This contribution deals with the optimization of the frequency response of a multi-area, multi-energy HVDC-HVAC cyber-physical power system, representing a power electronic-dominated power system. The system consists of a three-area system, modified so that the areas are electromagnetically decoupled through MMC-based HVDC links, and different controllable energy sources, such as fully decoupled wind turbines type IV and proton exchange membrane electrolysers, are installed at various points of the system. The modified system exhibits three decoupled areas with different generation and demand mixes characterized by different inertia levels and increased controllability due to the converters’ capabilities. The outer controllers of the power electronic interfaced elements installed have been modified with the active power gradient control scheme to respond to frequency excursions and provide fast frequency support to the grid in case of commonly occurred active power-frequency imbalances. A problem formulation for coordinated optimization is presented, aiming at a coordinated tuning of the parameters of the frequency controllers of the synthetic inertia elements participating in the frequency regulation against critical commonly occurred active power-frequency imbalances. The formulations consider the minimization of the dynamic displacements of the areas’ speed following an active power imbalance. To effectively solve the optimization problem and enhance the frequency stability of the system, a powerful metaheuristic optimization algorithm, the mean-variance mapping optimization (MVMO) algorithm, has been utilized. The optimization results can effectively highlight the tuning strategy that achieves the best frequency response of the system under various commonly occurred active power frequency disturbances. It can also provide further insight on the proper utilization of various sources of synthetic inertia with respect to their response capabilities. Finally, the simulation results can also clarify the importance of the location of installation of converter-based elements providing fast frequency support with respect to the grid node the imbalance occurs.

HVDC-HVAC power systems dominated by power electronic converter interfaced elements are exposed to frequency instability risk due to low levels of system inertia and ineffective primary frequency control. Hence, significant research is devoted to new control concepts to enable fast active power (P) - frequency support by power electronic converters. Furthermore, when multiple elements attempt to arrest P imbalances, a coordinated strategy is required to avoid adverse consequences of concurrent and interfering control actions such as steep rate-of-change-of-frequency and over/under frequencies during the frequency containment period. To tackle this issue, in this paper, three different optimization strategies are formulated aiming at a cooperative reaction of fast P controllers attached to the outer control layer of modular multilevel converters (MMCs) applied in HVDC links and proton exchange membrane (PEM) electrolyzers. Each formulation is implemented by combining DIgSILENT PowerFactory 2024 SP2 as a power system simulation tool with a Python-based optimization solver that adopts the mean variance mapping optimization algorithm (MVMO). A comparative analysis performed on a multi-area multi-energy hybrid HVAC-HVDC power system to evaluate the proposed formulations in terms of their applicability, effectiveness according to P reserve availability, optimization convergence rate, and the suitability of the frequency response due critical sudden P imbalances.

Modernization of power systems leads to more power electronic interfaced units in the generation, demand, and transmission. Examples are remotely installed renewable energy sources, loads with constant power, or high voltage direct current (HVDC) corridors. These changes significantly affect the frequency stability margins of the system and thus special control techniques should be applied in the converters of the new installed units so as to shoulder the frequency regulation in case of commonly occurred active power imbalances. The response of such units has to be cooperative in order to avoid problems such as insufficient reactions or overshoots. In this chapter, a coordinative tuning approach of the active power gradient control scheme applied to the controllers of modular multilevel converter (MMC)-based HVDC links and proton exchange membrane electrolyzers with the provision of fast frequency support in a multiarea hybrid HVDC-HVAC power system with responsive demand units is proposed. This tuning uses an optimization approach based on mean variance mapping optimization and is able to minimize the frequency excursions in all interconnected areas participating in the frequency regulation even without communication between the system nodes. This technique has shown great results in terms of quality and convergence rate within a short number of fitness evaluations achieving a set of frequency responses within acceptable limits set by operators even in case of the loss of the largest generating unit in the weakest system area. It has also revealed the applicability of such a method in more complex systems and the necessity for sophisticated tuning methods according to the application needs and the system characteristics.

Power electronic dominated power systems formed nowadays are characterized by fast and frequent dynamics, limited short circuit support, low inertia conditions and lack of inertial support. Under these conditions, coping with active power imbalances in a power system may becomes a significant challenge for transmission system operators (TSOs) that may experience extensive frequency deviations and steep rates of change of frequency (RoCofs). To deal with the frequency stability issues encountered, power electronic interfaced (PEI) units can rapidly respond to provide fast frequency support (FFS) taking advantage of their controllability levels and their rapid response to setpoint changes. FFS may depend on the active power gradient (APG) control strategy that determines the required amount of active power, and the rate the power injection takes place. However, when multiple elements try to regulate simultaneously the frequency adverse control actions such as insufficient or over frequency regulation may be encountered. To solve this issue, this paper proposes a formulation for the optimal and coordinative tuning of the APG controllers of PEI elements installed in a multi-area, multi-energy hybrid HVDC/HVAC power system with modular multilevel converter (MMC) HVDC links and proton exchange membrane (PEM) electrolyzers. This formulation focuses on creating an artificially coupled frequency response for an electromagnetically decoupled multi-area system taking advantage of the available active power reserves and the inertia levels of each area. In that way, an active power imbalance can be optimally shared among the interconnected areas leading to effectively improved frequency response for the affected and supporting areas. The proposed formulation is solved using the mean variance mapping optimization (MVMO) algorithm after a series of RMS simulations is performed in DIgSILENT PowerFactory 2021.