Power & Energy Engineering · grid connection studies · reactive power capability
The capability stack
Slice by slice: the reactive power a modelled 300 MW offshore wind park can deliver at its connection point, and where it falls short.
Overview
We modelled a 300 MW AC-connected offshore wind park, from its turbines' converters through the 66 kV array, the offshore substation and a 60 km export cable, and ran 107,291 steady-state load flows (104,111 converged) to map the reactive power it can deliver at its onshore connection point. Each slice of the stack is one connection-point voltage, from 0.875 to 1.100 pu. Each solved point is checked against every limit in the model: the converters' current, terminal-voltage and DC-link limits, the cable and offshore transformer ratings, and the highest voltage the 66 kV and 220 kV equipment is rated for.
We checked the stack against an example profile we drew inside the envelope of the EU generator connection code (Regulation (EU) 2016/631, Art. 21(3)(b)–(c), Figure 8 with Table 9's ranges, Pmax = 300 MW, the turbines' ratings). We ask for the same band at every power level, a choice the Regulation leaves to the system operator. With a fixed 65 Mvar onshore reactor in service, the stack falls short in two regions:
- Producing at full power, it is short at every voltage: 20–45 Mvar, set by the converters' DC-link limit. The gap deepens to 57.6 Mvar at 1.100 pu, where the last limit reached is the offshore 220 kV busbar at 245 kV.
- Absorbing at 0.875–0.900 pu, it is short by up to 44.4 Mvar at zero power, where the converter terminals reach 0.90 pu with the tap changers at their end stop.
These are the two corners the Regulation itself flags as costly: production at high voltage, consumption at low voltage.
The production gap is mostly our own reactor's doing. Without it, the park meets the production side everywhere; at 1.100 pu the fixed reactor absorbs 79 Mvar. Equipment on the connection-point busbar changes nothing inside the network, because that voltage is held fixed in each slice, so compensation is sized as an exact final step. Beside the fixed reactor, a ±52.4 Mvar STATCOM closes both regions. Switching a 125 Mvar reactor out when the park produces and in when it absorbs closes them with no STATCOM at all.
The arrangement is representative, not a real project. The connection point is onshore, as when the park builds its own export system. Where it sits depends on the country, and the article that applies follows it: with an onshore connection point the Regulation treats the park as an onshore module (Art. 23(1)). The Regulation also lets the system operator ask the cable's owner for extra reactive power to cover the export cable (Art. 21(3)(a)); our profiles do not. Whether tap changer steps may count toward the capability depends on the system operator, so the stack is computed both ways.
What we built
- The park. A 300 MW offshore park model:
- 20 × 15 MW full-converter turbines on four 66 kV strings;
- two 180 MVA offshore transformers with on-load tap changers;
- an 80 Mvar offshore reactor;
- a 60 km 220 kV export cable in 12 sections.
Cable data is computed from the cable geometry.
- The converter. Each turbine converter has three limits: current, AC terminal voltage (0.90–1.10 pu) and a DC-link limit on its internal voltage, which caps over-excited output as the terminal voltage rises.
- The sweep. It runs over connection-point voltage, active power, 17 tap positions and the turbines' reactive setpoint. Bisection finds each edge of the capability to 0.01 Mvar per turbine, and every edge records the limit that sets it.
- The profile checker. It tests the stack against three example profiles we drew inside the Figure 8 envelope, with Table 9's ranges. It sizes the onshore reactor, fixed or switched, and the STATCOM that close the gaps.
- An interactive stack. You can:
- scrub the voltage slices;
- free or freeze the tap changers;
- switch the reactor between fixed and switched;
- change the profile;
- move the STATCOM rating.
Tech stack
Python, pandapower (Newton–Raphson load flow), NumPy; three.js for the stack; a headless browser for the film frames.
Numbers
| Number | How we measured it |
|---|---|
| 107,291 load flows, 104,111 converged | The sweep for the onshore connection point: 19 voltages × 11 power levels × 17 tap positions × 13 or 25 reactive setpoints, plus the bisection steps at each edge. The 3,180 that did not converge count as outside the limits. None of the edges was set by a non-converged point. |
| 211 s | Wall-clock time for that sweep on 5 processes of an M1 Pro laptop (about 10 ms per load flow per process). |
| 169 Mvar | Charging of the 60 km export cable at 220 kV, by hand: U²·ω·C·l with C = 184.9 nF/km from the cable geometry. Fed from one end with the far end open, the cable generates 170.1 Mvar, both in the exact distributed-line solution and in our 12-section model. |
| 57.6 Mvar short (producing) | The deepest over-excited shortfall: 1.100 pu, full power, with the 65 Mvar onshore reactor fixed in service. The last limit reached is the offshore 220 kV busbar at 245 kV. Taps free, example profile A. |
| 44.4 Mvar short (absorbing) | The deepest under-excited shortfall: 0.875 pu, zero power. The converter terminals are at 0.90 pu and the tap changers at their end stop. Same conditions. |
| ±52.4 Mvar | STATCOM rating at 1.0 pu that closes every shortfall against profile A with the tap changers free and the 65 Mvar reactor fixed in service. It is the largest shortfall divided by its voltage, because a current-limited STATCOM delivers its rating times the voltage (we assume rated current up to 1.10 pu). |
| 125 Mvar, switched | A breaker-switched onshore reactor (out when producing, in when absorbing) that closes every shortfall against profiles A, B and C with free taps and no STATCOM. It is the smallest size in 5 Mvar steps that does so. |
| 177.4 Mvar | The STATCOM rating with the tap changers frozen at neutral (fixed reactor). Even that leaves three operating points open: at 0.875–0.900 pu the converters cannot deliver full power at all. |
| 11.1 and 33.3 Mvar | STATCOM ratings for example profiles B (relieved corners) and C (±0.33 band), with the fixed reactor and free taps. |
| 54.7 Mvar | The same check with the connection point on the offshore 220 kV busbar instead, as on a system-operator-owned offshore hub. There the export cable and both reactors sit outside the park, and the STATCOM would sit offshore (106,039 more load flows). Art. 25(5) and Table 11 apply; for Continental Europe, Table 11 has the same limits as Table 9. |
| 7.0 MW | Losses from the turbine terminals to the connection point at full power, 1.000 pu, turbines at zero reactive power, taps at neutral (293.0 MW delivered). |
| 0.0000002 Mvar | Largest difference in connection-point reactive power between the load-flow engine and our own Newton–Raphson, written from the same documented data, at 60 random operating points. This checks the code, not the physics. |
All numbers are steady-state results from our model of a representative park. They are not a compliance assessment.
Stills
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