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By Charles Rhodes, P.Eng., Ph.D.

It has been experimentally observed that no real electricity grid without energy storage is able to obtain more than about 20% of its average energy requirement from wind and solar electricity generation. On clean electricity grids this issue forces 80% of the grid supplied energy to come from hydro and nuclear generation. This web page identifies the cause of this practical constraint on supply of wind and solar energy.

A synchronous electricity generator usually consists of a fluid turbine prime mover, a flywheel, and an electromagnetic magnetic rotor spinning inside stationary wound copper stator coils. The magnetic rotor is excited with DC. The AC line frequency applied to the stator coils causes a rotating stator magnetic field. The physical rotation of the rotor occurs at exactly the same angular velocity and direction as the rotation of the stator magnetic vector. Hence at torque balance there is a nearly constant angle between the magnetic vector of the rotor and the magnetic vector of the stator. If the magnetic vector of the rotor leads the stator there is a torque on the rotor which tends to make it slow down and hence the machine acts as a generator. If the magnetic vector of the rotor lags the magnetic vector of the stator there is a torque on the rotor which tends to make it accelerate and hence the machine acts as a motor. Changing the rotor excitation current changes the strength of the magnetic interaction between the rotor and the stator.

A synchronous generator has an electromechanical controller that uses a precise external 60 Hz reference signal to contol the flow of energy source fluid through the turbine so as to maintain stable 60 Hz electricity generation at a constant phase with respect to an external 60 Hz time base reference signal. The reference signal usually originates at a quartz crystal oscillator or an atomic clock. All the synchronous generators of a particular electricity system use the same reference signal with different time offsets, depending on their geographical positions.

In some situations the time offset of a particular synchronous generator is fixed by a constant time delay with respect to the external 60 Hz reference signal. In other situations the required time delay is obtained from the AC grid. Note that if there is a large fraction of asynchronous generation connected to the grid it can slightly affect the time delay through the AC grid which can contribute to grid instability.

The rotor excitation current in a particulat generator sets the strength of the rotor magnetic field which sets the amount of locally generated power.

Large electricity generators, such as those used at hydraulic power stations or nuclear power plants are usually synchronous generators. Usually synchronous generators are dispatchable.

In order to ensure grid stability at all times there must be enough operating fast response generation to follow rapid uncontrolled load changes.

An important feature of large synchronous generators is that they can be used to black start the AC grid.

An asynchronous generator uses the signal on the AC line as its frequency and phase reference. Thus an asynchronous generator relies on the proper operation of external synchronous generators for its own proper operation.

A simple type of asynchronous generator is an induction generator, which is just an over sped AC induction motor. For example an induction motor excited at 60 Hz with a nominal speed of 1800 RPM acts as a motor exporting torque at 1780 RPM. The same machine externally driven at 1820 RPM will import torque and act as an induction generator. In both cases the machine relies on the existence of an externally supplied 60 Hz AC voltage to provide both a frequency and a phase reference. Induction machines can be power factor corrected by addition of appropriate shunt capacitance to make them parallel resonant at or near 60 Hz.

A potential danger with such resonant generators is that if unloaded and disconnected from the grid their output voltage can quickly become very high.

Typically smaller economy generators, such as those at wind turbines or solar power installations, are asynchronous generators. Frequently these small generators are unconstrained and not dispatchable. Usually they do not provide grid stabilizing moment of inertia.

A disadvantage of asynchronous generators is that they cannot black start an AC power system unless that system is parallel resonant at approximately 60 Hz. In practice stand alone resonant systems are so difficult to manage during black start that they are seldom used for that purpose. Most resonant equipment relies on the AC line for a frequency and phase reference.

A solid state power inverter can in principle be programmed to act as either a synchronous or an asynchronous generator. However, the battery and the solid state switching devices required to properly simulate the behaviour of a synchronous generator with a flywheel are so large and expensive that this simulation capability is seldom used. As a result, use of solid state inverters as asynchronous generators at wind and solar generation sites leads to grid instability due to lack of moment of inertia. This issue is further discussed on the web page titled: Generation Valuation.

Solid state inverters programmed to act as asynchronous generators usually rely on a Phase Lock Loop (PLL) circuit to match the inverter phase to the grid phase. These PLL circuits operate over a limited frequency range. However, if the grid to which such a power inverter is connected lacks sufficient synchronous generation with good frequency control, the PLLs lack a stable frequency reference and the entire grid can drift in frequency over the PLL operating frequency range. If the grid contains long transmission lines this frequency drift will change the reflected power, which change will further contribute to grid instability.

Many environmentalists erroneously assume that if an electricity grid needs more generation capacity that capacity can be provided simply by connecting more asynchronous solar and wind generation.

There is a fundamental grid stability issue which limits to 20% the maximum fraction of average grid power that can be supplied by unconstrained asynchronous wind and solar electricity generation. Exceeding the 20% limit by use of generation constraint and/or energy storage substantially increases the electricity cost per kWhe. The purpose of this section is to show how the 20% limit arises.

A consequence of this stability limit is that if all of the electricity provided by the electricity grid must come from clean sources, then for economy about:
100% - 20% = 80%
must come from a combination of hydraulic and nuclear electricity generation. In many jurisdictions there is little or no opportunity for hydraulic electricity generation, so when fossil fuel electricity generation is phased out it must be replaced by nuclear generation.

Pp = Annual peak grid load. This peak load usually occurs during a hot day in the summer when air conditioning is running at maximum capacity

Pl = Annual lowest grid load. This low load typically occurs during a mild night in the spring or the fall when little space heating or air conditioning is running.

Pa = Average grid load through the year;
= (Total annual kWhe generated) / (8766 h)

To a first approximation:
Pa = (Pp + Pl) / 2
and in a typical electricity system:
Pp = 2 Pl

Pa = (3 Pl) / 2
= 1.5 Pl

Pwsa = annual average value of combined wind and solar generation power
Pwsp = peak value of combined wind and solar generation power
Cf = capacity factor of wind and solar generation

By definition:
Cf = Pwsa / Pwsp

Cf = 0.30

Pwsa = Cf Pwsp

Fws = fraction of annual grid load kWhe provided by wind and solar electricity generation

Fws = Pwsa / Pa
= (Cf Pwsp) / Pa
= 0.30 Pwsp / 1.5 Pl
= 0.20 (Pwsp / Pl)

However, as is shown below:
(Pwsp / Pl) < 1
which gives:
Fws < 0.20

Thus the fraction of annual grid energy provided by unconstrained asynchronous wind and solar generation is limited to about 20%.

PROOF THAT (Pwsp / Pl) < 1:
It is now necessary to show the source of the constraint: [Pwsp / Pmin] < 1

This constraint is easier to understand from a mechanical perspective than from an electrical perspective.
A synchronous turbo-generator has an electro-mechanical controller which uses a slotted wheel pulse counter to sense the cumulative angle of rotation:
(Theta - Thetao):
with respect to Thetao where:
Thetao = shaft angle of rotation at time:
t = to

Assume that the generator is wound 4 pole and is intended for 1800 RPM opertion. At time t the ideal shaft angular position with respect to Thetao is given by:
(Theta - Thetao) = Pi F (t - to)
F = 60.000000000 Hz.

At time t the actual measured shaft angular position with respect to Theto is:
(Theta - Thetao)

At time t the shaft angle error in radians is:
Angle Error = [(Theta - Thetao) - Pi F (t- to)]

The electromechanical controller then calculates the instantaneous rotor angular velocity W using:
W = [d(Theta) / dt].

The ideal rotor angular velocity is:
d[Pi F (t - to)] / dt = Pi F

The electromechanical controller then calculates the angular velocity error:
Angular velocity error = (W - Pi F)
= {[d(Theta) / dt] - [Pi F]}

In these expressions:
t = time
to = a reference initial time
Thetao = shaft angle at time t = to
Theta = shaft angle at time t
Pi = 3.14159265 F = a precise 60 Hz frequency reference, typically derived from a quartz crystal frequency standard that is phase lock coupled to a broadcast reference frequency.

The electro-mechanical controller uses these parameters to control the flow of an energetic fluid (steam or water) which impacts the turbine and sets the amount of turbine positive torque. The generator's load causes formation of magnetic torque of the opposite sign. If the load is steady, after a brief settling period the net torque on the generator shaft converges to zero, the angular velocity error converges to zero and the shaft angle error converges to zero so that the generator produces exactly 60 Hz at a specified phase shift with respect to reference frequency signal F.

Following a step change in load, there are damped oscillations in the angular speed error:
{[d(Theta) / dt] - [Pi F]}
and in the cumulative angle error:
{[Theta - Thetao] - [Pi F (t – to)]}

At any instant in time the angular speed error can be either negative or positive and the cumulative angle error can be either negative or positive. The electromechanical controller is programmed to make these two errors both converge to zero. It does so by changing the energetic fluid flow impacting the turbine so that the net torque on the turbine shaft which is
(energetic fluid torque – load induced magnetic torque)
converges to zero. Note that at any instant in time the net torque may be either positive or negative. The net torque causes the flywheel to either accelerate or decelerate.

Now assume that an asynchronous electricity generator is also connected to the same circuit. The asynchronous generator does not know frequency F. It can only sense the line frequency:
W = d(Theta) / dt
which is an approximation of [Pi F].

A gradual increase in the asynchronous generator power output while holding the load constant causes a corresponding gradual decrease in the load torque on the synchronous generator. In order to keep the synchronous generator running at 60 Hz its electro-mechanical controller reduces the flow of energetic fluid impinging on the turbine. However, when this fluid flow reaches zero the controller can no longer generate a negative net torque to properly control the synchronous generator shaft angular speed error or the cumulative angle error.

However, the asynchronous generator relies on proper:
W = d(Theta) / dt
values to determine its own frequency and phase. Hence both the synchronous generator and the asynchronous generator lose their frequency and phase control. The synchronous generator rotor spins freely but there is no mechanism to cause a net negative torque to slow it down. The asynchronous generator is not aware that its reference frequency:
W = [d(Theta) / dt]
and phase angle
are drifting away from their reference values. Hence both of these generators will likely gradually over speed until they trip a high frequency limit which will generally shut down the grid.

Electricity grid protection systems rely on detecting frequency deviation from the nominal 60 Hz. Typically the low frequency trip is set at 57 Hz and the high frequency trip is set at 63 Hz.

The frequency and phase control of an AC grid relies on the synchronous generation experiencing sufficient load torque that its electro-mechanical controller(s) can cause formation of both positive and negative net torque. As asynchronous generation forces synchronous generation to zero the synchronous generation can no longer lock onto its fixed angular velocity reference [Pi Fo] and the frequency of the asynchronous generation drifts with the frequency of the synchronous generation. That frequency soon drifts significantly away from 60 Hz and triggers a safety trip.

As previously shown this form of grid instability manifests itself when the annual average power supplied by unconstrained asynchronous wind and solar generation reaches about 20% of the annual average grid power.

Electricity system "stability" usually refers to the transient change in frequency caused by a step change in generation or load. This frequency change must be limited to prevent grid shutdown due to frequency based safety trips. A frequency change also affects any party that relies on the AC line frequency for timing or for determining the RPM of a synchronous motor. A transient frequency change is also accompanied by a transient change in system voltage. Electricity system stability is particularly important for paper mills, plastic film facilities and wire producers that need to precisely control the RPM of large high speed rollers and winding equipment. A practical effect of the electricity system stability degradation in Ontario that occurred subsequent to the 1970s was to drive newsprint paper mills into insolvency.

Electricity system transient stability is set by the ratio of system mechanical moment of inertia to peak power. When fossil and nuclear generators are displaced by solid state asynchronous wind and solar generation the ratio of the moment of inertia to peak power decreases which degrades the frequency and voltage stability of the entire electricity system.

A major problem with unconstrained (wind + solar) generation occurs when this average asynchronous generation supplies more than about 20% of the grid's annual average power. The solid state asynchronous generation lacks the moment of inertial needed to provide electricity system stability and from time to time shuts down its stable frequency reference.

Under the Ontario electricity market rules prevailing today to maintain grid stability during low load periods it is necessary to pay wind and solar generation to not generate, which is financially ludicrous. To economically use the available surplus clean electrical energy for fossil fuel displacement it is necessary to adopt an interruptible electricity rate.

In parts of the USA such as California and Texas there is regulatory failure to recognize that sufficient grid connected synchronous generation is required at all times to maintain grid stability, no matter how much (wind + solar) energy is available. In order to avoid burning fossil fuels the required synchronus power must come from a combination of dependable hydro and nuclear generation.

In order to keep the grid frequency stable the dispatch rules must ensure that the synchronous generation never goes to zero. A synchronous capacitor connection is not sufficient. The synchronous generation must actually be generating real power to stabilize the grid frequency and phase to an external time reference.

The underlying problem is that wind and solar power sources almost always rely on some form of asynchronous generation. This asynchronous generation relies on the frequency and phase of the grid voltage to set its own frequency and phase. As asynchronous generation pushes synchronous generation off the grid, the grid frequency and phase become progressively more unstable. When there is no synchronous generation there is no longer a rigid time base for the asynchronous generation.

Hence, the fraction of average total grid energy that can be provided by unconstrained asynchronous wind and solar generations has a maximum of about 20%.

This issue is independent of whether the generation is realized with electromagnets or solid state electronics. The issue that matters is the time base. Synchronous generation is generally referenced to a time base that is set by a crystal controlled clock or an atomic clock. The various synchronous generators on the same electricity system all use the same time base transmitted either by a stable radio signal or a propagation time stable hard wired connection. The asynchronous generators derive their phase and frequency reference from the grid itself. However, that phase and frequency information relies on proper operation of the synchronous generation. When the synchronous power goes to zero the synchronous generators keep spinning but their control systems can no longer stabilize the grid frequency and phase to the external time base. The grid frequency will tend to drift until it causes a high or low frequency trip.

The underlying cause of this instability problem with electromechanical generation at low synchronous power levels is that power turbines are unidirectional. To stabilize the frequency and phase at low power there needs to be a generator speed retarding mechanism. Once a synchronous generator is transmitting power into a real load it can be retarded by reducing the prime mover water or steam flow while outputting power to a real load. However, at zero power output there is no energetic fluid flow to reduce, so the mechanism for frequency and phase control to the reference time base can no longer operate.

It might be possible to address this issue by dispatching additional electrical load on, but few parties have properly thought through all the implications of interruptible electricity and real time load dispatch.

Unconstrained generators are output limited by their immediately available power. If the generator is unconstrained there is no additional power available for stabilizing frequency and phase. Hence an unconstrained generator cannot provide frequency and phase stabilization.

Gene Preston advises that in ERCOT they have wind generation which claims to be self synchronous. In reality these wind generators are solid state power inverters controlled by phase lock loops. Each phase lock loop has an oscillator that varies in frequency enough to allow the generator to lock onto the grid provided that the grid frequency is within the oscillator's lock range. In this manner the various generators can synch themselves to the grid and each other. However, the grid frequency then becomes uncertain because it can potentially be anywhere in the lock range of the various phase lock loops.

The solid state inverters also lack the rotating moment of inertia necessary for grid frequency stability in the presence of step load changes. There are also other ways in which this arrangement can become unstable. Experimentally ERCOT has found that due to grid instabilities it cannot exceed an average wind energy component of about 20%.

This web page last updated November 8, 2021.

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