Ultra-high-power　arc　furnace　is　the　main　equipment　of　modern　smelting.　It　is　very　important　to　accurately　model　it　in　order　to　understand　the　time-varying　and　non-linear　of　arc　and　realize　the　targeted　research　of　power　quality.　In　this　paper,　a　new　model　of　ultra-high-power　electric　arc　furnace　for　the　study　of　low-frequency　and　non-stationary　inter-harmonics　is　proposed.　Firstly,　according　to　the　law　of　conservation　of　energy,　a　static　model　of　an　ultra-high-power　arc　furnace　is　established.　Then,　based　on　the　static　arc　model　and　the　chaotic　theory,　a　dynamic　mathematical　model　of　ultra-high-power　electric　arc　furnaces　is　established　to　describe　the　characteristics　of　inter-harmonic　emission　between　low-frequency　and　non-stationary.　Finally,　the　feasibility　and　correctness　of　the　model　is　verified　in　Matlab/Simulink　simulation　environment.　The　simulation　results　show　that　the　model　of　the　ultra-high-power　electric　arc　furnace　proposed　in　this　paper　can　accurately　reflect　the　operation　characteristics　of　ultra-high-power　electric　arc　furnace　in　practical　industrial　applications,　and　can　reveal　the　low-frequency　non-stationary　inter-harmonic　emission　characteristics　of　the　ultra-high-power　electric　arc　furnace.　In　addition,　it　reflects　the　influence　of　ultra-high-power　electric　arc　furnace　equipment　on　the　stability　of　distribution　network.　©　2020　IEEE.