Department of Electrical, Electronic and Computer Engineering, Cape Peninsula University of Technology, Symphony Way, Bellville, Cape Town, 7535, South Africa.
Sci Rep. 2023 Feb 16;13(1):2752. doi: 10.1038/s41598-023-29317-1.
The increasing complexity and difficulty of the Automatic generation control (AGC) problem has resulted from the increasing scale of interconnected power networks and changing daily demands. The primary goals of AGC are to control frequency variations at nominal levels and tie-line power variances at planned levels. To effectively deal with AGC control difficulties, this study introduces Discrete Optimal Quadratic Automatic Generation Control (OQAGC). One advantages of this method is the differentiation of quadratic cost function results into linear terms while minimizing control actions and minimizing state deviations. This developed control method leads to a simple and easy discrete control law that can be implemented for both linear and nonlinear systems. For optimizing the controller, this research work utilized an optimum control theorem using Lagrangian multipliers, while the functional minimization technique is used for systematically selecting the state and control weighting matrices in discrete form for N control regions (where N is the number of interconnected power systems). The discrete cost function needs are derived using this technique in terms of area control errors, integral area control errors, and control energy expenditure. Four interconnected power systems were analyzed with/without disturbances and area control errors, each with one thermal, hydro, and gas-generating unit. A two-area multi-source power system with renewable energy in control area 2 is analyzed for the performance of the proposed controller with generation rate constraints (GRCs). The functional minimization technique simplifies and eases the choosing of weighting matrices. Furthermore, the simulation findings suggest that the developed discrete optimum quadratic AGC control-based cost functional minimization approach enhances power system dynamics in terms of stability, steady-state performance, and the closed-loop control system's robustness to input load disturbances. As a result, the newly developed OQAGC approach demonstrates the significance of the discrete LQR controller for N multi-area power systems.
自动发电控制（AGC）问题的日益复杂性和难度源于互联电网规模的不断扩大和日负荷需求的变化。AGC 的主要目标是将频率变化控制在额定水平，并将联络线功率偏差控制在计划水平。为了有效应对 AGC 控制难题，本研究引入了离散最优二次自动发电控制（OQAGC）。该方法的一个优点是，在最小化控制作用和最小化状态偏差的同时，将二次成本函数的结果区分成线性项。这种开发的控制方法导致了一种简单且易于实现的离散控制律，可以应用于线性和非线性系统。为了优化控制器，本研究工作利用拉格朗日乘子的最优控制定理，同时利用泛函最小化技术系统地选择离散形式的 N 个控制区域（N 是互联电力系统的数量）的状态和控制加权矩阵。该技术根据区域控制误差、积分区域控制误差和控制能量消耗来导出离散成本函数需求。分析了四个具有/不具有干扰和区域控制误差的互联电力系统，每个系统都有一个热力、水力和燃气发电机组。分析了具有可再生能源的两区域多源电力系统在控制区域 2 中的控制性能，以评估具有发电率约束（GRC）的所提出控制器的性能。泛函最小化技术简化并方便了加权矩阵的选择。此外，仿真结果表明，所开发的基于离散最优二次 AGC 控制的成本函数最小化方法提高了电力系统的动态稳定性、稳态性能和闭环控制系统对输入负荷干扰的鲁棒性。因此，新开发的 OQAGC 方法证明了离散 LQR 控制器在 N 个多区域电力系统中的重要性。
