Real-time Synchrophasor Applications for Power System Control

Authors: Ken Martin, Neeraj Nayak, Iknoor Singh, Electric Power Group, CA, USA, and Ian Dobson, Iowa State University, USA

Area Angle Stability Assessment

Concept of Area Angle:  It is well known that power flow through an AC transmission line is directly related to the phase angle of the voltage across the line and inversely related to the line impedance. This is conveniently expressed as:

where V1 and V2 are the voltages at busses at the ends of the line, X is the line impedance, and θ is the voltage phase angle across the line. It turns out that these relationships can be extended to the power flow through and angle across an entire area of the grid. This "area angle" is proportional to the power flow. Moreover, if lines outage inside the area, then the area impedance increases, tending to increase the area angle even if power flows stay much the same. Thus, the area angle can respond to changes inside the area. The area angle can be evaluated by suitably combining together the PMU measurements of voltage angle around the border of the area.

The challenge is finding a way to relate this concept to grid capacity and control action. This project developed a monitor and control application based on this concept. The first offline step selects an area of the transmission grid that has a significant power flow through the area from one side of the area to the other (Figure 8). The area can have a number of power entry and exit points. The next offline step is reducing a base case model of the network inside the area to equivalent connections between boundary busses using the Kron reduction. We then use the reduced system to determine weights for the boundary busses that indicate their contribution to the area angle (Figure 7). In online application, a phase angle measurement is required from each bus at the boundary of the area and the measured angles are summed with their precomputed weights to determine the angle across the area. A minimum time interval is applied in alarm detection to prevent swings from triggering alarms.

This area angle provides a good measure of the power flow through the area in relation to the grid within it but thresholds for the area angle need to be related to line limits. By determining the angle across the system at maximum loading under single, double and triple line outages, we can find angle limits for the area offline. Two thresholds are defined, i.e. a warning and an emergency threshold. If either limit is exceeded, the operator will be alerted in real-time.

Case Study for Area Angle Monitoring: We use PMU measurements from an event to track the variation of area angle. The event is the loss of two transmission lines between John Day and Grizzly.  The calculated area angle values are shown in Figure 9. The warning and emergency thresholds are indicated by blue and red lines respectively. We can see that this event will trigger warning since it crosses the warning threshold of area angle for a certain period of time but is not severe enough to indicate an emergency. This alerts the operator to watch the trend. If the emergency area angle threshold is exceeded, the operator can consider redispatch to reduce the power flow through the area or take other actions, depending on operating orders.

Conclusion:  Phasor measurement systems are widely used for analysis and model validation. However, application to protection and control has proceeded slowly. It is anticipated that deployment of these applications will steadily increase as the technology matures and system coverage increases.
This article presents three applications utilizing phasor data for power system operations control. The RTCA is a standard application used at most utilities. This RTCA is unique in that it operates from phasor data and provides fast contingency analysis independent of the EMS state estimator. The VSI and AAM applications operate directly from phasor data and at the data reporting rate, typically 1/50 or 1/60 of a second. The VSI application takes advantage of the independent time-synchronized measurement of voltage and current to quickly monitor voltage collapse proximity in a predefined power transfer corridor with multiple lines. The area angle provides a unique measurement of stress due to power transfer through a predefined area by combining together measurements at the border of the area. The VSI and area angle applications can back up other monitoring types to provide additional security in controlling the grid and are intended to quickly indicate emergency actions when the conventional state estimator does not converge. The combined applications are anticipated to provide an important step towards the acceptance of phasor measurements for grid control.

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