Optimal Power Flow for AC–DC Grids: Formulation, Convex Relaxation, Linear Approximation, and Implementation

Abstract

HVDC is becoming an increasingly important part of the present day transmission systems. Accurate models of active and reactive power control capabilities of HVDC converter stations are required to analyse the operation of power systems consisting of ac and dc grids, including ancillary services and security. Different converter station technologies exist, with varying control characteristics. This paper develops an optimal power flow model for ac and dc grids. A variety of formulations, from non-linear to convexified to linearized, are developed and implemented in an open-source tool. A convex relaxation formulation of a parameterized ac/dc converter model is developed. The hierarchy of common ac optimal power flow formulations is mapped to formulations for converter stations and dc grids. Numerical illustrations for a number of test cases, up to 3120 ac nodes and up to 10 dc nodes and converters, are provided.

Universal branch model for the solution of optimal power flows in hybrid AC/DC grids

“…The optional control constraints (23) to (27) are modelled in order to capture maximum operational flexibility for the EPS. Further description of each optional control constraint within the FUBM is included below.…”

“…The results are compared against the open-source tool for electric power system simulation and optimization MATPOWER [20]. AC/DC cases compare the FUBM OPF results with the results obtained in [27], where a Bus Incidence Model (BIM) for ACDC OPF is implemented as an extension of the 'PowerModels.jl' package [49], which is built on top of Julia/JuMP [50]. Both AC and AC/DC cases showcase the scalability and computational performance of the FUBM formulation.…”

“…This modified large scale system has a total of 3125 buses, 3703 lines and 505 generators, full AC data can be found in [51] and the DC data in [53]. Table 17 presents a comparison of the simulation results reported in [27] for the BIM-JuMP approach, and the AIMMS-FUBM approach. For the FUBM, the AC/DC cases are solved using KNITRO, CONOPT and IPOPT in AIMMS.…”

“…As a result, the equations per model and grid vary accordingly. Meanwhile, there are two open source non linear AC/DC OPF formulations presented in [27] and [28] to solve the AC and DC grids at the same time. The first one is an extension of the 'PowerModels.jl' package, and the second one is a Pythonbased framework.…”

“…The main contributions of this paper can therefore be summarised as follows: (i) The FUBM provides a direct link between AC and DC grids when modelling an AC/DC EPS allowing for solutions on a unified frame of reference, this is in essence di erent from existing unified models like the ones presented in [28] and [27], (ii) the FUBM provides a general framework for modelling a wide variety of AC, DC, and AC/DC elements in just one compact model to be used in operational planning problems and optimization applications in power systems, (iii) The FUBM allows the incorporation of the voltage and power control features from each one of the control elements to the optimization problem to achieve a fully flexible EPS, (iv) formulation of FUBM can be solved using a variety of optimization solvers, and as such, it is flexible enough to be incorporated in general-purpose model-based languages such as AIMMS as a mathematical programming problem.…”