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# Electrical engineering for hydropower, from run-of-river to pumped storage plants

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## Hydropower Energy

Nowadays, when we all see and feel the colossal crisis looming on the horizon, the question of energy security is among the first things on the table in each country’s management. It’s now essential more than ever for each country to use all its energy resources wisely. This is where we come to one of my favourite topics (for a reason) – Hydroelectricity.

Hydropower plants (HPPs) are the critical elements in every power system. This technical article discusses the essential electrical engineering for hydropower, from run-of-river to pumped storage plants (PSPs).

## 1. Basics of Hydropower plants

Hydroelectricity is the oldest yet in many terms the most efficient renewable energy source. Prime mover uses a combination of potential power of water column H or head [m] and discharge flow Q [m3/h] to develop mechanical power that will keep generator rotor running and producing electricity at stator leads thanks to electromagnetic induction.

There is indeed a direct correlation with these parameters and active power available at dispatchment point, being:

𝑃 ≈ 9,81 × 𝑄 × 𝐻 × 𝜂 [W]

where η is efficiency of all components (turbine, alternator and transformer).

Without entering in details of hydromechanics and turbine components that stand upstream the generating station, all the hydro turbines will run at a fraction of the grid synchronous speed. This is particularly the case of impulse turbine (Pelton type), where rotating speed is proportional to head. Reaction turbines (hence where the mechanical power is exploited from water leaving the vane geometry) rotate faster than impulse turbines given the same head and flow conditions.

This contributes to a relative reduction of generator polarity and allows a gearless solution that is however far different from the direct coupling of large gas turbines where the rotating speed is usually 3000/3600rpm.

Figure 1 – Pelton (impulse type), Francis and Kaplan (reactive type) turbine runner

While prime mover speed is in fact directly linked with turbine geometry, water head and flow, generators above a certain rating shall operate at synchronous speed with electrical grid, being either 50Hz or 60Hz. Small hydro plants, especially low head recovery solutions below 500kVA will use induction generators or permanent magnet generators (PMG) that are exceptions to this rule.

Speed multiplier gearboxes are rarely used for large units, at contrary the pole/frequency equation is exploited:

n = 60 × f / 2Np [rpm]

where f is grid frequency in [Hz] and Np is number of poles and n is rotor speed in [rpm].

Hydro turbine governor will maintain the shaft close to the design rotation speed, overspeed mechanical protection being a critical turbine design aspect, hence grid frequency of produced sinusoidal waveform at generator leads is guaranteed, at cost of very large alternator rotor.

Pelton units have indeed a dedicated mechanical component (diverter plate) to prevent this risk that can lead to catastrophic consequences since although absolute speed is definitely lower than turbogenerators, considering rotor inertia and fact that contrary to gas turbines (and partly to steam turbines) you cannot simply cut-off turbine fuel and damper the speed overshoot only.

Table 1 – Turbogenerator classification in regards to the poles number and rotation speed

 Poles Rotation Speed (rpm) Type 50 Hz 60 Hz 2 3000 3600 Turbo 4 1500 1800 6 1000 1200 Fast Hydro 8 750 900 10 600 720 12 500 600 14 429 514 16 375 450 18 333 400 20 300 360 Slow Hydro 40 150 180

Finally, although this has no impact on rotating equipment per se, plant electrical balance of plant and operation philosophy will be impacted by hydro plant type either a run of the river installation with minor civil works (and possibly even off grid) or a conventional scheme involving an upstream dam or even a pumped storage scheme with two reservoirs / dams.

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## 2. Hydro generators, speed/polarity and mounting types

Hydro generators differs significantly from turbounits in terms of rotor geometry, while a four pole generator is the standard for industrial power generation or six poles motors are used only in mills or wherever an high efficiency and torque at low speed is needed, even the fastest Pelton runners will most probably require an higher polarity.

As a note the absolute speed of the prime mover shall not be confused with the characteristic hydro turbine speed (or Nq) that counterintuitively is very high for very slow runners, e.g. Kaplan units.

Hydroelectric generator rotor will have to host a corona of salient poles hence its diameter is usually larger, sometimes much larger than shaft length. This will have a positive side effect on machine inertia constant, a key parameter for grid stability that we will analyze further.

Airgap between stator and rotor will significatively different for high polarity hydro generators, having in fact almost a linear gap that will impact the electromagnetic design and generator equivalent circuit.

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