How to model a three-phase motor feeder system with VFD, Soft Starter, and DOL in Simscape Electrical?

Hello MathWorks Community,

I would like to create a simulation model of the attached single-line electrical diagram using Simscape Electrical. My goal is to create a model that is as faithful as possible to the provided specifications to study dynamic events like motor starting, load changes, and short-circuit scenarios.

I am looking for advice on the best practices and the most appropriate blocks to use for each component.

System Main Bus Parameters:

• Voltage: 380/254V, 3-Phase + Neutral
• Frequency: 60 Hz
• Prospective Short-Circuit Current (Icc): 42 kA
• Nominal Bus Current (In): 4000 A

The system has three main circuits, each with a different motor and starting method:

Circuit 1: 45kW Motor with a VFD

• Motor: 45 kW Asynchronous Machine.
• Starter: A 170A Variable Frequency Drive (VFD).
• Protection: 250A Circuit Breaker (Device 52.1).
• Cable: 3-core, 35mm² (+ 16mm² Neutral).

Circuit 2: 160kW Motor with a Soft Starter

• Motor: 160 kW Asynchronous Machine.
• Starter: A 300A Soft Starter (PD-01).
• Protection: 320A Circuit Breaker (Device 52.2).
• Cable: 3x single-core, 185mm² (+ 95mm² PE).

Circuit 3: 1.1kW Motor with a DOL Starter

• Motor: 1.1 kW Asynchronous Machine.
• Starter: A 9A Direct-On-Line (DOL) contactor (PD-02).
• Protection: 4A Circuit Breaker (Device 52.3).
• Cable: 4-core, 4mm².

My specific questions are:

1. Source Modeling: How can I accurately model the main source to reflect the 42 kA short-circuit current? Should I use the Three-Phase Source block and calculate the corresponding source impedance?
2. Starter Blocks: What are the recommended blocks or modeling approaches for the three different starters?

• For the VFD, is the AC-DC-AC Converter (Three-Phase) a good choice, or is there a more abstract block?
• For the Soft Starter, should I model it using antiparallel thyristors with a controlled firing angle ramp?
• For the DOL Starter, is the Three-Phase Breaker block sufficient, or should I use a separate contactor model?

1. Cable Modeling: What is the best way to model the impedance of the cables based on their cross-sectional area (e.g., 185mm²)? Should I use the PI Section Line block and estimate the R/L/C parameters?
2. Protection: How can I simulate the overcurrent trip characteristics of the circuit breakers (Device 52)?

I have attached the single-line diagram for reference. Any guidance, examples, or pointers to relevant documentation would be greatly appreciated.

Thank you!

Answer 1

[Umar]

Hi @Douglas Junio Pereira,

Thank you for your detailed question about modeling your industrial electrical distribution system in Simscape Electrical. I had already reviewed your single-line diagram and afterwards did thoroughly research the MathWorks documentation since you posted your comments on the forum, and I'm pleased to confirm that your project is absolutely achievable. Please review attached pdf to walk you through everything step by step.

[Douglas Junio Pereira]

Hello!

Thank you so much for your detailed and helpful response. It has given me a much clearer understanding of the general approach to modeling my system.

I have a follow-up question regarding the specific block library. I noticed that the solution provided uses blocks from the Simscape Foundation Library (e.g., the ideal Voltage Source from simscape/Foundation Library/Electrical/Electrical Sources).

However, for my project, I need to build the model using the specialized blocks from Simscape Electrical (Specialized Power Systems), which are specifically designed for power system analysis. I have attached a screenshot of the blocks I am using, such as the Voltage Source (Three-Phase) block that includes parameters like Short-circuit power level and X/R ratio.

Could you please provide some guidance on how to "translate" the concepts from your Foundation Library-based solution to this Specialized Power Systems environment?

For example:

1. Source Modeling: How would I configure the Voltage Source (Three-Phase) block (as shown in my screenshot) to accurately represent the 42 kA short-circuit current from my diagram? It seems this block handles it differently than manually calculating a series impedance.
2. Component Equivalence: What are the equivalent blocks in this library for modeling the VFD, Soft Starter, and DOL starter? I see blocks like AC Drive and specific Asynchronous Machine models, and I want to ensure I'm using the intended workflow for this library.

My apologies for not specifying this library constraint initially. Any help in bridging this gap between the two modeling environments would be greatly appreciated.

Thank you again for your time and expertise.

[Umar]

Hi @Douglas Junio Pereira,

Thank you for your follow-up comment and for sharing the screenshot of your Voltage Source (Three-Phase) block configuration. I appreciate you clarifying that you need to use the Simscape Electrical Specialized Power Systems library rather than the Foundation Library blocks. This is actually the correct choice for industrial power system analysis, and I'm glad you're using these specialized blocks because they're specifically designed for the type of study you're conducting. Let me address your questions in the order you raised them with detailed guidance based on the MathWorks documentation for Specialized Power Systems.

For your first question about source modeling with the Voltage Source (Three-Phase) block, looking at your screenshot I can see you're using the correct block and it's already configured to use the X/R Ratio approach for source impedance which is perfect for representing your 42 kA short-circuit current. From your screenshot I see the rated voltage is set to approximately 122 volts, frequency is 60 hertz, source impedance is X/R Ratio mode, short-circuit power level is 1e6, and source X/R ratio is 15. However, based on your single-line diagram showing 380 volts line-to-line, 254 volts line-to-neutral, 60 hertz, and 42 kiloampere short-circuit current, here's how to configure this block correctly: First set the rated voltage phase-to-phase parameter to 380 which is your system line-to-line voltage, then calculate the short-circuit power level using the formula square root of 3 times the line-to-line voltage times the short-circuit current, which for your system equals 1.732 times 380 times 42000 equals 27,626,400 volt-amperes or 27.63 megavolt-amperes, so enter 27.63e6 or 27626400 in the short-circuit power level field. For the X/R ratio which represents the ratio of reactance to resistance in the source impedance, typical values for industrial systems fed from utility transformers range from 5 to 15, and I recommend using 7 for a typical industrial installation, though your current setting of 15 is acceptable but represents a very stiff source with high reactance. Keep the phase shift at 0 degrees, frequency at 60 hertz, and modeling option as Composite three-phase ports. The Voltage Source (Three-Phase) block in Specialized Power Systems automatically calculates the internal source impedance based on the short-circuit power level and X/R ratio you provide which is much more intuitive than manually calculating impedance values. According to the MathWorks documentation at https://www.mathworks.com/help/sps/powersys/ref/threephasesource.html the block calculates source impedance as Z equals voltage squared divided by short-circuit power, then X equals Z times X/R divided by square root of 1 plus X/R squared, then R equals X divided by X/R, and finally L equals X divided by 2 times pi times frequency. The documentation states you can specify the source internal resistance and inductance either directly by entering R and L values or indirectly by specifying the source inductive short-circuit level and X/R ratio. For your second question about component equivalence in Specialized Power Systems for the three motor starter circuits, let me address each one: For Circuit 1 the Variable Frequency Drive rated at 170 amperes driving the 45 kilowatt motor, you have two main approaches for VFD modeling. The simplified averaged model which I recommend for motor starting studies uses the Universal Bridge block configured as a three-phase inverter found at Simscape then Electrical then Specialized Power Systems then Power Electronics, configure it to Inverter mode, set the power electronic device to Averaged for faster simulation without modeling individual switching events, and use default or infinite snubber values for ideal switches. This approach models the fundamental frequency behavior making it perfect for studying motor starting transients, load current profiles, system voltage stability, and interaction between multiple motors. The detailed switching model for harmonic analysis requires building a full AC-DC-AC converter with a Three-Phase Diode Bridge for the rectifier stage, a Series RLC Branch capacitor for the DC link, a Universal Bridge with IGBTs and PWM control for the inverter stage, and Simulink blocks to implement voltage per hertz control or field-oriented control. The Universal Bridge documentation is at https://www.mathworks.com/help/sps/powersys/ref/universalbridge.html and you can search in MATLAB for ac3_example or Motor Control in the Specialized Power Systems examples. For Circuit 2 the Soft Starter rated at 300 amperes driving the 160 kilowatt motor, use thyristor-based voltage control with these component blocks: six Thyristor blocks total with two per phase in antiparallel found at Simscape then Electrical then Specialized Power Systems then Power Electronics then Thyristor, configure two thyristors per phase for bidirectional AC current flow by connecting them in antiparallel with cathode of one to anode of the other. Create a firing angle control system using a ramping signal in Simulink that goes from approximately 90 degrees down to approximately 5 degrees over your desired start time typically 10 to 15 seconds, where at 90 degrees minimal voltage reaches the motor for soft start and as the angle decreases voltage increases and the motor accelerates, then connect this signal to the gate pulse inputs of all thyristors. Model your current-limiting reactor RI-01 using the Three-Phase Series RLC Branch block found at Simscape then Electrical then Specialized Power Systems then Elements, set R to a small value like 0.01 ohms, set L to 3 to 5 percent impedance on motor base calculated as L equals 0.04 times rated voltage squared divided by angular frequency times motor power, and set C to infinity for no capacitance. Model the bypass contactor CS-01 using a Three-Phase Breaker block found at Simscape then Electrical then Specialized Power Systems then Elements with control logic to close when motor reaches approximately 90 to 95 percent rated speed detected using motor speed measurement, which bypasses the thyristors during normal operation eliminating continuous losses. The Thyristor documentation at https://www.mathworks.com/help/sps/powersys/ref/thyristor.html notes that the thyristor turns on when voltage across the device becomes positive and a pulse is applied at the gate terminal, and you should look for Soft-Start Induction Motor Drive examples in Specialized Power Systems or check MathWorks File Exchange for soft starter implementations. For Circuit 3 the reactor-limited Direct-On-Line Starter rated at 9 amperes driving the 1.1 kilowatt motor, this is the simplest configuration using these component blocks: the main contactor CS-02 uses a Three-Phase Breaker block found at Simscape then Electrical then Specialized Power Systems then Elements, set initial state to open, create a Simulink Step signal to control closing time, and add 50 to 100 milliseconds delay to represent realistic contactor operation. The current-limiting reactor RI-02 uses a Three-Phase Series RLC Branch with R set to small resistance between 0.01 and 0.05 ohms, L set to your inductance value if known or 3 percent impedance, and C set to infinity. Use a Simulink Step block set to your desired start time and feed this signal to the control port of the Three-Phase Breaker which closes when signal goes from 0 to 1, as documented at https://www.mathworks.com/help/sps/powersys/ref/threephasebreaker.html .

For motor modeling in all three circuits use the Asynchronous Machine block found at Simscape then Electrical then Specialized Power Systems then Machines with these key configuration parameters: for your 45 kilowatt motor in Circuit 1 set nominal power to 45e3 watts, voltage to 380 volts line-to-line, frequency to 60 hertz, and rotor type to Squirrel-cage. For your 160 kilowatt motor in Circuit 2 set nominal power to 160e3 watts, voltage to 380 volts, frequency to 60 hertz, and rotor type to Squirrel-cage. For your 1.1 kilowatt motor in Circuit 3 set nominal power to 1.1e3 watts or 1100 watts, voltage to 380 volts, frequency to 60 hertz, and rotor type to Squirrel-cage. Important settings include using Stationary reference frame for power system studies, connecting a torque input representing the load characteristic, and setting initial slip to 0 for steady-state initialization or using the Start motor at initial slip option, as documented at https://www.mathworks.com/help/sps/powersys/ref/asynchronousmachine.html

For cable modeling use the Three-Phase PI Section Line block found at Simscape then Electrical then Specialized Power Systems then Elements which is specifically designed for three-phase power cables and transmission lines. Configure it with these parameters: for Circuit 1 with 35 square millimeter conductors use R equals 0.49 ohms per kilometer, L equals 0.35e-3 henries per kilometer, and C equals 0.25e-6 farads per kilometer. For Circuit 2 with 185 square millimeter conductors use R equals 0.093 ohms per kilometer, L equals 0.25e-3 henries per kilometer, and C equals 0.35e-6 farads per kilometer. For Circuit 3 with 4 square millimeter conductors use R equals 4.3 ohms per kilometer, L equals 0.35e-3 henries per kilometer, and C equals 0.15e-6 farads per kilometer. Note that if your cable runs are short less than 50 meters and you're primarily studying motor starting you can use the simpler Three-Phase Series RLC Branch with just R and L values to speed up simulation, as documented at https://www.mathworks.com/help/sps/powersys/ref/threephasepilinesection.html

For circuit breaker protection implementation for breakers 52.1, 52.2, and 52.3 use the Three-Phase V-I Measurement block found at Simscape then Electrical then Specialized Power Systems then Sensors and Measurements, place one after each breaker to measure current and convert output to Simulink signal. Create a subsystem with two protection functions: instantaneous trip using Simulink Compare blocks where if current exceeds 10 to 15 times the breaker rating it trips immediately such as for your 320 ampere breaker in Circuit 2 trip if current exceeds 3200 amperes, and time-delayed trip implementing inverse-time characteristic using an integrator with current squared times time calculation that trips when accumulated energy exceeds threshold. Feed the trip signal to the Three-Phase Breaker control port where when signal equals 1 the breaker opens and add reset logic if desired, as documented at https://www.mathworks.com/help/sps/powersys/ref/threephasevimeasurement.html

Don't forget these essential configuration steps: add the powergui block which is required as every Specialized Power Systems model must include exactly one powergui block found at Simscape then Electrical then Specialized Power Systems then Utilities and place it anywhere in your model typically in the upper-left corner. Configure the solver by opening the powergui block, selecting Continuous for your application, choosing ode23tb solver which is good for stiff power system problems, and setting max step size to capture fast transients such as 1e-6 initially, as documented at https://www.mathworks.com/help/sps/powersys/ref/powergui.html

I recommend this implementation sequence: Phase 1 build the basic power structure by adding the powergui block, adding and configuring the Three-Phase Source with your 27.63 megavolt-ampere short-circuit level, adding three branches for your three circuits, and adding measurement scopes for bus voltage and current. Phase 2 start with the simplest Circuit 3 by adding the Three-Phase Breaker rated at 4 amperes for breaker 52.3, adding Series RLC for reactor RI-02, adding the Asynchronous Machine rated at 1.1 kilowatts, adding mechanical load, and testing motor starting with simple breaker closing at time equals 0.1 seconds. Phase 3 add medium complexity Circuit 1 by adding Three-Phase Breaker rated at 250 amperes for breaker 52.1, adding PI Section Line for cable, adding Universal Bridge in averaged inverter mode, adding Asynchronous Machine rated at 45 kilowatts, and implementing basic voltage per hertz frequency ramp control. Phase 4 add complex Circuit 2 by adding Three-Phase Breaker rated at 320 amperes for breaker 52.2, adding thyristor pairs with 6 total in antiparallel, adding reactor RI-01, adding bypass breaker CS-01, adding Asynchronous Machine rated at 160 kilowatts, and implementing firing angle control and bypass logic. Phase 5 add protection systems by adding V-I measurement blocks, implementing overcurrent protection logic, connecting trip signals to breakers, and testing protection during motor starting. Phase 6 run studies including individual motor starts, sequential starts, simultaneous starts, and short-circuit studies.

Regarding the key differences between Specialized Power Systems versus Foundation Library since you asked about translation between libraries: Specialized Power Systems which is what you're using is designed specifically for power system transient analysis, includes built-in power electronics like thyristors IGBTs and diodes, has three-phase blocks with composite connections, requires the powergui block for simulation, uses phasor or time-domain simulation, is optimized for electrical power applications, and has pre-built machines transformers and protection devices. Foundation Library uses a physical modeling approach for multi-domain systems, provides component-level modeling that is more granular, has no built-in three-phase composite blocks, is more flexible but requires more manual construction, and is better for mixed physical systems combining mechanical thermal hydraulic and electrical domains. For your industrial power system analysis Specialized Power Systems is definitely the correct choice.

MathWorks provides several relevant examples in the Specialized Power Systems library which you can access by typing sps_examples in the MATLAB Command Window or going to Home then Help then Examples then Simscape Electrical then Specialized Power Systems. Relevant example models to study include Motor Starting Studies where you should look for Induction Motor Start examples, Soft Starter examples by searching for Thyristor-based soft start, VFD Systems by searching for AC Drive or Vector Control, and Power System Transients for general electrical distribution examples. Additional documentation links include the main Specialized Power Systems Getting Started guide at https://www.mathworks.com/help/sps/getting-started-with-simscape-electrical.html , the Modeling Electric Motors guide at https://www.mathworks.com/help/sps/motor-control.html , and you should also search for soft starter at the MATLAB File Exchange at https://www.mathworks.com/matlabcentral/fileexchange/ where many community-contributed models are available for motor control and power systems.

To directly summarize the answers to your original questions: for source modeling configure your Voltage Source (Three-Phase) block with rated voltage set to 380 volts, short-circuit power level set to 27.63e6 volt-amperes, and X/R ratio set to 7 as a typical industrial value, noting that the block automatically calculates source impedance with no manual calculation needed. For component equivalence use Universal Bridge in averaged mode plus Asynchronous Machine for the VFD, use six Thyristors in antiparallel configuration plus firing control plus bypass breaker plus Asynchronous Machine for the Soft Starter, and use Three-Phase Breaker plus Series RLC for the reactor plus Asynchronous Machine for the DOL Starter. All components are available in the Specialized Power Systems library which is exactly the right toolset for your industrial power distribution analysis.

Again your project is absolutely feasible and you're on the right track as the screenshot you shared shows you're using the correct block library and approach, with the main adjustment needed being configuring the source block with your actual 27.63 megavolt-ampere short-circuit level and 380 volt base voltage. Please feel free to ask if you need clarification on any specific component or implementation detail as I'm happy to provide more detailed guidance on any particular aspect of your model. When you build your model I recommend enabling data logging in the powergui block so you can easily post-process your simulation results and generate professional plots of motor currents voltages and speeds during starting transients.