Passivity based stability analysis of the power control of interconnected droop-based grid-forming inverters
Authors
Christiansen, Jan Peter Mortensen ; Jørgensen, Jonas Lillelund
Term
4. term
Education
Publication year
2023
Submitted on
2023-05-31
Pages
81
Abstract
Efterhånden som flere vedvarende energikilder tilsluttes via effekt-elektronik, bliver grid-formende invertere stadig vigtigere. De kan selv sætte spænding og frekvens og dermed opføre sig lidt som traditionelle generatorer. Det gør spørgsmålet om stabilitet i elnet med mange invertere centralt. Denne afhandling vurderer stabiliteten ved hjælp af passivitetsanalyse – en energibaseret metode, der groft sagt undersøger, om et system ikke kan generere mere energi, end det modtager. Vi tilpasser en tilgang, der tidligere er brugt til net domineret af synkrongeneratorer (Spanias m.fl.), hvor busdynamik og koblingen mellem busser behandles som to forbundne delsystemer. Der anvendes en tidsvarierende fasormodel, og generatorer erstattes af invertere. Resultaterne viser, at det samlede net i denne opdeling ikke er passivt. Hvis man derimod ser den komplekse effekt som input til inverterens dynamik og spændingsniveau og fasevinkel som output, kan selve inverterdynamikken vises at være passiv. For at bevise stabilitet af en sammenkobling af invertere med den såkaldte circle criterion (et matematisk stabilitetskriterium for feedback-systemer) kræves imidlertid, at selve sammenkoblingen er strengt passiv, hvilket den ikke er. En feedback-passivisering kunne i princippet opfylde kravet, men det vil koste i form af meget præcis tids-synkronisering. Ved at bruge invariansprincippet (fra Lyapunov-teorien) vises stabilitet, hvis man antager, at nettet er tabsfrit, og at fasevinkelforskellene mellem invertere er små. For at undersøge, hvordan systemet opfører sig uden disse stramme antagelser, udføres simuleringer på to velkendte testsystemer: Kundurs Two Area Network og IEEE Reliability Test System.
As more renewable energy sources connect through power electronics, grid-forming inverters are becoming central to power system operation. They can set voltage and frequency, acting in some ways like traditional generators, which makes the stability of inverter-heavy grids a key concern. This thesis assesses stability using passivity analysis—an energy-based method that, roughly speaking, checks whether a system cannot generate more energy than it receives. We adapt an approach previously used for grids dominated by synchronous generators (Spanias et al.), splitting the problem into two interconnected subsystems: bus dynamics and the network interconnection. A time-varying phasor model is used, with generators replaced by inverters. The findings show that, under this decomposition, the overall grid is not passive. However, if complex power is taken as the input to the inverter dynamics and voltage magnitude and phase angle as the outputs, the inverter dynamics themselves can be shown to be passive. To establish stability of a network of inverters via the circle criterion (a mathematical test for feedback stability), the interconnection must be strictly passive, which it is not. A feedback passivization could, in principle, enforce strict passivity, but it would require very accurate time synchronization. Using the invariance principle (from Lyapunov theory), stability is guaranteed under the assumptions that the system is lossless and that phase angle differences between inverters are small. To explore behavior beyond these strict assumptions, simulations are conducted on two standard test systems: Kundur’s Two Area Network and the IEEE Reliability Test System.
[This summary has been rewritten with the help of AI based on the project's original abstract]
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