Q-V droop Q(V)

What it is (precise)

Written in per-unit, the law is Q = −(V − V_ref) / k, with Q in per-unit of rated reactive capability and k the droop setting in per-unit voltage. The minus sign carries the physics: injecting Q raises local voltage, so the line falls from left to right, and a bus above reference calls for absorption.

Droop and gain are reciprocals of each other, and vendors quote both — a 4% droop means 25% of rated Mvar per 1% of voltage deviation, and the same behaviour appears on a smart-inverter datasheet as four (V, Q) corner points rather than a coefficient. Establish which convention a document uses before comparing two settings, because a number that looks conservative in one form looks aggressive in the other.

Inside the deadband the law commands no reactive movement at all. That flat middle exists so a plant does not chase the normal daily drift of a healthy bus, and so it does not respond to every step a mechanical regulator elsewhere on the network makes.

Outside it, the line runs until the plant's capability clips it: the droop describes intent, the P-Q envelope decides delivery, and at high plant loading or at the ends of the voltage range the envelope may hand back less Mvar than the slope is asking for. MVA headroom and the POI capability envelope carry that side of the arithmetic; what belongs here is the consequence, which is that a droop line drawn past the envelope simply saturates and stops regulating.

The absence of integral action is deliberate. A proportional law settles with a standing voltage offset equal to slope times delivered reactive power, so a plant holding 0.5 pu of its rated Q on a 4% droop sits 2% off the reference and stays there.

Operators who want the reference recovered add a slow reset that walks the reference or the Q schedule back over minutes, which restores the target at the cost of reintroducing the integrating behaviour that droop was chosen to avoid. Whether such a reset is enabled, and how slow it is, is one of the first questions to ask about any voltage-control specification.

The network sets what a given slope actually does

How far a Mvar moves the bus is a property of the network, not of the plant. To first order the voltage sensitivity at a bus is the reciprocal of its short-circuit level: ΔV in per-unit ≈ ΔQ divided by the fault level in MVA. At a point of interconnection with a 1,000 MVA short-circuit level, the roughly 33 Mvar that accompanies 100 MW at 0.95 power factor moves the bus about 3.3%; take the same plant to a node half as strong and the same Mvar moves it twice as far.

Choosing a droop is therefore choosing a loop gain against that sensitivity, which is why an identical 4% setting is comfortable at one connection point and twitchy at another, and why the interconnection study rather than the PCS datasheet is where the number is settled.

Whether reactive power is even the right lever depends on the X/R ratio of the network behind the connection. Voltage change follows roughly (R·ΔP + X·ΔQ) / V, so on a transmission network where reactance dominates resistance the Q term controls voltage and the plant's own MW barely shows.

Down at distribution voltages X/R approaches unity, real power moves the bus about as much as reactive power does, and rulebooks written for that environment pair a volt-var function with a volt-watt function for exactly this reason. A Q-V droop specified without regard to where it lands can be asked to hold a voltage that its own active-power dispatch keeps pushing around.

One more geometric detail: the droop is written at the connection point, but the inverters live behind the unit transformers and the collection system, so the voltage they measure is not the voltage the meter reads. The plant controller closes that gap, trimming per-unit setpoints so the sloped line is honoured where the obligation is measured.

Some agreements go further and ask the plant to regulate a remote busbar through line-drop compensation, which puts an estimated impedance inside the control law and makes the estimate itself a setting worth auditing. Note that BESS unit transformers normally carry off-circuit taps rather than on-load tap changers, so the fast regulator on site is the power electronics, not the transformer.

Voltage control, power factor, or fixed Q — and which one is armed

Three reactive control modes are in common use, and only one of them looks at the grid. Voltage control with droop closes on measured voltage and moves Q to defend it. Power-factor control slaves Q to P at a fixed ratio, which means the reactive output collapses to zero whenever the plant sits at zero MW — for a battery that spends much of the day parked between dispatches, that is the difference between a voltage regulator and a bystander.

Constant-Q control holds a fixed Mvar figure and ignores voltage entirely, which is what a network operator wants when the plant is being used to offset a known, static reactive demand rather than to regulate.

Codes generally require the capability in all three modes and let the connection agreement pick one. EirGrid's Grid Code (Ireland) is explicit about it, requiring controllable power park modules made up of energy storage power stations to reach the same rectangular P-Q envelope — Q/Pmax of ±0.33, equivalent to 0.95 power factor either way — whether they are operating in power-factor control, voltage-control or constant-reactive-power mode, held from full export through zero MW down to maximum import.

ERCOT's Nodal Protocols (Texas) frame the Texas obligation around a Voltage Set Point at the Point of Interconnection Bus instead, requiring 0.95 or better lagging capability for any setpoint from 0.95 to 1.04 pu and 0.95 or better leading capability from 1.0 to 1.05 pu, at all MW levels and while charging as well as discharging.

Distribution connections often carry both a power-factor obligation and a voltage-dependent curve at once. Under California's Rule 21, a generating facility must hold power factor near unity at rated output or a value the distribution provider specifies inside a 0.9 leading to 0.9 lagging cone, while the same tariff's smart-inverter provisions carry a default volt-var curve for UL 1741 SB inverters.

The practical point is that mode, setpoint, slope and deadband are project data rather than product data: they belong in the executed interconnection agreement, they go into the dynamic model the developer submits, and the witnessed capability test is run against them. A plant that ships in power-factor mode when the agreement assumed voltage control has a settings problem, not a hardware problem, but it fails the test either way.

Reading a published curve

California's Rule 21 default volt-var curve is a useful worked example because every corner is published. It commands unity power factor between 97% and 103% of nominal voltage — a ±3% deadband — then ramps to 30% reactive injection at 92.0% voltage and to 30% absorption at 107.0% voltage.

Convert those corners into slopes and the two halves are not the same: 5 percentage points of voltage buys 30% of rated Q on the injection side, a droop of about 16.7%, while 4 percentage points does the same work on the absorption side, about 13.3%. Asymmetry of that kind is normal and usually intentional, since the consequences of high and low voltage on a distribution feeder are not symmetric either. These are settable defaults for one jurisdiction, not a universal curve.

Two boundaries constrain any curve drawn this way. The first is category capability: IEEE 1547-2018 Category B, the usual assignment for a utility-scale battery interconnecting at distribution level, calls for injection and absorption on the order of 44% of nameplate apparent rating, where Category A absorption is 25% — a curve cannot ask for reactive power the category does not require the equipment to have.

The second is that the envelope itself moves with voltage. Great Britain's G99 makes this explicit for power park modules at connection points of 33 kV and below, where the reactive envelope is sloped rather than rectangular: full lagging capability is required only at or below 1.00 pu and full leading capability only at or above 1.00 pu. That is precisely the interaction to check, because the far end of a droop line is exactly where the envelope has narrowed.

Several regulators on one bus

The reason droop exists rather than plain setpoint tracking becomes obvious with two plants on the same bus. Give both an integrating voltage regulator and the same target, and the small differences between their measurements decide the outcome: one drives toward maximum injection, the other toward maximum absorption, the bus ends up near target, and neither has any dynamic reactive headroom left for the disturbance the whole arrangement exists to handle.

Droop replaces that contest with arithmetic. Each device settles where its own sloped line crosses the achieved voltage, so the share is deterministic and inversely proportional to droop — a shallower slope than the neighbour makes a plant the passenger, a steeper one makes it the workhorse, and the network operator can allocate the duty by handing out settings.

Steady-state sharing is only half the problem; the other half is timescales. A plant-level loop settles reactive power in roughly 1 to 5 seconds, while the utility's substation tap changers and switched capacitor banks act in discrete steps after an intentional time delay measured in tens of seconds. If the fast loop erases the voltage error just before the mechanical device would have corrected it, the tap either never operates or operates and is immediately countered, and both outcomes end in excess operations and a wandering bus.

The defences are a deadband at least as wide as the step the mechanical device makes, deliberate separation between the two response times, and setpoints coordinated by the network operator rather than chosen independently by each connectee. Loop interaction inside the plant, between the plant controller and the inverters' own local loops, is a separate problem that the power plant controller entry covers.

Control mode changes the timescale as well. A grid-forming plant carries the Q-V relation inside its voltage-source behaviour and responds within cycles, whereas a grid-following plant implements it as an outer regulator working in seconds — put one of each plus a utility tap changer on the same bus and there are three laws running decades apart in speed.

Fault-time behaviour is different again: the dynamic reactive current a code demands during a voltage dip is a faster, separate requirement that belongs to ride-through, not to this steady-state law. Where the fast interactions matter, the positive-sequence study is not enough and the EMT model is where the answer lives.