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Location

This example model can be found in the software under the category "How to" with the file name "ePHASORSIM_CO_SIMULATION.ecf".

Description

This example demonstrates a multi-rate PHASOR-EMT co-simulation. The PHASOR subsystem 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 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 models a 5-node distribution feeder with an induction motor operating under constant torque (Figure 2). The EMT subsystem, running with a time-step of 20 us, is connect to bus 6 of the PHASOR subsystem, which runs with a time-step of 10 ms.

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Figure 1. WSCC 9-bus power system [1] and Feeder connected to the PHASOR/EMT simulation.

Co-Simulation Coupling Interface

In a co-simulation, the coupling interface is a mechanism for data exchange between subsystems, 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.

1. 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 impedance is used to couple the EMT subsystem, with the voltage magnitudes described by equation (1). It is noted that for simplicity, a fixed equivalent impedance is employed in this example.

2. 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 subsystem. 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 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:

1. Incoming pins (control command)

   • Three-phase Fault: Activation/deactivation of a solid three-phase fault on the bus of interest.

   • load: Active and Reactive power of the load located on bus 6 (MW, MVar).

2. Outgoing pins (measurements)

   • Vmag: Voltage magnitude of all the buses (p.u.).

   • Vang: Voltage angle of all the buses (degree).

More information about I/O pins configurations can be found at https://opal-rt.atlassian.net/wiki/x/6PqcC.

Simulation and Results

To assess the co-simulation dynamic performance, along with its numerical stability, tests are carried out considering two different scenarios, as indicated in Table bellow.

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 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 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 subsystem, which serve as inputs to the PHASOR subsystem. 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 subsystem, along with the fault current in the feeder circuit. Finally, Figure 8 displays the stator currents and angular velocity of the induction machine.

References

[1] Identification of a continuos time nonlinear state space model for the external power system dynamic equivalent by neural networks, DOI:10.1016/j.ijepes.2009.03.016.