Better solutions provide primarily better regulation of voltage, thus create less flicker and less penalty. However, in the case of a STATCOM, the voltage is so well regulated that a secondary benefit emerges; the wear‐and‐tear on the electrodes in an electric arc furnace application becomes more uniform than in any other solution; this results in less frequent replacement of the electrodes, which reduces the overall operating cost of the plant. When all the costs, benefits, and penalties are taken into account, there may be a case where the cost of the added features of a particular solution outweighs the benefits. In between, there lies the cost‐effective solution that provides the most features at the least total cost.
Consider the solution cost (C1) is a combination of a fixed cost (FC1) and a variable cost (m1 x), which is given by
where m1 is the slope 1 and assumed to be 0.4, x is the number of features, and FC1 is the fixed cost 1 and assumed to be 0.
Consider the opportunity cost (C2) is a combination of a fixed cost (FC2) and two variable costs (m2 x and 2−wx ), which is given by
where m2 is the slope 2 and assumed to be –0.2, x is the number of features, FC2 is the fixed cost 2 and assumed to be 1.3, and w is the weighting factor and assumed to be 1.
Therefore, the total cost (C) is given by
(1‐10)
where C1 and C2 are given in Equations (1-8) and (1-9), respectively. All the parameters may be assigned suitable values to represent cost versus features of a solution realistically.
1.4.2 Payback Time
Consider a transmission line with an ATC of 500 MW during the peak load of 200 hours per month. A $10 M solution utilizes 50% of the ATC and its payback time is 10 months. What is the cost of power delivery in $/hour/MW?
If an ST or a UPFC is used, what would be the payback time in each case? Assume the costs of a 100 MVA‐rated ST and a 160 MVA‐rated UPFC are $10 M and $80 M, respectively. It is calculated in Chapter 3 that a 30 MVA‐rated ST or UPFC enhances the power flow in a particular line about 60 MW.
ST Data:
UPFC Data:
For a 60 MW of power flow enhancement, both the ST and the UPFC will generate a yearly revenue of
Note that the base case is related to a solution of voltage regulation where the power flow in the line is enhanced by 250 MW. Since the voltage regulation in the line cannot be increased beyond the statutory limitations, the 100% of the ATC cannot be realized using the voltage regulation solution. However, the full ATC can be achieved by using an impedance regulation method, offered by an ST or a UPFC. If the slow response time in 3–5 s is acceptable, an ST is a preferred solution over a UPFC, since the fast response time in <0.010 s from a power electronics inverter is not required in most utility applications and the payback time of the ST is 20% of the cost of a UPFC.
1.4.3 Economic Analysis
A comparison of the sizes and footprints of the world’s first UPFC and an equivalent ST is shown in Figure 1-25. The UPFC applications estimate the project cost to be twice the equipment cost. Conservatively, the assumed project cost of the ST is also estimated to be twice the equipment cost, even though the footprint of the ST is much smaller than that of the UPFC. The Operation & Maintenance (O&M) costs, O&MUPFC, for UPFC are easily an order of magnitude higher than the (O&M) costs, O&MST, of the ST. Since there is very little published data on actual annual operating costs of GTO switches and required maintenance, the O&M costs are ignored for this analysis.
Figure 1-25 World’s first UPFC at the AEP Inez substation (left) versus a comparably rated ST (right).
The life‐cycle cost of a given type of solution (ST or UPFC) is the present value, determined from all cost categories for each design option over a time cycle that is equivalent for all alternatives. Appropriate discount rate for interest is applied. When comparing the ST and the UPFC, one should estimate the life of power electronics inverter‐based UPFC as 15 years and that of the transformer/LTCs‐based ST to be 45 years, although 50 years is a typical life span of power transformers. With alternatives that have unequal lives, it is customary to compare the alternatives over a period of time equal to the Least Common Multiple (LCM) of their lives using the best estimate for future renewal of shorter life alternative life cycle costs. In the case of the ST versus the UPFC, it is estimated that the UPFC costs for years 16–30 and years 31–45 to be same as the costs from years 1–15.
The equivalent future amount (F) at time, t = n, of any present amount (P) at time, t = 0, are related by
(1‐11)
where i is the discount rate or interest