Power grid in a changing world
Part 2: System Inertia
Introduction
In part 1 of this series, we discussed the essence of a stable power system — one that continuously adapts to power and frequency imbalances, making required adjustments within a remarkably brief timeframe to adequately compensate for the disturbances.
Given that electricity needs to be consumed as soon as it is generated, keeping a stable grid 24/7 is for me without doubt one of the most amazing feats of engineering.
Today, our focus shifts to system inertia, the grid’s first defence mechanism against grid instability. System inertia instantly kicks in following a supply-demand mismatch, offering power plants the time needed to activate their frequency responses.
We will also delve into the challenges posed by the grid of tomorrow, where the majority of electricity comes from renewable, low-inertia sources.
Inertia 101
Inertia is defined as the resistance of a physical object to a change in its state of motion including changes in speed and direction (Newton’s first law of motion).
With reference to the power systems, inertia is the rotational kinetic energy stored in the rotating masses of generators and motors synchronously connected to a grid:
J is the moment of inertia (the resistance to change in rotational speed) and ω the angular velocity (the rotor’s frequency).
The ratio between this embedded kinetic energy and the system base power (a reference power level of a grid) is called the inertia constant H, the most used value to characterise synchronous generators:
It is interpreted as the duration (in seconds) during which a generator can provide nominal power only using the kinetic energy stored in the rotating mass.
(Notice that for wind and solar, H = 0. You can sense where we are heading…)
As discussed in the previous article, a sudden imbalance between the electrical power being generated and the power being consumed in the system leads to a deviation in the system frequency. This disturbance is translated into a electromagnetic power Pₑ that acts on the machine rotor, in addition to the mechanical power Pₘ from its prime mover.
In those situations, inertia is the energy that is exchanged with the system (either released or absorbed) to restore the balance:
We now substitute J by H, the inertia constant of the generators:
We can normalise both sides by the system base power S to get the per-unit reference:
The initial value of dω/dt after an imbalance of power in the grid system and before any control action is called Rate of change of frequency (RoCoF): an important notion qualifying the robustness of an electrical grid.e
The equations above show that for the same degree of per-unit power imbalance, the inertia constant H is inversely proportional to the rate of change of frequency.
This reflects the fact that a system with higher inertia will experience a slower rate of change in rotor speed and, consequently, a slower change in system stability during transient events.
Inertia and frequency control strategies
In the previous article, we have seen the below graph about different stages of frequency responses:
The immediate and automatic injection of energy to balance rapid frequency deviations, slowing the rate of change of frequency is formally called inertial response.
Traditionally, inertia response is taken for granted: it is considered as a natural characteristic of the power system. Its capability to damp immediate oscillations gives operators a window for their primary, secondary, and tertiary control plans to step in if needed. Typically, in gas-fired power stations, the power output can be changed by about 8% per minute, while for nuclear plants, the rate of power change ranges from 1 to 5% per minute.
Inertia in renewable sources
Till now we only consider rotating synchronous generators, which are used in all conventional thermal power plants. However, this is no longer the case with the new generation of electricity sources, the renewable ones, which have inverter-based generators. Their systems are characterised as inertia-less and non-synchronous: the electro-mechanical coupling mechanism with the grid system discussed so far is gone.
Consequently, as more renewable power plants are connected to the grid and as more traditional (carbon-heavy) sources of inertia go away, it becomes more difficult for system operators to manage grid frequency in a timely and stable manner.
Coupling that with the intermittent nature of the renewable sources, the constant variations in output make balancing supply and demand even more challenging.
This can lead to situations in which traditional frequency control strategies become too slow with respect to the disturbance dynamics for preventing large frequency deviations and the resulting consequences. The loss of rotational inertia and its increasing time-variance lead to new frequency instability phenomena in power systems. Frequency and power system stability may be at risk.
Conclusion
In conclusion, the critical role of system inertia and the instantaneous response it provides to maintain a stable power grid cannot be overstated.
However, the landscape is evolving quickly with the rise of renewable energy sources. The absence of direct electromagnetic coupling with the grid in these sources challenges their ability to contribute to system inertia. This shift comes with serious consequences: reduced inertia paves the way for faster frequency dynamics, leading to more significant frequency deviations and transient power exchanges, especially during power faults.
As we embrace the future of energy, understanding and addressing these challenges in maintaining system inertia will be pivotal for ensuring the reliability and resilience of our power grids. Balancing the innovation of renewable sources with the foundational principles of grid stability will be the key to navigating the complexities that lie ahead.
