# A New Passive Islanding Detection Solution Based on Accumulated Phase Angle Drift
## 2 Principles of ROCOF and VVS Relays
### VVS Relay  
Voltage vector shift (VVS) is also referred to as vector surge or phase jump. The VVS relay monitors the phase angle change of the local voltage in real time. Under the steady state condition, the phase angles calculated each cycle are the same and the voltage cycle length is also fairly constant. Hence the phase angle change is zero. However, at the instant of islanding, the current will change suddenly if the power between load and generation does not closely match. The sudden change of current will cause a sudden jump of the voltage vector, as shown in Figures 1 and 2.  
Figure 1: Voltage vector shift illustration.  
In Figure 1, \(\dot{E}\) is the rated electromotive force; \(\dot{U}_{n}\) is the rated voltage; \(\dot{U}^{\prime}\) is the new voltage after the vector shift; \(X_{d}\) is the synchronous reactance; \(X_{d}^{\prime\prime}\) is the sub-transient reactance; \(\dot{I}_{L}\) is the load current; and \(\Delta\dot{I}_{L}\) is the current change.  
The resultant voltage vector is dependent on the current change and the sub-transient reactance of the machine, which is the reactance of the generator under a sudden load change. The voltage phase angle change can be approximately expressed as:  
\[\Delta\theta=arcsin(\frac{\left|\Delta\dot{I}_{L}\right|\cdot X_{d}^{\prime \prime}}{\left|\dot{U}_{n}\right|}) \tag{2}\]  
If the generator is running at the rated condition before the voltage vector shifts, then Equation (2) can be approximately deduced as:  
\[\Delta\theta\approx arcsin(\frac{\Delta P}{P_{n}}\cdot X_{d}^{\prime\prime}) \tag{3}\]  
In Equation (3), \(\Delta P\) is active power change; and \(P_{n}\) is the rated active power of generator.  
Here it is necessary to emphasize that VVS relay in a practical engineering application usually detects the sudden change of the voltage phase angle due to the sudden change of load current. However, a change of system frequency can also cause the change of the voltage cycle length and hence the change of phase angle between two consecutive cycles. The value of angle change due to the frequency change is expressed as:  
\[\Delta\delta(\Delta T)=\pi\cdot\frac{df}{dt}\cdot\Delta T^{2} \tag{4}\]  
In Equation (4), where \(\Delta\delta\) is the angle change due to frequency change; \(df/dt\) is the rate of change of frequency; \(\Delta T\) is the phase angle calculation interval.  
When the rate of change of frequency is 1.0 Hz/s, the angle change between two consecutive power cycles is only. However, the typical angle threshold of VVS relay is from 6.0\({}^{\circ}\) to 10.0\({}^{\circ}\). Hence, the VVS relay is not sensitive to the voltage phase angle change caused by change of frequency alone [21]. In some of the literature [15; 16; 22], the VVS relay is described to detect the phase angle change caused by the change of frequency. Such analysis is not consistent with the operating principle of practical commercial VVS relays.  
If the current change at the instant of islanding is large enough to cause a voltage phase angle change larger than the angle threshold, the VVS relay will operate and islanding is detected. In addition to the inherent NDZ, the VVS relay cannot effectively distinguish islanding conditions from system faulted conditions. At the instant of system faults or fault clearance, the VVS relay can sense the sudden change of the voltage phase angle. Other system events, such as load or generation switch operation, could also cause the sudden change of voltage phase angle. To enhance the reliability and  
Figure 2: Transient voltage change.  
reduce the possibility of nuisance tripping, it requires a relatively higher angle setting for the VVS relay. Hence the VVS relay is relatively less sensitive for islanding detection.