Applying the Product Mix and Output Algorithm

Two Simple Examples

Example 1 – Single Product Site

A - Linear Regression using Base Year Data

1.1 Analyse weekly production and energy data from the base year period:

Total Production = x tonnes
Total Delivered Gas Energy Use = Eg kWh
Total Delivered Electricity Energy Use = Ee kWh

1.2 Plot weekly total gas use (Eg) against weekly total production (x) to gain equation:

Eg = 39.8 x + 7,786

1.3 Plot weekly total electricity use (Ee) against weekly total production (x) to gain equation:

Ee = 128.5 x + 60,230

1.4 Derive the Product Output Algorithm for the site:

Total Weekly Primary Energy: E = Eg + ( 2.6 x Ee )

E = 373.9 x + 164,384

Therefore, Specific (primary) Energy Consumption:
SEC = 373.9 x + 164,384 = 373.9 + 164,384
....................x ...................................x

1.5 Adjust target using MS1 production levels:

Original target = 1,128.8 kWh/tonne

Base Year SEC at MS1 production levels would have been:

SEC = 373.9 + 164,384 .......................................NB. x is weekly production
. ....................(9,300/52)

SEC = 1,293.0 kWh/tonne

Adjusted MS1 target of 2% reduction = 1,267.2 kWh/tonne

Actual MS1 performance = 1,194.1 kWh/tonne

Therefore site has passed by adjusting the target.

B - Linear Regression using Recent Data

1.6 Analyse recent weekly production and energy data:

Total Production = x tonnes
Total Delivered Gas Energy Use = Eg kWh
Total Delivered Electricity Energy Use = Ee kWh

1.7 Plot weekly total gas use (Eg) against weekly total production (x) to gain equation:

Eg = 38.2 x + 7,177

1.8 Plot weekly total electricity use (Ee) against weekly total production (x) to gain equation:

Ee = 120.7 x + 55,331

1.9 Derive the Product Output Algorithm for the site:

Total Weekly Primary Energy: E = Eg + ( 2.6 x Ee )

E = 352.0 x + 151,038

Therefore, Specific (primary) Energy Consumption:

SEC = 352.0 x + 151,038 = 352.0 + 151,038
......................x .................................x

1.10 Calculate Base Year performance at reduced MS1 output (SEC4) and adjust target:

We know SEC1 and SEC2 from the derived equation and SEC3 from the base year annual data. To calculate SEC4 we assume:

SEC4 = SEC3 x (SEC2 / SEC1) SEC3 = 1,151.9 SEC2 = 352.0 + 151,038 ........................(9,300/52) SEC2 = 1,196.5

SEC1 = 352.0 + 151,038 = 1,035.0
.....................(11,500 / 52)

SEC4 = 1,151.9 x (1,196.5 / 1,035.0) = 1,331.6

Adjusted Target = 2% reduction on SEC4 = 1,305.0

Actual SEC achieved during the milestone year = 1,194.1

Actual Milestone Year SEC is less than the adjusted target, therefore the site passes.

Example 2 - Two Product Site, No Sub-metering

A - Multiple Regression using Base Year Data

2.1 Analyse weekly production and energy data from the base year period:

Total Production of Product A = A tonnes
Total Production of Product B = B tonnes
Total Delivered Gas Energy Use = Eg kWh
Total Delivered Electricity Energy Use = Ee kWh

2.2 Perform a multiple regression analysis on the weekly gas use (Eg) against weekly total production for Products A and B to gain equation:

Eg = 6,302 + 10.4 A + 212.0 B

Where R2 = 0.96

2.3 Perform a multiple regression analysis on the weekly electricity use (Ee) against weekly total production for Products A and B to gain equation:

Ee = 57,959 + 83.5 A + 392.1 B

Where R2 = 0.83

2.4 Derive the Product Output Algorithm for the site:

Total Weekly Primary Energy: E = Eg + ( 2.6 x Ee )

E = 150,693 + 227.5 A + 1,231.5 B

Therefore, Specific (primary) Energy Consumption:

SEC = 150,693 + 227.5 A + 1,231.5 B
..........................( A + B )

2.5 Adjust target using MS1 production levels:

Base Year SEC at MS1 production levels would have been:

SEC = 150,693 + (227.5 x (6,000/52)) + (1,231.5 x (3,300/52))
...................................( (6,000/52) + (3,300/52) )

NB. A and B are weekly production

SEC = 1,426.4 kWh/tonne

Adjusted MS1 target of 2 % = 1,397.9 kWh/tonne

Actual MS1 performance = 1,194.1 kWh/tonne

Therefore site has passed by adjusting the target.

B - Multiple Regression using Recent Data

2.6 Analyse recent weekly production and energy data:

Total Production of Product A = A tonnes
Total Production of Product B = B tonnes
Total Delivered Gas Energy Use = Eg kWh
Total Delivered Electricity Energy Use = Ee kWh

2.7 Perform a multiple regression analysis on the weekly gas use (Eg) against weekly total production for Products A and B to gain equation:

Eg = 7,671 + 48.1 A + 8.6 B

Where R2 = 0.90

2.8 Perform a multiple regression analysis on the weekly electricity use (Ee) against weekly total production for Products A and B to gain equation:

Ee = 53,660 + 87.1 A + 220.9 B

Where R2 = 0.82

2.9 Derive the Product Output Algorithm for the site:

Total Weekly Primary Energy: E = Eg + ( 2.6 x Ee )

E = 147,185 + 274.6 A + 582.9 B

Therefore, Specific (primary) Energy Consumption:

SEC = 147,185 + 274.6 A + 582.9 B
..........................( A + B )

2.10 Calculate Base Year performance with MS1 product mix and outputs and adjust target:

We know SEC1 and SEC2 from the derived equation and SEC3 from the base year annual data. To calculate SEC4 we assume:

SEC4 = SEC3 x (SEC2 / SEC1) SEC3 = 1,151.9 SEC2 = 147,185 + (274.6 x (6,000/52)) + (582.9 x (3,300/52)) .................................( (6,000/52) + (3,300/52) ) SEC2 = 1,206.97 SEC1 = 147,185 + (274.6 x (9,300/52)) + (582.9 x (2,200/52)) ......................................( (9,300/52) + (2,200/52) )

SEC1 = 999.1

SEC4 = 1,151.9 x (1,206.97 / 999.1) = 1,391.56

Adjusted Target = 2% reduction on SEC4 = 1,363.73

Actual SEC achieved during the milestone year = 1,194.1

Actual Milestone Year SEC is less than the adjusted target, therefore the site passes.