Hydropower Engineering

Firm energy is the energy a hydropower plant or system can generate reliably and continuously, even in the critical dry period, because it is based on the dependable (firm) flow, usually the flow available about 90% of the time. On the load curve it supplies the base load, the minimum demand present throughout all 8,760 hours of the year. In Nepal most plants are run-of-river, so firm energy is limited by low dry-season flows (December to May).

Secondary energy is the extra, non-guaranteed energy generated when river flow exceeds the dependable flow, mainly in the monsoon (June to September). It is the energy above the firm-energy level and serves intermediate and peak demand on the load curve, or is exported or spilled if there is no demand.

Nepal context: demand peaks in winter while river flow peaks in the monsoon, so the system has a dry-season deficit (met by imports from India and by storage plants such as Kulekhani) and a monsoon surplus of secondary energy. Firm energy is sold at a higher price, and secondary energy at a lower price or not at all. This is why storage and peaking (PRoR) projects are valued.

1. Losses in the hydraulic system (tunnel conveyance scheme)

Water flows from intake, through desilting basin, headrace tunnel and surge shaft, to penstock, turbine and draft tube. Losses occur in the following forms.

A. Major (friction) losses, given by Darcy-Weisbach:

$h_f = f\frac{L}{D}\frac{V^2}{2g}$

1. Friction in the headrace tunnel (long length, rough concrete or rock surface).
2. Friction in the penstock.

B. Minor (local) losses, given by

$h_m = K\frac{V^2}{2g}$

3. Entrance loss at the intake ($K\approx 0.1$ to $0.5$ depending on shape).
4. Trash rack loss (bar thickness, spacing, clogging).
5. Gate and valve losses (intake gate, butterfly or spherical inlet valve).
6. Contraction and expansion (transitions) losses.
7. Bend losses in horizontal and vertical bends, depending on $R/D$ and the angle.
8. Junction or bifurcation (manifold) losses.
9. Surge shaft junction and orifice (throttling) loss, if provided.
10. Exit loss, since the velocity head leaving the draft tube is not recovered.

In addition, water hammer causes a transient pressure rise. It is not a steady loss but is considered in penstock design.

2. Steps in calculating net head

1. Gross head: $H_g = \text{forebay/surge level (or intake water level)} - \text{tailrace water level}$ (for a Pelton turbine, to the nozzle centre line).
2. Fix the design discharge $Q$ and the conduit diameters, so velocity $V = 4Q/\pi D^2$ is known for each reach.
3. Friction losses: find $f$ from the Moody chart, or use Manning's/Hazen-Williams formulas, and compute $h_f$ for the tunnel and penstock.
4. Minor losses: select $K$ values and compute $h_m = \sum K\,V^2/2g$.
5. Total loss: $h_L = h_f + h_m$ (usually 3 to 8% of gross head in a well-designed scheme).
6. Net head:

$H_n = H_g - h_L$

7. Check at different flows: compute $H_n$ at design, minimum and maximum flow and for clean and clogged trash racks. Use the minimum net head for turbine selection and the maximum (plus surge) for penstock design.

Power is then $P = \rho g Q H_n \eta_o$.

Types of Turbines Used in Hydropower Projects

Turbines are classified mainly by the head available and the direction of water flow.

1. Pelton Turbine (Impulse Turbine)

• Suitable for high head (above ~250 m) and low discharge.
• Water is directed through nozzles as high-velocity jets striking bucket-shaped runners.
• The pressure drop occurs only in the nozzle; the runner operates at atmospheric pressure.
• Used in projects like Khimti, Chilime.

2. Francis Turbine (Reaction Turbine)

• Suitable for medium head (roughly 30–250 m) and medium discharge.
• Water enters radially and leaves axially; both pressure and velocity change across the runner.
• The runner is fully enclosed in a spiral casing (volute) and operates under pressure.
• Used in projects like Kulekhani, Middle Marsyangdi.

3. Kaplan / Propeller Turbine (Reaction Turbine)

• Suitable for low head (below ~30 m) and high discharge.
• Water flows axially through the runner; blades may be fixed (propeller) or adjustable (Kaplan).
• Double-regulated Kaplan has adjustable both guide vanes and runner blades for high part-load efficiency.
• Used in projects like Gandak, Koshi type run-of-river schemes.

4. Cross-Flow (Banki-Michell) Turbine

• Suitable for low to medium head and small discharge; simple and cheap.
• Common in micro-hydro (pico/micro) projects in Nepal.

5. Turgo and Cross-Flow variants — used for small/medium heads as impulse alternatives.

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Key Factors Governing Selection of Appropriate Turbine

1. Net head (H) — the single most important factor; determines whether impulse (high head) or reaction (medium/low head) type is chosen.
2. Design discharge (Q) — fixes the size and specific speed of the runner.
3. Specific speed (Ns) — must fall within the recommended range for each turbine type to ensure good efficiency and cavitation-free operation.
4. Efficiency and part-load performance — plants with varying load need turbines (e.g., Kaplan) that stay efficient over a wide range.
5. Cavitation and setting level — reaction turbines require proper suction head (NPSH) to avoid cavitation.
6. Runner size and rotational speed — must match the synchronous speed of the generator (governed by grid frequency, 50 Hz in Nepal).
7. Cost and ease of manufacture/maintenance — local fabrication and spare parts availability matter, especially for micro-hydro.
8. Sediment load — high sediment rivers (typical in Nepal) require erosion-resistant materials and suitable turbine type.
9. Site topography and layout — determines head, penstock length, and powerhouse arrangement.

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Types of Generators and Their Use

1. Synchronous Generator

• Most common in hydropower; rotor speed is synchronized with grid frequency (N = 120f/P).
• Requires DC excitation (via slip rings or brushless exciter).
• Can supply both active and reactive power; controls voltage and power factor.
• Used in almost all grid-connected hydropower plants.

2. Induction (Asynchronous) Generator

• Speed slightly above synchronous speed (slip ~1–5%).
• Simple, rugged, cheap, no separate excitation needed.
• Cannot control voltage or supply reactive power; draws reactive power from grid.
• Used in micro-hydro and small isolated/captive plants.

3. Permanent Magnet Synchronous Generator (PMSG)

• Uses permanent magnets instead of field winding; no excitation loss.
• High efficiency, compact, low maintenance.
• Used in modern small hydro and variable-speed applications.

4. DC Generator

• Produces direct current; used only in very small isolated plants or for excitation purposes (older systems).

Summary: For grid-connected hydropower, synchronous generators are standard; for micro-hydro, induction or PMSG types are preferred due to simplicity and low cost.

Optimization of hydropower components

Optimization means selecting the dimensions, capacity, material or arrangement of a component so that it performs its function at the least total cost (or greatest net benefit) while satisfying hydraulic, structural and site constraints. Component costs are linked: a larger penstock costs more but loses less head and so produces more energy. Optimization is therefore a trade-off between capital cost and the capitalized cost of lost energy.

Objectives

1. Minimize the total cost (capital plus operating and energy-loss cost) over the project life.
2. Maximize energy generation and net benefit by reducing hydraulic losses.
3. Ensure technical feasibility and safety (velocity limits, water hammer, buckling, stability).
4. Use materials and construction effort economically.
5. Make the component fit the optimum of the whole scheme, not just a local optimum.

Optimization of the penstock

Notation: $D$ diameter, $L$ length, $Q$ discharge, $H$ head, $f$ friction factor, $t$ thickness, $t_c$ corrosion allowance, $\rho_s$ steel density, $C_s$ steel cost per kg, $C_e$ energy price per unit, $T$ operating hours per year, $n$ life, $i$ interest rate, $\sigma$ allowable stress.

1. Capital cost. Steel weight is $W=\pi D t L\rho_s$, with thickness from the hoop formula

$t=\frac{\rho g H D}{2\sigma}+t_c$

$C_{cap}=K_1D^2+K_2D,\quad K_1=\frac{\pi L\rho_s C_s\rho gH}{2\sigma},\quad K_2=\pi L\rho_s C_s t_c$

2. Cost of energy lost. With $V=4Q/\pi D^2$,

$h_f=\frac{8fLQ^2}{\pi^2 gD^5},\qquad P_{loss}=\rho gQh_f=\frac{8\rho fLQ^3}{\pi^2D^5}$

Capitalizing the annual loss over $n$ years at rate $i$:

$C_{loss}=\frac{K_3}{D^5},\quad K_3=\frac{8\rho fLQ^3TC_e}{\pi^2}\cdot\frac{(1+i)^n-1}{i(1+i)^n}$

3. Total cost.

$C_{total}=K_1D^2+K_2D+\frac{K_3}{D^5}$

4. Optimum. Setting $dC_{total}/dD=0$:

$2K_1D^7+K_2D^6=5K_3$

Neglecting $t_c$ ($K_2=0$), $D^7=5K_3/2K_1$. Here $\rho$ and $L$ cancel, giving

$D_{opt}=\left[\frac{40fQ^3TC_e\sigma}{\pi^3\rho_sC_sgH}\cdot\frac{(1+i)^n-1}{i(1+i)^n}\right]^{1/7}$

5. Minimum check. $\dfrac{d^2C_{total}}{dD^2}=2K_1+\dfrac{30K_3}{D^7}>0$, so this is a true minimum.

6. Constraints. The result must satisfy the velocity limit (about 2 to 6 m/s), a minimum thickness for handling and buckling, and $p_{max}=\rho g(H+\Delta H_{surge})\le 2\sigma t/D$.

Under the DoED Guidelines for Study of Hydropower Projects, a medium project (10 to 50 MW) needs a feasibility-level study. The survey requirements are as follows.

1. Topographical survey

Purpose: to give an accurate base for layout, design and quantity estimates of all structures.

• Control survey: a permanent network of benchmarks and control points tied to the national datum (Survey Department), with traverse and levelling closed to accepted accuracy; coordinates in the national grid (MUTM).
• Catchment and general area maps: 1:25,000 or 1:50,000 Survey Department maps for the catchment, project area and access routes.
• Project area maps (contour interval and scale by component):

• Longitudinal profiles and cross-sections along the headrace, penstock, tailrace and river reach (for example river cross-sections at the weir axis and gauging site) to fix levels, gross head and water surfaces.
• Marking of the proposed axes of the structures on the ground and showing them on the maps, together with landslides, gullies, settlements, forest and land-use features that affect layout and land acquisition.

2. Construction material survey

Purpose: to identify adequate local sources of materials at economical distance.

• Identification of sources for fine aggregate (sand), coarse aggregate/boulders, rock for riprap and gabion, and impervious or random fill soils, with location maps and haulage distances. Cement and steel are usually imported or purchased from outside and their availability and transport are reported.
• Quantity estimates: the available volume at each source (at least 1.5 to 2 times the project requirement), by test pits, trenches and borrow area mapping.
• Quality tests to relevant Nepal and IS/ASTM standards: for aggregate, gradation, specific gravity, water absorption, Los Angeles abrasion, soundness, alkali-aggregate reactivity and petrographic examination; for sand, fineness modulus and silt content; for soils, grain size, Atterberg limits, compaction and permeability.
• Rock quarry assessment for crushed aggregate and the suitability of excavated tunnel muck for reuse.
• Environmental and legal aspects of quarrying and river-bed extraction, royalties, access and disposal sites.

The results are presented in the feasibility report as source maps, test tables and quantity-versus-demand balance, and are used to estimate construction cost and plan the construction schedule.