Borehole Pump Design

The Design of a Deep Tube-Well Water

Pumping Installation
This excel tool has been developed for the detailed engineering design of deep tube-well
water pumping installations. These installations are used to pump water from underground
aquifers to reservoirs above ground. They typically comprise the following: a system of
pipes to convey the water, a submersible multi-stage borehole pump, a submersible squirrel-
cage induction motor, a submersible electrical cable (drop cable), and an electrical power
source.

The excel tool aims to provide a simple step-by-step methodogy for the design of these
installations that can be applied in a variety of contexts and with different equipment. The
tool provides help with the following:

Calculate head friction losses in pipework.

Calculate the total dynamic head.
Size pump and find duty point.
Check pump's Net Positive Suction Head.
Size electrical motor and check cooling flow.
Size electrical supply cable.
Calculate total power consumption and efficiency.
Size genset for continuous duty operation.
Size genset for motor starting.

This tool can be used with single- and three-phase induction motors, at different supply
voltages and frequencies (50 or 60 Hz).

The following sections in this manual provide guidance with each of the steps involved in
the design and includes a detailed worked example.

Excel Tool Deep Tube Well Pump Design_v2.0_365.xlsx - 74KB

1.1 Hydraulic Profile - Overall System
Characteristics
In this section, the user defines the main hydraulic characteristics of the installation at its
duty point: the flow rate and the total dynamic head. These two values are the basis for all
other calculations in this spreadsheet so it is important to get them right.

The pump's duty point is the point of equilibrium between the pump and the system it
serves, i.e. it is the flow rate where the pump's head equals the installation's total dynamic
head.

Finding the pump's duty point is an iterative process, requiring the calculation of total
dynamic head at different flow rates until this value matches the pump's head. The
installation's total dynamic head is the sum of total vertical lift (constant regardless of flow
rate) and total friction losses (increasing with higher flow rate).

When selecting a pump, it is important that its duty point is as close as possible to the point
of best efficiency (BEP). Running a pump near the point of best efficiency will reduce energy
costs and extend its life. A pump should never be run outside its Allowable Operating Range
(AOR). The AOR is the portion of the pump curve determined by the pump manufacturer
where the pump can be operated continuously without significantly affecting the
performance or life of the pump.

So the normal procedure is to first decide on a target flow rate based on the well pumping
test (the aquifer safe yield) and to select a pump with the BEP at this flow rate. The pump's
duty point is then found by an iterative comparison of pump head and the system's total
dynamic head. The spreadsheet includes a tool to record these iterations.
1.2 Hydraulic Profile - Calculation of Friction
Losses
This spreadsheet will calculate friction losses in pipes and fittings. The calculation of the
head loss in a pipe is done using the Darcy-Weisbach equation, where the Darcy friction
fator is calculated using the Swamee-Jain equation.

The user has to specify the pipe's internal roughness. Suggested design values are shown
below. Note that the roughness will vary with age and condition of the pipe.

Galvanised Iron : 0.15 mm

PE/PP/PVC : 0.005 - 0.01 mm

Carbon Steel Smooth : 0.05 - 0.15 mm

Carbon Steel Corroded : 0.15 - 1.0 mm

Smooth Concrete : 0.2 - 0.8 mm

Rough Concrete : 0.8 - 3.0 mm

In addition, all pipes and fittings have to be designed to the correct pressure rating. The user
is able to read the calculated working pressure on each section of pipe. An ample margin of
safety is required if there is a risk of pressure surges in the system.
2.1 Net Positive Suction Head (NPSH)
Calculation
The NSPH calculation is required to check the likelihood of cavitation in the pump. Three
factors determine this likelihood: the pump submersion, the site altitude and the water
temperature. The likelihood of cavitation is checked through the equation below.

NP SHa > NP SHr

NPSHa is the NPSH available;

NPSHr is the NPSH required.

The NPSH required is also referred to as the minimum inlet pressure required, and is
provided by the pump manufacturer in the form of a curve. The correct value should be
read at the pump’s duty point.

The NPSH available is calculated using the equation below.

NP SHa = Sp + Sa − Svp − Sm

Sp is the pump submersion, i.e. the vertical distance between the surface of the
liquid and the pump inlet;

Sa is the absolute pressure on the surface of the liquid, i.e. the atmospheric
pressure taking account of the site altitude;
 Svp is the absolute vapour pressure of the liquid at the pumping temperature;
and

Sm is a safety margin, typically no less than 1.0 metres.

If the water is flowing from below (well screen is below the level of the pump inlet), then
there are no friction losses to consider in the calculation of the NPSH available, i.e. the head
of water above the pump inlet is constant and is not reduced because of the movement of
water below.
2.2 Geometric Fit & Motor Cooling Check
These checks are carried out to ensure the motor/pump assembly fits inside the well casing
and that the motor is sufficiently cooled by the flow of water around it. Note that the
position of the motor inside the well casing can be eccentric and that the flow of water
around the motor will not be uniform. The calculated flow velocity is the therefore an
average value. In extreme cases, the pump inlet will be pressed against the well casing and
will experience extreme inlet turbulent flows.

To ensure the motor/pump assembly fits inside the well casing and flow velocities are
within acceptable limits, it is recommended that the inside diameter of the well casing
should be no less than 1.25 times the diameter of the motor/pump assembly (whichever is
the largest). Conversely, when the diameter of the well casing is too large, this will reduce
the motor cooling flow and a sleeve is required around the motor.

Adequate cooling of the motor requires the following checks: first, check that the motor
temperature rating exceeds the maximum water temperature in the well; and second, check
that the water flow velocity around the motor is adequate.

With regards to the first check, when the water temperature exceeds the motor temperature
rating, it is necesary to de-rate the motor – put simply, this is the provision of a larger
oversized motor. De-rating is done at a rate of 1.5% per degree Celsius up to a maximum of
20 degree Celsius. De-rating above this limit of 20 degree Celsius is not recommended.

With regards to the second check, where possible use the minimum flow velocity specified
by the motor manufacturer. Where published data is not available the minimum
recommended cooling flows around the motor are as follows: 0.2 m/s for non-de-rated
motors and 0.5 to 1.0 m/s for de-rated motors. Flows above 1.0 m/s should be avoided as
these can cause excessive turbulence at the pump inlet. Where required a sleeve can be
fitted around the motor to achieve the correct cooling flow.

The calculation of flow velocity is based on the assumption that all water flows
upwards from below the motor, i.e. the motor has been fitted above the level of
the well screen. Where the motor has been fitted below the level of the well
screen then a sleeve is always required. Where water flows from above and
below the level of the motor, and no sleeve has been installed around the motor,
then the calculated flow velocity should be halved, i.e. based only on half of the
pumping flow rate.
2.3 Motor Power Calculation & Selection
The power required of the motor (output) is linked to the power required by the pump
(input). The power required by the pump (shaft input power) is normally provided by the
pump manufacturer in a power curve. Two values from the power curve are important for
this calculation: the pump shaft power at duty point (P2) and the pump maximum shaft
power (P2max) at any point along the power curve.

The motor power requirement is here referred to as the motor design power (P2d) and is
calculated using the equation below.

P 2d = P 2max/Kt

P2max is the pump maximum shaft power at any point along the power curve;

Kt is the motor de-rating factor calculated in section (2.2);

The rationale of using P2max in the calculation of the motor design power is to ensure that
the motor is able to operate the pump at any possible point along its Allowable Operating
Range (AOR). The AOR is the portion of the pump curve determined by the pump
manufacturer where the pump can be operated continuously without significantly affecting
the performance or life of the pump.

In a case where it can be assured that the pump will not operate at P2max, the
motor may be sized for the 'worst credible' value of pump shaft power P2. This
would typically refer to the system with the 'lowest credible' head.

In addition, when selecting a motor, its nominal full-load power (P2n) needs to be limited so
that the motor operates in its high-efficiency range, namely 50 to 100% of its nominal full-
load. Therefore, when choosing a motor, ensure its nominal power (P2n) respects these two
constraints as reflected in the equation below.

P 2d < P 2n < 2 ∗ P 2

The motor manufacturer will publish motor performance data at various input
voltages. When selecting a motor make sure to use the correct input voltage
according to the actual supply on-site. Note also that published 3-phase motor
data will typically show line-to-line input voltage. However, this spreadsheet
requires the user to specify a line-to-neutral supply voltage, regardless of
whether a neutral line is present or not.

Where a pump power curve is not available, the pump shaft power can be determined from
the pump efficiency curve using the equation below. The point of maximum shaft power
(P2max) can be assumed to be the curve's cut-off point to the right of BEP (runout point).

P 2 = (3.6 ∗ Q ∗ H)/(367 ∗ Ƞ)
2.4 Motor Efficiency and Power Factor at
Duty Point
The motor manufacturer will normally provide motor efficiencies and power factors at 50,
75 and 100% of nominal full-load. The motor efficiency and power factor at duty point are
calculated by linear interpolation between these values.

These motor efficiencies and power factors are required for the electrical calculations in the
following sections. If published data is not available, it is suggested to use the values
published for a similar motor (same geometric size and nominal full-load). The results of
the calculation should then be treated with caution, adding where appropriate a margin of
safety of say 10%.
3.1 Supply Cable Current-Carrying Capacity
Calculation
The sizing of the supply cable involves two separate calculations that must always be done
at motor full-load. First, checking that the cable current-carrying capacity exceeds motor
full-load current rating. And second, checking the voltage drop along the supply cable is
within acceptable limits.

The cable current-carrying capacity should exceed the motor full-load current rating. The
motor full-load current rating is provided by the motor manufacturer and shown on the
motor nameplate. If this value is not available, an approximate value can be calculated
using the equation below.

P 2n/EF 100 = k ∗ V n ∗ In ∗ P F 100

k is a factor with value k=1 for single-phase motor or k=3 for three-phase motor;

P2n is the motor nominal full-load power;

Vn is the line-to-neutral voltage of the supply;

In is the motor full-load current rating;

EF100 and PF100 are the motor full-load efficiency and power factor
respectively;

The current-carrying capacity of the cable depends on the following factors: the conductor
cross-sectional area, the cable insulation type (70°C PVC or 90°C XLPE/EPR), the method of
installation, and the maximum ambient temperature.
The calculation of the cable current-carrying capacity is based on the the values published
in Table C.52.1 of IEC 60364-5-52 and based on installation method C (single-core or multi-
core cables on unperforated tray).

Table C.52.1 of IEC 60364-5-52

Cable de-rating is based on ambient temperature and using the correction factors from
Table B.52.14 of IEC 60364-5-52. The maximum ambient temperature should be taken as
the worst value of water and air temperature, allowing for any possible seasonal variations.
Table B.52.14 of IEC 60364-5-52.
3.2 Supply Cable Voltage Drop Calculation at
motor full-load
The voltage drop in the supply cable is calculated using equation below.

∆V n = k ∗ Ib ∗ (Rcosφ + Xsinφ) ∗ Lc

ΔVn is the line-to-neutral voltage drop in the supply cable;

k is a factor with value k=2 for a single phase motor or k=3 for a three-phase
motor;

Ib is the line current in the supply cable at motor full-load;

Lc is the total length of the supply cable including any length of cable above
ground;

R is the resistance of the cable conductor in Ω/km;

X is the inductive reactance of the cable conductor in Ω/km;

φ is the phase angle between voltage and current for the complete circuit (cable
plus motor).

A voltage drop in the supply cable reduces the supply voltage to the motor which in turn
raises the line current. It is of critical importance to limit voltage drop in the supply cable to
prevent damage to the electrical motor. Motor under-voltage is associated with a rise in
motor temperature that will cause a breakdown of insulation in the windings and shorten
the life of the motor. The voltage drop in the supply cable should therefore be limited to a
maximum of 5%, i.e. the voltage at the motor is within 5% of its rated nominal value.
This spreadsheet provides a precise voltage drop using calculated values of
circuit current and power factor, which are obtained resolving the electrical
circuit.

A simplified approach is to calculate the voltage drop using motor full-load

current rating (FLA) and power factor.
3.3 Overall Efficiency of Installation at Duty
Point
The electrical power demand for the complete circuit, including motor and supply cable, is
calculated using equation below.

P t = St ∗ P F t = k ∗ V n ∗ Idp ∗ P F t

k is a factor with value k=1 for a single-phase motor or k=3 for a 3-phase motor;

Pt is the circuit total real power at duty point;

St is the circuit total apparent power at duty point;

Vn is the line-to-neutral supply voltage;

Idp is the line current in the supply cable at duty point;

PFt is the circuit power factor at duty point.

The overall efficiency of the installation is calculated using the equation below:

Ƞ = (3.6 ∗ Qdp ∗ Hdp)/(367 ∗ P t)

A useful way to assess the efficiency is to calculate the energy required to abstract a unit of
water and per unit of vertical lift. This value provides a useful comparison for different
installations. It is calculated using the equation below.
 E = P t/(Qdp ∗ Hv)

E is the energy required per cubic metre of water and metre of vertial lift;

Pt is the circuit total real power at duty point;

Qdp is the water flow rate at duty point;

Hdp is the total dynamic head at duty point;

Hv is the total vertical lift disregarding drawdown.

4.1 Genset Sizing for Continuous Duty
Operation
The sizing of the genset is based on the total circuit load as calculated in the sections
above. De-rating of the genset is required for ambient air temperature, altitude and load
power factor as detailed below.

Most modern gensets are rated for maximum air temperature of 40°C. This refers to the
temperature of the cooling air as it enters the ventilating openings in the machine. Where
the air temperature exceeds this value, de-rating is required at a rate of 3% for every 5°C, up
to a maximum air temperature of 60°C.

Similarly, genset ratings are based on peformance at a maximum altitude of 1,000 m above
mean sea level. At higher altitudes, the air becomes thinner and loses its cooling
effectiveness. Therefore, genset de-rating is done at a rate of 3% per 500 m, up to a
maximum altitude of 4,000 m above mean sea level.

Genset are normally rated for a power factor of 0.8. Gensets alternators are limited in their
ability to deliver power at lower power factors. This is shown in the alternator reactive
power capability curve. Genset de-rating is required for inductive loads (motors) with a
power factor below 0.8. De-rating used in this spreadsheet is based on values shown in
table below.

Power Factor De-rating Factor

0.8 1.00

0.7 0.95

0.6 0.91

0.5 0.88

0.4 0.86

0.3 0.85
Finally, in sizing the genset, it is also important to consider the load duty cycle. A
continuous duty cycle requirement is assumed, meaning that the genset is required to
operate at full-load for an unlimited number of hours per year. For a genset that has been
rated for prime power duty, this requirement translates in the duty load not exceeding 70%
of its prime power rating. Therefore, taking all of the above into account, the genset primer
power rating requirement is calculated using the equation below.

Sg = St/(Kg ∗ 0.7)

Sg is the genset minimum prime apparent power rating;

St is the circuit total apparent power at duty point;

Kg is the total de-rating factor taking account of temperature, altitude and power
factor.
4.2 Motor Starting – Genset Capacity
Large motor starting requires two separate calculations/checks. First, checking that the
supply is able to provide the required starting power with limited disruption. For a genset,
this means providing the required starting current whilst maintaining a limited voltage dip
(typically 30%) and without stalling. And second, checking that the motor starting torque is
sufficient to start the pump (covered in section 4.3 below).

A motor starter is used to reduce motor current demand during startup. This spreadsheet
allows calculations to be performed for a variety of motor starters including the
autotransformer, the star-delta and the soft-start. A summary of the characterisitcs of each
of these starting methods is shown in the table below. Note that these values are the
theoretical values that can be expected in a circuit with a short supply cable, i.e. with no
voltage losses.

Vm/Vn Iu/Ist Id/Ist Tm/Tst Kst

Direct-on-Line 1.00 1.00 1.00 1.00 1.00

Autotransformer 80% 0.80 0.64 0.80 0.64 0.64

Autotransformer 65% 0.65 0.42 0.65 0.42 0.42

Star-Delta 1.00 0.33 0.33 0.33 0.33

Soft Start
X X2 X X2 X2
(setting X%)

Vm is the line-to-neutral starting voltage applied downstream of the motor

starter;

Vn is the line-to-neutral supply voltage;

Iu is the starting line current upstream of the motor starter;

Id is the starting line current downstream of the motor starter;

 Ist is the starting line current based on DOL starting (no starter) aka locked-rotor
current (LRC or LRA).

Tm is the motor starting torque based on the starting method used;

Tst is the motor starting torque based on direct-on-line starting (no starter) aka
locked-rotor torque (LRT).

Sizing the genset for motor starting requires two checks: checking the ability of the
alternator to start the motor with a limited voltage dip, and checking that the genset has
sufficient real power and will not stall during startup.

The first check requires the calculation of the apparent power demand during startup using
the equation below. This calculated value must then be compared with the alternator
performance data published by the manufacturer. The published alternator motor starting
capability must exceed the calculated apparent power demand.

Sst = k ∗ V n ∗ Ist ∗ Kst

Sst is the apparent power demand during motor startup;

k is a factor with value k=1 for a single-phase motor or k=3 for a 3-phase motor;

Vn is the line-to-neutral supply voltage;

Ist is the starting line current based on DOL starting (no starter) aka locked-rotor
current (LRA or LRC);

Kst is a factor that takes account of the starting method used (from the table
above).
Note that the motor starting capability of the genset will depend on the motor power factor.
As a rule, the same genset will be able to start a larger motor with a lower power factor.
Published alternator capability will typically be based on a conservative upper-bound power
factor of 0.5 or 0.6. This means that the published motor starting capability will be valid for
any motor with a starting power factor lower than this value. The motor starting power
factor will likely not be available but can be safely assumed to be lower than 0.5.

The second check involves checking that the genset engine is able to provide the required
real power during startup without stalling. The maximum real power the engine is able to
provide during startup is assumed to be the genset's standby power rating at a power factor
of 1. However, genset standby power ratings are typically declared at a power factor of 0.8.
Therefore, at a power factor of 0.8, the genset minimum standby real power rating is
calculated using the equation below.

P = Sst ∗ P F st ∗ 0.8

P is the genset minimum standby real power rating at a power factor of 0.8.

Sst is the apparent power demand during motor startup calculated above;

PFst is the motor power factor during startup.

As noted above, the motor starting power factor will likely not be available. Using a value of
0.5 provides a conservative answer when calculating the minimum genset standby power
rating.

No genset de-rating is required for motor starting.

4.3 Motor Starting – Torque Calculation
The purpose of using a motor starter is to reduce the demand on the power supply during
startup. The danger with using a motor starter is that by reducing the power demand, the
motor starting torque is also reduced. Reduce the power demand too much, and the motor
will be unable to start the pump!

In addition, another important factor in the calculation of the motor starting torque relates
to the voltage losses in the supply cable. Whilst the supply cable is not sized for starting
currents, the reality is that voltage losses in the supply cable are an important factor to be
considered in the calculation of the motor starting torque.

The calculation of the motor starting torque (T’m), is therefore based on the motor starting
method used and taking account of any voltage losses along the supply cable. The motor
starting torque is calculated using the equation below.

T ′ m/T n = (T st/T n) ∗ (V ′ m/V n)2

T’m is the motor starting torque based on starting method used and taking
account of any voltage losses in the supply cable;

Tst is the motor starting torque based on direct-on-line starting (no starter) aka
locked-rotor torque (LRT);

Tn is the motor nominal full-load torque;

V’m is the line-to-neutral voltage applied to the motor based on starting method
used and taking account of any voltage losses in the supply cable;

Vn is the line-to-neutral supply voltage.

Calculating the torque required to accelerate a load from standstill to operating speed is a
complex calculation requiring a number of parameters of both the motor and the pump that
are likely not known. As a simplified approach, the method suggested here is to compare
the motor starting torque with the pump ‘breakaway’ torque. The pump ‘breakaway’ torque
is the torque required to set the pump in motion from a stationary position (the friction
torque in a stationary position aka ‘stiction’). For a submersible borehole pump, the
breakaway torque may be as much as 50% of its torque at the best efficiency point.

Since the pump breakaway torque is likely not known, the suggestion is to ensure that the
motor starting torque calculated in the equation above is no less than 60% of the pump’s
torque at the best efficiency point (BEP). The pump’s torque at BEP is calculated from the
pump’s shaft power at BEP, which can be read from the pump’s power curve (refer to section
2.3 above regarding the pump power curve).
4.4 Motor Starting – Voltage Drop in Supply
Cable
In this section, the user has access to the calculated values of starting line current
(downstream of the starter), the voltage drop in the supply cable, and the actual starting
voltage applied to the motor. These are the values that are used in the calculation of the
motor starting torque in section 4.3 above.

The calculation of these values is done by resolving the electrical circuit formed by supply
cable and motor. During startup, the motor is assumed to behave as a resistive load.
Annex - Worked Example
Problem conditions:

Static water level is 400 m below ground.

Level of discharge into reservoir is 20 m above ground.
Total length of pipework above ground is 30 m.
Water temperature in well is 50°C.
Site altitude is 2,200 m above mean sea level.
Maximum ambient air temperature is 45°C.
Well pump test results are available.
Total daily water requirement is known.

Worked Example Borehole Pump_Worked Example_Feb21.pdf - 2MB

1.1 Duty Point

Based on the well pump test and the total daily water requirement, a target flow rate of 15
m3/hr is chosen. This flow rate has been chosen also to match the BEP of a Grundfos
SP17 pump.
 Grundfos SP17 Pump Curve

From the well pump test, the drawdown at this flow rate is 2 m. Therefore the total vertical
lift Hv is 422 m.

Total friction losses in the pipework at this flow rate (from section 1.2) is 13.0 m. Therefore
total dynamic head is 435.0 m.

Reading the SP17 pump curve, the point (15,435) is somewhere between 48 and 51 stages
(the number of impellers). Choosing 48 stages means the duty point will be to the left of
BEP and the flow rate is slightly below 15 m3/hr. Conversely, choosing 51 stages means the
duty point is to the right of BEP and the flow rate is above 15 m3/hr. I decide on using a
SP17-48.
At a flow rate of 15 m3/hr, the SP17-48 pump has a head of approx 422 m compared to the
system's total dynamic head of 435 m.

A second iteration at 14.5 m3/hr, reveals a pump head of approx 433 m compared to the
system's total dynamic head of 434.2 m. This difference represents less than 1% and is as
close one can get in practical terms when using a paper graph. The pump duty point is
therefore taken at a flow rate of 14.5 m3/hr.

1.2 Calculation of Friction Losses

For the calculation of the friction losses, I have selected a locally available galvanised steel
pipe with an internal diameter of 67.1 mm. I use an internal roughness value of 0.15 mm.

I have also included 4 (90 deg) elbows, 4 check valves and 1 gate valve.

The total calculated head loss at a flow rate of 15.0 m3/hr is 13.0 m.

The total calculated head loss at a flow rate of 14.5 m3/hr is 12.2 m.

In addition, it is also important to check that the pipes and fittings have the
correct pressure rating for the application, including allowance for any possible
pressure surges.

2.1 Net Positive Suction Head (NPSH)

From the pump curve I read the required NPSH at a flow rate of 14.5 m3/hr to be 4.0 m.

The pump inlet is installed at a depth of 410 m below ground level so that it has a
submersion of 8 m. At an altitude of 2,200 m and a water temperature of 50°C, the NPSH
available is calculated to be 13.6 m, which exceeds the required value of 4.0 m.
2.2 Geometric Fit & Motor Cooling

The Grundfos SP17-48 pump has an outside diameter of 175 mm.

The Grundfos MS6000 30kW motor (from section 2.3) has an outside diameter of 140 mm
and a temperature rating of 40°C.

The minimum casing internal diameter recommended for this pump/motor assembly is
1.25x175=219 mm.

The maximum water temperature is 50°C so the motor requires de-rating. The temperature
de-rating factor is 0.85.

A locally available casing has an internal diameter of 225 mm. Without the use of a sleeve
around the motor and assuming all water flows from below (the well screen is below the
level of motor), then the water around the motor has a flow velocity of 0.17 m/s. This is
insufficient for a de-rated motor.

We will use a sleeve to increase the flow around the motor. A sleeve with a diameter of 170
mm will provide a flow velocity of 0.55 m/s.

Note that since the pump is larger than the motor, the sleeve will need to widen as it extends
around the pump inlet. The casing size will need to be re-checked after finalising the sleeve
design.

2.3 Motor Power Calculation

From the pump's power curve I read the following:

P2 = 23.2 kW at duty point (14.5 m3/hr)

P2be = 23.4 kW at BEP (15.0 m3/hr)
P2max = 25.6 kW at runout (22 m3/hr)

The motor design power based on P2max and temperature de-rating factor: 25.6/0.85=30.1
kW.
Note that at runout the pump has a head of approx. 250 m. Given that the static vertical
head to ground is 400 m, one could argue that the pump will never be required to operate at
this point.

If I argue that the minimum credible head is 400 m, then the flow rate is 16.5 m3/hr and P2
is 24.2 kW. In this case the motor design power is 24.2/0.85=28.5 kW.

I settle on a motor with a nominal power P2n of 30 kW.

2.4 Motor Efficiency and Power Factor

I confirm that the power supply on site has a line-to-neutral voltage of 230 V. The three-
phase line-to-line voltage is 400 V.

Grundfos MS6000 Motor Data

From published motor data at the correct supply voltage, I read and insert in the
spreadsheet the motor's efficiency and power factor at 50, 75 and 100% load.

At duty point the pump shaft power P2 is 23.2 kW. Therefore the motor load is 77% of its
full-load nominal power.

3.1 Supply Cable Current-Carrying Capacity

The Grundfos MS6000 30 kW motor has a current rating of 64 A.

I will be using a submersible cable for drinking water with insulation and sheath rated for a
conductor temperature of 90°C.

The cable will need to be de-rated for an ambient temperature of 50°C - worst value of water
and air temperature.

A cable with a cross-section area of 50 mm2 has a current-carrying capacity of

0.82x179=147 A. This value exceeds the motor current rating of 64 A.

3.2 Supply Cable Voltage Drop

The voltage drop calculation has to be done at motor current rating of 64 A. The total
length of cable assumed is 420 m, which includes 10 m of cable above ground.

The calculated line-to-neutral voltage drop is 12.2 V, which represents a 5.3% of the rated
voltage of 230 V. The recommended limit is 5% so the small excess is acceptable.

3.3 Power Consumption

The power demand of the complete circuit (motor and cable) at duty point is as follows:

Real Power Pt = 29.0 kW

Apparent Power St = 35.1 kVA
Power Factor Pt = 0.825

The total energy consumption required to produce a cubic metre of water is 29/14.5 = 2.0
kWh. The total energy consumption per cubic metre of water and metre of vertical lift
(disregarding drawdown) is 29/14.5/420 = 4.75 Wh. These values are important to assess
the efficiency of the installation.
 It is useful to assess the cost of providing a larger cable size compared to the
savings that can be done by reducing the energy consumption. For example a
cable with a cross-section area of 95 mm2, will reduce the power consumption
from 29.0 to 28.2 kW.

4.1 Genset for Duty Operation

Site altitude 2,200 m requires de-rating of 7%. Air temperature of 45°C requires de-rating of
3%. Power factor of 0.825 does not require de-rating.

The genset minimum prime power rating is 35.1/0.93/0.97/0.7 = 55.6 kVA.

4.2 Genset Motor Starting

Starting method is autotransformer with tapping at 65%.

From motor data, locked-rotor current is 500% of rated current, 5*64=320 A. Locked-rotor
torque is 160% of rated torque, 1.6*100=160 Nm. The starting power factor is not known, a
conservative value of 0.5 is assumed.

Check the genset meets the following two requirements:

The alternator minimum motor starting capability is 3*230V*320A*0.42 = 93 kVA.

The genset minimum standby real power rating (at a PF of 0.8) is 93*0.5*0.8 = 37.2
kW.

4.3 Motor Starting Torque

Using the autotransformer at 65% and taking account of voltage losses in the supply cable,
the motor starting torque is reduced from the DOL value of 160 Nm down to 45.4 Nm. The
actual starting voltage applied to motor after losses in cable is 122.7 V (see calculation is
section 4.4).

The pump's breakaway torque is not known. It is suggested that the motor starting torque
be no less than 60% of the pump's torque at the point of best efficiency: 0.6 * 77.9 = 46.7
Nm.

The motor starting torque of 45.4 Nm is slightly under the minimum of 46.7 Nm. Providing
a larger cable size will increase the motor starting torque.

Providing a cable with a cross-section area of 95 mm2, will increase motor

starting torque from 45.4 to 53.5 Nm, which is 68% of pump's torque at BEP.