---
title: "Design: 230 m head plant, 45 km line"
subject: "Power Plant Design"
chapter: 4
key: "semester_8/power_plant_design:design-2071-230m-45km"
source: https://www.bctengineer.com/q/semester_8/power_plant_design/design-2071-230m-45km
site: BCT Engineering
---

# Design: 230 m head plant, 45 km line

Power Plant Design · Chapter 4: Electric System Design of a Power Plant

- Asked in: 2071 Bhadra, 16 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/power_plant_design/design-2071-230m-45km
- Whole chapter: https://www.bctengineer.com/md/semester_8/power_plant_design/chapter-4

## Question

A typical hydro power plant has the following details.

| Month | Discharge (m³/s) | Flow duration | Discharge (m³/s) |
|---|---|---|---|
| January | 4.62 | Qmax (Q0) | 210.00 m³/s |
| February | 3.80 | Q25% | 18.24 m³/s |
| March | 3.55 | Q45% | 7.82 m³/s |
| April | 4.55 | Q65% | 4.7 m³/s |
| May | 3.5 | Q85% | 3.10 m³/s |
| June | 12.70 | Q95% | 2.17 m³/s |
| July | 32.98 | Qmin | 0.64 m³/s |
| August | 40.26 |  |  |
| September | 31.23 |  |  |
| October | 15.00 |  |  |
| November | 7.37 |  |  |
| December | 4.80 |  |  |

| Turbine type | Head range (m) |
|---|---|
| Kaplan | 2 < H < 40 |
| Francis | 10 < H < 350 |
| Pelton | 50 < H < 1300 |

| Parameter | Value |
|---|---|
| Gross head | 230 m |
| Turbine efficiency | 90% |
| Generator efficiency | 97% |
| Transformer efficiency | 98% |
| Head loss | 5% |
| Riparian release | 10% |
| Generator sub-transient reactance | 21% |
| Transformer reactance | 9.15% |
| Transmission line inductance | 0.95 mH/km |
| Transmission line length | 45 km |
| Transmission voltage level | 33 kV |
| Generator voltage level | 11 kV |
| Transmission circuit | Double circuit |

Design a power plant so as to obtain the following parameters:
a) Electrical power output taking design discharge as Q45%.
b) Select the numbers of units and installed capacity.
c) Select the type of turbine.
d) Draw the single line diagram showing number of units, generator, power transformer, station transformer and diesel generator for black start.
e) Suggest the type of bus bar to be used.
f) Calculate the rating of the generator circuit breaker (GCB) to be used in your design.

## Short answer

Design discharge Q45% after riparian release is 7.47 m³/s, net head 218.5 m; output to 33 kV bus is 13.7 MW. Install two 7 MW Pelton turbines (4‑jet, 375 rpm), total 14 MW.

## Answer

Assumptions: riparian release = 10% of the driest monthly mean flow; net head = gross head minus 5% loss; $\rho g = 9.81$ kN/m³; generator power factor 0.85; base = 100 MVA. For fault levels the grid is taken as a source of 500 MVA at the 33 kV grid substation at the far end of the line (an assumed typical value, since grid data is not given).

#### a) Electrical power output at $Q_{45\%}$

Driest month = May (3.5 m³/s), so riparian release $Q_r = 0.1 \times 3.5 = 0.35$ m³/s.

$$
\begin{aligned}
Q_d &= Q_{45\%} - Q_r = 7.82 - 0.35 = 7.470\ \text{m}^3/\text{s} \\
H_n &= H_g(1 - 0.05) = 230 - 11.50 = 218.50\ \text{m} \\
P_{hyd} &= \rho g Q_d H_n = 9.81 \times 7.470 \times 218.50 = 16.012\ \text{MW} \\
P_{shaft} &= \eta_t P_{hyd} = 0.9 \times 16.012 = 14.411\ \text{MW} \\
P_{gen} &= \eta_g P_{shaft} = 0.97 \times 14.411 = 13.978\ \text{MW} \\
P_{out} &= \eta_{tr} P_{gen} = 0.98 \times 13.978 = 13.699\ \text{MW}
\end{aligned}
$$

**Answer:** generator output = 13.978 MW; power delivered to the 33 kV bus = **13.699 MW**.

#### b) Number of units and installed capacity

- Choose **2 units**. With a run-of-river flow that falls well below the design flow in the dry months, one unit can run near full load on half the design flow, so efficiency stays high in winter.
- One unit can be maintained while the other runs, and two units keep the number of machines (and cost) low for a plant of this size.
- Per unit: $Q = 7.470/2 = 3.735$ m³/s, generator output $= 13.978/2 = 6.989$ MW → rate each unit at **7 MW**.
- Generator rating: $S = 7/0.85 = 8.24$ MVA → **8.5 MVA, 11 kV, 0.85 pf, 50 Hz**.
- Step-up transformer, one per unit: **10 MVA, 11/33 kV, YNd11** (next standard size above 8.5 MVA).

**Answer: installed capacity = 2 × 7 MW = 14 MW.**

#### c) Type of turbine

$H_n = 218.50$ m lies in the Francis (10–350 m) and Pelton (50–1300 m) ranges, so the specific speed decides.

Shaft power per unit $P = 14.411/2 = 7205.3$ kW. With $N = 120f/p$ (synchronous speeds) and $N_s = N\sqrt{P}/H_n^{5/4}$, where $H_n^{5/4} = 840.1$:

| $N$ (rpm) | Poles | $N_s$ (metric, kW) |
|---|---|---|
| 1000 | 6 | 101.0 |
| 750 | 8 | 75.8 |
| 600 | 10 | 60.6 |
| 500 | 12 | 50.5 |
| 428.6 | 14 | 43.3 |
| 375 | 16 | 37.9 |
| 333.3 | 18 | 33.7 |

Usual ranges: Pelton about 10–30 per jet (multi-jet $N_s = N_{s,jet}\sqrt{z}$), Francis about 60–300, Kaplan 300–1000.

Choose $N = 375$ rpm (16 poles): $N_s = 37.9$. With **4 jets**, $N_{s,jet} = 37.9/\sqrt{4} = 18.9$, inside the Pelton range.

Check of jet ratio: jet velocity $V_j = 0.98\sqrt{2gH_n} = 64.2$ m/s; bucket speed $u = 0.46V_j$; runner diameter $D = 60u/(\pi N) = 1.50$ m; jet diameter $d = \sqrt{4(Q/z)/(\pi V_j)} = 0.136$ m; $D/d = 11.0 > 10$, acceptable.

A Francis at 1000 rpm ($N_s = 101.0$) is also possible, but the Pelton is preferred because (i) its efficiency stays nearly flat from about 20% to 100% load (jets can be switched off), which suits a run-of-river plant whose flow falls far below the design flow in the dry season, and (ii) it tolerates the heavy sediment of Himalayan rivers better, and worn buckets and needles are easier to repair.

**Answer: 2 × vertical-axis 4-jet Pelton turbines, 375 rpm, about 7.21 MW each.**

#### d) Single line diagram

```text
 Line-1          Line-2  (33 kV, 45 km)
    |               |
  [CB]            [CB]
    |               |
 ===+=====+=========+===+=== 33 kV bus
          |             |
        [CB]          [CB]
          |             |
        (T1)          (T2)
          |             |
        [CB]          [CB]
          |             |
 =========+====[BS]=====+=========+=== 11 kV bus
          |             |         |
        [GCB]         [GCB]     [CB]
          |             |         |
        (G1)          (G2)      (ST)
                                  |
 =================================+===+ 0.4 kV
                                      |
                                    [ACB]
                                      |
                                    (DG) black start
```

| Item | Rating |
|---|---|
| Generators G1–G2 | 8.5 MVA, 11 kV, 0.85 pf, 375 rpm, $X''_d$ = 21% |
| Step-up transformers T1–T2 | 10 MVA each, 11/33 kV, YNd11, $X$ = 9.15% |
| Station transformer ST | 250 kVA, 11/0.4 kV, Dyn11, 4.5% (aux load about 1.5% of capacity) |
| Diesel generator DG | 160 kVA, 0.4 kV (essential auxiliaries for black start) |
| Line | 33 kV, double circuit, 45 km to grid substation |
| NGR | neutral grounding resistor (low-resistance earthing, one generator earthed at a time if preferred) |

BS = bus section breaker, GCB = generator circuit breaker, ACB = air circuit breaker. Black start: with the grid dead, the DG energises the 0.4 kV auxiliary bus (governor oil pumps, cooling water, excitation field flashing, lighting and battery chargers), one unit is started and runs in island mode, and it then energises the step-up transformer and the line.

#### e) Type of bus bar

- **11 kV:** single bus bar with a **bus-section breaker**, units split between the two sections, so a bus fault or maintenance takes out only part of the plant.
- **33 kV:** single bus bar, sectionalised, with transformer bays and two line bays (double circuit).

Reason: for a 14 MW plant a sectionalised single bus gives reasonable reliability at low cost; a double bus or main-and-transfer bus would cost much more and is normally used only for larger plants or grid substations.

#### f) Rating of generator circuit breaker (GCB)

Per-unit reactances on 100 MVA base:

$$
\begin{aligned}
x_g &= 0.21 \times \frac{100}{8.5} = 2.4706\ \text{pu}, \quad x_t = 0.0915 \times \frac{100}{10} = 0.9150\ \text{pu} \\
X_L &= 2\pi f L l = 2\pi \times 50 \times 0.95\times10^{-3} \times 45 = 13.430\ \Omega \text{ per circuit; two in parallel} = 6.715\ \Omega \\
x_l &= \frac{X_L \times 100}{33^2} = \frac{6.715}{10.89} = 0.6166\ \text{pu}, \quad x_{grid} = \frac{100}{500} = 0.2000\ \text{pu} \\
x_{grid\ path} &= 0.2000 + 0.6166 = 0.8166\ \text{pu}
\end{aligned}
$$

All generators feed the common 11 kV bus, so the GCB is rated for the full 11 kV bus fault level (generators plus the grid through the step-up transformers):

$$
\begin{aligned}
S_{gen} &= 2 \times \frac{100}{2.4706} = 81.0\ \text{MVA} \\
S_{grid} &= \frac{100}{x_t/2 + x_{grid\ path}} = \frac{100}{0.4575 + 0.8166} = 78.5\ \text{MVA} \\
S_{11kV} &= 81.0 + 78.5 = 159.4\ \text{MVA}
\end{aligned}
$$

$$
\begin{aligned}
I_{sc} &= \frac{159.4}{\sqrt{3} \times 11} = 8.37\ \text{kA}, \quad I_{make} = 2.55 \times 8.37 = 21.34\ \text{kA peak} \\
I_{FL} &= \frac{8.5}{\sqrt{3} \times 11} = 446\ \text{A}, \quad 1.25 I_{FL} = 558\ \text{A}
\end{aligned}
$$

| Parameter | Required | Selected |
|---|---|---|
| Rated voltage | 11 kV system | 12 kV |
| Rated normal current | ≥ 558 A | 630 A |
| Breaking capacity | 159.4 MVA (8.37 kA) | 25 kA (520 MVA at 12 kV) |
| Making capacity | 21.34 kA peak | 63 kA peak |
| Short-time current | – | 25 kA, 3 s |
| Type | – | Vacuum (or SF6), generator-duty tested (IEEE C37.013) |

**Answer: GCB fault level = 159.4 MVA; select a 12 kV, 630 A, 25 kA generator circuit breaker.** The margin covers the DC component and delayed current zeros of generator faults; surge arresters and surge capacitors are fitted at the generator terminals when a VCB is used.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Per unit generator output is about 7 MW at 0.85 pf. Which ratings were chosen?
   A. Generator 8.5 MVA, transformer 10 MVA (next standard size)
   B. Generator 7 MVA, transformer 7 MVA
   C. Generator 8.5 MVA, transformer 8.5 MVA
   D. Generator 10 MVA, transformer 8.5 MVA
   Answer: A. S = 7/0.85 = 8.24 MVA, so 8.5 MVA; the step-up transformer is the next standard size above that, 10 MVA. (Key point: Generator and transformer rating)

2. At 375 rpm, Ns = 37.9. How does this lead to a 4-jet Pelton?
   A. Ns per jet = 37.9 x 4 = 151.6
   B. Ns per jet = 37.9/sqrt(4) = 18.9, within the Pelton range
   C. Ns per jet = 37.9/4 = 9.5, so 4 jets are needed
   D. Ns above 30 means Kaplan
   Answer: B. Multi-jet Ns = Ns,jet x sqrt(z); 18.9 per jet lies in the usual 10-30 band. (Key point: Pelton jets)

3. How are the grid and the double-circuit line represented in the fault calculation?
   A. Grid ignored; one line only
   B. Grid as infinite bus with zero reactance; lines in series
   C. Grid as an assumed 500 MVA source (0.2 pu on 100 MVA); two lines in parallel give half the single-line reactance
   D. Grid as 100 MVA (1 pu); lines in series
   Answer: C. x_grid = 100/500 = 0.2 pu; two 13.43 ohm circuits in parallel give 6.715 ohm, then added to the grid reactance. (Key point: Fault source data)

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