By Kathryn Porter, Watt-Logic

The Iberian blackout demonstrated the importance of voltage control and reactive power, but these concepts are poorly understood even by people within the electricity sector. In this two-part series of posts I will look at voltage, active power and reactive power in power grids and how they relate to the blackout in Iberia on 28 April.

This first part will look at the physics of power grids and the general behaviour of both synchronous generation (gas, hydro and nuclear) and inverter-based generation (wind, solar and batteries), while the second post will address what we know about the Iberian blackout.

Reactive power, voltage and current

Few people really understand reactive power. They talk about power sloshing backwards and forwards in the circuit, but rarely explain what it is or why it behaves that way.

So from first principles, here is a primer on reactive power…

In a circuit containing only resistance, current and voltage are in phase with each other and related through Ohm’s Law: Voltage = Current × Resistance. Energy is lost from the circuit in the form of heat through the resistor. The power is doing real work: heating elements, running motors, lighting lamps.

In circuits containing capacitors and inductors, however, things are different, and not only do we have active power ie the power that drives loads, we have reactive power which does not. This power is stored in the magnetic and electric fields that are created and destroyed as the current and voltage cycle.

Inductors resist changes in current and store energy in magnetic fields, while capacitors resist changes in voltage and store energy in electric fields. In an already established circuit (powering a circuit for the first time has some differences), as voltage moves from zero towards its maximum, capacitors release their charge (energy) as the electric field collapses, and inductors begin to store energy as the magnetic field builds.

As voltage passes its peak and returns to zero, the magnetic field collapses (inductors discharge) and the electric field begins to build (capacitors charge) – energy is passed from the magnetic field to the electric field. This repeats as voltage passes through zero and builds to its minimum (negative maximum). So in every complete cycle of voltage, energy is exchanged from the magnetic to electric field and back twice. Most transmission loads are inductive, so current lags voltage in ac power grids.

People speak of inductors absorbing reactive power and capacitors creating it, but this is not accurate. Both capacitors and inductors store and release reactive power at different parts of the current and voltage cycle.

From this we derive something known as the Power Triangle: because all the power is no longer used to do work as it is in a purely resistive circuit, we have some power doing work (the base of the triangle) and some power being stored in the electric and magnetic fields (the height of the triangle). The hypotenuse is the apparent power (voltage x current) that the source must deliver.

Just as with Pythagoras’ theorem, the larger the reactive component, the greater the total current required to deliver a given amount of real power. This is inefficient, and one reason why we try to minimise reactive power demand in power systems.

Even without loads, power grids contain both resistance and impedance. Power lines don’t conduct electricity perfectly — some energy is lost as heat due to electrical resistance. Long power lines also behave like inductors because when ac current flows through a conductor, it constantly changes direction, and this changing current generates a changing magnetic field around the wire (by Ampère’s Law). This magnetic field, in turn, induces a voltage (by Faraday’s Law) that opposes the change in current. This opposition is inductive reactance, which is what inductors do.

Over a longer conductor, the total magnetic field created is larger, and the effect is stronger so the wire behaves more and more like an inductor the longer it gets. Similarly, the windings in transformers create magnetic fields and are a classic source of inductance in power grids. Then there is the effect of loads such as motors which can be both inductive and contain capacitors.

Voltage, current and impedance

In the same way that the speed with which current and voltage alternates is linked to supply and demand, so too is the actual amount of the current and voltage. In a purely resistive circuit, if demand exceeds supply, the current drawn increases, and from Ohm’s Law, voltage will also increase, which can cause generators to trip, motors to overheat, and other equipment failures. If supply exceeds demand, current drawn falls, and hence voltage also falls, leading equipment to stall.

But in ac systems with inductors and capacitors, we must use impedance instead of resistance, and the relationship between voltage and current changes – while supply and demand affect the amount of current drawn, the change in voltage is much harder to determine.

Ohm’s Law is amended to Voltage = Current x Impedance where Impedance = Resistance + (j x Reactance)… j is the SQRT (-1) (known in mathematical terms as i). This is quite hard to visualise…

Most people know that the square root of 4 is 2, but it’s also (-2): the product of two negative numbers is a positive number. So the roots of any positive number are both the positive and negative values: the square root of 9 is both 3 and -3 etc. This begs the question, what is the square root of -4 or -9? What is the number, which when multiplied by itself, gives the answer of -1?

We can picture this in geometric terms. Instead of thinking of numbers as being on a continuous line from -infinity to +infinity (one dimension), we can think in two dimensions and picture rotations. So this question is not what number multiplied by itself gives -1, but what transformation or rotation performed twice will convert +1 into -1. In two dimensions this is easy – a rotation anti-clockwise through 90o, twice.

To describe this in algebraic terms is pretty hard unless you invent a concept known in maths as i for imaginary number. i is defined as the square root of -1 and i squared is +1. So now we can say that the square root of -4 is the same as the square root of (4 x i2) or 2i. In electrical engineering we use j as the notation for i, for some reason.

Impedance is a mixture of an imaginary number and a real number and is therefore known as a complex number (just as the square root of -4 is a complex number). Resistance lies along the horizontal (real) axis, while reactance lies along the vertical (imaginary) axis, and impedance is the combination: a vector pointing at some angle, made of both real and imaginary parts.

When current flows through impedance, voltage and current are no longer in phase as they are in a purely resistive circuit – this means the peaks and troughs are not aligned. Because most grids contain more inductors than capacitors the current lags the voltage ie it reaches a peak after voltage does. Effectively the current is “rotated” backwards relative to the voltage.

This means increasing current doesn’t necessarily increase voltage – it might increase it less than expected, or it might voltage to drop, depending on the system. Current and voltage are no longer directly proportional.

The direction and magnitude of the reactance matters, and since reactance depends on frequency (the balance between supply and demand) and network conditions, the amount of voltage needed for a given current changes over time.

Unlike frequency, reactive power is more localised and is not the same across the entire grid. This is because the grid is made up of lots of circuits connected to each other, which have different devices connected to them providing different levels of capacitance and inductance.

Impedance in real grids

If there are no loads on the system and it has a single conventional synchronous generator, connected to a grid with no loads, no capacitor banks, and no transmission lines with appreciable impedance (idealised) and only its own internal components, then current and voltage would be in phase — the generator would supply zero current because there is no load to draw power, and therefore no phase shift. However, this is very idealised – in the real world, even without “loads”, the system includes equipment that inherently introduces reactance, beginning with both the generator and the wires constituting the circuit.

Within a synchronous generator, the stator windings have inductance which introduces some internal reactance. The excitation system (rotor magnetic field) determines the voltage magnitude, not the phase angle. Overall, the generator has what’s called a synchronous reactance, which is almost entirely inductive in nature, and naturally appears as an inductive source, even before external loads are connected.

The generator can still produce or absorb reactive power, by adjusting field excitation:

• Overexcited: internal voltage exceeds terminal voltage so current lags voltage and the generator behaves like an inductor
• Underexcited: internal voltage is lower than terminal voltage so current leads voltage and the generator behaves like a capacitor

But the internal inductive nature is always there as part of the fundamental magnetic characteristics of the machine.

Transmission lines also have impedance because they are not perfect conductors. They are usually inductive although over long distances as described above, but they can also behave like capacitors with the line itself acting as one plate and the ground the other. This impedance introduces phase shift, allowing current to flow even in the absence of conventional loads (the power line itself acts as a load). In a real grid circuit, the phase angle between voltage and current depends on:

• The internal impedance of the generator (inductive)
• Transmission line impedance (usually inductive but can be capacitive)
• The nature of the load (can be anything – resistive, inductive, or capacitive)
• The location of measurement and whether it is close to or far from the generator

In a circuit containing only a generator and a transmission line that is a perfect conductor, there would be no current flow.

What do we really mean by a “synchronous grid”?

It’s not enough for generators to all output current and voltage that has a consistent rate of change (ie frequency), it is important that they are correctly aligned. It’s interesting to think through what happens when a power grid is first energised eg after a blackout as happened in Iberia.

Most power stations actually rely on the grid to get going, but if there is no grid, special “black start” facilities are needed. In Britain these tend to be gas power stations with diesel generators that provide the startup power. In Spain, hydro is also used. In the same way that cars have a starter motor that gets the engine running, so power stations need input energy to get the turbines running.

So the first power station uses its onsite power supply to get started and bring its turbines up to speed – 3,000 RPM in Europe and 3,600 RPM in the Americas (for 2-pole systems). In fact there’s a whole list of tasks the starter motor must carry out:

• Compressor and turbine startup (main shaft spinning) – the turbine can’t ignite until it’s spinning at a certain speed (often ~20–30% of rated RPM). The starter motor handles this first
• Ignition systems – modern gas turbines use electrically powered igniters (spark plugs or plasma torches) to light the fuel-air mix. These require stable dc/ac auxiliary power, which comes from the diesel generator or black-start motor
• Fuel pumps and valves – gas needs to be delivered at the right pressure and flow rate
• Control valves, actuators, and fuel metering systems all need power
• Control and instrumentation systems – turbine control systems needs stable power for PLCs, sensors, pressure and temp monitoring etc, without these the turbine cannot be operated or regulated safely
• Air handling or lubrication systems – for cooling, sealing, and reducing friction. Lube oil pumps and seal oil systems are critical and need early power

Power is also needed to energise the electromagnets that actually generate the electricity: alternating current is generated when one magnet (the rotor) rotates inside the magnetic field of another magnet (the stator). As these are electromagnets, electricity is required to establish these magnetic fields, and this is also initially provided by the starting motor.

The black start power station will begin to generate electricity and will energise the high voltage power lines to which it is connected, allowing the nearest power station to start up its turbine. At this point it can also power its own site load and the starter motor can be disengaged.

However, there are no loads connected to the grid at this stage. The generators try to keep their voltages in phase so their maxima and minima perfectly align and in this way, no power is delivered to the grid. The energy provided by the gas burners is kept at the minimum needed to maintain 3,000 RPM and the turbines store this in the form of kinetic energy.

Magnetic and electric fields are being created and destroyed in each voltage cycle, but as there is almost no resistance present (only from the power lines) as there are still no loads, there is no electricity flowing.

The two generators will slightly vary the phase angles of their voltages to allow some power to be drawn by other generators, allowing them to start up. Since it is difficult to connect load in stages – generally loads are connected by area, so a grid supply point will be opened to energise the connected lower voltage network to which loads are automatically connected – there needs to be enough generation on the grid to meet the demand that is connected as soon as it is connected, otherwise the frequency will fall outside acceptable bounds, the generators will all trip off and the blackout will resume.

So loads cannot be connected to the grid until there is enough generation synchronised.

Typically the grid is divided into zones that are islanded from each other. Each zone is energised before demand is connected, and only after demand is connected and the island is running properly will the zones be connected or synchronised to each other. This staged process is necessary to ensure stability.

As demand is connected, the generators vary the phase angle of their voltage output by adjusting their rotation speeds for short periods of time. It is necessary for them to be almost but not exactly in phase – if they are exactly in phase there will be no power flows but if they are too much out of phase they will interfere with each other creating unstable voltages.

Generators convert torque into electrical power – a turbine (gas, steam, or hydro) provides mechanical torque to the rotor of the generator. The rotor spins within a magnetic field, inducing an alternating voltage and pushing current into the grid. The electrical power output is the result of electromagnetic resistance to the rotor’s motion — called electromagnetic torque or counter-torque. The turbine tries to spin the rotor, and the grid “pushes back” via the load it’s supplying. This opposition creates a balance.

At equilibrium, mechanical torque from the turbine is equal to the electrical (electromagnetic) torque from the generator’s magnetic interaction with the grid. The rotor spins at a constant speed (3,000 RPM in Europe) producing current and voltage that alternate at a stable frequency (50 Hz).

How do TSOs manage reactive power and voltage?

The main tool TSOs use to maintain system stability is frequency. Electrical equipment is very sensitive to changes in frequency and has protection measures that will disconnect it from the grid if frequency or the rate at which frequency is changing falls outside its programmed tolerance levels, potentially leading to blackouts. Frequency is also a measure of whether supply and demand are in balance, which can affect current and voltage, albeit in unpredictable ways, as noted above.

TSOs also manage voltage and reactive power – they measure voltage and current directly, as well as the phase angle between them which allows reactive power to be calculated at different parts of the grid. While frequency is managed by turning generation up and down (and to a lesser extent demand), voltage is controlled through reactive power services.

If we remember that alternating current is generated when one magnet rotates in the magnetic field of another magnet, inducing current and voltage in a wire, a generator can change its voltage by varying the strength of these magnetic fields. But reactive power isn’t simply the magnitude of the voltage, it depends on the phase angle (or lag) between the voltage and current waves.

By changing the excitation (field current) in the rotor, the internal voltage of the generator is altered, and this changes how much reactive power flows between the generator and the grid, and that changes the angle between the terminal voltage and current because reactive power is related to the angle between voltage and current.

The phase is not being controlled directly – the controlling field strength alters terminal voltage which alters current phase relative to voltage based on system conditions.

It should also be noted, that while in individual circuits voltage leads ie the changes in voltage cause energy to be stored and released from the magnetic and electric fields, at the grid level, containing multiple circuits, supplying reactive power (by over-exciting a generator or switching on capacitor banks) raises or supports local voltage while absorbing reactive power (under-excitation or inductive loads) lowers voltage. Reactive power is the control variable, and voltage is the outcome.

Although voltage changes trigger the energy storage, it’s the phase relationship between current and voltage that determines whether reactive power is flowing in or out, and this phase relationship is driven by amount of induction versus capacitance in the circuit.

There are other tools TSOs can use to manage voltage, some of which were employed by REE in an effort to prevent the Spanish blackout. These included coupling power lines, reducing export on interconnectors and setting them to constant power mode, and disconnecting shunt reactors.

Coupling transmission lines

“Coupling transmission lines” usually refers to a configuration where two or more transmission lines are electrically or magnetically coupled in a way that affects their impedance and power flow. There are two common interpretations, depending on the system layout:

Parallel Transmission Lines (mutual coupling) – this is the most likely meaning in the Spanish context. When two or more lines run in parallel, often on the same towers or very close together, their magnetic fields interact. This creates mutual inductance, which modifies the total impedance seen between sending and receiving ends – in effect, the total impedance between two substations becomes lower than the impedance of any single line, especially for the dominant mode of current flow.

When they are coupled, eg by closing switches or re-configuring breakers, operators electrically connect those circuits at one or both ends (and sometimes at intermediate points). This reduces impedance because the current now has more than one route it can follow and chooses the line of least resistance (or in this case, impedance). This can improve the angular stability of the corridor (critical during oscillatory events). The lines are connected in parallel rather than in series.

Series connection would be dangerous and unworkable at transmission level as it would double voltage, require exact impedance matching, and magnify instability risks. Parallel connection, by contrast keeps voltage the same, adds current-carrying capacity and provides redundancy.

The process can also be referred to as: bus coupler closure, mesh configuration, operational coupling of circuits, or paralleling of transmission lines.

“Coupling transmission lines” may also refer to capacitive coupling or reactive power compensation. This is less likely in the Spanish context, but sometimes “coupling” refers to the use of series capacitors or FACTS devices to “couple” parts of the grid and control impedance. This allows power to flow more freely across high-impedance paths, effectively lowering reactance.

Reducing export on interconnectors and setting them to constant power mode

When a HVDC interconnector runs in constant power mode, it attempts to maintain a fixed active power transfer, regardless of local voltage or frequency variations. This means it adjusts its current to keep power constant, so even if the voltage dips, it increases current to maintain the same megawatt output (up to equipment limits). This helps to mitigate voltage drops through current injection – when the ac side sees a drop in voltage, the HVDC control system compensates by increasing current injection to keep the power flow steady. This effectively props up the local voltage, since the receiving grid sees more current inflow.

A constant power mode stabilises active power flows, which can help reduce the chance of secondary voltage disturbances. But there’s a trade-off – if the voltage drops too much, trying to maintain constant power requires injecting very high current, which could exceed converter limits or worsen reactive power imbalance. Some interconnectors can automatically switch modes (eg from constant power to constant current or voltage droop mode) if system stability degrades too far.

In the Spanish context, Spain was exporting to France, and the interconnector was set to constant power mode after voltage drops and both frequency and voltage oscillations were detected. This meant that the system would aim to maintain a consistent power transfer in MW irrespective of changed in Spanish grid conditions. If voltage on the Spanish side dropped, the converter would increase current draw from the Iberian grid. However, this would increase electrical stress on the Spanish system as it’s having to supply more current under weakening voltage conditions, which can exacerbate the voltage drop:

• • The converter can act as a “power sink” drawing current from a weakening system
  • If multiple exporting elements behave this way during a disturbance, it can worsen reactive power imbalances or amplify instability.

To mitigate the effects of the higher current draw, the active power export capacity is reduced. In the Spanish case, the export capacity was cut to 1,500 MW and then constant power mode at 1,000 MW was implemented, which was a de facto capacity reduction to 1,000 MW. If the interconnector had been left in a voltage-following or frequency-sensitive mode, it might have responded unpredictably to ongoing oscillations, possibly creating new disturbances or cross-border propagation of instability.

In normal mode (voltage-following or frequency-following):

• • The converter lets power vary depending on system voltage or frequency
  • If voltage drops or frequency changes, the power flow adapts, even if that means amplifying oscillations
  • It’s reactive and may contribute to instability, especially in low-inertia or oscillating conditions

In constant power mode:

• • The converter holds the real power steady, but allows the current to vary to compensate for voltage drops
  • If voltage drops by 10%, current must rise by ~11% to keep power constant, which introduces greater current swings. These can increase losses, stress cables/converters, and may affect local voltages further if not managed carefully

This can be compared with the use of cruise control on a car going uphill. Here, normal mode is the foot on the accelerator pedal – if the speed drops you and you only increase acceleration after the drop in speed, you react late and may overcompensate. Constant power mode is like cruise control – the engine adjusts power to keep speed stable. It doesn’t make the hill go away, but it makes the car’s behaviour more predictable and avoids oscillating between accelerator and brake (or just pressing or releasing the accelerator). However, this does not account for the steepness of the hill (maybe a gear change is also required) or the even-ness of the road surface and/or incline.

Similar limitations apply to the grid context. Constant power mode trades voltage stress for frequency stability, but it’s a crude response because it treats the voltage instability as a static rather then dynamic problem and assumes you have correctly diagnosed it in the first place (ie there is only a need for cruise control and not a lower gear).

Disconnecting shunt reactors

A shunt reactor is a high-voltage electrical device designed to behave like an inductor. It is connected in parallel (or “shunt”) with the transmission line or busbar, and works by storing energy in its magnetic field. Shunt reactors help to control voltage levels, particularly by preventing overvoltage during periods of low load and high line capacitance (common on long transmission lines). They behave like a break – because like inductors, they absorb power when voltage is increasing, voltage increases less than it would in their absence. Their effect is steady and passive – they don’t actively respond to system conditions unless specifically switched or controlled via tap changers or power electronics.

Therefore, if shunt reactors are disengaged, they stop limiting the rise in voltage, allowing it to increase more on the upward cycle, and therefore mitigates low voltage conditions. Impedance is lower when shunt reactors are disengaged.

What are the limits of generator response?

While conventional generators support voltage by changing the excitation current of the electromagnets that generate electricity, this has no impact on the speed with which the rotating magnet rotates, so in theory it should have no impact on the frequency with which current and voltage alternate.

However, each generator has a physical limit to what it can produce at any given moment – it cannot produce unlimited active and reactive power simultaneously. This is described by the generator’s capability curve, which defines a boundary of permissible combinations of:

• Active power (MW) — from the turbine/fuel
• Reactive power (MVAR) — from excitation system

If a generator is operating near its thermal or stator current limit, supplying more reactive power (to support voltage) would require it to reduce active power, and vice versa. In this case, supporting voltage via excitation can reduce a generator’s headroom to respond to frequency deviations (which require changes to active power).

In a disturbance, the grid frequency drops because demand exceeds supply. The generator’s governor tries to increase mechanical power (active power output) to increase the amount of electricity being output to the grid. In some cases, the same disturbance can cause the voltage to also drop (as noted above, unlike in purely resistive circuits, this is not always the case due to the complex relationship between capacitance and inductance). In this case, the generator’s control systems will increase current to the electromagnets to increase reactive power output. Hence the generator is trying to simultaneously increase both active and reactive power output.

But sudden changes in excitation currents can cause changes in terminal voltage, affecting machine stability. If the voltage is unstable, generators might be unable to sustain or ramp active power as planned.

During a fault on the system such as a short circuit, current typically spikes since resistance greatly reduces (resistors are by-passed by the short circuit). This can cause voltage collapse local to the fault which can cause generators to trip, leading to loss of generation and a frequency drop.

Voltage disturbances can have serious consequences beyond just local voltage collapse. A drop in voltage reduces the generator’s electromagnetic (electrical) torque, because terminal voltage directly contributes to the torque produced in the rotor. If the electrical torque drops but the mechanical torque from the gas turbine remains unchanged, the imbalance causes the rotor to accelerate.

However, the generator’s control systems prevent it from speeding up arbitrarily — it stays at synchronous speed. Instead, the imbalance causes the generator’s internal angle to shift forward relative to the grid, a phenomenon known as “rotor angle swing.”

The power transferred to the grid depends on the sine of this phase angle. Power increases as the angle increases, peaking at 90°, and then begins to fall again. Like a spring that’s been wound up and released, the generator swings past 90° and then reverses, oscillating around its new equilibrium.

If the disturbance is cleared quickly, and the system has enough damping (from inertia, system controls or grid support), these oscillations will fade. But if the grid can’t absorb the shock, due to low inertia or weak damping, the swings can grow worse, and the generator can lose its synchronisation to the grid entirely. At that point, it will disconnect from the grid, triggering a loss of generation, and potentially a frequency drop or wider cascading instability.

Inverters generally operate with a fixed power factor that is a fixed relationship between active and reactive power (this is set out in Spain’s RD 413/2014 regulation governing the use of renewable generation). Wind and solar cannot provide dynamic voltage support unless they are configured for synthetic inertia or voltage control, but this is unusual because they would have to reserve headroom for inertia provision which has an adverse impact on the economics of the generator.

How do inverter-based resources behave differently?

Inverters convert direct current or asynchronous alternating current into a alternating current that can be injected into ac power grids. However, this output is often referred to as being “dirty” that is the waveform produced is not a clean, smooth sine wave like that from a synchronous generator. Instead, it may have the following issues:

• Harmonics: inverters use power electronics to approximate an ac waveform. This switching introduces harmonic distortion — additional frequency components at multiples of the fundamental frequency (e.g., 150 Hz, 250 Hz on a 50 Hz grid). These harmonics can cause heating in transformers and motors, interfere with sensitive electronics and reduce power quality and efficiency
• Noise / ripple: “dirty” output often includes high-frequency noise or voltage ripple superimposed on the main waveform. This results from imperfect filtering in the inverter’s output stage and can stress insulation on equipment and trigger false trips in protection systems
• Poor waveform fidelity (non-sinusoidal): basic inverters may produce a square wave, modified sine wave, or a poorly approximated sine wave (e.g., stepped waveform). Even advanced inverters that generate “pure” sine waves may not match the smoothness of a synchronous machine unless carefully filtered and synchronised
• Phase instability / jitter: particularly in grid-forming inverters, where the inverter sets the voltage and frequency reference (rather than following the grid), small timing errors or phase mismatches can appear. This can result in unstable interactions with other equipment, especially synchronous machines or other IBRs

A “dirty” output isn’t always a problem for the grid if it’s filtered properly and harmonics are controlled, but in high-IBR systems it becomes more serious because there are fewer synchronous machines to absorb or dampen harmonics, grid protection and measurement equipment may misread distorted waveforms, and interactions between inverters can create unpredictable, resonant or unstable behaviours (as seen in Spain).

Conventional synchronous generators provide frequency support (inertia and changes in active power) and voltage support (changes to excitation currents). However, inverter-based generators such as wind and solar do not provide inertia nor are they able to vary output to support frequency (there are very few inverters currently in operation that can provide inertia, so for the purposes of this discussion they will be ignored. To my knowledge there are no such grid forming inverters in Spain) but they do provide voltage support by injecting or absorbing reactive power.

Batteries are also inverter-based, but because they are able to rapidly change their active power output they provide synthetic inertia and frequency support and also provide voltage support in the same way that wind and solar do.

In the event of a fault, wind and solar can support voltage by altering their reactive power output, but if frequency falls outside their operational tolerances, they will disconnect (trip off), aggravating the grid disturbances. Batteries provide much more support but their impact is limited by their low levels of deployment – there are not enough batteries to support the grid in the absence of sufficient synchronous machines.

Power factor control is a key function in inverter-based resources (“IBRs”) such as wind, solar PV, and battery storage, and it has a direct effect on voltage control. As noted above, the power factor is the ratio of active (real) power to apparent power, and reflects how much of the power is doing useful work rather than circulating as reactive power, being stored in and released from the electric and magnetic fields in each voltage cycle. A power factor of 1 means all the power is active power and no reactive component (meaning there are no inductors or capacitors connected to the circuit).

Inductive devices absorb reactive power when voltage is rising, and release it as voltage falls. Capacitive devices do the opposite: they release reactive power when voltage is rising, and absorb it as voltage falls. This exchange doesn’t do real work, but it supports the voltage waveform and system stability. So, by adjusting how much reactive power an IBR provides or absorbs, local voltage can be regulated.

IBRs typically use power electronics that can decouple real and reactive power, by changing the phase angle between current and voltage. If it makes the current lag the voltage, it behaves like an inductor, while if it makes the current lead the voltage it behaves like a capacitor. This gives them the flexibility to control power factor, and thus influence voltage. Inverters control this phase angle using software.

There are several modes of power factor control:

• Fixed power factor: the inverter maintains a constant power factor (eg 0.95 leading or lagging). This sets a constant relationship between active and reactive power. It’s a simple process, less dynamic for voltage control
• Voltage-reactive power (Volt-VAR) mode: reactive power is adjusted automatically based on local voltage. If the voltage dips, the inverter injects reactive power, and if voltage rises, it absorbs it. This is more dynamic and therefore more helpful for voltage stability
• Power factor setpoint control: the inverter receives a power factor command (from the TSO or DSO) and adjusts reactive output accordingly. This is common in grid codes with coordinated voltage control schemes

Because IBRs can’t inherently supply inertial response, using them for voltage regulation becomes increasingly important in low-inertia grids. In traditional synchronous machines, voltage control was handled via excitation systems – in inverter-based generation (and batteries) voltage control is implemented via power factor and VAR control loops within the inverter – inverters emulate the effects of synchronous machines on voltage by precisely shaping voltage and current waveforms.

In Spain IBRs are required at certain times to maintain a constant phase angle (and failure to do so was one of the contributors to the blackout, as I will describe in the follow-up post where I will discuss the Spanish blackout in detail). This means they reacted to the grid instead, and were affected by the voltage oscillations. During a voltage oscillation the voltage magnitude and possibly the phase angle (between current and voltage) vary dynamically.

If an inverter tries to maintain a fixed power factor during this, but doesn’t adjust fast enough, it will lag the system and fail to keep up with the voltage changes. This leads to mismatched reactive power support, which can worsen the oscillations or allow them to grow.

Voltage oscillations don’t directly affect the phase angle, but they do create a moving reference making it harder to ensure the phase angle is maintained. If an inverter tries to hold a fixed power factor (constant phase angle relative to a fluctuating voltage), it may no longer deliver the intended reactive power. Worse, the delay or mismatch can feed instability if the inverter is slow to adjust or lacks adequate voltage sensing. The inverter fails to track the voltage waveform accurately, and its contribution becomes out-of-phase, which can increase the severity of the disturbance.

What are oscillations in frequency and voltage?

There has been a lot of discussion about “oscillations” in connection with the Iberian blackout. Both frequency and voltage oscillations are described in the official report, together with various illustrative graphs. So what are these oscillations, and how are they caused?

Frequency is the rate at which current and voltage vary in an alternating current grid, ie 50 Hz in Europe and 60 Hz in North America. A frequency oscillation occurs when that rate itself varies over time, meaning the system frequency is no longer holding steady at 50 Hz, but gently swings above and below it in a regular pattern.

When a 0.2 Hz oscillation was identified on the Spanish grid, this was a secondary variation in current and voltage changing at a rate of one cycle every 5 seconds. The table illustrates such an oscillation.

Here the frequency has a variation of ± 0.005 Hz that takes 5 seconds to complete its cycle. This means that the  0.2 Hz frequency oscillation identified in Spain saw the system frequency (the instantaneous rate of the 50 Hz waveform) gently rocking back and forth at one cycle every 5 seconds, typically with a small amplitude (eg ±0.005 to ±0.02 Hz). It was a slow sinusoidal variation in the frequency of the frequency, superimposed on the 50 Hz base — not a permanent step shift to 50.2 Hz.

A voltage oscillation is a cyclical fluctuation in voltage magnitude, not in the waveform frequency. When Spain had “voltage oscillations of up to 4 kV” this meant the voltage magnitude at 400 kV would have swung between 396 and 404 kV (or centred about some lower value since the fault was also associated with a reduction in voltage, so it might have been 394 – 402 kV). The term “oscillation” implies the voltage varied in a repeating, resonant fashion, not just a brief dip and recovery. These kinds of fluctuations, if not properly damped, can excite resonances in the system, especially with certain inverter-based resources, leading to wider instability.

It’s also worth considering what the 400 kV refers to in the first place, since voltage is alternating between zero, some maximum and some minimum in a sinusoidal pattern. In modern power grids, the constant voltage level cited for power lines, and other equipment is the dc equivalent of the alternating voltage, which is calculated from the root mean square (“RMS”) of the alternating voltage. The peak voltage is the RMS voltage x √2 which is approximately 566 kV for a 400 kV system.

What causes oscillations in frequency and voltage?

When there is a grid fault, such as a short circuit, impedance plummets at or near the fault site causing a surge in current, especially from nearby generators. Voltage can collapse locally, potentially rippling out across connected circuits. Protection systems try to isolate the fault, sometimes within milliseconds.

Even if protection systems clear the fault quickly and no machines trip the fault can cause a frequency disturbance. Generators close to the fault still react to the voltage drop and may momentarily increase their reactive current output. If the disturbance is large enough, it can affect the torque balance on generator shafts, causing oscillations in rotor speed which change the active power of the generator, creating frequency oscillations.

These frequency deviations are typically small and quickly damped, but in a weak or heavily inverter-dominated grid, they may persist or amplify. If enough machines respond asynchronously to the fault, especially if there’s low inertia, you can get

• system-wide electromechanical oscillations – small, system-wide frequency or angle swings
• sub-synchronous or inter-area oscillations, especially in weakly connected zones

These can destabilise the system over time and may trigger automated trips or control actions (like modulating excitation or curtailing IBRs) to suppress them.

Under certain conditions, inverter-based resources such as solar PV, batteries, and wind turbines can be the cause of grid oscillations. The purpose of an inverter is to convert dc electricity generated by solar panels, batteries and wind turbines (wind turbines generate alternating current, but not with constant frequency so they cannot synchronise to the grid. To get round this, the ac generated is converted to direct current and then back to ac for connection to the grid). Inverters not only convert from dc to ac, but they need to do so in a way that is compatible with the power grid. This means they must:

• Match the grid’s voltage and frequency (eg 240 V, 50 Hz in the UK)
• Synchronise phase angle and wave shape with the grid
• Inject power (active and reactive) into the grid as instructed by controls or markets

To do this, the inverter uses:

• A switching bridge (eg insulated-gate bipolar transistors (“IGBTs”) or metal-oxide-semiconductor field-effect transistors (“MOSFETs”))
• Filters (to smooth out the pulse width modulation (“PWM”) switching)
• A control system (to regulate output)
• A phase-locked loop (“PLL”) to “track” the grid voltage phase/frequency

Inverter controls assume they’re connected to a reasonably strong grid, where voltage is “stiff “(ie doesn’t sag or distort), impedance is low and inductive, and frequency is stable and easy to follow. However, real power grids don’t have low impedance as described above. In particular they have inductance, and this causes problems for inverters in a number of ways:

• Instability in control loops: if the inverter thinks the grid is stable but it’s not, its control loop can overshoot, oscillate or lose synchronisation (PLL unlock)
• Harmonic interaction: high impedance at certain frequencies can amplify harmonics – inverters create some harmonics by design (from switching) but normally, they’re filtered out or absorbed by the grid. In a weak grid, these harmonics reflect back and build up creating resonance
• Sub-synchronous resonance: at sub-50 Hz frequencies impedance may create oscillating power flows, current/voltage instability and damage to cables, filters, or transformer windings

Inverters can cause grid voltage oscillations through control interactions, lack of damping, or fast-acting power electronics responding poorly to weak grid signals. The key mechanisms of such oscillations are:

• Phase-locked loop instabilities: inverters need to synchronise with grid voltage and frequency via PLLs. In a weak or noisy grid, PLLs can lose lock or misinterpret disturbances, leading to unstable current injections and oscillatory feedback
• Low inertia and fast response: unlike synchronous machines, inverters don’t possess inertia, ie they don’t naturally resist changes in grid frequency. However, their response is not necessarily passive – their speed of response adjusting their power output can sometimes amplify grid disturbances instead of smoothing them as a heavy spinning mass would
• Resonance with grid impedance: inverters interacting with certain line or transformer impedances can excite harmonic or sub-synchronous resonances particularly in weak grids. In real world power grid applications, oscillations are seen in offshore wind farms due to long cables
• Poor coordination: if multiple inverters or parks use similar fast-reactive controls (eg droop response, virtual inertia), they may reinforce each other’s actions and create a positive feedback

Not only can inverters create grid voltage oscillations they can also amplify existing oscillations. This is actually more common than them creating oscillations in the first place. If a grid is already oscillating due to a disturbance such as a sudden large generator or interconnector trip, inverters can:

• Misinterpret voltage/frequency swings, causing over- or under-reaction
• Inject reactive power too aggressively (or with delay), adding energy to the oscillation rather than damping it
• Enter anti-islanding or fault ride-through modes erratically — some will stay connected, others may trip too fast, worsening the imbalance

Modern grid-forming inverters are designed to damp such oscillations, but almost all inverters currently deployed in western power grids are grid-following and were not designed to operate under stressed or low-inertia conditions.

Examples of the impact of IBR on power grids can be found in this paper from Dominion Energy Virginia, in which several instances of sub-synchronous oscillations events are described, how they arose, and how they were resolved.

“Since 2021, reports of abnormal events across the Dominion system have increased, due to the increase in IBRs,”
– Dominion Energy

Among the findings of the paper were that system operators can struggle to identify oscillations because traditional SCADA monitoring devices have sampling rates that are too low to capture them until they become large or of long duration, at which point either SCADA monitoring detects them or customers begin to complain about the impact on their equipment. For this reason, Dominion recommends the use of voltage oscillation detection at selected sites throughout the system and reactive power oscillation detection at all IBR and synchronous generation sites.

Note on mechanical inertia

In heavily IBR-dominated grids, TSOs look for alternatives to synchronous generators for the provision of inertia. In addition to synthetic inertia from batteries, they use spinning mass in the form of synchronous condensers and flywheels. Both are rotating machines synchronised to the grid frequency, and they provide inertia because they are heavy spinning lumps of metal.

However they differ in their primary function – synchronous condensers are synchronous machines (essentially generators) that are not connected to a mechanical power source – they spin freely and provide reactive power and inertia. Flywheels are usually mechanically spinning mass, sometimes coupled to a generator or a power electronics system, designed to inject or absorb power rapidly during transients.

Synchronous condensers are connected to the grid in the same way that synchronous generators are – via their stator windings. They maintain synchronism with the system frequency with the rotating magnetic field inside the machine locked in phase with the grid voltage. They also have a phase lock which ensures current and voltage are in phase meaning no current or active power flows.

When the grid frequency changes suddenly (for example after a trip or load event), the grid tries to accelerate or decelerate the rotating magnetic field in the condenser’s stator. Due to the electromagnetic coupling between stator and rotor, the inertia of the spinning rotor resists this change, absorbing or releasing kinetic energy into the grid through electromagnetic torque. This resistance provides inertial response automatically – it doesn’t require sensing or software as it’s a physical, instantaneous response governed by the physics of the coupling. Synchronous condensers provide reactive power in the same way that synchronous generators do: by changing the current through the electromagnets on the rotor.

Flywheels are synchronous machines that work almost identically to synchronous condensers in that they are electromagnetically coupled to the grid, although come flywheels are connected electrically via an inverter, in which case they store energy but don’t naturally provide inertia. In this case they behave like a battery, providing synthetic inertia and reactive power by manipulating the phase angle between current and voltage.

Power grids with more IBRs tend to be weaker and therefore less stable

In summary, the theory of power grids and the real-world experience of system operators tells us that grids with a higher proportion of inverter-based generation are less stable. Faults are more difficult to contain, and even absent fault conditions, inverters can mis-behave creating voltage disturbances that can lead to disconnections due to lack of grid resilience in the absence of sufficient synchronous generation.

Synchronous generation performs three very important functions that are difficult to replicate with IBRs. Firstly they create the current and voltage waveforms with a stable 50 Hz frequency and the correct amplitude (eg 240 V in the UK). Secondly they are able to maintain the stability of this voltage waveform, in part because their inertia resists changes to their speed of operation and in part because they can vary their active power output to respond to fluctuations on the grid. And finally, they are able to adjust the excitation levels of their electromagnets, which allows them to add or absorb reactive power to control voltage.

In contrast, not only do inverter-based resources not perform many of these functions, they can in some cases initiate voltage oscillations that destabilise power grids.

Original article   l   KeyFacts Energy Industry Directory: Watt-Logic