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This example demonstrates a multi-rate PHASOR-EMT co-simulation. The PHASOR subsystem subcircuit is integrated into HYPERSIM using the ePHASORSIM block interface. More details on how to use the ePHASORSIM interface can be found inhttps://opal-rt.atlassian.net/wiki/x/IoCGPg. The PHASOR subsystem ePHASORSIM Interface . The PHASOR subcircuit is based on the IEEE 9-bus system, which includes three generators with exciter control, three step-up transformers, three static loads, and six transmission lines (Figure 1). The EMT subsystem subcircuit models a 5-node distribution feeder with an induction motor operating under constant torque (Figure 2). The EMT subsystemsubcircuit, running with a time-step of 20 us, is connect to bus 6 of the PHASOR subsystemsubcircuit, which runs with a time-step of 10 ms.
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In a co-simulation, the coupling interface is a mechanism for data exchange between subsystemssubcircuits, often involving variables such as voltage, current, power, or states. The coupling interface is fundamental to ensuring the necessary data exchange at defined communication points, guaranteeing proper and stable operation of the co-simulation. In the approach used in this example, the PHASOR-EMT co-simulation framework includes two coupling interfaces as indicated in Figure 3: one for converting phasor quantities to instantaneous values and another for the inverse conversion from the EMT domain to the phasor domain, described as follows.
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Figure 3. Coupling between subsystemssubcircuits.
PHASOR TO EMT: This coupling interface computes a set of three-phase instantaneous voltage v_abc(t) based on the voltage angle (theta) and magnitude (V) from the phasor quantities. It is noted that considering ePHASORSIM pins outputs, the angle must be converted to radians and the magnitude must be multiplied by the appropriated base value. The phasor to EMT conversion is based on equation (1). A voltage source behind a equivalent impedanceis used to couple the EMT subsystemsubcircuit, with the voltage magnitudes described by equation (1). It is noted that for simplicity, a fixed equivalent impedance is employed in this example.
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EMT TO PHASOR: The PQ buses in the ePHASORSIM solver support dynamic active and reactive loads, allowing the PQ quantities to be set as inputs and to vary over time. In this context, the coupling interface involves calculating the PQ at the boundary bus with the EMT subsystemsubcircuit. Considering that the ePHASORSIM solver accounts only for the positive sequence of the grid network, the PQ calculations at the EMT boundary bus must also consider only the positive sequence components of the instantaneous currents and voltages. Additionally, the active power should be expressed in MW, while the reactive power should be provided in Mvar.
The PHASOR subsystem subcircuit is modeled using a standard ePHASORSIM Excel file (https://opal-rt.atlassian.net/wiki/x/jm2dC), where the I/O pins configurations and network/dynamic data for the transmission network are provided. For this example, the following incoming and outgoing pins are set:
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Scenario | Description | Fault applied | Event duration |
#01 | A three-phase-to-ground fault is applied at BUS 2 (69 kV) within the EMT subsystemsubcircuit | t = 1 s | 0.5 s |
#02 | A three-phase-to-ground fault is applied at BUS 4 within the PHASOR subsystemsubcircuit | t = 6 s | 50 ms |
The system operates under steady-state conditions until t = 1 s when a three-phase-to-ground fault is applied to BUS 2 within the EMT subsystem subcircuit for 0.5 s. Once the system returns to steady state, a second three-phase-to-ground fault is applied to BUS 4 at t = 6 s within the PHASOR subsystem subcircuit for 50 ms. Figure 4 illustrates the voltage sag at the coupling bus during both events.
Figure 5 presents the PQ quantities calculated at the boundary bus within the EMT subsystemsubcircuit, which serve as inputs to the PHASOR subsystemsubcircuit. Conversely, Figure 6 depicts the RMS voltages at the ePHASORSIM interface outputs, highlighting the voltage sags during transient events. Figure 7 illustrates the instantaneous voltage at BUS 2 within the EMT subsystemsubcircuit, along with the fault current in the feeder circuit. Finally, Figure 8 displays the stator currents and angular velocity of the induction machine.
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Figure 4. RMS and EMT voltages at coupling interface.
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Initial model validation
A validation.oprec file can be found in the validation repository of the project to validate that the model starts correctly.
References
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