With increasing global energy demands [
1], solar energy has become the most inexhaustible and ecologically beneficial renewable energy source today. It has drawn wide attention in industrial fields, such as desalination power [
2] and generation [
3]. According to the Ministry of Global Renewable Energy forecast, from 2020 to 2030, the global demand for waterborne photovoltaics (PV) are expected to grow at an average annual rate of 22%, and the installed capacity of waterborne PV will be more than 30 GW in 2030. Hencec waterborne PV has been hailed as a new energy source, “accelerating the transition of the solar energy−driven future of the most effective leverage”. Solar energy can be converted into electricity through both sides of the bifacial PV module to generate additional energy, making the bifacial PV module leap forward as the PV industry’s new favorite [
4,
5]. Based on data, bifacial photovoltaic modules comprised approximately 45% of the total photovoltaic module in the third round of the “Photovoltaic Leader” project, as per the statistics [
6].
The increased performance ratio, reduced operational expenses, and expanded usability of bifacial PV panels have garnered significant interest among scholars both nationally and internationally [
6,
7,
8]. Appelbaum et al. [
9] deliberated on the computation of yearly occurrence radiation for a PV facility comprised of bifacial PV modules organized in numerous rows with two arrangements. Gu W et al. [
10,
11] developed an integrated optical−electrical−thermal model of a bifacial PV module, where the overall irradiance of the tilted front and rear surfaces is obtained through an optical model, and the corresponding power output is obtained through an electrical model. Mouhib et al. [
12] described the current status of bifacial PV, introduced bifacial PV and its differences from conventional mono−facial PV, and identified different parameters characterizing bifacial performance. Current works on the bifacial PV generation system primarily focus on their generation principles, internal structures, and other related aspects, but they tend to neglect the modeling methodology for bifacial PV modules and the maximum power point tracking (MPPT) technique employed in bifacial PV generation systems. The maximum peak of the bifacial PV system could be influenced by external factors such as diurnal fluctuations, alterations in cloud cover, and variations in weather conditions. Ensuring an efficient and effective MPPT is crucial to enhance the power conversion efficacy of the PV generation system [
13,
14]. Currently, studies on MPPT, both in the domestic and international domains, can be broadly categorized into the following groups. Firstly, there are conventional MPPT algorithms, such as the perturbation observation (P&O) algorithm [
15] and the incremental onductance (INC) algorithm [
16,
17], which are widely adopted. Abdel-Salam et al. [
15] proposed the P&O algorithm that adds the change of PV outlet current as the third tracking index in the flow chart, which effectively increases the tracking efficiency of the traditional P&O algorithm’s tracking efficiency. Nevertheless, the conventional MPPT technique encounters challenges in precisely monitoring the maximum power point (MPP) amidst abrupt variations in environmental conditions. The other single category consists of intelligent algorithms, such as Particle Swarm Optimization (PSO) [
18,
19,
20,
21]. Koad R.B et al. [
18] proposed the use of the PSO algorithm to solve the problems of traditional MPPT algorithms, which are easy to fall into local optimum and slow convergence. However, the convergence of intelligent algorithms is difficult to determine, and if the parameters are not selected properly, it will lead to system operating point oscillation. In addition, bionic meta−heuristic algorithms have also received wide attention [
22,
23]. Moghassemi Ali et al. [
22] proposed to implement MPPT for partially shaded PV systems based on the whale optimization algorithm and differential evolutionary algorithm, and studied the performance evaluation of MPPT. Although it has a significant improvement in tracking accuracy, the bionic meta-heuristic algorithm leads to a significant reduction in tracking accuracy speed due to the huge computational cost [
24,
25]. In addition, the modern optimization algorithms exhibit greater advantages in the application of MPPT. Eltamaly [
26] proposed the musical chairs algorithm for the case of highly dynamic changes in shading conditions, which could significantly reduce the convergence time and failure rate, and improve the efficiency and stability of the PV system.
The model predictive control (MPC) strategy has been used in PV applications due to its ability to handle process variable constraints as well as optimize performance metrics [
27,
28,
29]. Sajadian et al. [
30] proposed a concept based on the combination of MPC and pole search optimization for tracking the maximum power point, with a simple control structure and a fast dynamic response. Metry M et al. [
31] applied the MPC principle to remove the usual current sensors needed for unconventional MPPTs in order to achieve a faster response and reduced power ripple in a steady state. Nonetheless, external disturbances result in alterations to the reference value, thereby rendering the conventional MPC oblivious to the system’s economic efficiency while undertaking real−time tracking. To solve this problem, economic model predictive control (EMPC) has attracted attention because it can consider the control and optimization problem of MPPT from a new perspective [
32,
33,
34,
35,
36,
37]. EMPC reflects the process economy directly or indirectly as the objective function and adjusts the optimal operation strategy in real time to improve the dynamic economy of the system while satisfying the operation constraints [
38,
39,
40,
41,
42].
In this paper, focusing on the bifacial PV power generation system, this work proposed an economic model predictive control-based MPPT strategy. This strategy aims to achieve real-time optimization of the system’s operating point by continuously monitoring the current economic performance index, while ensuring compliance with operation constraints. Shown in
Figure 1 is the tracking principle schematic of the MPP of the bifacial PV generation system. The innovations of this paper are: (1) By examining the phenomenon of light reflection and refraction on the water surface, this work developed an irradiance model for a bifacial PV module based on its solar operation mode and employed the bifacial coefficients to establish the module’s electrical characteristics. (2) The EMPC controller was designed based on the state−space model and combined with the equipment operation constraints of the bifacial photovoltaic power generation system. An economic objective function was established to solve the system, with the maximization of power generation as the economic performance index. (3) We analyzed and compared the control effects of EMPC and traditional MPPT, and verified that the algorithm can coordinate multivariable control actions according to internal and external operating conditions and improve the dynamic economy of the system.
The paper is organized as follows: a mathematical model of the waterborne bifacial PV power generation system, as well as an irradiance model, are developed in
Section 2. In
Section 3, the proposed EMPC strategy and the flow of controller design are derived. In
Section 4, a MATLAB (R2022a) simulation of the proposed EMPC strategy is performed, and the classical MPPT strategy and EMPC strategy are compared to verify the effectiveness and practicality of the EMPC strategy. In addition, in this section, the superiority of bifacial PV modules compared to mono-facial PV modules is comparatively analyzed. Finally,
Section 5 provides the conclusion.