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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



1
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




                                              2
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


                                                   3
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”.




                                                     5
                                        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


                                                     7
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.
                                                              8
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
                                                                                9
95% Confidence
6% Precision
                     CV1≤0.15




                                        65% Confidence
                                        28% Precision
                         0.15≤CV2≤0.5
                                                     10
        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)

                                                            11
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 
                                           
                                                        12
 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 )
                                                                    13
   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%
                       
                                                                       14
INITIAL VALUES


 Parameters                        Group I    Group II
 Overhead cost (R)                 b1=500     b2=1000
 Unit price of
                                   c1=500     c2=5000
 meter (R)
 CV value                          cv1=0.15   cv2=0.5

                 Table 4 The initial values




                                                         15
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.


                                                    17
Thanks!


      Questions?


                   18

				
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