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# Chapter 3: Calculations

ECO8 software has been developed by SCHNEIDER ELECTRIC with the aim of enabling quick evaluation of energy savings that can be achieved by installing an ALTIVAR variable speed drive in a pumping or ventilation application.

### 3.1 Reference curves

Active power consumed by a frequency converter associated with a variable load torque (quadratic) load can be calculated as shown below.

The load torque can be defined in the following way (mechanical friction is ignored):

C = k1 x n^2 (1)

with n = Motor rotation speed
k1 = Constant (varies as a function of application type)

Mechanical power of this drive is:

P = C x n
...using here expression (1), we obtain:

P = k1 x n^3

In addition, the frequency converter supplies electrical power to the motor at efficiency of around 97%:

P SPEED DRIVE = P / 0.97

Mechanical power required to obtain a given flow is extracted from the following POWER-FLOW curves:

##### Fans

Flow | Downstream | Upstream | Variable speed drive
10 | 0.18 | 0.34 | 0.1
20 | 0.36 | 0.36 | 0.1
30 | 0.55 | 0.39 | 0.1
40 | 0.71 | 0.42 | 0.13
50 | 0.85 | 0.46 | 0.18
60 | 0.92 | 0.51 | 0.24
70 | 0.98 | 0.57 | 0.37
80 | 1 | 0.64 | 0.54
90 | 1 | 0.76 | 0.77
100 | 1 | 1 | 1

#####

##### Pumping

Flow | Recirculation | With valve | Variable speed drive
10 | 0.71 | 0.39 | 0.1
20 | 0.79 | 0.49 | 0.1
30 | 0.86 | 0.58 | 0.1
40 | 0.9 | 0.68 | 0.13
50 | 0.94 | 0.75 | 0.18
60 | 0.97 | 0.82 | 0.24
70 | 0.98 | 0.89 | 0.37
80 | 0.99 | 0.94 | 0.54
90 | 1 | 1 | 0.77
100 | 1 | 1 | 1

For a valve according to manometric height H (with variable speed drive) :

Flow | H=0 | H=0.5 | H=0.85
10 | 0.06 | 0.15 | 0.35
20 | 0.08 | 0.18 | 0.37
30 | 0.1 | 0.22 | 0.41
40 | 0.11 | 0.27 | 0.45
50 | 0.13 | 0.35 | 0.52
60 | 0.22 | 0.43 | 0.58
70 | 0.34 | 0.53 | 0.66
80 | 0.51 | 0.66 | 0.78
90 | 0.73 | 0.82 | 0.9
100 | 1 | 1 | 1

The inclusion of a variable speed drive can satisfy these requirements by eliminating the use of control valves, which operate by reducing the effective cross-section of the pipe.

In addition, variation in motor efficiency as a function of its speed must be taken into account. To determine motor efficiency at a given speed, the following EFFICIENCY-SPEED curve is used:

Speed | Efficiency
10 | 0.7
20 | 0.78
30 | 0.85
40 | 0.89
50 | 0.93
60 | 0.96
70 | 0.97
80 | 0.98
90 | 0.99
100 | 1

### 3.2 Formulas

Without variable speed drive, active power consumed by a motor driving a pump or fan will therefore be:

P WITHOUT SPEED DRIVE = P RATED MOTOR x (1/s) x (I / In) x f1(Q)

... with s = Rated efficiency of motor according to speed

I / In = Current absorbed by the motor at 100% load / rated current

f1(Q) = Power as a function of flow for a fan or pump (see curves above for precise values)

The reactive power is obtained as follows:

Q = P WITHOUT SPEED DRIVE x (sin phi/cos phi)

With variable speed drive, active power consumed by a motor driving a pump or fan for a given flow will therefore be:

P WITH SPEED DRIVE = P RATED MOTOR x 1/s x (I / In) x f2(Q) x 1/v x f3(Q)

... with f2(Q) = Power as a function of flow with variable speed drive (see curves above for precise values)

f3(Q) = Efficiency as a function of speed (see curves above for precise values)

w = Motor efficiency correction factor as a function of speed
v = Variable speed drive efficiency

Reactive power consumption of the motor-variable speed drive assembly is zero.

When calculation of power consumed for a given flow has been completed, just multiply this by the number of hours of operation at this flow to obtain the energy consumption. The final result is obtained by adding together all the energy consumptions obtained for the various flows.

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