1. A method of determining a Security Constrained Economic Dispatch (SCED) solution for a hybrid power system comprising an Alternating Current (AC) grid interconnected with a multi-terminal High Voltage Direct Current (HVDC) grid at two or more Point-of-Common-Coupling (PCC) buses, wherein a control system is in communication with the hybrid power system, the control system including a processing circuit having a processor, the processing circuit being configured to output the SCED solution for implementation in the hybrid power system, the processing circuit configured to optimize a non-linear objective function, subject to a set of constraints that include AC grid constraints and DC grid constraints, for determining the SCED solution using successive linear approximation, the processing circuit configured to perform the following steps of the method: computing a power balance sensitivity for the AC grid, based on calculating AC grid power flow according to a reasonably assumed dispatch solution and initialized power injection values for the PCC buses; determining an initial dispatch solution by solving a linear programming (LP) problem that linearly approximates the non-linear objective function, subject to a limited subset of the constraints and based on assumed power injection values; adopting the initial dispatch solution as the SCED solution when the initial dispatch solution does not result in any new constraint violations, as determined by performing an AC grid power flow analysis according to the initial dispatch solution, and otherwise performing an LP problem iteration, including: calculating DC grid power flow in a DC grid power flow analysis, based on the injection values included in the current dispatch solution and correspondingly updating the DC grid constraints in the LP problem; solving the updated LP problem and adopting the resulting dispatch solution as the SCED solution if no new AC grid constraint violations are detected from repeating the AC grid power flow analysis, and otherwise adding a most-violated one of any newly-detected AC grid constraints to the LP problem and performing another LP problem iteration, and outputting the SCED solution or a control signal derived from the SCED solution determined by the processing circuit, the SCED solution based at least in part on monitored operating parameters of the AC grid and the HVDC grid received by the processing circuit, the SCED solution or control signal providing information to adjust the operation of one or more devices of the hybrid power system to implement the SCED solution.