Modular Controller Design applied to Network Reduction Suited for Offline and Online Simulation

Novel Modal Resonance Proximity Region between photovoltaic and multi‐machine subsystems under inertia and damping variations

“…Computing the eigenvalues of state matric A v of Equation (1) and eigenvalues of state matric A g of Equation ( 5) yields the open-loop VSC oscillation modes (VOMs) and the open-loop EOMs, respectively. The closed-loop oscillation modes can be yielded by Equation (5). EOMs' position variations, from open-loop to closed-loop, indicate the influence of the VSC subsystem on small-signal stability of the multimachine subsystem, whereas the VOMs' position variations indicate the influence of multi-machine subsystem dynamics on the small-signal stability of the VSC subsystem.…”

“…To reflect the impacts of various scenarios in the state space models as developed in Section 2, for one variable scaled generation plant, if there are k generators actually online and using the same base value, equivalent parameters for its state space model can be expressed as follows [5]:…”

“…To reflect the impacts of various scenarios in the state space models as developed in Section 2, for one variable scaled generation plant, if there are k generators actually online and using the same base value, equivalent parameters for its state space model can be expressed as follows [5]: $$$\left\{\begin{array}{@{}l@{}}{H}_{\mathit{eq}}=\sum\limits _{k=1}^{m}{H}_{k},{D}_{\mathit{eq}}=\sum\limits _{k=1}^{m}{D}_{k}\\ {X}_{\mathit{eq}}=1/\sum\limits _{k=1}^{m}\frac{1}{{X}_{k}},{T}_{\mathit{eq}}=\sum\limits _{k=1}^{m}\left({S}_{k}{T}_{k}\right)/\sum\limits _{k=1}^{m}{S}_{k}\end{array}\right.$$$ where H eq and D eq are the aggregated model's equivalent inertia and damping constant, respectively, X eq represents the aggregated model's equivalent reactance and T e represents equivalent time constant in the aggregated model. H k and D k are inertia and damping constant of the k th actually online generator in the generation plant, respectively, X k represents k th generator's reactance, whereas T k represents k th generator's time constant for its excitation system and governor.…”

“…To reflect analysed system's main characteristics and reduce the computational burden, a multi-machine system is simplified to a limited number of representative buses connected to equivalent generators with aggregated parameters in ref. [5], but the system parameter amendment for different operating states is not investigated. Considering the system changes in minutes, a measurement-based generator equivalent method is proposed in [6].…”