Technical worked example

Grundfos SPE + RSI:
solar pumping at variable speed

A Grundfos SPE set driven by an RSI converter has its own sizing logic: a cut-in threshold, a minimum continuous flow rate and three essential accessories. Here is how it works, figures included, and the method to size it.

Calculations based on the official curves Sources: Grundfos instructions and technical brochures
The three parts

A hydraulic end, a permanent magnet motor, a converter

An SPE system is made up of three components specifically designed to work as an integrated unit. The hydraulic end is based on the submersible pumps of the SP range, recognised for many years for their reliability and performance. The drive is provided by an MS6000P permanent magnet synchronous motor, of four-pole design, able to reach a maximum speed of 3,000 rpm at 100 Hz, supplied with three-phase 3 × 350 V. The set is driven by the RSI converter, which directly converts the DC power from the solar array into three-phase power and continuously adapts the motor's rotation speed to the solar power available, in order to optimise the pump's operation across the whole irradiance range.

SPthe hydraulic end of Grundfos submersible pumps, from 6 to 10 inches
MS6000Ppermanent magnet synchronous motor with buried magnets, 4 poles, 3,000 rpm at 100 Hz, 3 × 350 V
RSIsolar converter with integrated maximum power point tracking, IP66 rating
92.4%motor efficiency at full load, still 90.6% at half load

Efficiency is the main advantage of the permanent magnet motor. The absence of induced currents in the rotor limits motor heating and reduces the amount of heat transmitted to the pumped liquid, two factors that directly determine the lifetime of the submersible set. Grundfos states a gain of 8 to 10 efficiency points compared with an asynchronous motor of equivalent power, and publishes the detail of these values at 50, 75 and 100% load.

The key concept

The cut-in threshold, or why a pump can run without delivering water

A centrifugal pump only develops a useful head above a minimum rotation speed. Below this threshold, although the motor drives the hydraulic end and consumes energy, the head generated remains insufficient to overcome the static load of the circuit: no flow is then delivered at the outlet. The affinity laws for centrifugal pumps, published notably by Grundfos in its technical documentation, make it possible to determine this critical speed from which water actually begins to be delivered.

cut-in speed = √( TDH ⁄ shut-off head )

The shut-off head is the top of the flow-head curve, at full speed. A pump that reaches 189 m at zero flow and works at 75 m cuts in at √(75/189), that is 63% of its speed. Below this speed, the pump consumes energy without delivering any flow, while above it the flow rate increases rapidly with rotation speed. The lower this ratio, the wider the daily time window during which the pump runs.

Setting this threshold is provided for by the manufacturer. Commissioning the RSI includes setting a minimum delivery frequency, determined by progressively increasing the frequency until flow appears, a value the converter then stores. It also has a dedicated fault code, "low DC power", which stops the drive when the power delivered by the solar array becomes insufficient.
Worked example

An SPE 77-9 at 75 metres

Take an example: 75 metres of total dynamic head, with a target flow rate of around 100 m³/h. The SPE 77-9 meets this point: nine stages, 37 kW motor, shut-off head of 189 metres. It cuts in at 63% of its speed: the pump starts early in the morning and stops late in the evening. Here is its day, for a 47 kWp solar array and a system yield of 0.80.

IrradiancePower at converter inputFlow rateWhat happens
150 W/m²5.6 kW0 m³/hbelow the threshold: the pump delivers no flow
197 W/m²7.3 kWcut-inwater starts to rise
300 W/m²11.2 kW32 m³/halready a third of the maximum flow rate
500 W/m²18.7 kW61 m³/hmid-morning regime
700 W/m²26.1 kW80 m³/h 
900 W/m²33.6 kW95 m³/h 
1,000 W/m²37.3 kW101 m³/hfull speed, the converter caps it
197 W/m²the irradiance at which water starts to rise: well before mid-morning
5.1 : 1the ratio between full-speed power and cut-in power: the working window
101 m³/hthe flow rate at full speed, at 75 metres of head
7.7 m³/hthe minimum continuous flow rate of this pump, dictated by motor cooling

A window of 5 to 1 corresponds to a wide operating range. On a pump whose ratio of head to shut-off head was 0.85, cut-in would rise to 92% of speed and the window would fall to 1.3 to 1: the same installation would then only work during peak hours. This is the first point that sizing must check, even before the power of the solar array.

The converter

What the RSI requires from the solar array

The RSI comes in two voltage ranges, and this choice commits the whole solar array, since it determines the architecture of the module strings. The 3 × 380-440 V range covers 2.2 to 250 kW, while the 3 × 208-240 V range extends up to 15 kW and works at lower DC voltages.

Converter rangeMinimum MPP voltageRecommended MPP voltageMaximum input voltagePower
3 × 380-440 V450 V530 to 615 V800 V2.2 to 250 kW
3 × 208-240 V230 V290 to 336 V400 V1.5 to 15 kW

Two wiring sizing rules follow from this. The string must stay above 450 volts at the maximum power point even in high heat, when module voltage collapses, and below 800 volts in open circuit in extreme cold, when it peaks. The recommended band between the two has a physical reason: there must be enough DC voltage for the converter to deliver the motor's full voltage at its rated frequency.

The converter is sized not on the motor's rated power, but on its rated current. Grundfos technical documentation states this explicitly. MS6000P motors are designed for a 3 × 350 V supply, while RSI converters deliver an output voltage of between 380 and 440 V. This design difference leads Grundfos to use current as the selection criterion. In practice, a motor of a given power therefore frequently requires a converter from a higher power class. For example, a 37 kW MS6000P motor has a rated current of 85.6 A and must be paired with a converter able to supply at least 87 A, corresponding to the 45 kW model.
The three essentials

The three essentials

Three items of equipment accompany the set and protect the motor over time: the sine-wave filter, the flow sleeve and the temperature sensor.

The sine-wave filter

A converter does not deliver a sine wave but a series of pulses, and the resulting voltage spikes stress the winding insulation, all the more so when the drop cable is long. The SP pump instructions set clear limits: for an MS6000 motor supplied by a solar converter, without a filter, the array's open-circuit DC voltage is limited to 400 volts and the unshielded cable to 300 metres; with a sine-wave filter, these limits rise to 800 volts and 500 metres.

The 3 × 380-440 V range requires a minimum voltage of 450 volts at the maximum power point, and consequently an even higher open-circuit voltage, so it can never meet the 400-volt limit. On this range, the sine-wave filter is mandatory. The 3 × 208-240 V range, whose input is capped at 400 volts, is designed to do without it.

On a 3,000 rpm motor supplied at 100 Hz, the filter is selected from the 100 Hz column of the catalogue. A filter's permissible current is about a quarter lower at 100 Hz than at 50 Hz: a motor drawing 85.6 A at 100 Hz requires a filter rated for around 112 A at 50 Hz.

The flow sleeve

A submersible motor is cooled by the water flowing past it; Grundfos requires a velocity of at least 0.15 m/s along the motor, and gives the formula to check it:

V = Q × 353 ⁄ (D² − d²)   V in m/s, Q in m³/h, D the borehole or sleeve diameter in mm, d the pump diameter

In a wide borehole, the water slows down around the motor and cools it less. The sleeve, a simple tube placed around the motor, restores the flow velocity; Grundfos also recommends it in the presence of sand.

On the SPE 77-9 in the example, it becomes useful beyond a borehole diameter of about 190 mm; the threshold depends on the pump.

The temperature sensor

Grundfos submersible motors can be fitted with a built-in temperature sensor, and the technical brochure states unambiguously that these sensors are incompatible with a frequency converter. A fuse inside the transmitter blows as soon as it is connected to the converter, and the sensor is permanently lost. Grundfos recommends installing an external Pt100 or Pt1000 sensor instead.

The external sensor is the set's only thermal protection. The converter protects the motor against electrical overload; temperature, however, relies entirely on the sensor: the instructions state that the converter does not measure it.

Operating conditions

The operating range to respect

Sizing must guarantee that the pump always operates within its domain of use, whatever the climate conditions and site constraints.

LimitValueWhy
Minimum continuous flow rate0.1 × rated flowbelow this, water no longer circulates enough to cool the motor
Maximum continuous flow rate1.3 × rated flowrisk of reverse axial thrust and cavitation
Running with the valve closed30 seconds maximumthe liquid heats up locally
Overspeednot recommendedthe manufacturer advises against exceeding the rated frequency
Acceleration ramps3 seconds maximumprotection of the sleeve bearings and the seal
Number of starts120 per hour, 360 per dayworth checking on a site with frequent cloud passages
The non-return valve is an essential part of the installation. On a permanent magnet synchronous motor, any water flow through the pump while it is stopped, particularly if the riser column flows back, can cause the rotor to turn. The motor then behaves like a generator and produces a voltage at its terminals, even with no electrical supply. Grundfos technical documentation accordingly states that the motor terminals must be considered potentially live until the rotor's complete stop has been verified. Installing a non-return valve prevents this reverse flow, removes the risk of parasitic rotation and, as such, is a design requirement of the system.
The alternative

Converting an existing SP pump to solar

The RSI can also drive the standard asynchronous motors fitted to the submersible pumps of the SP range. A pump already installed in a borehole can therefore be converted to solar operation without modifying the hydraulic end, using the same converter and the same sizing method.

 SP + RSI (asynchronous motor)SPE + RSI (permanent magnets)
Motor efficiencyaround 82%92.4% at full load
Efficiency at partial loadrarely published90.6% at half load
Rated speed2,900 rpm at 50 Hz3,000 rpm at 100 Hz
Direct mains connectionpossiblenot possible, converter mandatory
Sine-wave filter on the 400 V rangemandatorysystematically included
Use caseconverting an already installed pumpnew installation, seeking the best efficiency

For the same solar array, the permanent magnet motor has more power at the shaft: it cuts in earlier in the morning and delivers a higher volume of water over the whole day. A gap of ten efficiency points therefore translates directly into a higher volume produced.

Sizing

What LE LAB does with all this

Sizing a variable-speed pumping system starts with determining the hydraulic cut-in threshold. It is first necessary to check that this threshold leaves a usable operating window under real irradiance conditions. It must then be ensured that the required flow rate remains above the pump's minimum continuous operating flow, then checked that the solar array respects the voltage window admissible by the converter, both at the maximum voltage in low temperatures and the minimum voltage in high heat. Only once these operating conditions have been validated can the month-by-month water production be assessed.

The thresholdcalculated for each pump and each head, and shown in the report's operating conditions
The voltage windowchecked at the minimum recorded over sixteen years and at hot-cell temperature, with the real coefficients of the selected module
The accessoriessine-wave filter and dry-run sensor systematically included, flow sleeve recommended according to the borehole's characteristics
The comparisonagainst the ranges with an integrated controller, which are the simplest solution when they reach the operating point

During sizing, LE LAB systematically compares SPE sets paired with an RSI converter against pumping solutions with an integrated controller. When several architectures can reach the required operating point, the application prioritises the simplest solution, in order to limit installation complexity, reduce costs and make installation and maintenance easier.

Sources

Where these figures come from

  • SPE 3,000 rpm technical brochure, Grundfos: description of the range, MS6000P motors, efficiencies and power factors, sine-wave filter selection, operating conditions, affinity laws, recommended borehole diameters.
  • SP and SPE installation and operating instructions, Grundfos: operation with a frequency converter, voltage and cable-length limits with and without a filter, minimum flow velocity along the motor, temperature sensors.
  • RSI 1.5 to 250 kW installation and operating instructions, Grundfos: voltages at the maximum power point, maximum input voltage, frequency range, output sizes and currents, minimum delivery frequency setting, fault codes.
  • RSI AC Drives instructions, Grundfos: technical specifications of the converter, types of motors driven, temperature ranges and derating.
  • Flow-head curves and power curves from the product data sheets on Grundfos Product Centre, for the pump used in the example.

Figures and constraints taken from official Grundfos documentation, versions in effect at the date of publication; the manufacturer's instructions remain the reference. A page published by SINES, official Grundfos distributor.