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Hidden moving target defense (HMTD) is a proactive defense strategy that is kept hidden from attackers by changing the reactance of transmission lines to thwart false data injection (FDI) attacks. However, alert attackers with strong capabilities pose additional risks to the HMTD and thus, it is much-needed to evaluate the hiddenness of the HMTD. This paper first summarizes two existing alert attacker models, i.e., bad-data-detection-based alert attackers and data-driven alert attackers. Furthermore, this paper proposes a novel model-based alert attacker model that uses the MTD operation models to estimate the dispatched line reactance. The proposed attacker model can use the estimated line reactance to construct stealthy FDI attacks against HMTD methods that lack randomness. We propose a novel random-enabled HMTD (RHMTD) operation method, which utilizes random weights to introduce randomness and uses the derived hiddenness operation conditions as constraints. RHMTD is theoretically proven to be kept hidden from three alert attacker models. In addition, we analyze the detection effectiveness of the RHMTD against three alert attacker models. Simulation results on the IEEE 14-bus systems show that traditional HMTD methods fail to detect attacks by the model-based alert attacker, and RHMTD is kept hidden from three alert attackers and is effective in detecting attacks by three alert attackers.