## 2 S-L Analysis Method
### Introduction of S-L Analysis Method  
Input/output bidirectional devices can become both power supply and load in the power system. They can also become participants of frequency regulation through automatic speed-regulating devices and demand side response. Therefore, the above frequency analysis should be extended. Generators not only refer to conventional power sources, but they also include input/output bidirectional devices operating in generator mode. Loads not only refer to traditional loads but also include input/output bidirectional devices operating in motor mode.  
Figure 2: The supplementary control for load increase \(\Delta P_{\rm G}\).  
The traditional frequency analysis method does not show the frequency regulation characteristic of the load, which is not able to visually display the power balance relations shown in Equations (1) and (2) in the power system. As a result, the frequency regulation process and mechanism of the input/output bidirectional devices in different modes (generator mode/motor mode) cannot be exhaustively analyzed. Aiming at such shortcomings, in this section, the S-L analysis method is presented. First, the application of this method is introduced under the conventional single-power system. Afterward, how this method can be applied to complex multi-power systems including input/output bidirectional devices is explained.  
In order to visualize the frequency characteristics of the load, the frequency characteristic in the first quadrant was extended to both the first quadrant and the second quadrant and a uniform power reference direction was established. As shown in Figure 3, the horizontal axis is the active power axis and the vertical axis is the frequency axis. Taking into account the cognitive habits, the motor practice is used to regulate the positive direction, which means the power absorbed by the motor is positive rather than the power generated by the generator. Regardless of power supply or load, the direction of power absorption from the grid is positive and the direction of power delivery to the grid is negative. In this way, it is possible to clearly distinguish between the power supply and the load in a unified power reference direction and give them a clear physical meaning. In order to visually represent the balance of the power system, the operation line was then defined. Therefore, the intersection of the operation line and frequency axis is the system frequency. The abscissa of the intersection of operation line and each power's frequency characteristic line is the power generated by that power supply and the abscissa of intersection of operation line and each load's frequency characteristic line is the electricity consumption by that load. If the sum of the abscissas of the intersections of the operation line and each power frequency characteristic line is equal to that of the operation line and each load frequency characteristic line, Equation (1) is satisfied, which achieves power balance. At this moment, the frequency corresponding to the running line is the steady state frequency. This method considered the source-load static frequency characteristics, which is hence abbreviated as the S-L analysis method.