Physical Anatomy of the Grid

Why there is a voltage hierarchy

Transmitting power P at voltage V requires current I = P / (√3 · V · cos φ) on a three-phase circuit. Resistive losses scale with I²R. Doubling the voltage therefore halves the current and quarters the losses for the same delivered power. This single relationship is why long-distance transport happens at hundreds of kilovolts and consumption happens at hundreds of volts, with transformers between.¹

A typical European hierarchy:

The boundary between “transmission” and “distribution” is regulatory as much as technical — it defines which operator (TSO or DSO) is responsible — and it varies by country. That boundary matters for modelling because it usually marks where your data ends.

Alternating current and the three-phase system

Power systems are three-phase AC: three conductors carrying sinusoidal voltages 120° apart. Balanced three-phase transport delivers constant instantaneous power (unlike single-phase, which pulsates at twice the fundamental frequency) and uses conductor material efficiently.

Two consequences dominate modelling:

Complex power. With voltage and current as phasors, apparent power is S = V I* = P + jQ. The real part P (watts) does useful work; the imaginary part Q (var) is the oscillating exchange associated with the magnetic and electric fields of inductive and capacitive elements. Reactive power does not “travel” well — it is a strongly local quantity — and managing it is a distinct operational task from managing active power.

Symmetrical components. Unbalanced conditions (most faults) are analysed by decomposing the three phases into positive-, negative-, and zero-sequence networks, a transformation due to Fortescue.² Positive-sequence-only models are the standard for bulk system studies; distribution studies frequently cannot make that assumption, because LV networks are genuinely unbalanced.

Lines and cables

An overhead line is modelled as a distributed-parameter element, but for the lengths encountered in most studies the lumped π-model is used: a series impedance R + jX with half the total shunt susceptance B/2 at each end.

• R — conductor resistance. Temperature-dependent, and the source of ohmic losses.
• X — series reactance, dominated by geometry (conductor spacing and height). For overhead lines X typically exceeds R by a factor of 3–10 at transmission voltage. This high X/R ratio is the assumption underpinning the DC power flow approximation in module 4.
• B — shunt capacitance to earth. Modest on overhead lines; large on cables.

Cables differ from overhead lines in ways that matter. Their capacitance per kilometre is roughly an order of magnitude higher, so a long AC cable generates substantial reactive power (charging current) that must be absorbed by compensation, and this places a practical length limit on AC cable connections — the reason long subsea links are almost always HVDC.³

Ratings. A line’s limit is thermal: excessive current heats the conductor, which sags, reducing clearance to ground. Ratings therefore depend on ambient temperature, wind, and solar irradiance, which is the basis of dynamic line rating — using real conditions rather than a conservative static assumption, often unlocking 10–30% additional capacity on wind-exposed corridors.⁴ Beyond a few hundred kilometres, the binding limit shifts from thermal to voltage-drop and then to stability, a progression usually summarised by the St. Clair curve.

Transformers

Transformers connect voltage levels and are modelled as a series impedance plus an ideal ratio. Two features have outsized modelling importance:

Tap changers. An on-load tap changer varies the turns ratio in steps (typically ±10% in 1–2% increments) to regulate voltage. In a power flow this is either a fixed parameter or a controlled variable with a target voltage — the latter making the problem harder, since taps are discrete.

Phase-shifting transformers (PSTs). By injecting a quadrature voltage, a PST changes the angle across itself and therefore directly controls active power flow through its branch. PSTs are the main means of steering flows in a meshed AC network and are deployed heavily on the borders of Poland, the Netherlands, Belgium, and Slovenia to manage loop flows.⁵ In a model, a PST introduces a controllable phase angle, which turns a linear flow problem into one with an additional decision variable.

Substations and switching

A substation is where branches meet. Its internal arrangement — single busbar, double busbar, breaker-and-a-half, ring bus — determines how much of the substation is lost when a single element fails, and therefore what N-1 means at that location.

For modelling, the key point from module 1 returns here: the electrical node is not the same as the physical substation. A double-busbar substation with a bus coupler open is two electrical nodes; with it closed, one. Operators use busbar splitting as a genuine congestion-management action, changing the network’s impedance matrix without moving a single megawatt of generation. Topology optimisation — treating switch states as decision variables — is an active research area precisely because this control is nearly free and largely unexploited.⁶

Reactive power and voltage support

Voltage is a local quantity, controlled by managing reactive power at or near the point of concern. The toolkit:

• Generator excitation — synchronous machines produce or absorb reactive power within a capability curve (the “D-curve”), and are the primary voltage regulators.
• Shunt reactors — absorb reactive power; used to counteract cable and lightly-loaded line charging.
• Shunt capacitors — supply reactive power; used to support voltage under heavy load. Their output falls with the square of voltage, which makes them least helpful exactly when voltage is already low.
• SVCs and STATCOMs — power-electronic devices giving continuous, fast reactive control. A STATCOM, being current-source-like, holds output better at depressed voltage than a capacitor bank.
• Synchronous condensers — synchronous machines without a prime mover, providing reactive power, short-circuit current, and inertia. Being retrofitted at scale in systems with high inverter penetration.

A model without reactive power (the DC approximation) is blind to all of this. That is acceptable for a market study and unacceptable for a connection study.

HVDC

High-voltage direct current links transfer power through converters at each end. Two technologies:

• LCC (line-commutated converter) — thyristor-based, mature, very high ratings, but consumes reactive power and requires a reasonably strong AC system at each end.
• VSC (voltage-source converter) — IGBT-based, can control active and reactive power independently, can energise a passive network (black start), and is the basis of essentially all new offshore and multi-terminal projects.⁷

Modelling-wise, an HVDC link is fundamentally different from an AC line: its flow is a decision variable, not a physical consequence. This is why HVDC is attractive for controlling flows and why embedded HVDC inside a meshed AC system changes the nature of the operational problem.

Generation

From the network’s point of view a generator is an injection with a reactive capability range and a control mode. The distinction that matters most today:

• Synchronous generation (thermal, hydro, nuclear) — rotating mass electromagnetically coupled to system frequency. Contributes inertia, which slows the rate of change of frequency after a disturbance, and high fault current, which protection relies on to detect and clear faults.
• Inverter-based resources (wind, solar PV, batteries, HVDC) — coupled through power electronics. No inherent inertia, fault current typically limited to ~1.1–1.5× rated, and behaviour defined by control software rather than physics. Grid-following inverters measure the grid’s voltage angle and inject relative to it, and therefore require a grid to already exist; grid-forming inverters impose a voltage waveform and can support or create one.⁸

The displacement of the first class by the second is the central technical challenge in grid modelling today, and module 6 returns to it.

Protection

Protection systems detect faults and open breakers within cycles. They rarely appear in steady-state models, but they constrain them in two ways: fault levels must remain high enough for relays to discriminate (a growing problem in inverter-dominated regions), and protection settings — particularly distance protection zones and load-encroachment behaviour — determine whether overloaded lines trip and turn a local overload into a cascade. Post-mortems of major blackouts almost always find protection acting correctly on a local view while worsening the system-wide outcome.⁹

Summary

The grid is a voltage hierarchy joined by transformers, carrying three-phase AC on lines and cables whose π-model parameters set how power divides, with reactive power managed locally and flows steered by phase shifters and HVDC. Each equipment class contributes specific parameters to a model — and each contributes behaviour that a coarser model deliberately discards.

Next: how this equipment becomes a dataset.

References