In the grid-connected photovoltaic system (GPVS), due to characteristics of fluctuation and intermittency for photovoltaic solar power, and high randomness for electric load, it is of great difficulty for integrating photovoltaic solar power into power grid. Therefore, an accurate prediction of short-term electric load and photovoltaic solar power is of great importance for balancing supply and demand. Currently, numerous isolated models about the forecasting o. In the grid-connected photovoltaic system (GPVS), due to characteristics of fluctuation and intermittency for photovoltaic solar power, and high randomness for electric load, it is of great difficulty for integrating photovoltaic solar power into power grid. Therefore, an accurate prediction of short-term electric load and photovoltaic solar power is of great importance for balancing supply and demand. Currently, numerous isolated models about the forecasting of electric load and photovoltaic solar power have emerged, while the coupling effect between them has been hardly considered and lower stability of existing methods brings great difficulty in providing reliable predictions at practical applications. To address this gap, this paper proposes an interpretable multi-prediction model for short-term (day-ahead) electric load and photovoltaic solar power forecasting. In the framework, a non-parametric functional principal component analysis (FPCA) is constructed to extract the overall trend and identify dominant modes of variation in the daily electric load and photovoltaic solar power data. Furthermore, state transition matrix is proposed to comprehensively interpret the coupling effect, with which a novel multi-prediction strategy that takes advantage of coupling effect is further introduced, where the Maximum Likelihood Estimation (MLE) is employed to estimate unknown parameters. Moreover, data from California Independent System Operator (ISO) is utilized to investigate the performance of proposed method,. ••A novel multi-prediction framework is proposed in this paper.••State transition matrix is proposed to interpret the coupling effects.••A non-parametric feature engineering approach is constructed to extract features.••Performance analysis including stability and feasibility is conducted.Grid-connected photovoltaic systemCoupling effectState transition matrixShort-term electric load forecastingWith increasing prominence of environmental problems and severe abuse of fossil fuel, policies have been announced worldwide to promote the development of renewable energies. Due to characteristics of zero-emission, sustainability and easy accessibility, solar energy has received much more attention. On such basis, installation of grid-connected photovoltaic system (GPVS) has grown rapidly all over the world in the last few decades. The photovoltaic solar market reached about 843 GW in 2021 with an increase of about 22.8%, and it is expected that the total installed capacity of GPVS will reach 1700 GW by 2030.However, in GPVS, photovoltaic solar power is typically fluctuating and intermittent and electric load is usually highly random, which would cause unexpected loss and might bring various types of failures in grid, such as power imbalances, voltage fluctuations, power outages, etc. Thus, an accurate short-term electric load and photovoltaic solar power forecasting is required to make a crucial instruction for energy utilization. Nevertheless, for the construction of existing models, electric load and photovoltaic solar power in GPVS are always in isolation from each other, which breaks the coupling effect among them, triggering that energy systems fail to ensure energy effective utilization. Therefore, it is necessary to introduce new models in interpretation with the co. The framework of proposed coupling forecasting method is shown in Fig. 1. It can be seen from the figure that the FPCA approach is firstly constructed to estimate the overall trend and dominant modes of variation of electric load and photovoltaic solar power. State transition method is then proposed to interpret the coupling effect between electric.
