Choosing an IBR topology under unbalance

This tutorial compares the implemented three-phase converter categories on the same balanced and unbalanced four-wire grid. Its purpose is to show when :THREE_LEG, :FOUR_LEG, and :SPLIT_DC cease to be interchangeable.

The experiment holds the AC rating and filter fixed. Only the physical neutral path and DC structure change.

1. Build two study networks

The source is deliberately stiff so the converter limits, rather than feeder voltage drop, dominate the comparison.

using PowerOptLab
using BMOPFTools: parse_bmopf

function four_wire_grid(; magnitudes, angles)
    parse_bmopf("""
    {"bus":{
      "grid":{"terminal_names":["a","b","c","n"],
              "perfectly_grounded_terminals":["n"]},
      "poc":{"terminal_names":["a","b","c","n"],
             "perfectly_grounded_terminals":["n"],
             "v_min":[180.0,180.0,180.0],
             "v_max":[270.0,270.0,270.0]}},
     "voltage_source":{"vs":{"bus":"grid",
       "terminal_map":["a","b","c"],
       "v_magnitude":$(magnitudes),"v_angle":$(angles)}},
     "linecode":{"lc":{"R_series_1_1":0.05,"R_series_2_2":0.05,
       "R_series_3_3":0.05,"R_series_4_4":0.05}},
     "line":{"l1":{"bus_from":"grid","bus_to":"poc",
       "terminal_map_from":["a","b","c","n"],
       "terminal_map_to":["a","b","c","n"],
       "linecode":"lc","length":1.0}}}
    """; from_string=true)
end

balanced = four_wire_grid(
    magnitudes=[230.0,230.0,230.0],
    angles=[0.0,-2.0944,2.0944],
)
unbalanced = four_wire_grid(
    magnitudes=[245.0,215.0,230.0],
    angles=[0.05,-2.15,2.0],
)

The unbalanced case contains both magnitude and angle asymmetry. A magnitude- only test is not enough to exercise every sequence pathway.

2. Define the physical alternatives

common = (
    bus="poc", phase_terminals=["a","b","c"], neutral="n",
    s_max=20e3, i_max=40.0,
    r_filter=0.05, x_filter=0.15, m_max=0.96,
)

devices = [
    AdvancedInverter(; id="three-leg", topology=:THREE_LEG,
        v_dc=700.0, c_dc=1.1e-3, common...),
    AdvancedInverter(; id="four-leg", topology=:FOUR_LEG,
        v_dc=700.0, c_dc=1.1e-3, In_max=40.0, common...),
    AdvancedInverter(; id="split-dc", topology=:SPLIT_DC,
        v_dc=800.0, c_dc=2.8e-3, In_max=21.0, common...),
]

The split-link unit uses a higher DC voltage because each phase is constrained against a half bus. This is a physical utilisation penalty, not a numerical adjustment intended to equalise the answers.

3. Solve and construct an auditable comparison

function study(network, device)
    r = solve_advanced_inverter(network, device)
    @assert r.termination_status in ("LOCALLY_SOLVED", "OPTIMAL")
    return (
        topology=r.topology,
        status=r.termination_status,
        export_kw=r.p_poc/1e3,
        neutral_a=r.i_neutral,
        zero_a=r.i_zero,
        negative_a=r.i_negative,
        bus_ripple_v=r.dv2,
        switching_headroom_v=r.switching_margin,
    )
end

balanced_results = study.(Ref(balanced), devices)
unbalanced_results = study.(Ref(unbalanced), devices)

foreach(println, balanced_results)
foreach(println, unbalanced_results)

Expected qualitative findings:

• the balanced case makes all three topologies look similar and produces almost no neutral current or double-frequency DC ripple;
• the 3-leg bridge still serves an unbalanced voltage set, but enforces Ia + Ib + Ic = 0 and therefore has no zero-sequence current;
• the 4-leg bridge uses its semiconductor neutral leg and must respect In_max;
• the split link returns neutral current through its two capacitors, coupling AC unbalance to midpoint and bank stress.

Do not rank the topologies from p_poc alone. Compare current paths, required DC voltage, capacitor stress, and switching headroom.

4. Make a sequence-current policy explicit

Hardware capability and grid-code policy are separate limits. For example, add a negative-sequence ceiling to the four-leg unit without changing its neutral- leg rating:

sequence_limited = AdvancedInverter(; id="four-leg-sequence-limited",
    topology=:FOUR_LEG, v_dc=700.0, c_dc=1.1e-3, In_max=40.0,
    i_negative_max=0.5, common...)

r_sequence = solve_advanced_inverter(unbalanced, sequence_limited)
@assert r_sequence.termination_status in ("LOCALLY_SOLVED", "OPTIMAL")
@show r_sequence.p_poc r_sequence.i_zero r_sequence.i_negative

i_negative_max does not stand in for In_max: negative sequence does not require neutral current, while zero sequence does. Keeping the two constraints separate is essential for a defensible four-wire study.

5. Publication checks

For every reported point, record:

1. termination_status and solve_status(result);
2. switching_margin, especially when DC utilisation affects the conclusion;
3. all three sequence currents rather than only i_neutral;
4. the physical reason each topology has its selected v_dc, In_max, and capacitor ratings; and
5. sensitivity to the unbalance scenarios, not just the balanced base case.

This remains a fundamental-frequency capability comparison. It does not prove dynamic neutral control, fault ride-through, or small-signal stability.