SWER case study: why optimisation matters

This case study follows one rural feeder — a Single-Wire Earth-Return (SWER) line — to show where optimisation earns its keep in distribution planning. Every code block runs when the docs are built, so the voltages below are real.

What SWER is, and why it is hard

A SWER line carries single-phase power on one conductor, using the earth itself as the return path. There is no second wire. A dedicated isolating transformer taps the three-phase medium-voltage network and feeds the SWER line; distribution transformers along the line step down to 230/240 V for customers, each earthed so the load current returns through the ground. By halving the conductor count and the pole hardware, SWER electrifies vast, sparsely populated areas at a fraction of the cost of a two- or three-wire line. It is the backbone of rural electrification in Australia, New Zealand, Brazil and southern Africa — Ergon Energy alone operates ~65,000 km of it in Queensland, at 12.7 kV (off 22 kV feeders) and 19.1 kV (off 33 kV).

The economy comes at a price: voltage regulation. A SWER line is long, lightly built and high-impedance, so it sits on a knife-edge between two opposite failure modes that the literature documents well:

• Peak demand → undervoltage. Rural load has grown far beyond the original design — air-conditioning, variable-speed-drive motors, irrigation pumps — and the voltage drop along a high-impedance single conductor with an earth return is severe (Sultan & Hawkins, Rural SWER networks — associated problems and cost-effective solutions, IJEPES 2011).
• Light load + rooftop PV → overvoltage. Modern rural customers export solar. Reverse power flow on the same high-impedance line pushes the far end above its limit (the North Jericho SWER study, Capacity improvements for rural SWER systems, IEEE). On real, very long SWER lines the light-load line-charging (Ferranti) rise adds to this; the fixture used below models no shunt capacitance, so the overvoltage demonstrated here is purely PV reverse flow.

Because voltage regulation is the capacity-limiting factor, the cheapest way to carry more load or host more PV is not a bigger conductor — it is better voltage control. The North Jericho study found that replacing fixed shunt reactors with controllable ones raised feeder capacity by ~85 %. That is the thread this case study pulls on: a single fixed setting cannot serve both failure modes, but an optimiser dispatching a controllable device per operating point can.

1. Load and diagnose

The case ships with the package: a Queensland-style isolated-SWER feeder — a 22 kV three-phase source, a phase-to-phase isolating transformer to a 12.7 kV single-wire backbone, a single-ended distribution transformer (dx1 → lv_1) and a split-phase centre-tapped one (dx2 → lv_2).

using BMOPFTools

dss = joinpath(pkgdir(BMOPFTools), "test", "data", "SWER", "Master.dss")
net = from_dss(dss)

report = analyze(net)
println("SWER zones         : ", report.results[:connectivity]["n_swer_zones"])
println("split-phase zones  : ", report.results[:connectivity]["n_split_phase_zones"])
println("lv_1 nominal (V)   : ",
        round(report.results[:voltage_levels]["bus_voltage_map"]["lv_1"], digits=1))

 Downloading artifact: powerio_capi
┌ Warning: from_dss: 11 parsing and conversion diagnostic record(s) in 5 class(es) (full list on net["_meta"]["powerio_warnings"]):
│   EMIT.BMOPF.FIELD_DROPPED: `units` has no place in the BMOPF schema; dropped from 3 elements
│   EMIT.BMOPF.FIELD_DROPPED: `units` has no place in the BMOPF schema; dropped from 3 elements
│   EMIT.BMOPF.FIELD_DROPPED: 4 occurrences, e.g. `kv` has no place in the BMOPF schema; dropped from 3 elements
│   EMIT.BMOPF.FIELD_DROPPED: 3 occurrences, e.g. voltage source source: `angle` has no place in the BMOPF schema; dropped from the output
│   EMIT.BMOPF.RETAINED_SOURCE_ONLY: 3 occurrences, e.g. transformer dx1: no_load_shunt have no single_phase slot in BMOPF schema 0.1.0; kept under extras.transformer
└ @ BMOPFTools ~/work/BMOPFTools.jl/BMOPFTools.jl/src/io/from_dss.jl:853
SWER zones         : 2
split-phase zones  : 1
lv_1 nominal (V)   : 240.0

analyze recognises the topology directly: the single-wire, transformer-isolated sections are flagged I.PROV.SWER_ZONE, and the centre-tap-fed section as split-phase.

for f in report.findings
    f.code in ("I.PROV.SWER_ZONE", "I.PROV.SPLIT_PHASE_ZONE") &&
        println(f.code, " — ", f.message)
end

I.PROV.SWER_ZONE — Galvanic zone anchored at bus 'swer_0' is single-wire and transformer-isolated — a SWER (single-wire earth-return) section.
I.PROV.SPLIT_PHASE_ZONE — Galvanic zone anchored at bus 'lv_2' is split-phase (fed by center_tap transformer 'dx2'): legs ["a", "b"] are anti-phase about the centre-tap neutral.
I.PROV.SWER_ZONE — Galvanic zone anchored at bus 'lv_1' is single-wire and transformer-isolated — a SWER (single-wire earth-return) section.

2. Stress it into a realistic feeder

The committed fixture is a deliberately small canonical case (it is also a unit-test network). Real SWER lines run tens of kilometres on a high-resistance conductor and carry an aggregated peak up to the isolating-transformer rating. We stretch the backbone to ~96 km and use a realistic 2.5 Ω/km conductor, and size the two distribution transformers to their customers (the canonical stubs ship at a token rating) — plain edits to the network dictionary, which doubles as a tour of the data model.

for (_, l) in net["line"]; l["length"] *= 8.0; end       # 12 km → 96 km
net["linecode"]["swer"]["R_series_1_1"] = 2.5 / 1000      # Ω/m

# Right-size the transformers (the OPF enforces each nameplate `s_rating` as a
# per-winding apparent-power cap, so an undersized unit is flagged as overloaded
# rather than silently run past its rating). The distribution transformers are
# sized to the ~40 kW leg they each serve; the isolating transformer must carry
# the whole 80 kW peak PLUS the reactive support the compensator (below) pushes
# through it, so it is the larger 150 kVA unit.
for (_, sub) in net["transformer"], (id, x) in sub
    id == "dx1" && (x["s_rating"] = 63_000.0)      # single-ended distribution xfmr
    id == "dx2" && (x["s_rating"] = 50_000.0)      # split-phase distribution xfmr
    id == "iso" && (x["s_rating"] = 150_000.0)     # isolating xfmr (peak + reactive)
end

println("backbone length (km): ", sum(l["length"] for l in values(net["line"]))/1000)

backbone length (km): 96.0

The LV taps must stay inside the Australian AS IEC 60038:2022 supply-voltage range (230 V nominal, −10 %/+10 % → 207–253 V) — the same window that inverter standards such as AS/NZS 4777.2 key their responses off; we hold the 12.7 kV backbone to ±10 %.

function set_limits!(n)
    for b in ("lv_1", "lv_2")
        nph = count(t -> t != "n", n["bus"][b]["terminal_names"])
        n["bus"][b]["vpn_min"] = fill(207.0, nph)
        n["bus"][b]["vpn_max"] = fill(253.0, nph)
    end
    for b in ("swer_0", "swer_1", "swer_2")
        n["bus"][b]["v_min"] = [11430.0]; n["bus"][b]["v_max"] = [13970.0]
    end
    n
end

Next, the measurement helper and the operating points. vpn reads the phase-to-neutral magnitude out of a solved result — the quantity the limits bind. An operating point is just a scaled copy of the loads: the fixture ships 5 kW of canonical load, so scale(16.0) lifts it to an 80 kW aggregated peak — the whole of it crossing the 150 kVA isolating transformer (real SWER peaks are transformer-limited), while the two distribution transformers (63 and 50 kVA above) each carry their ~40 kW leg. scale(2.0) is a 10 kW light-load trough. The OPF enforces every transformer's nameplate as a hard per-winding apparent-power cap, so the dispatch we compute below respects the thermal limits as well as the voltage window — no operating point runs a transformer past its rating. That coupling is the point of the isolating transformer's headroom: it has to carry the peak and the reactive support the compensator injects to hold the far-end voltage.

using JuMP, Ipopt, Printf
const OPT = optimizer_with_attributes(Ipopt.Optimizer, "print_level" => 0)

# Phase-to-neutral voltage magnitude at bus `bid`, terminal `ph`, from a result.
vpn(res, bid, ph) = (b = res["bus"][bid];
    abs((b[ph]["vr"] + im*b[ph]["vi"]) -
        (haskey(b, "n") ? b["n"]["vr"] + im*b["n"]["vi"] : 0.0 + 0im)))

# Operating point = the fixture's loads scaled by K (deepcopy → scenarios stay independent).
scale(K) = (n = deepcopy(net); for (_, ld) in n["load"]
    ld["p_nom"] = ld["p_nom"].*K; ld["q_nom"] = get(ld,"q_nom",[0.0]).*K; end; n)

The overvoltage driver is rooftop PV at the lv_1 tap. 55 kW — roughly a dozen 5 kW rooftop systems behind one tap — pushes ~45 kW back up the line against the 10 kW trough. The IBR dict pins the unit at full, unity-power-factor output, so the power flow sees a fixed injection rather than a dispatchable device:

function add_pv!(n, kw)
    n["ibr"] = get(n, "ibr", Dict{String,Any}())
    n["ibr"]["pv"] = Dict{String,Any}(
        "bus" => "lv_1", "terminal_map" => ["a","n"], "topology" => "SINGLE_PHASE",
        "prime_mover" => "PV",
        "s_max"   => [kw*1100.0],   # VA rating: 10 % headroom over P, typical sizing
        "p_min"   => [kw*1000.0],   # p_min = p_max pins P at full output —
        "p_max"   => [kw*1000.0],   #   a fixed injection, not a decision variable
        "q_min"   => [0.0],
        "q_max"   => [0.0],         # q pinned to 0: unity power factor
        "p_avail" => [kw*1000.0])   # irradiance-limited available power (= P here)
    return n
end

Finally the two candidate devices. The fixed reactor is a constant inductive shunt (no decision variable), at 120 kVAr sized by trial so the light-load PV overvoltage comes back inside 253 V. The controllable compensator is an IBR with p = 0 and reactive power free in a band, which the OPF dispatches (STATCOM-like); its 180 kVAr band gives headroom in both directions so the voltage limits, not the device rating, are what bind. Both sit at the SWER end, swer_2 — the classic location for a SWER line reactor. Vpf solves a power flow; Vopf solves an OPF and returns the voltage plus the compensator dispatch, erroring readably if the solve fails.

add_reactor!(n, kvar) = (n["shunt"] = get(n, "shunt", Dict{String,Any}());
    n["shunt"]["reac"] = Dict{String,Any}("bus"=>"swer_2", "terminal_map"=>["a"],
        "B_1_1" => -kvar*1000.0 / 12700.0^2); n)   # fixed inductive susceptance (S)
add_comp!(n, kvar) = (n["ibr"] = get(n, "ibr", Dict{String,Any}());
    n["ibr"]["comp"] = Dict{String,Any}("bus"=>"swer_2", "terminal_map"=>["a","n"],
        "topology"=>"SINGLE_PHASE", "s_max"=>[kvar*1000.0], "p_min"=>[0.0],
        "p_max"=>[0.0], "q_min"=>[-kvar*1000.0], "q_max"=>[kvar*1000.0],
        "p_avail"=>[0.0]); n)

Vpf(n)  = vpn(solve_pf(n; optimizer=OPT, per_unit=true), "lv_1", "a")
function Vopf(n)
    r = solve_opf(set_limits!(n); optimizer=OPT, per_unit=true)
    st = r["termination_status"]
    st in ("LOCALLY_SOLVED", "OPTIMAL") || error("OPF did not solve: status = ", st)
    vpn(r, "lv_1", "a"), r["ibr"]["comp"]["a"]["qg"]/1000
end

3. The two failure modes

A determined power flow (solve_pf) at each operating point shows the feeder fall out of the AS IEC 60038:2022 supply-voltage window at both ends of its operating range.

v_peak_nc = Vpf(scale(16.0))
v_pv_nc   = Vpf(add_pv!(scale(2.0), 55.0))

println("PEAK demand            lv_1 = ", round(v_peak_nc, digits=1),
        " V   (< 207    → UNDERVOLTAGE)")
println("LIGHT load + 55 kW PV  lv_1 = ", round(v_pv_nc, digits=1),
        " V   (> 253    → OVERVOLTAGE)")

PEAK demand            lv_1 = 202.3 V   (< 207    → UNDERVOLTAGE)
LIGHT load + 55 kW PV  lv_1 = 255.2 V   (> 253    → OVERVOLTAGE)

4. A fixed reactor cannot serve both

A fixed shunt reactor sized to cure the light-load PV overvoltage absorbs reactive power all the time — so at peak demand it deepens the undervoltage. This is the exact mechanism the North Jericho study gives for why fixed reactors cap SWER capacity.

v_peak_fr = Vpf(add_reactor!(scale(16.0), 120.0))
v_pv_fr   = Vpf(add_reactor!(add_pv!(scale(2.0), 55.0), 120.0))

println("PEAK  + fixed 120 kVAr reactor  lv_1 = ", round(v_peak_fr, digits=1), " V   (WORSE)")
println("PV    + fixed 120 kVAr reactor  lv_1 = ", round(v_pv_fr, digits=1), " V   (better)")

PEAK  + fixed 120 kVAr reactor  lv_1 = 188.5 V   (WORSE)
PV    + fixed 120 kVAr reactor  lv_1 = 236.3 V   (better)

5. One controllable compensator, optimally dispatched

Replace the fixed reactor with a controllable compensator and let solve_opf choose its reactive output subject to the voltage limits. The same device now injects vars at peak and absorbs vars under PV — the degree of freedom that a fixed setting lacks.

vp, qp = Vopf(add_comp!(scale(16.0), 180.0))
vl, ql = Vopf(add_comp!(add_pv!(scale(2.0), 55.0), 180.0))

println("PEAK  + compensator  lv_1 = ", round(vp, digits=1),
        " V   (OPF injects ", round(qp, digits=0), " kVAr)")
println("PV    + compensator  lv_1 = ", round(vl, digits=1),
        " V   (OPF absorbs ", round(ql, digits=0), " kVAr)")

PEAK  + compensator  lv_1 = 219.4 V   (OPF injects 119.0 kVAr)
PV    + compensator  lv_1 = 246.8 V   (OPF absorbs -52.0 kVAr)

Both operating points are now inside the AS IEC 60038:2022 window, served by one device, only because the OPF dispatches it per operating point.

Why optimisation matters

The table is computed from the results above — the same live numbers, side by side:

@printf("%-18s | %-14s | %-20s | %s\n",
        "operating point", "no control", "fixed 120 kVAr", "compensator (OPF)")
println("-"^85)
@printf("%-18s | %6.1f V under | %6.1f V worse      | %6.1f V ok  (%+.0f kVAr)\n",
        "peak demand", v_peak_nc, v_peak_fr, vp, qp)
@printf("%-18s | %6.1f V over  | %6.1f V ok         | %6.1f V ok  (%+.0f kVAr)\n",
        "light + 55 kW PV", v_pv_nc, v_pv_fr, vl, ql)

operating point    | no control     | fixed 120 kVAr       | compensator (OPF)
-------------------------------------------------------------------------------------
peak demand        |  202.3 V under |  188.5 V worse      |  219.4 V ok  (+119 kVAr)
light + 55 kW PV   |  255.2 V over  |  236.3 V ok         |  246.8 V ok  (-52 kVAr)

Voltage regulation is the SWER capacity limit, and no single static setting spans the operating range — the optimiser's per-operating-point reactive dispatch is what unlocks capacity (the controllable-reactor capacity gains of the North Jericho study). On a high R/X SWER feeder reactive support is a limited lever, which is itself worth seeing in the numbers; where it runs out, the same OPF machinery sizes and dispatches real-power DERs and smart-IBR Volt-var.