# Metering cost minimization of M_V projects - Eskom

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```					    Metering cost minimisation of
M&V Projects

Xianming Ye

M&V Workshop 22 Aug 2012

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OUTLINE
 1. Introduction
 2. Lighting retrofit project

 3. Assumptions for the modelling

 4. Metering cost minimisation model

 5. Solution for the optimal metering cost

 6. Conclusion

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1. INTRODUCTION

   Minimal metering cost VS expected measurement
accuracy

   Key factor: optimal decisions of the sample size
according to the required measurement accuracy

   Sample size     Accuracy      Metering Cost

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M&V ACCURACY REQUIREMENT: 90/10
CRITERION

   IPMVP:

   Precision is an assessment of the error margin of
the final estimate.

   Confidence is the likelihood that the metering
target will fall within the precision range.

x                    x 
p                       z
                    n                 4
   Statistical statement: “the best estimate of
savings is 2000 kWh annually with 90%
(confidence) that true mean value falls within
±10% (precision) of 2000”.

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90/10 Criterion
0.0035

0.003

0.0025
Probability

0.002

0.0015

0.001

0.0005

0

1200   1400   1600    1800    2000    2200   2400   2600   2800
Observed Value

90% chance that true mean value                     6
falls between 1800 to 2200
SAMPLE SIZE CALCULATION

   As provided by the sampling technology:

z 2 cv2
n0 
p2                   Nz 2 cv 2
n 
n0 N                 Np 2  z 2 cv 2
n 
n0  N

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COEFFICIENT OF VARIANCE
   The coefficient of variance (CV) is defined as the
ratio of the standard deviation  to the mean µ

cv=/µ
   CV value is in the range (0, 1).
 Low CV (close to 0) indicates low uncertainty of the
sampling target.
 High CV (close to 1) exhibits high uncertainty of the
sampling target.
 CV can be obtained from previous sampling
knowledge or experience.
 When the CV is unknown, a default value of 0.5 is
recommended.
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2. LIGHTING RETROFIT PROJECT
Existing Lighting System      Proposed Technologies
Operation
Quantity
Schedule
Type           Wattage       Type      Wattage
Incandescent         60 W        CFL        20 W       8:00-22:00   10 000
Halogen                                               Based on
75 W        LED        15 W                        3000
downlighters                                           occupancy
Metering
Average daily energy consumption per lamp
target
Expected
90/10 Criterion
accuracy level

Table 1 Details of a lighting retrofit project
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95% Confidence
6% Precision
CV1≤0.15

65% Confidence
28% Precision
0.15≤CV2≤0.5
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Overall accuracy: 90/10 Criterion
COMBINED CONFIDENCE AND PRECISION FOR 90/10

Parameters            Group I     Group II       Overall

Confidence            89.20%        56.50%         90%
Precision              7.77%        20.55%         10%
Table 2 Combined solutions for 90/10 criterion (1)

Parameters           Group I      Group II     Overall
Confidence             90.60%       59.61%         90%
Precision               6.97%       25.68%         10%
Table 3 Combined solutions for 90/10 criterion (2)

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3. ASSUMPTIONS

   In the two sampling groups


X ~ N 1 ,1
2
             
Y ~ N 2 , 2
2

   Sampling distribution

X ~ N  1 ,12 n1              
Y ~ N 2 , 2 n2
2        
   By linear combination of the normal distributions

N1X  N2Y      N  N   2 N2  2 N2 
~ N  1 1 2 2, 1  1  2  2 
N              N    n1 N 2 n2 N 2 
                        
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4. METERING COST MINIMISATION MODEL
   Objective function
f     b1  c1n1  b2  c2n2

      2 2                               2 2       
 b1  c1  ceil 
N1z1 cv1 
 b2  c2  ceil 
N2 z2 cv2 
 N p2  z 2cv2                    N p 2  z 2cv 2 
 1 1 1 1                          2 2 2 2

   Design Variables

  ( z1 , z2 , p1 , p2 )
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   Constraints
   The overall project confidence level is higher than 90%,
which is:

x 
z       1.645
 n
   The overall project precision is within 10% margin of error,
which is:

x 
p             10%

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INITIAL VALUES

Parameters                        Group I    Group II
Unit price of
c1=500     c2=5000
meter (R)
CV value                          cv1=0.15   cv2=0.5

Table 4 The initial values

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5. SOLUTIONS
Parameters           Group I     Group II       Overall

Confidence             90%          90%         94.83%
Precision              10%          10%          9.44%
Meter number             7           67            74
Metering cost (R)      4000       336 000       340 000
Table 5 Metering cost without optimisation

Parameters          Group I      Group II      Overall
Confidence            90.60%       59.61%       90.53%
Precision              6.97%       25.68%        9.74%
Meter number             13           3            16
Metering cost (R)      7000        16 000       23 000
Table 6 Optimal metering cost              16
6. CONCLUSION
 Sampling groups are classified by different CV.
 A metering cost minimisation model is built,
optimal sample sizes for each sampling group
are determined, minimal metering cost for the
entire project is achieved.
 The model is proved to be useful, reliable and
flexible.
 The proposed model can be applied to other
projects, e.g. heat pump, air conditioning.

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Thanks!

Questions?

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