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

Acknowledgement:  
This article is based upon work supported by the Department of Energy (DOE) under Award Number DE-OE0000849. Opinions and claims expressed here are strictly the work of the authors and not that of DOE or any of its representatives.
EPG expresses appreciation to project advisors Prof. Anjan Bose (WSU) and Dejan Sobajic (GEng), and Utility leads Tony Faris (BPA) and Atena Darvishi (NYPA). EPG team members include Wenyun Ju, Simon Mo, and Uday Kothapa.
For references, please see “Real-time Synchrophasor Applications to Support Power System Operations” by Zhang, et al from Pac World Conference, Raleigh NC, August 2019.

Addressing these challenges calls for new technologies and solutions. The recent expansion of synchrophasor measurement systems can be used to serve these needs. Phasor Measurement Units (PMUs) are widely distributed across the electric power network. They provide a wide area view that is well suited to assessing power flows in any pattern. They provide complex bus voltages that can be used directly for computing the system state. Unlike traditional state estimation, phasors can provide power system state even in disconnected regions, such as when a system is islanded. Their high rate measurements enable the tracking of dynamics and an immediate real-time response.
Many synchrophasor based applications have been developed that take advantage of the time-stamped high-resolution PMU data. Most of these are for off-line analysis, and they have proven very useful for operation analysis, network assessment, and model validation. Acceptance of applications for real-time uses such as operation monitoring and automatic controls has been slow. This is due to several factors including limited need for additional information beyond what SCADA provides, few applications that provide critical information, and lack of confidence in synchrophasor data. In addition, there is limited PMU coverage, due to the high cost of installation and commissioning of PMU devices, communication bandwidth limits, and cyber security concerns. The applications described in this article are targeted to provide usable, actionable information to operators by addressing these problems.

The system described in Figure1 inputs synchrophasor data from PMUs and runs it through a Linear State Estimator (LSE). The LSE performs the same basic functions as a traditional state estimator (SE) except that by using synchrophasor data the problem can be reduced to a linear problem. This allows it to run at measurement speed (50-60 solutions/second) and it always solves. The LSE provides confidence in the data by noting discrepancies and rejecting clearly bad data. It also extends the measurement set by using the model to estimate values in some places that do not have a PMU. The output of the LSE is then sent to applications that perform analysis for operations. Three applications have been developed for this project. The first is a real-time contingency analysis (RTCA) application. This application uses the system solved case from the LSE to test for problems that could be caused by contingencies and provide alerts to the operators. The second is a voltage security index (VSI) that monitors voltage through a transmission corridor and quickly provides a warning if the voltage is risking collapse. The third application is an area angle monitor that compares the phase angle across an area of the power grid with angle limits that indicate overloaded conditions and warns the operator if there is a severe condition meriting quick action.

The work presented here is based on a US Department of Energy project titled “Real Time Applications Using Linear State Estimation Technology,” which develops real-time synchrophasor applications based on PMU measurements that have been processed and augmented by the LSE.

Synchrophasor Measurements and the LSE Enhancement
Synchrophasor measurement is provided by a PMU installed at a substation where it can access voltage and current quantities. A synchrophasor includes the magnitude and phase angle of the ac voltage or current waveform. The phase angle is referenced to universal time to allow comparing all the measured phase angles together. These measurements provide the complex voltages at all measured busses in the grid along with the associated branch currents. PMUs are usually distributed across the grid, so they provide a wide area view of voltages and currents across the area of the power grid. This wide area view can provide a good overall assessment of the voltage profiles and key power flows but is generally not comprehensive enough to provide a complete measurement of state since there are rarely enough PMU measurements to cover the entire grid. Eventually PMUs may cover the entire grid with enough measurements to provide direct state measurements, but this has not been the case so far.
To respond to the need for complete state solutions and redundancy to detect errors, the linear state estimator (LSE) has been developed. The LSE can provide a state solution in real-time at the same speed as the measurements since PMUs reduce state estimation to a linear problem. LSE can validate and improve the measurements as well as extend the measurement set over a wider-area of the grid.
The LSE provides more accurate data than the raw measurement by linking the measurements together with the system model. This allows detecting most error types, including those introduced by the PMU, data communication, and the PT/CT transformation. The LSE provides a consistent set of bus voltages (i.e., steady state of the system) which can be used to compute all parameters of interest including line currents, active and reactive power flows as well as active and reactive contributions from generating units and loads.

The LSE uses the same system model (Y matrix and associated topology) as a traditional EMS but has the key advantage of working with linear equations. LSE finds the system state that is the best least square fit to the PMU complex current and voltage measurements. The LSE also checks and corrects for data and topology errors.
In practice, the LSE system model has to be reduced to the PMU observable subset. The measurement data is applied to the model and the model is kept up to date by breaker status reports included with the PMU data or reported through an ICCP link with the EMS (Figure 2). Topology changes can also be inferred by looking at the branch current, but low current flows can give false readings.
 Due to the limited coverage of PMU devices, the LSE solution will be a partial set of buses out of the entire system. In most utility phasor measurement systems, these observable buses are usually at the highest voltage levels and represent the most important nodes of the system.
The LSE can extend PMU voltage estimates one bus away from the PMU using the voltage and current measurement with the branch line characteristics, but even this may leave a substantial number of busses and lines unsolved. This sparse measurement problem posed a major problem in implementing the applications in this project.

Real-Time Contingency Analysis

RTCA background:  Power system operators strive to keep the power system stable and secure at all times. During operation, the system can be observed to assure voltages, frequency and power flows are stable and within acceptable limits. But there is always the question as to what will happen if any element fails. Will it be stable? Or will the problem lead to further problems or even (gasp!) a blackout? The RTCA addresses the what-if problem by removing one or more element at a time and solving the power flow to find out if the system is stable and the flows and voltages are within prescribed limits. Power systems are designed and tested to be N-1 (one element removed) secure, but they may not be with a sudden N-k (k elements removed) condition. Further, sometimes removal of one element will automatically cause removal of others, such as by remedial action or network separation. RTCA applications use a power flow model that shows steady-state violations and does not address dynamic stability.

This RTCA uses a base case of system model covering the utility area that has been updated with the solution provided by synchrophasor data. The base case is a complete set of bus voltages and branch flows that match with each other and the power system model. For this application, it is reduced to the utility of interest and its direct neighbors. It can be updated on a daily basis to keep it current. This case is then updated with the latest PMU measurements and resolved so all the measurements are consistent. This approach of updating a base case model was found to provide a more comprehensive and accurate contingency analysis than only using the PMU data subset by itself. In the next step, the RTCA applies each contingency, such as removing a line from service, to the solved case. The power flow solver updates the model topology for changes caused by the contingency and recomputes all the power flows and bus voltages. Then it tests the new values against limits specified in the model and notes any violations. It will run through the entire contingency set and report all violations. In the automatic mode, the RTCA will take a new case as soon as one is complete and repeat the process. Violations are reported in a user display (Figure 3). This display shows the history of runs (left side), a chart of category 1-3 results (top), and drill down panels where an operator can examine detailed results (center-right). Detailed results include the list of contingencies that cause violations as well list of violations caused by individual contingencies (bottom-right).

RTCA application example: Figure 3 shows an example of contingency violation identified by the RTCA. Loss of a 500-kV line from Bus A-C causes a category 1 limit violation for the power flow on the 500 kV/230 kV transformer A – D. A one-line diagram from the PowerWorld simulator shows this case and the resulting overload of 12% on the transformer A-D.

Voltage Stability
Concept of VSI application:  This Voltage Stability Index (VSI) application assesses the voltage stability of a pre-defined corridor by calculating an index using PMU data. The calculation uses the complex voltage and current measurements from the corridor boundary busses and can be done at the speed of measurement (eg, 60/second) since it does not require iterations. The approach has the effect of reducing a complicated transmission corridor to a single line equivalent. It can be applied to a corridor with multiple lines and several connection points (Figure 4). This approach is particularly useful in quickly assessing the impact of multiple outages which may require emergency action to forestall subsequent cascading events.
The first step in configuring this application is to define the corridor to be monitored. The corridor is chosen so that a typical power flow from generation at one end to load at the other end can stress the system towards a voltage collapse. It works best if there are no significant branches cross-wise through the corridor but will accommodate some input and output taps. A phasor measurement of the voltage and current of each line at the boundary of the corridor is required. The lines in the transmission corridor are reduced to a single line equivalent as follows:

The complex power S for each line at the boundary is computed from the phasor measurements, S=VI*. These are then summed to determine the total power flow at the sending (generation) end, Ss, and the receiving (load) end, Sr. The sending and receiving currents are also summed and used with the complex power sums to find the equivalent voltage across the system Vsr and at the receiving Vr end.

The VSI is simply the voltage across the corridor divided by the load voltage, calculated in %:

It is well known that voltage stability can be strongly affected by generators reaching their maximum reactive power output limits.  Accordingly, the VSI index calculation must monitor the generators providing significant reactive power to the corridor, and, if the limit is reached, change the modeling of the generator in the calculation to a negative load with the constant maximum value of reactive power. If the generator is not directly monitored by a PMU, its reactive power limit status could in some cases be estimated from nearby PMUs or by other signals.
The index is calibrated in an offline model by stressing the transmission corridor by gradually increasing the power flow through the corridor until voltage collapse and then finding the VSI threshold corresponding to the utility-defined emergency margin to voltage collapse. Additional alert thresholds can also be assigned at lower levels of stress, thereby allowing the operator to take precautionary corrective steps.

Application example:  As an example, we consider a transmission corridor through Oregon in the western US. Power flow is predominantly from Pacific North-West to California over a primarily 500 kV transmission corridor. The section from Grizzly substation to Captain Jack and Malin substations was chosen for the study.  Figure 5 shows a schematic layout of the corridor. A high load study case has 4308 MW entering the corridor at Grizzly substation and 3808 MW leaving the corridor at Captain Jack and Malin substations (with the difference leaving the corridor at Ponderosa substations). The power flows and the index are calculated using measurements from Malin, Captain Jack, and Grizzly. 

Loss of two Palo Verde Generating Units: As shown in Figure 6, loss of two Palo Verde Generating Units caused VSI to jump from 12.81% to 16.61% indicating a stressed voltage condition. The stressed voltage condition can also be verified from the Malin voltage subplot, where the voltage decreased from 535.7 kV to 514.8 kV.
Table 1 summarizes the results for a few scenarios. It is evident that VSI increases (worsens) with severity of the voltage issues.
In all cases, the index clearly indicated a stressed condition across the voltage corridor. The next steps are to test enough cases to determine index threshold values that differentiate between critical outages that need emergency action, those that only serve as an alert, and those that do not require special attention.  Emergency actions include adding reactive support at the load end of the corridor or reducing the corridor power transfer. Based upon the study results, we can assign an alert threshold of 19% and an alarm threshold of 23%.

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.

Biographies

Ken Martin is a principal engineer with the Electric Power Group (EPG).  He has over 40 years' experience in the electric utility industry, first at the Bonneville Power Administration (BPA).  He started working with synchrophasor measurement with the original PMUs in 1987 and went on to develop the measurement system at BPA. He chaired the development of the IEEE C37.118 Synchrophasor standard series and convened the current IEC-IEEE 60255-118-1 synchrophasor measurement standard.  He is a Fellow of the IEEE, a registered Professional Engineer and has authored/co-authored more than 60 papers and articles.

Neeraj Nayak is a Senior Power Systems Engineer at EPG and has over 5 years of experience in Synchrophasor Technology – research, design, development, training and support. He has provided training and support to major ISOs and Utilities for implementing synchrophasor applications. He has extensive experience in synchrophasor applications research and development including – Real-time Contingency Analysis, Generator Model Validation, Phasor Simulator for Operator Training, Oscillation Detection and Monitoring. He managed the development of the on-line synchrophasor training portal. He has a master's degree in Electrical Engineering from University of Southern California (USC) which was focused on power systems analysis and impact of renewable energy on the power grid.

Iknoor Singh is a Senior Power Systems Engineer at EPG and is involved in research and development of synchrophasor applications. He has also performed analytical studies for establishing alarm thresholds and various event analysis based upon synchrophasor data. Prior to joining EPG, Iknoor was a Graduate Research Assistant at Arizona State University, where his MS thesis focused on effect of increased renewable resource penetration on power system transient and small signal stability. Previously, he worked as a power plant layout engineer at Siemens, India.

Ian Dobson was educated at Cambridge and Cornell universities and previously worked as an operations analyst in British industry and as a professor at the University of Wisconsin-Madison.
He is currently Sandbulte professor of electrical engineering at Iowa State University. Ian is a fellow of the IEEE, and has worked on voltage collapse, nonlinear dynamics, and cascading failure risk in electric power systems.

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