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This paper studies the decentralized <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> secure load frequency control issue and circuital realization of multi-area networked power systems subject to random transmission delays and deception attacks. To make full use of the stochastic feature of the network-induced transmission delay, its distribution described by the probability density function is utilized. Due to this feature, the normal control signal and the injected deceptive attack signal transmitted over the network can be formed as two distributed delay terms. Then, the <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>th load frequency control area is established as a new distributed delay system, in which the delay probability density is treated as the distributed kernel. By utilizing an integral inequality dependent on the kernel, new sufficient controller design conditions are derived to guarantee the system stability with given <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance. Moreover, a physical execution approach is addressed to transfer the load frequency control systems into electrical analogy circuits. The effectiveness of the proposed approach is illustrated via the professional simcape toolbox in Simulink/MATLAB for circuit simulations.

Probability-Density-Dependent Load Frequency Control of Power Systems With Random Delays and Cyber-Attacks via Circuital Implementation