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For simplicity, suppose temporarily that we have only one lower-level problem. T . T . 110) The meanings of coefficients are analogous to those in the t­ wo-­level optimization problem. Conceptually, we can replace the lower-level optimization problem with its Kuhn–Tucker condition and thus the ­bi-­level optimization problem can be reformulated as a regular nonlinear program that is unfortunately highly ­nonconvex. T . 113) where Bb′′ is a basis of the lower-level problem and Bb′ and bb′′ are the corresponding submatrices.

The drawback is the presence of frequency deviation after the system settles down. In other words, this method cannot restore the system frequency to a nominal value (for example, 50 Hz). 11. Modern power systems are generally controlled in a decentralized way. 12). For purposes of electricity energy settlements among regional subsystems, control of interconnection line flows is required. This interconnected flow control system is integrated into the frequency control system shown. The combination of secondary frequency control and interconnection line flow control is called automatic generation control (AGC).

In other words, the Lagrangian multiplier corresponding to the inequality constraint must be positive. To unify the optimality conditions, let the Lagrangian multiplier μ = 0 when the inequality constraint is not active. We thus obtain a Lagrangian function that has a unified form Γ = c(x) + μ[h(x) − b]. In this way, when building Lagrangian functions, we will not worry about whether the inequality is active. Therefore we will not deal with different constraints (equality or inequality) explicitly.

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