Power Flow Control Solutions for a Modern Grid Using SMART Power Flow Controllers. Kalyan K. Sen

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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 rate per period and n is the number of compounding periods. The notation, (F/P, i%, n), is interpreted as “Find F, given P, using an interest of i% over n years.” The factor, (1+i) ⁿ , referred to as single payment compound amount, converts P to F.

      The uniform series compound amount converts an annual amount (A) to future amount (F) and is related by

      (1‐12)

      Therefore, the uniform series present worth that converts an annual amount (A) to present amount (P) is related by

(1‐13)

Using Equation (1-13), (P/A, 10%, 45) = 9.8628 and (P/A, 10%, 15) = 7.6061. Therefore, (A/P, 10%, 45) = 1/9.8628 = 0.10139 and (A/P, 10%, 15) = 1/7.6061 = 0.13147.

      Consider the baseline designs of an ST and a UPFC of 100 MVA rating, each of which costs $10 M and $50 M, respectively. Therefore, the first cost of the project for the ST is $20 M and for the UPFC is 100 M.

      The Annual Cost of UPFC for 15 years with a first‐year installed cost of $100 M

       = the Annual Cost of UPFC for 45 years, since a second UPFC will be operational during 16–30 years and a third UPFC will be operational during 31–45 years.

      The Annual Cost of ST for 45 years with a first‐year installed cost of $20 M

      Annual Savings per year for using an ST, instead of a UPFC

      Equivalent Present Value of UPFC for 45‐year period (ignoring O&M costs)

The Economic Analysis of ST versus UPFC over a 45‐year time period is shown in Table 1-1.

1.5 Independent Active and Reactive PFCs

The independent control of active and reactive power flows requires the simultaneous control of the magnitude and phase angle of the transmission line voltage, which can be achieved by a shunt‐compensating voltage, using a Shunt–Shunt Compensator as shown in Figure 1-26. This concept dates back to the time when rectifiers and inverters were introduced to convert AC power from one voltage and frequency level to another with active power (P_link) transfer through a DC link. The most frequently‐used topology is an AC–DC rectifier followed by a DC–AC inverter for variable speed motor drives and, if combined with a local energy storage, an Uninterruptible Power Supply (UPS). To improve the power quality at the rectifier’s AC terminal and to accomplish a bidirectional power flow, two DC–AC inverters are connected back‐to‐back via their DC links as shown in Figure 1-26. This configuration in electric utility applications is known as Back‐To‐Back STATic synchronous COMpensator (BTB‐STATCOM).

Table 1-1 Economic Analysis of ST versus UPFC over a 45‐year time period.

Compensators	UPFC	ST
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