Mathematical Problems in Engineering

Volume 2018 (2018), Article ID 9049215, 9 pages

https://doi.org/10.1155/2018/9049215

## An Evaluation Method of the Photovoltaic Power Prediction Quality

School of Electrical Engineering, Northeast Electric Power University, Jilin 132012, China

Correspondence should be addressed to Mao Yang

Received 22 August 2017; Revised 29 December 2017; Accepted 13 February 2018; Published 15 March 2018

Academic Editor: Emilio Turco

Copyright © 2018 Mao Yang and Xin Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Photovoltaic (PV) output power has regularity, volatility, and randomness. First of all, this paper carried on a metrological analysis to PV system data. Then, this paper analyzed the relationship between PV historical data, PV power forecasting model, and forecast error. By spectrum analysis of PV power, the PV power is decomposed into periodic components, low frequency residual components, and high frequency residual components. Making a specific analysis of these three components determines the minimum modeling error value, which reflects the unpredictable part of the PV power. Determining the minimum modeling error for PV forecasting not only objectively evaluates the quality of the PV forecasting model but also can determine the prediction accuracy standard according to different PV power generation targets. The examples given in this paper illustrate the effectiveness of the method.

#### 1. Introduction

Renewable energy power is an important solution to global warming. Solar energy generated from PV systems is one of the fastest and the most promising growing renewable energy types [1]. PV power has a large randomness and volatility due to the light intensity, humidity, battery temperature, and so forth [1–3]. This randomness and volatility of PV output cause some adverse effects on the grid when it is connected in a large scale. Therefore, accurate PV power prediction is of great significance to the safe and economical operation of power system.

The prediction of PV power is to use a certain modeling method based on historical data [1, 3–5]. In recent years, a large number of studies have focused on the method of PV power prediction. In [2], based on the analysis of the system structure, two-phase orthogonal currents were constructed, the DC component of the reactive current of the loads is acquired by the algorithm based on the instantaneous reactive power theory, the DC component of the active current is derived from the PI controller, and thus the grid-connected command current is obtained. The distance analysis method was employed in [5] to analyze the correlation between PV power generation and weather factors. In order to adapt to the weather mutation, the self-organizing feature map was used to identify the weather clustering from the cloud forecast information; the corresponding forecasting network was used for each weather class. In [6], a combined forecasting model was proposed based on the rough set. Three kinds of single prediction models were firstly established based on similarity date, support vector machine, and persistence forecasting method. Then, the weight was then assigned to the forecast produced by each prediction model through determining their attribute importance in rough set theory. In the literature [3], considering the influence of wind speed and light on the power flow of microgrids, the prediction of the combined probability distribution of microgrid trend can reduce the adverse effect of wind speed and mild randomness on microgrid operation. According to the prediction of wind power and PV power generation, the qualitative prediction of the trend of microgrid was carried out, and then the conditional joint probability distribution and the unconditional joint probability distribution of the microgrid trend were predicted by combining the Markov chain.

The above methods only focus on finding effective forecasting methods and do not take into account the predictability and unpredictability of the PV power time series itself. In this paper, the regularity of the PV power is fully excavated, as well as its physical explanation, so as to achieve the greatest modeling accuracy. Firstly, the periodic characteristics of PV power are analyzed. Then, the PV power is decomposed by Fourier decomposition to extract the corresponding periodic component including daily cycle components, low frequency components, and high frequency components which are analyzed and explained physically. Finally, the minimum modeling error is determined from the high frequency components. In order to verify the effectiveness of the method, the minimum error of PV power is analyzed under different forecast horizons and different locations. The minimum modeling error determined is then compared with the standard deviation of the prediction error obtained from the three PV power prediction modeling methods, that is, continuous method, artificial neural networks, and generalized regression audit network of PV power generation combined forecast, respectively. The prediction of PV power is similar to the load forecasting, and the research on the evaluation of the load regularity has existed. The necessity of the evaluation of the load regularity has been expounded in [10], and a method of load regularity evaluation was put forward based on statistical analysis. The minimum modeling error of the PV power can be obtained by the method of PV power regularity. When the error is compared with the results of each prediction model, the quality of each model can be evaluated objectively. Furthermore, the result obtained may provide a reference for the relevant departments to develop the forecasting error standard for a specific PV power plant.

This paper is organized as follows. Section 2 carries on a metrological analysis to PV system data. Section 3 analyzes the relationship between the prediction error and the regularity of the PV power. Section 4 demonstrates an evaluation method of PV power regularity. Section 5 analyzes the modeling error. Section 6 verifies the effectiveness of the proposed method. Section 7 offers the conclusions of this study.

#### 2. The Metrological Analysis to PV System Data

When sunlight shines on the surface of a solar cell, its semiconductor interface converts light energy into electrical energy due to the PV effect. Solar cell output power by the solar radiation intensity, temperature, humidity and wind speed, and other factors, the equivalent circuit shown in Figure 1. In the figure, is the current generated by the photovoltaic cell, which is strongly related to the light-receiving area and the illumination condition of the PV cell; is the equivalent diode current; is the bypass resistor, which has a great resistance value and can be neglected in the ideal circuit; is the series resistance; is the equivalent load resistance of PV cells; is the load current; is the load voltage.