# Chapter 5: Tariff¶

### Example 5.1, Page Number: 91¶

In :
#Variable declaration:
M = 200                          #max demand(kW)
LF = 0.4                         #load factor
c1 = 100                         #tarif(Rs/kW)
c2 = 10                           #tariff(pais/kWh)

#Calculation:
E = M*LF*8760                    #units consumed/year
T = c1*M+E*c2/100                #annual charges(Rs)
OC = T/E                          #overall cost(Rs/kWh)

#Results:
print "Overall cost per kWh is ",round(OC*100,2),"paise"

Overall cost per kWh is  12.85 paise


### Example 5.2, Page Number: 91¶

In :
from __future__ import division

#Variable declaration:
V = 220                         #voltage(V)
I = 20                          #current(A)
E = 8760                        #kWh
c1 = 20                         #tariff part1(paise/unit for 500hrs)
c2 = 10                          #tariff part2 for additional unit(paise/unit)

#Calculation:
#assuming power factor to be unity.
M = V*I/1000                       #max demand(kW)

#part (i):
E1 = M*500                       #kWh
C1 = c1*E1/100                   #Rs
E2 = E-E1                      #kWh
C2 = 10*E2/100                 #kWh
T = C1+C2                       #total annual bill(Rs)
T2 = T/E                       #equivalent flat rate(Rs/kWh)

#Results:
print "(i) Annual bill is Rs",T
print "(ii)Eqv flat rate is ",round(T2*100,1),"paise"

(i) Annual bill is Rs 1096.0
(ii)Eqv flat rate is  12.5 paise


### Example 5.3, Page Number: 92¶

In :
from sympy import *

#Variable declaration:

#for tariff (a):
c1 = 100                   #tariff part1(Rs)
c11 = 15                   #tariff part2(paise/kWh)

#for tariff (b):
c2 = 30                   #paise/kWh

#Calculation:
#Let x be the number of units at which charges
#due to both tariffs become equal.

x = symbols('x')
x1 = solve(c1+c11*x/100 - c2*x/100 , x)

#Results:
print "Tariff(a) is economical if consumption is more than",round(float(x1),2),"units."

Tariff(a) is economical if consumption is more than 666.67 units.


### Example 5.4, Page Number: 92¶

In :
from __future__ import division
from sympy import *

#Variable declaration:
#for 1t tariff:
c11 = 30                           #Rs/annum
c12 = 3                            #paise/unit

#for 2nd tariff:
c21 = 6                            #paise/unit for 1st 400 units
c22 = 5                            #paise/unit for extra units

#Calculation:
#Let x (> 400) be the number of units taken per annum
#for which the annual charges due to both tariffs become equal.

x=symbols('x')
T1 = c11+c12*x/100                  #charges due to 1st tariff(Rs)
T2 = c21*400/100+c22*(x-400)/100                  #charges due to 2nd tariff(Rs)
x1 = solve(T1-T2,x)

#Results:
print "Required no. of units are ",round(x1),"kWh"

Required no. of units are  1300.0 kWh


### Example 5.5, Page Number: 92¶

In :
#Variable declaration:
M = 50                           #max load on the station(MW)
AD = 75                          #aggregate demand by consumers(MW)
E = 18*10**7                      #units/annum

#for annual fixed charges:
c11 = 28*10**5                    #for generation(Rs)
c12 = 32*10**5                   #for transmission & distribution(Rs)
c13 = 90*10**5                   #for fuel(Rs)

#for running charges:
c21 = 0.9*90*10**5               #fuel cost(Rs)
r = 85                           #% of power transmitted

#Calculation:
T1 = c11+c12+c13*0.1            #10% of fuel used for fixed charges(Rs)
C1 = T1/(AD*10**3)                       #Rs/kW

E1 = r*E/100                        #units delivered to consumers
C2 = c21/E1                     #cost per kWh

#Results:
print "Tariff is",C1 ,"Rs/kW of maximum demand plus",round(C2*100,1),"paise per kWh."

Tariff is 92.0 Rs/kW of maximum demand plus 5.3 paise per kWh.


### Example 5.6, Page Number: 93¶

In :
from __future__ import division

#Variable declaration:
M = 75*10**3                           #Max emand(kW)
LF = 0.4                               #load factor

c1 = 60                                #1st part of generating cost(Rs/kW)
c2 = 4                                 #2nd part of generating cost(paise/kW)

CT = 2000000                         #annual capital charges for transmission system(Rs)
CD = 1500000                         #annual capital charges for distribution system(Rs)

dt = 1.2                             #diversity factor of tr. system
dd = 1.25                            #diversity factor of tr. system

nt = 0.9                             #efficiency of tr system
nd = 0.85                            ##efficiency of distribution system

#Calculation:
#(i) Cost at substation:
#(a)Annual fixed charges:

Tafc1 = c1*M+CT                      #total annual fixed cost(Rs)
S1 = M*dt                            #sum of all the max demands(kW)
AC1 = Tafc1/S1                        #Annual cost per kW of max. demand(Rs)

#(b) Running Charges:
Cs1 = c2/nt                        #Cost/kWh at substation(paise)

#(ii) Cost at consumer’s premises:
Tafc2 = Tafc1+CD             #Total annual fixed charges at consumer’s premises(Rs)
S2 = S1*dd                   #sum of of maximum demands of all consumers(kW)
AC2 = Tafc2/S2                      #Annual cost per kW of maximum demand(Rs)
#As the distribution efficiency is 85%, therefore, for each kWh delivered from
#substation, only 0·85 kWh reaches the consumer’s premises
Cs2 = Cs1/nd                        #Cost/kWh at consumer premises(paise)

#Result:
print "(i)At sub-station, the cost is Rs",round(AC1,2),"per annum per kW maximum demand "
print "   plus",round(Cs1,2),"paise per kWh"
print "\n(ii)At consumer’s premises, the cost is",round(AC2,2),"per annum per kW maximum demand"
print "    plus",round(Cs2,2),"paise per kWh."

(i)At sub-station, the cost is Rs 72.22 per annum per kW maximum demand
plus 4.44 paise per kWh

(ii)At consumer’s premises, the cost is 71.11 per annum per kW maximum demand
plus 5.23 paise per kWh.


### Example 5.7, Page Number: 94¶

In :
from __future__ import division
from sympy import *

#Variable declaration:
#     Fixed charges    Running charges       #Station
#          (per kW)     (paise/kWh)
Cf1 =  300;         Cr1 = 25                 #Diesel
Cf2 =  1200;        Cr2 = 6.25               #Steam

#Calculation:
#Suppose energy supplied in one year is 100 units i.e., 100 kWh.

#Diesel Station:
L = symbols('L')                   #load factor
E = 100                            #kWh(say)
P = E/8760                         #avg power, kW
M = P/L                             #max deamnd(kW)
C1 = Cf1*M+E*Cr1/100             #Fixed and running charges for 100 kWh

#Steam station
C2 = Cf2*M+E*Cr2/100            #Fixed and running charges for 100 kWh

L1 = solve(C1-C2,L)

#Result:
print "The load fctor is ",round(L1*100,2),"%"

The load fctor is  54.79 %


### Example 5.8, Page Number: 95¶

In :
#Variable declaration:
M = 100                           #max demand(kW)
LF = 0.6                          #load factor
pf = 0.8                          #power factor
c1 = 75                           #1st part tariff(Rs/kVA)
c2 = 15                           #2nd part tariff(paise/kWh)

#Calculation:
E = M*LF*8760                    #units consumed/year
M1 = M/pf                        #max demand in kVA
AB = M1*c1+E*c2/100              #annual bill(Rs)

#Result:
print "Annual bill is Rs",AB

Annual bill is Rs 88215.0


### Example 5.9, Page Number: 95¶

In :
#Variable declaration:
M = 240                             #max load(kW)
pf = 0.8                             #power factor
E = 50000                            #annual units consumption(kW)
c1 = 50                              #1st part tariff(Rs/KVA)
c2 = 10                              #2nd part tariff(paise/unit)

#Calculation:
M1 = M/pf                          #KVA
AB = M1*c1+E*c2/100                 #annual bill(Rs)
FR = AB/E                          #Rs

#now
pf1 = 1
M2 = M
AB1 = M2*c1+E*c2/100               #Rs
S = AB-AB1                         #annual saving(Rs)

#Result:
print "Flat rate of energy consumption is ",FR*100,"paise"
print "Annual saving is Rs",S

Flat rate of energy consumption is  40.0 paise
Annual saving is Rs 3000.0


### Example 5.10, Page Number: 96¶

In :
from __future__ import division
import math

#Variable declaration:
M = 50                            #max demand(kW)
E = 36000                         #energy consume(kWh)
R = 23400                         #reactive power(KVAR)
c1 = 80                              #1st part tariff(Rs/kW)
c2 = 8                              #2nd part tariff(paise/unit)
c3 = 0.5               #3rd part tariff(p/kWh)for each 1% of pf below 86%

#Calculation:
L = E/(24*30)                   #avg load(kW)
RP = R/(24*30)                  #avg reactive power(kVAR)

theta = math.atan(RP/L)         #power factor angle
pf = math.cos(theta)
PFS = E*c3*(0.86-pf)               #power factor surcharge(Rs)
MB = c1*L+c2*E/100+PFS           #monthly bill(Rs)

#Result:
print "The monthly bill is Rs",round(MB,1)

The monthly bill is Rs 7268.0


### Example 5.11, Page Number: 96¶

In :
#Variable declaration:
c1 = 150                              #1st part tariff(Rs/KVA)
c2 = 8                              #2nd part tariff(paise/unit)
LF = 0.3                            #load factor

#Calculation:
#suppose max demand is 1kVA

#(i)When p.f. is unity:
pf = 1
OC1 = c1*100/(8760*LF)+c2              #operating cost(Rs)

#(ii) When p.f. is 0·7
pf1 = 0.7
OC2 = c1*100/(8760*LF*pf1)+c2         #operating cost(Rs)

#Result:
print "At unity p. f., overall cost is Rs",round(OC1,2)
print "At 0.7 p. f., overall cost is Rs",round(OC2,2)

At unity p. f., overall cost is Rs 13.71
At 0.7 p. f., overall cost is Rs 16.15


### Example 5.12, Page Number: 97¶

In :
from __future__ import division

#variable declaration
L = 200                        #avg load(kW)
pf = 0.8                       #power factor
M = 250                        #max demand(kW)
l = 4                          #losses(%)
r = 12                          #interest & depreciation(%)
C = 50                         #high voltage equipment cost(Rs)
t = 8                          #working hours
n = 300                        #no. of working working

#for system(i)high voltage supply:
c11 = 5                        #1st part tariff(paise/unit)
c12 = 4.50                    #2nd part tariff(per month per kVA)

#for system(ii)low voltage supply:
c21 = 5.5                      #1st part tariff(paise/unit)
c22 = 5                        #2nd part tariff(Rs per month per kVA)

#Calculation:
#(i) High voltage supply:

M1 = M/pf                      #Max. demand in kVA
#As the losses in h.v. equipment are 4%, therefore,
#capacity of h.v. equipment:
Cap = round(M1/(1-l/100),1)            #capacity of h.v. equipment(kVA)
C1 = C*Cap                     #Capital investment on h.v. equipment(Rs)
E1 = L*t*n/(1-l/100)           #units consumed(kWh)
T1 = C1*r/100+Cap*c12*12+c11*E1/100                #Total annual cost(Rs)

#(i) low voltage supply:
M2 = M/pf                      #Max. demand in kVA
E2 = L*t*n                     #units consumed(kWh)
T2 = M2*c22*12+E2*c21/100      #kWh

T = T2 - T1

#Results:
print "Difference in the annual costs of two systems is Rs",T

Difference in the annual costs of two systems is Rs 620.0


### Example 5.13, Page Number: 97¶

In :
from __future__ import division

#Variable declaration:
#(i) Purchasing diesel set:
M1 = 1000                      #kW
C1 = 400                       #Rs/kW
r1 = 10                         #annual interest depreciation(%)
c11 = 75                       #Rs/kW
c12 = 5                         #paise/unit

#(ii) Purchasing from grid supply:
r1 = 10                         #annual interest depreciation(%)
c21 =120                       #Rs/kW
c22 = 3                         #paise/unit
#after 2 years:
M2 = 2500                        #kW
E = 5.5*10**6                   #units reached

#Calculation:
#(i) Purchasing diesel set:
CC = M1*C1                     #Rs
#The present capacity of the station is 2000 kW and the expected
#maximum demand after two years is 2500 kW.
P = 2500-2000                   #extra power to be generated(kW)
T1 = CC*r1/100+P*c11+E*c12/100       #total annual cost(Rs)

#(ii) Purchasing from grid supply:
T2 = P*c21+E*c22/100           #total annual cost(Rs)

#Result:
print "Alternative (ii) is cheaper by Rs",T1-T2,"per annum"

Alternative (ii) is cheaper by Rs 127500.0 per annum


### Example 5.14, Page Number: 98¶

In :
from __future__ import division
from pylab import *
from sympy import *
import math

#Variable declaration:
#H.V supply:
c11 = 70                         #1st part tariff(Rs/kVA)
c12 = 3                          #2nd part tariff(paise/kWh)

#L.V supply:
c21 = 65                         #1st part tariff(Rs/kVA)
c22 = 4                          #2nd part tariff(paise/kWh)

c = 50                           #cost of transformer & switchgear for HV side(Rs/kVA)
r1= 2                            #transformer losses(%)
r2 = 15                 #annual fixed charges(%) of transformer & switchgear
n = 6                            #no of working hours

#Calculation:
(x,y) = symbols('x y')              #say x = Factory load in kW
#y = No. of working days above which H.V.
#supply is cheaper
#for HV side:
r = x*round(1/(1-r1/100),4)                #rating of transformer & switchgear(kVA)
E1 = x*y*round(n*1/(1-r1/100),2)                       #units consumed per annnum
T11 = x*math.floor(1/(1-r1/100)*c11*100)/100+x*round(1/(1-r1/100)*r2*c/100,2)          #total fixed charges(Rs)
T12 = E1*c12/100                 #total running charges(Rs)
T1 = T11+T12                     #total annual charges(Rs)

#for LV side:
E2 = x*y*n                      #units consumed per annnum
T21 = c21*x                     #total fixed charges(Rs)
T22 = c22*E2/100                #total running charges(Rs)
T2 = T21+T22                   #total annual charges(Rs)
y11 = solve(T1-T2,y)

#Result:
print "If the factory is run for more than",math.floor(y11),'days' #the ans. is different from that in book
print "then H. V. supply will be cheaper."                         #due to calculation using improper rounding.

If the factory is run for more than 249.0 days
then H. V. supply will be cheaper.