Power Factor and Sweep Frequency Testing in Transformers

Matthew Wallace, CBS Field ServicesFeatures, Summer 2024 Features

At best, an equipment failure is a costly inconvenience. At worst, it can affect the entire country and impact Wall Street.

Consider BP’s refinery in Whiting, Indiana — the largest in the Midwest, according to BP, producing 440,000 barrels per day of crude oil. On February 1, 2024, Reuters reported that the refinery had shut down unexpectedly, and in a news report in the Indianapolis Star, witnesses said they saw flames “shooting out the stacks” at the refinery.

The cause? A transformer failure that shut the plant down, forcing all but the most essential workers to evacuate, according to Reuters. It was a failure that would have an impact on drivers across the country. The average price of regular and diesel gasoline rose in the following weeks, which Fox Business attributed to the Whiting Refinery shutdown. Two weeks after the incident, with the refinery still shuttered, investors were dumping their oil investments.

The Whiting Refinery incident is a cautionary tale about how catastrophic a transformer failure can be, not only for the company in question but also for customers and related stakeholders. One way to mitigate such failures is routine inspections and testing of transformers.


There is no one-size-fits-all test to evaluate a transformer’s overall health and reliability. However, a number of basic transformer tests can identify potential problems before they fail. Some evaluate the insulation in the transformer. The insulation resistance, or Megger test, measures the resistance of electrical insulation to assess its ability to prevent current leakage. A dissolved gas analysis looks at the gasses dissolved in the insulating oil to determine whether certain processes occurring in the transformer might indicate an issue.

Other tests look at the integrity of the transformer’s core and windings. The turns ratio test (TTR), for instance, compares the number of turns between windings to ensure proper voltage transformation ratios. The winding resistance test measures the resistance of each winding to identify potential issues, such as loose connections or damaged conductors. The exciting current test helps evaluate the core and windings by measuring the current drawn when the transformer is energized but not loaded.

Certain diagnostic tests for transformers assess the health of bushings and insulation in the load tap changer mechanism and test the functionality of protective relays, circuit breakers, and other devices that are important for safe operation.

Two additional transformer tests will be the focus of this article:

  • Power factor testing evaluates the condition of the transformer’s entire insulation system
  • Sweep frequency response analysis (SFRA) compares the transformer’s frequency response fingerprint to a baseline to detect internal faults or mechanical issues


Power factor is a measure of the capacitance between isolated areas of the transformer. In a transformer, there is no single insulator to be evaluated. Instead, insulation comprises several systems:

  • Transformer insulating fluid
  • Winding-to-ground insulation
  • Winding-to-winding insulation
  • Primary (H) bushing insulation system
  • Secondary (X) bushing insulation system
  • Load tap changer (LTC) insulation system

Power factor testing allows for evaluation of the transformer’s insulating system as a whole by testing each of these systems individually. It is calculated as a ratio of resistive current to total current.

In its simplest form, power factor testing is a three-step process:

  1. Apply a controlled AC voltage across the insulation system within the transformer to simulate operational conditions.
  2. Analyze and measure the total current (It) flowing through the insulation system, dissecting it into its resistive component (Ir) and capacitive component (Ic). This step provides critical insights into the impedance characteristics of the insulation under test.
  3. Utilize the derived resistive current (Ir) and total current (It) to determine the power factor, a vital parameter indicating the efficiency of the insulation system in maintaining electrical integrity. This calculation is performed through the formula: cos(θ) = Ir/It, elucidating the phase relationship between voltage and current.

In the simplest terms, the lower the power factor percentage value, the healthier the insulation system.

  1. However, from a practical standpoint, there are three primary test modes for performing power factor testing on a transformer (Figure 1):
  2. Ungrounded specimen test (UST) mode, which isolates an individual section of the system under test
  3. Grounded specimen test (GST) mode, which measures the total current leaking to ground
Figure 1: Wiring Diagrams for Three Power Factor Test Modes

Grounded specimen test with guard (GST-guard or GST-g) mode, in which a guard circuit is used to isolate and measure different pieces of insulation while reducing the number of test connections required 

On a two-winding transformer, power factor testing examines the insulation in three different areas (Figure 2):

  1. CH: The high-voltage winding-to-ground insulation system, including the primary-side (H) bushing insulation
  2. CL: The low-voltage winding-to-ground insulation system, including the secondary-side (X) bushing insulation
  3. CHL: The high-voltage to low-voltage (inter-winding) insulation system, which does not include the bushing insulation
Figure 2: Power factor testing examines three areas in a two-winding transformer: H = high-voltage winding; L = low-voltage winding; and G = ground.

For a three-winding transformer, the test focuses on three areas (Figure 3):

  1. CT: The tertiary winding-to-ground insulation system, including the tertiary-side bushing insulation
  2. CLT: The low-voltage to tertiary-voltage (inter-winding) insulation system, which does not include any bushing insulation
  3. CHT: The high-voltage to tertiary-voltage (inter-winding) insulation system, which does not include any bushing insulation
Figure 3: Power factor testing examines three areas in a three-winding transformer.

The guard circuit is used to isolate and measure different pieces of insulation while reducing the number of test connections required to do so (Figure 4).

Figure 4: A guard circuit isolates and measures insulation.

There are a number of ways to ensure success in power factor testing. 

  1. Make sure to clean all bushings and connections before performing the tests. 
  2. Make connections carefully and ensure the ground connection is metal-to-metal, not over a painted, oxidized, or coated surface. 
  3. Confirm that the jumpers to the short windings are taut and don’t touch surrounding surfaces. 
  4. Keep the high-voltage hook’s ground and guard rings away from the surface being energized. 
  5. Detach the bus whenever possible and attempt to guard off any left attached. Don’t forget to remove bonds, high-resistance grounding systems (HRG), or other devices that may be connected to neutrals.
  6. Don’t wait until the test is over to examine your data. Check your work after the first test and compare it to previous test data. Review current/capacitance and watts, not just the percent power factor.
  7. Do not exceed the withstand voltage of the insulation being tested. Power factor testing is non-destructive.


Sweep frequency response analysis (SFRA) is used to detect a variety of internal faults or mechanical issues that could lead to problems:

  • Mechanical displacements or deformations in the transformer’s core or winding structure
  • Shifts in the transformer core or any problems related to its mechanical integrity
  • Issues such as short circuits, ground faults, or mechanical stress that may impact the transformer’s performance
  • Mechanical damage during transportation, installation, and operation
  • Problems with bushings, such as misalignment or deformation, and issues with terminal connections
  • Issues between winding layers, such as shorted turns or displaced windings
  • Problems related to the clamping and bolting systems that hold the transformer’s components together
  • Changes in frequency response that can indicate certain mechanical and electrical issues

Changes in the phase shift and magnitude of the response curves that point to potential problems

SFRA can also indirectly identify corona discharges or partial discharges within the transformer, which are indicators of insulation issues.

SFRA testing is appropriate in a variety of situations. These include immediately after transformer production, before and after transporting the transformer, and after commissioning the unit. It’s also relevant after an incident in which electromechanical changes are suspected. These could be catastrophic events, such as earthquakes or hurricanes. Similarly, if any vibration or high-temperature alarms occur or short-circuit faults occur, SFRA testing should be undertaken.

SFRA testing begins with the application of an excitation signal, typically a sinusoidal waveform, to the transformer winding. The test signal covers a range of frequencies, from a few hertz to a few megahertz. As the excitation frequency changes, the transformer responds by producing an output signal, which is recorded. This signal contains valuable information about the transformer’s behavior at different frequencies. 

The recorded data is used to create a frequency response curve, often represented graphically.  Different parts of the response curve reveal different conditions of the transformer. Significant deviations from a reference curve, which is typically created when the transformer is known to be in good condition, are analyzed, as they can indicate various mechanical and electrical issues within the transformer.

Various issues are seen in different parts of the response curve (Figure 5). The very-low frequencies indicate core problems and shorted or open windings. In the middle frequencies, winding deformations are indicated. The high frequencies reveal tap connections and other winding connection problems.

Figure 5: Different transformer issues are seen at different frequencies in the response curve.

The following frequencies are associated with specific issues:

  • 20 Hz–2 kHz: Core deformation, core ground problems, shorted turns, open circuits, and residual magnetism
  • 2–20 kHz: Winding movement and shunt impedance
  • 20–400 kHz: Deformation of the main and tap windings
  • 400 kHz–2 MHz: Movement of the main and tap windings and ground impedance variations

Software analysis of response curves makes it easy to detect deviations from the reference curve. Typical SFRA tests include end-to-end open circuit, end-to-end short circuit, capacitive inter-winding (CIW), and inductive inter-winding (IIW).

  • The end-to-end open circuit test examines both the windings and core. It is commonly used because of its simplicity and the ability to examine each winding separately. A test signal is applied to one end of a winding, with the transmitted signal measured at the other end. In this configuration, the magnetizing impedance of the transformer is the main parameter characterizing the low-frequency response (below the first resonance).
  • The end-to-end short circuit test is similar to the end-to-end open circuit, but a winding on the same phase is short-circuited. It provides the ability to examine an individual winding. The influence of the core is removed below 10–20 kHz because the low-frequency response is characterized by the short-circuit impedance/leakage reactance instead of the magnetizing inductance. The test’s response at higher frequencies is similar to end-to-end open circuit measurements.
  • The CIW test looks at the capacitance between windings. It requires a test signal to be applied to one end of a winding and the response measured at one end of another winding on the same phase that is not connected to the initial winding. The response using this configuration is dominated at low frequencies by the inter-winding capacitance.
  • The IIW test evaluates the inductance of both windings. For this test, the signal is applied to a terminal on the high-voltage side, with the response measured on the corresponding terminal on the low-voltage side. Both windings must be grounded. The low-frequency range of this test is determined by the winding turns ratio.
  • The CIW curve is capacitive at low frequencies, whereas the IIW curve reflects the turn ratio at low frequencies, as seen in Figure 6. Both curves have a similar response at high frequencies.
Figure 6: The CIW curve is capacitive at low frequencies, whereas the IIW curve reflects the turn ratio at low frequencies. Both curves have a similar response at high frequencies.

SFRA analysis relies on comparative results. Repeatability is critical over the life of the transformer. Three types of data analysis are related to SFRA testing: time-based, type-based, and design-based.

  1. Time-based analysis uses test results from the same transformer. Any deviations between the curves indicate potential problems. Time-based analysis is the most reliable comparative SFRA testing approach.
  2. To evaluate transformers of the same design run, type-based analysis is appropriate. It does, however, require knowledge of the transformer design. With this kind of analysis, small deviations do not necessarily indicate a problem.
  3. When the design of the transformer winding legs and bushings are identical between transformers, a design-based analysis can be performed. As with type-based analysis, small deviations do not necessarily indicate an issue.

In any event, successful data analysis of SFRA test results means following some best practices:

  • Use high-quality, high-accuracy instruments and the same applied voltage in all SFRA measurements.
  • Ensure good connections on the measurement terminals.
  • Use the shortest braid grounding from the shields of coaxial cables to the flange of the bushing.
  • Ensure transformer conditions are similar (taps, oil level, etc.).
  • Make sure all connections are clean.
  • Document tests well. Photos of connections can help.
  • Research the transformer ahead of testing and have any past results in hand.
  • Because SFRA is an AC test, perform it before DC testing or ensure the core is demagnetized.


Power factor and sweep frequency tests are an important part of a comprehensive transformer maintenance plan. When combined with routine inspections, these tests can mitigate costly failures. 


[1] bp America. BP Refineries Fact Sheet, Updated March 2024. Accessed at:

[2] Seba, Erwin and Somasekhar, Arathy. “Power loss forces BP to shut biggest US Midwest refinery,” Reuters, February 1, 2024. Accessed at: www.reuters.com/business/energy/power-loss-forces-bp-shut-biggest-us-midwest-refinery-2024-02-02/. 

[3] Sims, Chris. “BP Whiting power outage spawns fire, evacuations. What to know in Indiana refinery shutdown,” Indianapolis Star, February 2, 2024. Accessed at: www.indystar.com/story/news/2024/02/02/bp-refinery-whiting-indiana-fire-february-1-2024-oil-power-outage-evacuations/72448317007/.

[4] Murray, Christopher. “Gas prices jolted up by 12 cents as Indiana oil refinery remains closed: AAA,” Fox Business, February 16, 2024. Accessed at:

Matthew Wallace is President of Field Services at CBS Field Services. A graduate of Iowa State University and the U.S. Navy Nuclear Program, he has more than 25 years of experience in the electrical testing and commissioning industry. Wallace is a NETA Level 4 Certified  Technician.