDefined5ZoneAirCooled.idf example file that comes with EnergyPlus shows a case where a PlantComponent:UserDefined object represents a chiller, so it uses the PlantEquipmentOperation:CoolingLoad object to control how it meets chilled water loads. See an excerpt below for the plant loop and related operation scheme settings, with a "*" next to the important input fields for your question.

PlantLoop,
  Chilled Water Loop,      !- Name
  Water,                   !- Fluid Type
  ,                        !- User Defined Fluid Type
* CW Loop Operation,       !- Plant Equipment Operation Scheme Name
  CW Supply Outlet Node,   !- Loop Temperature Setpoint Node Name
  98,                      !- Maximum Loop Temperature {C}
  1,                       !- Minimum Loop Temperature {C}
  autosize,                !- Maximum Loop Flow Rate {m3/s}
  0.0,                     !- Minimum Loop Flow Rate {m3/s}
  ,                        !- Plant Loop Volume {m3}
  CW Supply Inlet Node,    !- Plant Side Inlet Node Name
  CW Supply Outlet Node,   !- Plant Side Outlet Node Name
  Cooling Supply Side Branches,  !- Plant Side Branch List Name
  Cooling Supply Side Connectors,  !- Plant Side Connector List Name
  CW Demand Inlet Node,    !- Demand Side Inlet Node Name
  CW Demand Outlet Node,   !- Demand Side Outlet Node Name
  Cooling Demand Side Branches,  !- Demand Side Branch List Name
  Cooling Demand Side Connectors,  !- Demand Side Connector List Name
  SequentialLoad,          !- Load Distribution Scheme
  CW Avail List;           !- Availability Manager List Name

PlantEquipmentOperationSchemes,
  CW Loop Operation,       !- Name
* PlantEquipmentOperation:CoolingLoad,  !- Control Scheme 1 Object Type
* Central Chiller Only,    !- Control Scheme 1 Name
  PlantOnSched;            !- Control Scheme 1 Schedule Name

PlantEquipmentOperation:CoolingLoad,
  Central Chiller Only,    !- Name
  0,                       !- Load Range 1 Lower Limit {W}
  900000,                  !- Load Range 1 Upper Limit {W}
* Cooling Plant;           !- Range 1 Equipment List Name

PlantEquipmentList,
  Cooling Plant,           !- Name
* PlantComponent:UserDefined,  !- Equipment 1 Object Type
* Central Chiller;         !- Equipment 1 Name

More specifics about your controls need to be defined in the Plant Connection Loading Mode input field of the user-defined plant component, as well as the EMS programs used for initialization and simulation of the user-defined plant component.

Yes, you should be able to use any of the PlantEquipmentOperation:### objects with the PlantComponent:UserDefined object. The EMSUserDefined5ZoneAirCooled.idf example file that comes with EnergyPlus shows a case where a PlantComponent:UserDefined object represents a chiller, so it uses the PlantEquipmentOperation:CoolingLoad object to control how it meets chilled water loads. See an excerpt below for the plant loop and related operation scheme settings, with a "*" next to the important input fields for your question.making references between objects.

PlantLoop,
  Chilled Water Loop,      !- Name
  Water,                   !- Fluid Type
  ,                        !- User Defined Fluid Type
* CW Loop Operation,       !- Plant Equipment Operation Scheme Name
  CW Supply Outlet Node,   !- Loop Temperature Setpoint Node Name
  98,                      !- Maximum Loop Temperature {C}
  1,                       !- Minimum Loop Temperature {C}
  autosize,                !- Maximum Loop Flow Rate {m3/s}
  0.0,                     !- Minimum Loop Flow Rate {m3/s}
  ,                        !- Plant Loop Volume {m3}
  CW Supply Inlet Node,    !- Plant Side Inlet Node Name
  CW Supply Outlet Node,   !- Plant Side Outlet Node Name
  Cooling Supply Side Branches,  !- Plant Side Branch List Name
  Cooling Supply Side Connectors,  !- Plant Side Connector List Name
  CW Demand Inlet Node,    !- Demand Side Inlet Node Name
  CW Demand Outlet Node,   !- Demand Side Outlet Node Name
  Cooling Demand Side Branches,  !- Demand Side Branch List Name
  Cooling Demand Side Connectors,  !- Demand Side Connector List Name
  SequentialLoad,          !- Load Distribution Scheme
  CW Avail List;           !- Availability Manager List Name

PlantEquipmentOperationSchemes,
  CW Loop Operation,       !- Name
* PlantEquipmentOperation:CoolingLoad,  !- Control Scheme 1 Object Type
* Central Chiller Only,    !- Control Scheme 1 Name
  PlantOnSched;            !- Control Scheme 1 Schedule Name

PlantEquipmentOperation:CoolingLoad,
  Central Chiller Only,    !- Name
  0,                       !- Load Range 1 Lower Limit {W}
  900000,                  !- Load Range 1 Upper Limit {W}
* Cooling Plant;           !- Range 1 Equipment List Name

PlantEquipmentList,
  Cooling Plant,           !- Name
* PlantComponent:UserDefined,  !- Equipment 1 Object Type
* Central Chiller;         !- Equipment 1 Name

More specifics about your controls need to be defined in the Plant Connection Loading Mode input field of the user-defined plant component, as well as the EMS programs used for initialization and simulation of the user-defined plant component.