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Abstract

This article introduces two models based on the IEEE [1] and IEC [2] loading guides to compute the HST of a transformer winding. The models are solved numerically using arbitrary load and top oil temperature profiles. The results are then compared to highlight relative characteristics of the models.

Introduction

The Transformer Loss of Life (LoL) is based on knowing the HST [3]. It is generally adopted that the HST is given by (1).

Where:

θ_H is the HST;

θ_A is the average ambient temperature during the load cycle;

∆θ_TO is the top oil temperature rise; and

∆θ_H is hot-spot to top oil temperature rise.

Traditional models [1, 2] estimate the HST based on (1) and require inputs that include: (i) parameters specific to the transformer; and (ii) real-time measurements of ambient temperature, top oil temperature and load current. In recent years transformer manufacturers have included fibre optic sensors (FOS) distributed throughout the windings which conveniently provide an accurate HST measurement leading to a better estimate of the LoL. There are still many transformers in the field that do not incorporate FOS and rely on traditional models for maximising their useful lifespan. This work describes two traditional models for estimating the HST in oil immersed transformers; the models are solved for the HST and compared.

HST models

In our applications, the top oil temperature is provided (measured) and therefore analysis is limited to models that consider only the hot-spot to top oil temperature rise.

Model 1: The model referred to in Clause 7 [1] as ‘transient heating equation’ is based on work by Kennelly [4] who showed that the winding temperature rise above room temperature is exponential, and Cooney [5] who proposed that the winding temperature rise above top oil and the top oil temperature rise can be treated separately. The model assumes an average ambient temperature of 30°C and step changes in load.

The transient winding HST rise over top oil temperature is given by (2).

Where:

t is the duration of the load;

∆θ_H is the hot-spot to top oil temperature rise.

∆θ_H,u is the ultimate winding hottest-spot rise over top oil temperature for the load;

∆θ_H,i is the initial winding hottest-spot rise over top oil temperature for t=0; and

τ_W is the winding time constant at the hot-spot location (4.8 minutes [6]).

The initial and ultimate HST rises over top oil temperature are given by (3).

Where:

m is an empirically derived exponent to calculate the variation of ∆θ_H with changes in load (this varies with the type of cooling and equal to 0.8 for ONAN cooling [1];

K_u is the ratio of ultimate load to rated load;

K_i is the ratio of initial load to rated load; and

∆θ_H,R is the winding hottest-spot rise over top-oil temperature at rated load (typical values range from 20°C to 35°C [6]).

Model 2: The most recent model [2], is based on work by Swift [7] who proposed a thermal model of a power transformer based on heat transfer theory with an equivalent electrical circuit for determining the HST, shown in Figure 1.

Figure 1: Thermal model of winding-to-oil heat transfer

The current source q_wdn is the heat generated by the winding losses, C_th-wdn is the thermal capacitance of the winding, R_th-hs-oil is the non-linear winding to oil thermal resistance, and θ_hs is the HST. Swift’s model is further extended by considering the hot-spot rise dynamic as differences between the fundamental hot-spot rise and the effect of the varying oil flow that influences the HST given by (4).

∆θ_h1 represents the change in the fundamental hot-spot rise given by (5).

∆θ_h2 epresents the varying rate of oil flow past the hot-spot, a phenomenon which changes much more slowly and given by (6).

The combined effect of (5) and (6) account for the scenario where a sudden rise in the load current may cause an otherwise unexpectedly high peak in the HST rise, very soon after the sudden load change [2]. Additionally, k₂₁ and k₂₂ are dimensionless parameters and shape (5) and (6) according to Table 1.

Table 1: Recommended thermal characteristics for exponential equations [2]

Model solutions

In this section equations are solved numerically for various scenarios. The actual time is equal to the time increment, set to 0.0167 minutes, multiplied by the time index shown in the graphs. Distributions of Load Factor (LF) and top oil temperature, shown in Figures 2 and 4, are created for the purpose of highlighting the characteristics of the models.

The thermal effect of the oil on the winding HST rise in Model 2 is further investigated by setting k₂₁ to 1 and 3 and by applying the distributions shown in Figure 4. When k₂₁ is set to 1, the effect of oil is not included and the transient behaviour is solely due to the winding constant. Setting k₂₁ to 3 ensures the contribution of the oil time constant in (6) and with (4) now resulting in a subtraction of two first order step responses. The effect is shown in Figure 5, with the response initially exhibiting significant overshoot in the first three excursions and eventually settles to a final value. The effect is due to the inertia of the oil, and is more prevalent in ONAN^a and ONAF^a transformers where oil circulation is restricted, refer to Table 1. The slow decay in the response is due to the oil constant which is ~ 21 times that of the winding constant.

Transformer Monitoring
CHK Power Quality Pty Ltd offers the Miro-F TXM Transformer Monitor and Logger (TxM), an instrument purposely suited for comprehensive monitoring of transformer health and can provide LoL calculations based on the IEC and IEEE Standards.

The TxM includes two temperature sensors which can be software configured to measure the top oil and ambient temperatures. Where the transformer is equipped with multiple winding temperature sensors the TxM, together with the Miro Auxiliary I/0 module (Miro Aux), can utilise these inputs in its LoL calculations.

Setting up and configuring the TXM requires the user to populate a template with relevant transformer ratings and other known parameters specific to the transformer. Alternatively, the user can use default values, provided in the TxM, for parameters that are not readily available on the transformer’s name plate.

The TxM together with the Miro Aux can expand the monitoring to include geomagnetic DC current; dissolved gases such as oxygen; moisture; on load tap changer (OLTC) operation; bushing leakage current; and fan operation. All these parameters can, not only be displayed alongside critical power quality information but also correlated for in depth analysis.

References

[1] “IEEE Guide for loading mineral-oil-immersed transformers and step-voltage regulators”, IEEE Standard C57.91, 2011.

[2] “IEC Power transformers, Part 7: Loading guide for oil-immersed power transformers”, IEC 60076-7, 2018.

[3] “Introduction to Transformer Loss of Life – based on models from IEC and IEEE loading guides”, Transmission and Distribution, Issue 3, June-July 2021, pp. 38-40.

[4] A. E. Kennelly, “The Thermal Time Constants of Dynamo-Electric Machines”, Winter Midwinter Convention of the A.I.E.E Transactions, New York, USA, Feb. 9-13, 1925, pp. 137-154.

[5] W. H. Cooney, ”Predetermination of Self-Cooled Oil-Immersed Transformer Temperatures Before Conditions are Constant”, A.I.E.E Transactions, vol. 44, pp. 611-618, 1925.

[6] “American National Standard guide for loading mineral-oil-immersed power transformers up to and including 100MVA with 55°C or 65°C winding rise”, ANSI/IEEE Standard C57.92, 1981.

[7] G. W. Swift, T. S. Molinski, and W. Lehn, “A Fundamental Approach to Transformer Thermal Modeling – Part 1: Theory and Equivalent Circuit”, IEEE transactions on power delivery, vol. 16, No. 2, pp. 171–177, April 2001.

Technical note – OTA Upgrade for the HL7650 Modem F/W, Using the AirVantage platform, 29 June 2022, rev 1.00

Telephone: +61 2 8283 6945; Fax: +61 2 8212 8105

Website: www.chkpowerquality.com.au

Updating the Firmware of the Miro’s Wireless 3G/4G HL7650 Modem Remotely, via the Sierra Wireless AirVantage Platform

This guide illustrates how to update the firmware of the Miro instrument’s Sierra Wireless HL7650 modem remotely via the AirVantage platform, for the Miro instrument to be able to operate over Telstra’s upgraded 4G LTE network. The AirVantage platform is provided by Sierra Wireless, the manufacturer of the modem.

Overview

Requirements

The following are required to carry out and complete the upgrade:

• Citrus_v1.3.0.10.exe
• miro_v3.16_May04.fw
• An operating Miro instrument that can be communicated with and installed with a Sierra Wireless 3G/4G HL7650 modem for 3G/4G remote cellular communications
• SIM card installed in the Miro instrument that can connect to the ‘telstra.internet’ APN. Contact service provider if unsure or if it is not available on the SIM card
• Internet access and a PC or laptop
• Basic working knowledge on installing, accessing, and using the Citrus software.

Setting up the Miro instrument for upgrade

Step 1: Install Citrus version 1.3.0.10 using the Citrus_v1.3.0.10.exe file provided.

Step 2: open the Miro instrument’s operation page using Citrus version 1.3.0.10. The Miro’s operations window will appear as shown in Figure 1.

Step 3: Click on ‘Upgrade Firmware’ and navigate to the folder containing the miro_v3.16_May04.fw firmware. Select the firmware file and click ‘Open’. This will start the firmware upgrade. Firmware upgrade progress will be indicated by the green progress bar at the bottom of the operations window.

Please note that during any restart process in this instruction, it may take several minutes to restart the Miro instrument along with its communications. Multiple connection attempts may also be needed, especially with the SSH secure connection which can take longer to connect.

Once the upgrade is complete the Miro instrument will reset, causing loss of connection as shown below in Figure 2. Open the Miro operations window and note the firmware listed should be ’3.16’.

Step 4: On the operations window, click on ‘Configuration’ to open the Miro configuration page. Navigate to the ‘Cellular OTA Updates’ tab. Tick ‘Enable OTA updates’ and enter ‘telstra.internet’ in the ‘APN:’ box as shown in Figure 3. Please note that “telstra.internet” is used only by the modem to retrieve firmware from the AirVantage website; the Miro instrument itself is not exposed to the internet. Care should be taken that changes are made only in the ‘Cellular OTA Updates’ tab, to prevent loss of remote cellular communication with the Miro instrument. Following the example shown in Figure 3, set ‘Polling interval (minutes):’ to 60 minutes (recommended polling interval). Once done, click ‘Save Config To Device’ and click ‘OK’ in the ‘Configuration set’ pop up.

Step 5: In the Miro operations window, restart the Miro instrument to apply the configuration changes made in the ‘Cellular OTA Updates’ tab. After restart is complete, navigate to the Miro operations window. Download a Miro datafile of the Miro instrument and open the datafile. Click on the ‘Diagnostics’ tab and from the drop-down menu click ‘Comms’ then ‘Network Status’. Choose where to save the Network Status file and then click ‘Yes’ on the ‘Network Status exported. Open file now?’ popup to open the Network Status file as shown in Figure 4.

From the Network Status log, scroll down to the bottom where the latest network status is and note both the IMEI and serial number of the HL7650 modem. As shown below in the Figure 5 example, the IMEI number is listed after the word ‘IMEI:’ i.e., ‘354940080029209’ (underlined in red). The serial number is the number listed after the word ‘+KGSN:’ i.e., ‘TD724385541410’ (underlined in blue). The current firmware version of the modem is also listed i.e., ‘SWIMCB71XX-TIM3.23.01.173400.201708251955.01’ (underlined in green). Note down these values as they will be required later when registering the modem on the AirVantage platform. Repeat Steps 2 to 5 for each Miro Instrument.

Website: www.chkpowerquality.com.au

Creating an AirVantage account

Step 6: Using your internet browser, open the link https://eu.airvantage.net/accounts/signup?type=UFOTA. At the bottom of the page click on ‘SIGN UP’. A new page will then open, enter your details as required to create a user account as seen in Figure 6. Once done, click on ‘SIGN UP’. An activation email will be sent to your email address upon successful sign up as seen in Figure 7. Click ‘SIGN UP ACCOUNT’ to activate account.

Step 7: Log into the newly created account using the following link: https://eu.airvantage.net/start. Upon successful login, the following account page is shown as seen in Figure 8. From the example in Figure 8, we can see that there is a total of two modem units registered on AirVantage with this account. Click on ‘Register new Systems’ (boxed in green in Figure 8).

Step 8: On the registration page under the ‘Register AirPrime HL Series’ box, register the HL7650 modem in AirVantage by choosing the ‘Type’ as ‘HL7650 (GENERIC)’ and inputting the ‘Serial Number’ and ‘IMEI’ that was noted in Step 5 into the corresponding fields. For the ‘Name’, this will be the name of the modem and is up to the user on what name is given. In this example, the modem was given the name ‘demonstration modem’ as seen in Figure 9. Select ‘Pre-configure system’ and then click ‘Register’

Note that multiple HL7650 modems can registered at once by clicking on ‘import a list’ and uploading a CSV file in the required format. For more details see: https://doc.airvantage.net/fota/reference/register/howtos/registerListOfSystems/.

Step 9: A ‘Pre-configure System(s)’ popup will appear as seen in Figure 10. Click on the bins on the right-hand side of the ‘Basic Workflow’ and ‘Send Wakeup’ boxes (boxed in red in Figure 10) to remove the boxes from the workflow.

Under ‘Individual actions’ on the left-hand side of the ‘Pre-configure System(s)’ popup, drag (press and hold left mouse button) the ‘Install Firmware’ (boxed in green in Figure 10) to the right side of the popup and release. This will now bring up an ‘Install Firmware’ box as seen in Figure 11.

In the ‘Install Firmware’ box, from the dropdown menu, select firmware version ‘HL7650 (Generic) (SWIMCB71XX-TIM3.26.00.A01.173700.201804050215.01)’. Note the ‘A01’ which indicates the latest version of the firmware as of March 2022. Once done, click on ‘Pre-configure’. This will close the popup.

Step 10: Upon successful registration of the modem, the modem will appear in the ‘Registered Systems’ box underneath the ‘Register AirPrime HL Series’ box as seen below in Figure 12. If it doesn’t appear, the ‘Registered Systems’ box can be manually refreshed by pressing the refresh button seen in Figure 12 (boxed in red) and the modem should appear in the list. Note that the refresh icon is normally not visible until the mouse cursor is hovering over the area as indicated in Figure 12.

Click on the purple cloud icon (boxed in green in Figure 12) which says ‘See the System details in the Upgrade activity’ when the cursor is put over it. This will take you to the upgrade page for that modem.

Step 11: With the modem set for pre configuration, AirVantage will automatically attempt to synchronise to the modem after registration as seen in the ‘Systems Operations’ box in Figure 13.

For successful synchronising with the modem and later the firmware upgrade, the modem needs to poll the AirVantage platform. With the polling interval set to 60 minutes, wait for the modem to poll AirVantage and wait for successful synchronisation as seen in Figure 14. The refresh icon may need to be clicked (boxed in red in Figure 14) to see the successful synchronisation.

Step 12: After AirVantage has successfully synchronised with the modem, the modem will automatically attempt to install the firmware for the modem and the ‘Install application’ task will appear in the ‘System Operations’ box as seen in the ‘Upgrade’ page of the modem in Figure 15 (refresh icon may need to be

Step 13: During modem firmware upgrade, 3G/4G connection will be reset and so connection of the Miro instrument to Citrus will be lost. Once the upgrade has been completed, the ‘Install application’ progress bar in the ‘Upgrade’ page will be completely green and the ‘Firmware’ version will be displayed in ‘System Info’ as shown in Figure 16 (boxed in red). The refresh icon on the ‘Upgrade’ page (boxed in green in Figure 16) may be required to be clicked more than once during and after upgrade to see the updated statuses on the ‘Upgrade’ page.

Alternatively, to check that the modem has the latest version of the firmware installed, check the network status log of the Miro instrument and note the firmware number now listed as ‘SWIMCB71XX-TIM3.26.00.A01.173700.201804050215.01’ (underlined in red in Figure 17).

Step 14: With the modem firmware update done, the OTA updates for the Miro instrument needs to be turned off. To do this, untick the ‘Enable’ box on the ‘Cellular OTA Updates’ page on Citrus (see Figure 9). Repeat Steps 8 to 14 for each Miro Instrument as necessary.

Step 15: Once upgrade of all HL7650 modem firmware is successful, the Citrus software needs to be reverted back to the latest released version. This can be found on CHKPQ’s website via the link: https://www.chkpowerquality.com.au/downloads/

and as seen in Figure 18. The link to download the Citrus software on this page is underlined in red.

Install the Citrus software version available for download from the CHKPQ website to the same folder where Citrus version 1.3.0.10 is located. This will overwrite Citrus version 1.3.0.10. The upgrade process is now complete.

Technical note – OTA Upgrade for the HL7650 Modem F/W, Using the AirVantage platform, 29 June 2022, rev 1.00

Telephone: +61 2 8283 6945; Fax: +61 2 8212 8105

Website: www.chkpowerquality.com.au

Abstract

Transformer harmonic current derating metrics; Harmonic Loss Factor, K-Factor, and Factor K are introduced, and used to calculate derating factors for dry and oil-filled type transformers.

Introduction

The introduction of Switched Mode Power Supplies (SMPS) in office equipment and LED lighting, Variable Frequency/Speed Drives (VF/SDs) to operate induction motors, and inverters that change DC, from photovoltaic cells, to Mains Frequency AC to drive Mains Frequency equipment or even feed upstream into the power grid are just some examples of how electronics are helping to increase efficiency in power usage. One drawback is their non-linear nature, which can yield significant voltage and current harmonic content both at the input and output, if not appropriately filtered. Harmonics on supply lines feed upstream into transformers, causing higher than expected heating and ageing. Excessive heating could lead to catastrophic outcomes (Picture 1). This work introduces three metrics; Harmonic Loss Factor, K Factor, and Factor K; developed to assess the impact of current harmonic heating of transformers.

Transformer losses

The IEEE Standard C57.110-1986 [1] is developed to limit transformer temperature rise due to non-sinusoidal load currents [2]; it describes the load losses and a method to calculate load reduction required, so as to not exceed rated losses given the harmonic spectra of the load current.

Total transformer loss P_T (1) is the sum of no-load loss (excitation loss) P_NL and load loss (impedance loss) P_LL.

It is assumed in the proceeding work that the voltage harmonic distortion does not significantly increase the excitation loss, leaving the load loss the dominating source of loss at rated load. The load loss consists of copper loss, P (also referred to as I²R) and stray losses P_SL. Stray loss is due to stray electromagnetic flux in the winding, core, core clamps, magnetic shields, enclosure, or tank walls [1]. The stray losses can be decomposed into eddy current losses in the winding P_EC and other stray losses P_OSL (2).

The copper loss is given by (3) and where the RMS current is decomposed into its harmonic content.

Winding eddy current loss in the power frequency spectrum is proportional to the square of both the load current magnitude and its frequency; and can cause excessive heating and abnormal temperature rise in the presence of non-sinusoidal load current.

It is found that other stray loss increases with the square of the current magnitude and by a harmonic exponent factor no greater than 0.8 [3].

P_EC-R and P_OSL-R are losses under rated conditions, and where I_R and is the rated current.

K-Factor

Underwriters Laboratories (UL) developed a metric called the K-factor [4], (6), a rating optionally applied to a dry-type transformer indicating its suitability for use with loads that draw non-sinusoidal currents and weights the harmonic currents according to their effect on transformer heating. The K-factor requires the rated current of the transformer.

The K-factor is used to specify a class of transformers capable of serving non-sinusoidal loads. K-factor rating of a transformer e.g. (4, 9, 13, 20, 30, 40 or 50) is an indication of the amount of harmonic current the transformer is capable of handling without overheating. The measured K-factor of the load must be below the K-factor rating of the transformer.

When comparing (4) and (6), the K-factor provides a measure of the ratio of the winding eddy current loss P_EC to the eddy current loss under rated conditions P_EC-R and therefore, a K-factor greater than unity indicates heating exceeding the rated operating conditions of the transformer. A standard transformer that is designed for linear loads is said to have a K-factor of unity.

Harmonic Loss Factor

Harmonic loss factor F_HL is defined in (7) as the ratio of the total winding eddy current losses due to the harmonics, P_EC, to the winding eddy current losses at operating current and power frequency, as if no harmonic currents existed, P_EC-O [1].

Similarly, the harmonic loss factor for other stray loss F_HL-STR is calculated using (8) but not critical in estimating the derating in dry-type transformers [3].

Note: is other stray losses at operating current and power frequency, as if no harmonic currents existed.

The K-factor and harmonic loss factor are related using (9).

From (9), the K-factor and F_HL are equal only when the RMS current value is equal to the rated current of the transformer. Under normal operating conditions the RMS current value should be less than the rated current and so the K-factor is less than F_HL .

Derating

The maximum amount of harmonic load current that a standard transformer can deliver without exceeding rated operating conditions is given by (10) [5]. I­_max (pu) is also used as a derating factor.

For dry-type transformers P_OSL-R (pu) is zero and (10) reduces to (11).

From (11) no derating is required when F_HL is unity. Equation (11), rewritten in terms of K-factor will yield the same value of derating. The UL standard [4] prescribes another method for derating dry-type transformers using K-factor.

Factor K

Another method used to derate a standard oil-filled transformer to harmonic load is referred to as Factor K [6] and given in (12).

e is the eddy current loss due to sinusoidal current at the fundamental frequency, divided by the loss due to DC current equal to the RMS current of the sinusoidal current value, both at reference temperature. The exponent q is dependent on the type of windings and on the frequency. As a guide, q is set to 1.7 for transformers with round or rectangular wire in both low and high voltage windings and to 1.5 for transformers having low voltage foil windings. The derating factor is given by 1/F_K.

Worked example

A VSD is connected to a transformer rated at 200A. The input current spectrum to the VSD resembles that of a six-pulse rectifier and normalised to 104.1A RMS. The rated eddy current loss P_EC-R , e and q are set to 10%, 0.1 and 1.7 respectively. The transformer harmonic derating metrics are calculated using equations (6), (7), (8) and (12). Equations (11) and (12) are used to calculate the derating of dry-type and oil-filled type transformers respectively.

The maximum harmonic number is limited to 25 as provided in the IEEE Standard C57.110-1998 [3]. It is noteworthy that the skin effect becomes more pronounced with frequency and eddy-current loss is smaller than predicted; values are conservative in particular above the 19^th harmonic [3].

In Figure 1 at each harmonic number, the harmonic derating metrics are calculated considering contributions of harmonics up to and including the harmonic number; and as expected the metrics increase in value with increasing harmonic number. The values at the 25^th harmonic for F_HL , K-factor, F_HL-STR and Factor K are 8.35, 2.26, 1.34, and 1.15 respectively.

In Figure 2 the derating factors for dry-type and oil-filled type transformers are 77.4% and 87.2% respectively with equivalent operating currents of 155A and 174A.

Please contact CHK Power Quality for a free and no obligation demonstration or trial.

Phone: +61 2 8283 6945
Email: sales@chkpowerquality.com.au

References

[1] IEEE C57.110-1986, “IEEE Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents”.

[2] M.A.S. Masoum, P.S. Moses, A.S. Masoum, “Derating of Asymmetric Three-Phase Transformers Serving Unbalanced Nonlinear Loads”, IEEE Transactions on Power Delivery, Vol. 23, No. 4, October 2008, pp. 2033-2041.

[3] IEEE C57.110-1998, “IEEE Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents”.

[4] UL-1561-1994, “Dry-Type General Purpose and Power Transformers”.

[5] S.B. Sadati, A. Tahani, M. Jafari, M. Dargahi, “Derating of Transformers under non-sinusoidal Loads”, International Conference on Optimization of Electrical and Electronic Equipment, Brasov, Romania, pp. 263-268, 2008.

[6] EN50464-3: 2007, “Three-phase oil-immersed distribution transformers 50Hz, from 50kVA to 2500kVA with highest voltage for equipment not exceeding 36kV – Part 3: Determination of the power rating of a transformer loaded with non-sinusoidal currents”, April 2007.