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𝑇 Δ , 𝑇 𝑟 temporal window length and resetting period of the modulation integral observer 𝑡 time variable 𝑡 𝑘 time instant of the k th resetting sequence 𝑑 process disturbance 𝜙 ℎ general modulation functions, h = 1, 2, 3 𝜙 𝑝,ℎ , 𝜙 𝑒,ℎ polynomial and exponential modulating functions, h = 1, 2, 3 𝑤 ℎ weighting parameters of the modulating functions, h = 1, 2, 3 Γ, Γ ) , Γ * general modulating function matrix and the variants formed by 𝜙 𝑝,ℎ and 𝜙 𝑒,ℎ 𝑣 ϕ,h auxiliary modulated signals Subscripts, superscripts and accents 𝑥 ! estimated signal 𝑥 " estimation error 𝑥 𝑖 𝑖th component of the vector 𝑥 (𝑖) 𝑖th order time-derivative of the signal 𝑥 ⊤ transpose

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This paper proposes a dual-layer modulation technique that combines two-and three-level modulation techniques to control the average neutral-point current (ANC) in neutralpoint-clamped (NPC) converters. In the proposed technique, two modulation layers are employed to independently synthesize the desired ac-side voltage reference and ANC reference. The first (outer) modulating layer operates at a lower frequency and synthesizes the ANC reference from the three phase currents. It determines the duration of applying each modulation technique, based on the ANC reference and the maximum ANC injection limits of the converter. The second (inner) modulating layer operates at the switching frequency and synthesizes the three phase voltages of the NPC converter from the common dc voltages by comparing the calculated duty cycles and a carrier waveform. The proposed dual-layer modulation technique has advantages of faster dynamics and reduced mathematical computations compared to the conventional approach. The feasibility of the proposed modulation technique is demonstrated experimentally on a laboratory prototype. A detailed performance comparison among different modulation techniques is also presented.