With the gradual expansion of the grid-connected capacity of renewable energy sources, such as wind power and photovoltaics, the intermittent and stochastic volatility of their output power has brought huge scheduling and control pressure to the frequency stability of power systems [
1]. On the one hand, each control area performs zoning control according to the AC/DC tie-line transmission plan. Each control area can only cover its own power imbalance and maintain the planned power exchanges of the tie-lines, thus it cannot support other areas of regulation capacity shortages through the tie-lines [
2,
3]. On the other hand, the multi-area AGC units are not taken as a whole to suppress the total power fluctuation. Therefore, making full use of the ability of transregional AC/DC tie-line transmission to achieve multi-area coordination has become a major concern for the secure operation of multi-area interconnected power systems [
4].
In recent years, many advanced control schemes have been applied to design a control system for multi-area AGC units, such as the intelligent optimization control method, which is widely used due to its simple control structure for effectively optimizing the parameters of proportional-integral-derivative (PID) controllers. However, intelligent optimization methods—such as particle swarm optimization (PSO) [
8], ant lion optimizer algorithm (ALO) [
9], imperialist competitive algorithm (ICA) [
10], grey wolf optimizer algorithm (GWO) [
11], and so on—may become trapped at local minima, leading to worse dynamic response performance. In order to overcome this deficiency, model predictive control (MPC) [
12] has become a promising research interest over the past decade and has been applied to the design of a control system for multi-area AGC units. In [
13], the authors recalled some achievements of MPC over the past decades, and in [
14], some guides to design MPC controllers using MATLAB were presented. A comparison between MPC and conventional PI control in AGC system design was made in [
15] to demonstrate the benefits of MPC, such as having flexibility and coordination between multiple inputs, taking into account system limitations, and exploiting knowledge about disturbances acting on the system. In [
16], the authors studied the merging of wind turbines in a multi-area power system controlled by a robust AGC based on the MPC technique. In [
17], the parameters of the MPC controller were determined by a bat-inspired algorithm to deal with system nonlinearities comprising generation rate constraints (GRCs) and governor dead bands (GDBs). However, these centralized control solutions are often impractical for application to a large-scale power system for computational reasons and the lack of error tolerance. When the centralized MPC controller or a control component fails, the entire AGC system gets out of control, and the control integrity cannot be guaranteed [
18]. The distributed MPC approach, whereby each control area is controlled by an independent MPC controller, has the advantages of error tolerance, less computational effort, and flexibility regarding the AGC system structure. A distributed MPC approach with a terminal state penalty for multi-area power systems was presented in [
19], but did not consider the system constraints. In [
20], a distributed MPC technique was presented for a multi-area interconnected power system, in which the distributed MPC controllers coordinated with each other by exchanging their information. In [
21], the authors proposed a distributed MPC scheme for a four-area hydrothermal interconnected power system, in which the limit position of the governor valve was modeled by a fuzzy model and the local predictive controllers were incorporated into the nonlinear control system. In order to better deal with the constraints, a distributed MPC was proposed in [
22] based on discrete-time Laguerre functions for multi-area interconnected power systems. Moreover, a multi-area AGC dynamic model integrated with a simplified wind turbine model was solved by a distributed MPC approach in [
23]. In [
24], the authors proposed a coordinated distributed MPC for an AGC system that included inherently variable wind-power generation.
However, to the best of our knowledge, while these distributed MPC methods can reduce the AGC regulation resource demands of the entire power system [
25], they cannot effectively improve the economics of AGC units while ensuring AC tie-line safety. In addition, a great deal of attention has been paid to AC interconnections between areas but not to AC/DC parallel interconnections between areas [
26,
27]. In this paper, a two-level hierarchical control framework is proposed to guarantee the safety of AC/DC tie-lines and reduce the cost of cross-regional support, and further, to achieve better frequency control performance for multi-area interconnected systems. The innovations of the proposed control approach are described as follows: the control framework of the proposed method consists of two layers, with a steady-state power allocation layer at the upper level and a dynamic frequency control layer at the lower level. The upper-level economic MPC (EMPC) controller is used to realize the steady-state power optimal allocation of multi-area AGC units under tie-line support constraints. The AGC units’ participation factors are sent to each control area through the steady-state power allocation layer. The lower-level distributed MPC (DMPC) controller is used to realize dynamic frequency optimization control of the multi-area interconnected system. The control signals of the distributed MPC controller are acted on each control area through the dynamic frequency control layer, so that the area error signal can be restored to zero. This bi-level model predictive control (BMPC) method optimizes the steady-state power and dynamic frequency control of cross-regional AGC units progressively, which can effectively guarantee the safety and economy of optimal cooperation frequency control of multi-area AGC units.
The remainder of this paper is organized as follows. An AGC model of a multi-area power system with a wind farm is established in
Section 2. Subsequently, in
Section 3, the systematic formulation of the BMPC for multi-area AGC units is developed, which consists of two layers, with the steady-state power allocation layer at the upper level and the dynamic frequency control layer at the lower level. Then, in
Section 4, case studies on a three-area AC/DC interconnected power grid are conducted to validate the better performance of the proposed BMPC method. Finally, some concluding remarks are presented in
Section 5.