GridLAB-D™ Model Validation Process: Example Application to Power Supply Circuit

The framework is applied to the example case of the design of a simple DC power supply, which converts 120V, 60Hz AC to 10V DC. Boxes in the flowchart below contain clickable content with questions and statements specific to implementing this example within a software environment.

A model of a power supply is developed with the goal of modeling the output voltage given loading conditions, focusing on characteristics like VRMS and ripple in steady state. The model will be used to choose the proper components to construct the power supply in order to meet power quality specifications. The model is validated by comparing simulated results to the measurements taken in a simple benchtop experiment.

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Project Scope

These blocks address questions and process steps related to the overall scoping and goals of the final model. They are meant to provide an initial guide to translating high-level requirements towards a specific final model.

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Software

These blocks address questions related to the software model and the modeling environment. This will include questions on the actual implementation, as well as limitations imposed by the chosen environment/platform on both the model implementation and subsequent simulations.

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Hardware

These blocks address questions relating to the physical device being modeled and the testing environment. This will include specifics properties of the physical device, testing capabilities of the available facility and equipment, and the process to obtain validation data for refining the software model.

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Decision

These blocks represent decision points or development of evaluation criteria in the framework process. They often represent a point in the process where the effectiveness of the approach or sufficiency of information must be decided. Affirmative outcomes result in progression through the flowchart. Negative outcomes don't necessarily constitute a failure, but may require a reiteration within the current section to refine details of the approach or implementation.

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Problem Statement/Goals of Study

Mission statement: create a model that can be used to help design a simple power supply for a given load and power quality specification.

The device is a simple unregulated power supply, fed by 120V, 60Hz wall power, with a fuse, transformer, full bridge rectifier, capacitor, and bleeder resistor (Figure 1). The goal is that given the impedance of a load, target VRMS and maximum ripple (Figure 2) we can model the output waveform and choose the proper fuse rating, transformer rating, capacitor size, and resistor size. The model will be limited to steady state behavior.

circuit diagram

Figure 1. Circuit Diagram

ripple

Figure 2. Definition of Ripple

Time Scale

Because stated power quality requirement concerns ripple, VRMS, and power rating, EMTP scale modeling is unnecessary. To accurately measure and model ripple, a few data points per 60Hz cycle are necessary, so millisecond level modeling and testing is a good goal. Because the focus is steady state behavior, a single time scale is sufficient. The duration to capture the behavior of interest is a few cycles at 60Hz, or less than a second. It is necessary to repeat both the test and the simulations with different combinations of components. Given the ms scale and short duration, the total number of calculation cycles should be very reasonable.

Quantities of Interest

The primary goal is to model voltage as a function of time, V(t), across the load.

The model will also be able to output V(t) and current as a function of time, I(t), at the input to the power supply, across the fuse, across the transformer, across the rectifying bridge, across the capacitor, and across the load. These are fundamental quantities, not derived. All voltages should be modeled with better than 0.01V accuracy.

Measurement of V(t) across the load are the primary quantity of interest, but it should be possible to measure the voltage and current at the input, across the fuse, across the transformer, across the rectifier, across the capacitor, and across the load. Measurements have better than 0.01V accuracy and it is possible to measure both the input voltage, 120V, and the voltage across the load, approximately 10V DC.

This is a device-level, steady state model, so there will not be multiple levels of detail or any aggregation.

Decision Point: Goals

Yes, the project goals can be met given the time step and duration. Yes the project goals can be met given the resolution and dynamic range of quantities of interest.

Fatal

  • Can this problem be fixed with a parameter or procedural adjustment?
  • Is the process missing any equipment or software capabilities needed?
  • Does this require starting the model validation process from the beginning?

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Model Capabilities

This problem requires a device-level model. Quantities that are modeled are V(t) and I(t) at input, across each circuit component, and across the load.

The input to the modeled device is a modeled wall supply, an infinite bus with a perfect 120V, 60Hz sinusoidal waveform. At the output the load is modeled, separately from the device, as a black box with specified impedance. The power supply reacts to characteristics of the load. The focus is the supplied steady state voltage, and there are no perturbing events.

All quantities are modeled with 1ms resolution. There are no relevant control states, as this is a passive device.

Available computing resources can easily model a device consisting of five parts, at ms level, for less than a second for each run.

Test Capabilities

For this test, a benchtop laboratory setting is optimal. Since the goal is to design an ideal power supply given a stated load and power quality requirement, it must be possible to swap in and out each component. A breadboard-style setup is required, as well as a varied set of components.

To stand in for the load, a tunable or swappable load is ideal, in which 0.1W to 10W can be consumed at ~10V. To provide the supply, a function generator that can generate a clean 120V, 60Hz sinusoid is required.

To make measurements, an oscilloscope is required, with a data link to a computer. The scope must have better than 0.01V resolution and the ability to probe both 120VAC and 10VDC. The scope must also have at least 1ms resolution.

Acceptance Criteria

The most pertinent point of comparison is V(t) supplied to the load across a single typical cycle, at 1ms time resolution. The largest source of inaccuracy is the uncertainty in component specification, and therefore that uncertainty will directly inform the acceptance criteria. VRMS should agree to within the accuracy of the transformer rating and the accuracy of the voltage drop across the rectifier, and the magnitude of the ripple should agree to within the fractional accuracy of the capacitor magnitude and accuracy of combined load and bleeder resistor impedance. The focus of the comparison will be on steady state behavior.

If V(t) across the load does not agree within limits, V(t) and I(t) at intermediate points of the power supply circuit are compared to determine the source of the inaccuracy.

The transformer model is a simple perfect voltage transformation, so the leakage across the transformer is not modeled. Noise due to the measurement tools is expected and disregarded; this noise source will be significantly lower than the required accuracy with a standard scope.

Decision Point: Capabilities

Yes, simulations and hardware tests are capable of addressing the acceptance criteria. The simulations capture all of the quantities of interest, as do the hardware tests. The fit criteria are compatible with expected noise levels.

Structure

The boundaries of the model are the infinite bus at the input and the output voltage supplied to the load. At each time step, V is specified to the downstream component and I is returned to the upstream component. The overall structure of the model is a series of very simple sequential blocks. The starting point is the infinite bus, then the fuse, then the transformer, then the rectifier, then the capacitor, bleeder resistor, and load impedance.

The fuse is modeled as a simple binary switch at the rated power. The transformer is modeled as a simple linear voltage transformation, and is exactly solvable. The rectifier is modeled as a simple voltage drop. The exponential decay due to the combination of the capacitance, the bleeder resistance, and the load impedance is calculated as a linear approximation; only the linear term of the Taylor expansion is kept. No transformations are required.

The system and device are single-phase. The harmonic signals are all represented in point-on-wave.

Parameters

The required parameters are as follows:

  • time step
    • 1 ms
  • input power
    • input voltage: fixed at 120V, uncertainty is 0.01V
    • frequency: fixed at 60Hz, uncertainty is 0.01Hz
    • impedance: assumed infinite bus
  • fuse
    • power rating: fixed, swappable, uncertainty given by specifications of chosen component
  • transformer
    • voltage ratio: fixed, swappable, uncertainty given by specifications of chosen component
    • power rating: fixed, swappable, uncertainty given by specifications of chosen component
  • bridge rectifier
    • voltage drop: fixed, swappable, uncertainty given by specifications of chosen component
    • power rating: fixed, swappable, uncertainty given by specifications of chosen component
  • capacitor
    • magnitude: fixed, swappable, uncertainty given by specifications of chosen component
  • bleeder resistor
    • magnitude: fixed, swappable, uncertainty given by specifications of chosen component
  • load impedance
    • magnitude: fixed, swappable

The operating point of interest is steady state, but the device will be initialized with a "cold start" with the capacitor voltage and transformer currents initialized to 0.

Simulation

Simulation executed as expected.

System Staging

Environment is laboratory bench. Device is constructed for testing purposes on a breadboard with swappable components. Input is from function generator that can generate a 120V, 60Hz sinusoid. Output is V(t) across a load, which has variable impedance.

Measurements are of steady state behavior. The oscilloscope is used to measure one point at a time, and measurements do not need to be simultaneous or share a timebase. Test equipment is non-invasive while measuring V(t) at various places through the use of a 1MOhm scope probe. Data is saved to the oscilloscope and later transferred to a computer via a USB connection.

Tests are repeatable, and are repeated for different load characteristics and combinations of components. A lab log is used to record the data about each test; the record for each test includes the specifications for every component, the load impedance, and the observed VRMS and ripple.

Test Procedure

The expected output of each test is V(t) across the load. If it is discovered that V(t) as measured and as modeled do not agree, then V(t) is measured across each component of the circuit and compared to V(t) at each stage of the model, in order to find the source of the discrepancy. V(t) is measured for a few cycles, in order to establish steady state behavior, and then is recorded and compared across a single 60Hz cycle. In order to fully validate that the model can be used to aid power system design, an array of different load characteristics, power quality requirements, and component choices must be tested and compared to the model. An example is given below; a complete test procedure would encompass all of the combinations.

  • Power Supply Specifications:
    • load impedance is 120 Ohm
    • target voltage is 10VDC
    • target ripple is less than 1V
  • Test Procedure:
    • Tune adjustable load impedance to 120 Ohm
    • The load will consume 0.83W, so insert a transformer with a 10:1 ratio and a rating of 1W
    • Insert a fuse rated to 0.1A
    • To get a ripple of 1V, a capacitor of 800µF is required
      • Repeat test for 5 different capacitance values, centered about 800µF, with a range of at least an order of magnitude
    • Record V(t) across load in oscilloscope, transfer data to computer, and compare to model output
      • If V(t) across load does not agree within previously stated acceptance criteria, measure V(t) across each circuit component and compare to modeled values.

Carry Out Tests

The tests are carried out as expected.

Apply Acceptance Criteria

Acceptance criteria applied to comparison of simulation results and hardware test results.

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Decision Point: Acceptance

The simulation results match the hardware test results.

Apply Acceptance Criteria

Finished

    Congratulations! You have successfully implemented and validated your model!

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Restart or Exit

    Reaching this block represents a problem in the model validation process. Early discovery of this problem prevents excess time and effort from being invested in a model validation that may be impossible, or require a change in scope.

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