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

Consider the three cases (Case 1: “do nothing;” Case 2: “do something;” and Case 3: “go above‐and‐beyond”) of solutions for voltage regulation.

Figure 1-24 Cost versus features in various solutions (Case 1: “do nothing;” Case 2: “do something;” and Case 3: “go above and beyond.”)

Case 1 represents a “do nothing” approach where the solution cost ( i.e . cost #1) is zero; but the lost opportunity cost ( i.e . cost #2), which is the cost of not providing a solution, such as penalty for causing a voltage flicker may be the highest as shown in Figure 1-24.

Case 2 represents a “do something” approach where the solution cost (cost #1) increases as the number of features in the solution increases. For example, a shunt‐connected reactor or capacitor with a breaker may seem to be the simplest solution where the solution cost (cost #1) is greater than zero; however, the lost opportunity cost (cost #2) that accounts for the (1) penalty for not providing var support and (2) penalty for creating voltage flicker may be less than that in Case 1.

Case 3 represents a “go above‐and‐beyond” approach where the solution cost (cost #1) increases further as the number of features in the solution increases. When various other solutions options, such as SynCon, SVC, STATCOM, and so on with faster response times are considered, the solution cost (cost #1) goes up further; however, the rate of decrease in lost opportunity cost (cost #2) may be less than the rate of increase of the solution cost (cost #1). So, the optimum cost is where the total cost is the minimum. This is the intersection of the regions where Case 2 ends and Case 3 starts.

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 ( C 1) is a combination of a fixed cost ( FC 1) and a variable cost ( m 1 x ), which is given by

(1‐8)

where m 1is the slope 1 and assumed to be 0.4, x is the number of features, and FC 1is the fixed cost 1 and assumed to be 0.

Consider the opportunity cost ( C 2) is a combination of a fixed cost ( FC 2) and two variable costs ( m 2 x and 2 −wx), which is given by

(1‐9)

where m 2is the slope 2 and assumed to be –0.2, x is the number of features, FC 2is 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 C 1and C 2are 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.

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 3that 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.