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
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 (Plink) 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 |
|---|---|---|
| Base Equipment size | 100 MVA | 100 MVA |
| Life | 15 years | 45 years |
| Equipment First Cost | $50 M | $10 M |
| Project First Cost | $100 M | $20 M |
| Annual Operation & Maintenance (O&M) Costs | $X | $0.1 X |
| Discount Rate | 10% | 10% |
| Equivalent Present project Cost over 45‐year life | $129.66 M | $20 M |
| Equivalent Present Project Cost over 45‐year life ratio | 6.483 | 1 |
| Equivalent Annual Cost over 45‐year life | $13.147 M | $2.0278 M |
| Equivalent Annual Cost over 45‐year life ratio | 6.483 | 1 |
| Annual Savings of ST over UPFC | $11.1192M | |
| Present Value of Savings of ST over UPFC | $109.66 M |
Figure 1-26 Point‐to‐point transfer of power with local reactive power compensation using a Shunt–Shunt Compensator‐based BTB‐STATCOM.
Assuming that the sending‐end voltage (Vs = Vs ∠ δs), receiving‐end voltage (Vr = Vr ∠ δr), and the line reactance (X) remain unchanged, the compensated active and reactive power flows (Pr and Qr) at the receiving end are