## 4 Power System Protection
### Reversed Power Flow Detection  
Reversed Power Relay (RPR) are power directional relays, which are used to monitor the power flow and enact appropriate actions during abnormal conditions. Under an exceptional condition, the power direction changes from the Busbar to the generator. This situation usually occurs when the prime mover has failed. It is natural for the power in the grid to be sufficiently lower than the rated power of the generator [26].  
The current stator phase shift is commonly referred to as the Maximum Torque Angle (MTA). The system uses a power directional relay with a MTA of 180\({}^{\circ}\), which is shown in Figure 2. As a result, the system can detect the loss of the prime mover. Accordingly, the phasor current is reversed and enters the trip zone. However, the reverse flow of the current is smaller than the moving average and the current of the actual power generator should only be carried out in the off-turbine loss and driving. Therefore, directional relays in detecting loss require a higher degree of sensitivity compared to overcurrent relays [27; 28].  
The best protection can be achieved using a Rogowski coil current sensor instead of the current transformer (CT), which avoids the erroneous behavior caused by the fault [29; 30]. When the power response provided by the generator is substantially closer to the zero power factor, incorrect behavior is avoided due to the phase-angle error of the current transformer. If the angle between the vector of the current and voltage is \(\Delta\), the load flow in the normal direction is between \(-90^{\circ}<\Delta<90^{\circ}\) in the reverse case, while the flow of power is at \(+90^{\circ}<\Delta<270^{\circ}\). The overlap between the voltage and current ranges is greater than their non-overlapping intervals under normal circumstances. Nevertheless, this overlap reduces to a lower level when reversing the flow of energy. The difference in the overlap interval during natural flow is used and the flow of energy is reversed in the implementation of the directional relay component [31].  
Figure 3 shows the implementation of the RPR component. The low signals of the current and voltage of the current transformer and voltage transformer have been found to change to the form of a square wave, which has a value of \"\(\pm 1\)\". After this, these levels of signals are multiplied to yield a positive number in the overlap interval and a negative number in the non-overlap interval [32].  
In the diagram, the upper limit of integration for the system is set to zero, so that the integral of the load is always less than zero in normal conditions. However, in the reverse trend, the production conditions include integral parts that tend to decline until they reach a threshold constant. In this case, the constant is set to 0.01. However, no value can be selected according to the reverse power amount. The application of RPR for directional characteristics based on Simulink is shown in Figure 4. The output of the element Block RPR is sent to a decision, in which the output is 1 for the tripping signals during normal operations and 0 under abnormal conditions [33].  
Figure 3: Implementation of a directional component.  
Figure 2: Vector diagram of current and voltage according to the Reversed Power Relay in the system.  
Figure 5a shows the three-phase current directions, \(\cos\)\(\mathbf{e}\) and power factor, while Figure 5b shows the same concepts of the PQ power plane.