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In smart grid, malicious customers may compromise their smart meters (SMs) to report false readings to achieve financial gains illegally. Reporting false readings not only causes hefty financial losses to the utility but may also degrade the grid performance because the reported readings are used for energy management. This paper is the first work that investigates this problem in the net-metering system, in which one SM is used to report the difference between the power consumed and the power generated. First, we prepare a benign dataset for the net-metering system by processing a real power consumption and generation dataset. Then, we propose a new set of attacks tailored for the net-metering system to create malicious dataset. After that, we analyze the data and we found time correlations between the net meter readings and correlations between the readings and relevant data obtained from trustworthy sources such as the solar irradiance and temperature. Based on the data analysis, we propose a general multi-data-source deep hybrid learning-based detector to identify the false-reading attacks. Our detector is trained on net meter readings of all customers besides data from the trustworthy sources to enhance the detector performance by learning the correlations between them. The rationale here is that although an attacker can report false readings, he cannot manipulate the solar irradiance and temperature values because they are beyond his control. Extensive experiments have been conducted, and the results indicate that our detector can identify the false-reading attacks with high detection rate and low false alarm.