Unformatted text preview: ed above ii) The current growth rate iii) The highest growth rate for the highest scenario specified above The modelling also provide options for “one step” or “more than one step”
jumps between growth rates. If for example three growth rates are specified
(low, medium and high) and the current load growth is at the low growth rate.
Then if the “one step” option has been selected, the next growth rate will be
the medium growth rate rather than the high growth rate. 48 The saturation level (maximum load possible) and saturation impact level
(SLB) loads are entered next. The load growth starts to slow down at the
saturation impact level, the saturation impact level is specified as: 0 < SLB <
0.95 of saturation. The transition matrix is then determined. If three scenarios are specified then
the transition matrix is normally determined as a 3 X 3 matrix. However the
transition matrix can be determined as a 5 X 5 matrix (maximum), especially
for wide growth ranges.
The user manual does not describe the transition probabilities, only the
diagonal probabilities.
Again, not many details are given, except for the following formula. Average time in trend = 1 1 − P Staying in same trend (3.2.6) There are cases, when the diagonal probabilities are not exactly determined
by equation (3.2.6).
Markov processes are used to calculate the future loads. A Markov process is
a probabilistic process for which the future (next step) depends only on the
present state; it has no memory of how the present state was reached. Each
state can be seen as a percentage growth and to move to the next year is to
move to the next step. The probabilities to move between steps are summarised in a matrix called the transition matrix (P). p11
P = p 21 p12
p 22 p13
p 23 p 31 p 32 p33 The sum of the transition matrix rows must always be one. 49 State 1 State 2
State 3 Figure 3.2.2  Markov process in terms of states The probability p 11 is the probability to stay in state 1 with the next movement,
similar is probability p 32 to move from state 3 to state 2.
The program provides satisfactorily results, but there are a number of
shortcomings:
1) The program cannot handle negative growths.
2) The program cannot handle large step load changes.
3) The program assumes the growth rates and the growth rate
holding times are constant over time. This is seldom true,
therefore the growth rates and holding times are specified as
average expected results over the forecasting horizon. Beasley explains a Markov process as follows. A manufacturer (K) has 25 %
of the market. Data from the previous year indicates that 88 % of K’s customers remained loyal that year, but 12 % switched to the competition. In 50 addition, 85 % of the competition’s customers remained loyal to the
competition but 15 % of the competition’s customers switched to K. What is
the expected market for K next year? 0.88
K 0.15 0.12 Competition
0.85
Figure 3.2.3  Markov process for K’s Market We know K has 25 % of the market. Hence the row matrix representing the
initial state of the system is given by: State
1 2 s 1 = [0.25 0.75] then s 2 = s 1 P
=[0.25, 0.75] 0.88 0.12 0.15 =[0.3325, 0.6675] 0.85 The expected market share for K is thus 33.25 %. [31 – 38] 51 Until now the term “transmission substation” has been used to define the load
that flows between transmission and distribution. In almost 90 of the cases
percent (see Chapter 5) the balanced loads are equal to the total load that
flows throw the transformers, for example TX1 (Figure 1.2.2). There are three exceptions to the rule. The first exception is the backbone
substation B1 (Figure 1.2.2). The three substation loads (TX1, TX2 and TX3)
are summated and electrical losses are added to determine the load for
substation B1.
For the second exception, see Figure 1.2.3. The balanced load is the sum of
the 220/132 kV and 220/66 kV loads. Depending on the transmission and
distribution network topology, certain arithmetic rules are defined to determine
the loads for the 400/220 kV, 220/132 kV and 220/66 kV transformations. The last exception is quite complex. Multiple regression has been considered
to determine the loads for the backbone substations B1, B2 and B3.
However, because of multicollinearity problems (between the independent
variables used to model the TX loads and net output for the power stations),
regression is no longer applied. Different network operations and generation
patterns have in some cases a significant impact on the backbone substation
loads. These backbone substation loads are determined by the weighted sum
of certain TX loads and power station net power outputs (see Chapter 5).
Very important: all these results are verified with power flow results. 3.2.8 Distribution Substations The spatial lo ad forecast starts at the supply point to customers. Enduse
load profiles are used to determine the expected loads on feeders and
substations. In addition, the forecast identifies areas with growth or areas with
no growth. The end ...
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This document was uploaded on 03/04/2014.
 Spring '14

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