Effects of load modelling on Voltage Impasse Regions (VIR)
Abstract: Voltage Impasse Region (VIR) is a phenomenon in power systemswhose dynamics are describe by a set of Differential AlgebraicEquations (DAE). VIR denotes a state-space area where voltagecausality is lost, i.e. the Jacobian of the algebraic part of DAEis singular. In a Time Domain Simulation (TDS) once system trajectoriesenter VIR, TDS experiences non-convergence of the solution.Then, there is no reason to continue with the simulation. Thisis why it is important to understand the mechanisms that introduceVIR. It is known that VIR appears in relation to static, non-linearload models. However, it remained unknown what the cumulativeeffect of several static, non-linear loads would be.This master thesis has further expanded the concept of VIRby carrying out a structured study on how the load modelling affectsVIR. For this purpose, this thesis proposes a quasi-dynamicmethodology to map VIR in the relative rotor angle space. Themethodology introduces a new discrete index called Voltage ImpasseRegion Flag (VIRflag), which allows to determine if the algebraicequations of DAE are solvable or not and, thus, to locate VIR.A test system is used to test the proposed quasi-dynamic approach.The VIRflag was first used to map VIR for various load combinations.Then, the relationship between TDS non-convergence issuesand the intersection of a trajectory with VIR is examined toverify the proposed methodology.The proposed method has been proved to be efficient in the determinationof VIR regardless of the number of non-linear loads inthe power system. Among the static exponential load models, theConstant Power (CP) load component has been identified as theone with the largest influence on VIR appearance and shape. TheConstant Current (CC) loads induce ”smaller" VIR areas and theConstant Impedance (CI) load can only alter the shape of VIR inthe presence of non-linear load models.
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