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After the digital revolution, the power system security becomes an important issue and it urges the power producers to maintain a well secured system in order to supply a quality power to the end users. This paper presents an integrated Corrective Security Constrained Optimal Power Flow (CSCOPF) with Flexible Transmission Line Impedance (FTLI) to enhance the power system security. The corrective approach of SCOPF is chosen, because it allows the corrective equipment to bring back the system to a stable operating point and hence, it offers high flexibility and better economics. The concept of FTLI arises from the ability of FACTS devices such as Thyristor Controlled Series Capacitor (TCSC), which can vary the line reactance to a certain extent. An enhanced security can be achieved by incorporating FTLI into the CSCOPF problem, since the power flow in a system is highly dependent on the line reactance. FTLI based CSCOPF can reduce the amount of rescheduling of generators, but it will result in an increased number of variables and thus, the complexity to the optimization process is increased. This highly complex problem is solved by using nonlinear programming. The AC based OPF model is preferred, since the corrective security actions require highly accurate solutions. IEEE 30 bus system is used to test the proposed scheme and the results are compared with the traditional CSCOPF. It can be seen that the proposed idea provides a notable improvement in the reduction of cost incurred for restoring the system security.

In the contemporary power scenario, the power system security has obtained much attraction due to the rapid increase in the power demand. Due to the increase in the consumption of electrical energy over the years, the generation has to be increased accordingly, in order to obtain a balanced system. But, the existing transmission system is designed to carry a certain amount of power only. However, the violation in the prescribed limit will result in a damage of transmission equipment and imposes a threat to overall security of the system. Either new line(s) should be added to the system or the existing transmission system must be used more efficiently to meet the increase in load demand and to preserve the security. The addition of new line is often impractical, because it is a very time-consuming task and sometimes becomes impossible with environmental limitations. Therefore, the efficient use of existing lines provides a better solution and hence, this work involves such an approach to enhance the system security. The problem of security is often incorporated with optimal power flow to achieve an added economical advantage and termed as Security Constrained Optimal Power Flow (SCOPF). There are two major types of SCOPF namely, Preventive SCOPF (PSCOPF) and Corrective SCOPF (CSCOPF). PSCOPF tries to obtain a normal state power flow solution, which is also feasible for all contingency conditions being considered with minimum cost [

CSCOPF allows varying the control variables by adjusting the control equipment after a contingency occurrence [

However, the procedures that are discussed so far have considered the transmission elements as fixed resources. But, by installing more flexible elements such as, FACTS devices, the operation becomes more flexible and the transmission line impedances can be changed by most of the FACTS devices. But, the variation in the characteristics of transmission lines may affect the operation of protective devices [

These works validate the cost reduction alone, when incorporating flexible Line impedance in OPF, but don’t consider this flexibility as a viable solution to other power system problems such as, security, congestion management etc. Hence, this work proposes the use of FTLI to enhance the security of power system by a corrective approach. First, the problem is formulated into an AC-OPF for real time feasibility then, the impedance of transmission lines are taken as a variable and incorporated into that model. The nonlinear programming technique is used to solve this proposed problem by using MATPOWER [

The remaining structure of this manuscript is given as follows. Section 2 describes about FTLI. Section 3 presents the formulation of the CSCOPF. Section 4 provides the solution methodology to solve the CSCOPF problem. Section 5 presents the results obtained from the traditional and proposed CSCOPF method and comparisons, discussions related to it. Section 6 concludes the overall work.

Traditionally, the transmission system is treated as a static component of a power system, except during the maintenance or outage conditions. However, the operation of power system can be made more flexible by installing more flexible elements, such as FACTS. It is known that the transmission line impedances can be changed by FACTS devices, such as TCSC to increase the transfer capacity. In near future, it is expected that sophisticated components can be developed and employed in power systems with advancements by further research in the area of materials and sensors, adaptable and economically viable devices such as piezo-resistor and thermistor impedance. These advanced components will allow the system operator to vary the transmission line impedance smoothly and make the power system with flexible impedance transmission lines. In this paper an optimal power flow model with the consideration of such flexible transmission line impedances (FTLIs) is proposed to achieve a better operational economics and enhanced security. The incorporation of FTLI means the inclusion of all line reactances as control variables in the optimization process. So, in the case of the IEEE 30 bus system, which has 41 branches it involves the addition of another 41 control variables and they are varied optimally along with other control variables (i.e., real power output of generators). The mathematical model of the proposed FTLI based CSCOPF is discussed in the subsequent section. This work is based on a futuristic view of the transmission system that can dynamically change its nature with respect to the changes in system state, rather than being static. This could impart commendable controllability and thus, provides a higher security to the system.

Here, the traditional C-SCOPF refers as CSCOPF without considering FTLI (i.e. without having line reactance as a variable). Traditional CSCOPF involves in the adjustment of control variables, such as real power output of generator, transformer tap settings, etc. The major control action that is widely followed is the rescheduling of generator output. The mathematical formulation of a CSCOPF without FTLI is done and they are presented below. The objective function is the minimization of a function and it is given in Equation (1). The various constraints that are involved in this problem formulation are presented in Equations (2)-(7).

Objective function:

Equality constraints:

Inequality constraints:

where,

where,

Depending upon the application, the objective function can be taken as cost or loss function. In this work, the minimization of the cost incurred in preserving security is taken as the objective. The equality constraints constitute the real and reactive power balance equations of the system as given in Equation (5).

where,

Whereas, the inequality constraints constitute the MVA flow limits (security constraints) on the branches, upper and lower bounds on the control variables and it is given in Equation (6).

where,

The proposed CSCOPF involves adjustment of control variables, such as real power output of generator, transformer tap settings, along with the line reactance. The adjustment of line reactance just after an outage, which minimizes the rescheduling of generators, is the major control action followed here. The formulation of the proposed CSCOPF is similar to the formulation of the traditional CSCOPF as discussed above, except considering the line reactance as a variable and it is shown below.

where,

All the Equations (1)-(3) and Equations (5)-(6) are applied to the proposed CSCOPF formulation, but the new z is given by the Equation (7).

Today, most of the market based dispatch procedures are executed using a DC model. Therefore, DC model based variation of line reactance (FACTS settings) seems to be compatible with the current practices. However, AC-based modeling of FACTS adjustment is essential for the real-time contingency analysis, where FTLI can be used to perform corrective actions. So, the AC model is chosen for this proposed CSCOPF problem and is solved by using interior point method. First, the state and cost of the system are derived for the operation of the system under normal state. The performance index for each line is calculated by using the formula as given in Equation (8). Then, an outage is assumed on the selected line and the new state of the system and its cost are derived after optimal rescheduling. The deviation in cost due to rescheduling is also recorded for the comparison with the results of proposed method. Normally, a contingency analysis is carried out on the system in order to perform a SCOPF. The performance indices (PI) of all lines are obtained by assuming the outage of various lines and then, performing a power flow. The lines with higher performance index, whose outage would cause severe impacts on the system, are considered as various cases in this analysis. The formula for the calculation of performance index of jth line is given by,

where,

The interior point method is a gradient based iterative procedure and that is used to solve linear and nonlinear convex optimization problems. The CSCOPF problem consists of quadratic objective function (i.e. the cost function), nonlinear equality and inequality constraints. Therefore, it lies in the class of nonlinear programming (NLP) problem and thus, the interior point method is used. In this work, the formulated problem is solved by using the “fmincon” function, which is used to solve linear and nonlinear optimization problems in MATLAB.

The simulation tests are performed in IEEE 30 bus system [

The PI of all the 41 lines are calculated as described above with the help of power flow and it is as given in

The top n branches in the sorted list are chosen for further analysis. A plot of performance index versus branch number is shown in

CASE 1A: In this case, the outage line is line number 1, which connects the buses 1 and 2. The generation and the associated cost corresponding to before and after an outage are given in

It can be noted that rescheduling introduces an increase in the operating cost of 575.34 $/hr. The system is then solved by considering FTLI i.e. the line reactance is considered as a variable. The results before and after outage for this consideration are tabulated. As the line reactance is being taken as a variable, it is bounded in a

Sl. No. | Outage of line | PI | Sl. No. | Outage of line | PI |
---|---|---|---|---|---|

1 | 1 - 2 | 22.5578 | 22 | 12 - 14 | 10.4877 |

2 | 2 - 5 | 17.5271 | 23 | 10 - 17 | 10.4576 |

3 | 4 - 12 | 17.3503 | 24 | 25 - 27 | 10.3775 |

4 | 28 - 27 | 15.4378 | 25 | 10 - 22 | 10.3688 |

5 | 1 - 3 | 14.1156 | 26 | 22 - 24 | 10.3627 |

6 | 3 - 4 | 13.9107 | 27 | 15 - 18 | 10.2438 |

7 | 4 - 6 | 12.9821 | 28 | 9 - 11 | 10.2425 |

8 | 6 - 8 | 12.1546 | 29 | 16 - 17 | 10.1778 |

9 | 9 - 10 | 11.9785 | 30 | 29 - 30 | 10.1759 |

10 | 6 - 9 | 11.9019 | 31 | 12 - 13 | 10.1719 |

11 | 10 - 20 | 11.7978 | 32 | 2 - 4 | 10.1667 |

12 | 2 - 6 | 11.5760 | 33 | 23 - 24 | 10.1439 |

13 | 6 - 28 | 11.3785 | 34 | 8 - 28 | 10.1304 |

14 | 12 - 15 | 11.2342 | 35 | 21 - 22 | 10.1153 |

15 | 19 - 20 | 11.1419 | 36 | 14 - 15 | 10.0778 |

16 | 27 - 30 | 11.0040 | 37 | 18 - 19 | 10.0185 |

17 | 10 - 21 | 10.8074 | 38 | 24 - 25 | 10.0050 |

18 | 15 - 23 | 10.5931 | 39 | 5 - 7 | 9.7258 |

19 | 6 - 10 | 10.5742 | 40 | 6 - 7 | 9.5125 |

20 | 12 - 16 | 10.5440 | 41 | 25 - 26 | 9.4631 |

21 | 27 - 29 | 10.5016 | - | - | - |

Gen. Bus No. | Before the outage | After the outage | Cost deviation ($/hr) | ||
---|---|---|---|---|---|

Generation (MW) | Cost ($/hr) | Generation (MW) | Cost ($/hr) | ||

1 | 199.28 | 8915.04 | 129.88 | 9490.38 | 575.34 |

2 | 37.22 | 40.75 | |||

5 | 35.99 | 66.21 | |||

8 | 15.09 | 29.69 | |||

11 | 6.33 | 24.03 | |||

13 | 0 | 3.98 |

certain range given by [1 − α, 1 + α], where α is taken as 20%.

CASE 1B: In this case, the line 1, which connects the buses 1 and 2, is considered as out of service and the system is rescheduled along with FTLI (i.e. considering line reactance as a variable). The results are tabulated in

It can be seen from

The control action against this line outage is made easy by considering the line reactance as a flexible control variable. Hence, the action of real power allocation to all the participating generators is easily accomplished with the reduced level of total generation cost. This reduction in cost deviation shows the supremacy of this proposed method over the other conventional methods.

The change in reactance of all lines after an outage in line 1 - 2 is tabulated in

It is proved that there is a notable improvement in cost due to the use of FTLI as a corrective variable. Particularly, the post contingency cost deviation is negative in CASE 3B and it indicates a reduction in cost even after an outage. It is also worth to mention that the percentage improvement is more than 100 in such case, which indicates the effectiveness of flexibility offered by the transmission system.

In this work, the incorporation of FTLI into CSCOPF was proposed, in which the line reactance is taken as a control variable and it is varied optimally with respect to contingencies. The proposed idea is tested in IEEE 30 bus system and the results have proved that improvement in cost and reduction in rescheduling are phenomenal. The idea, which is used to view the transmission system as a dynamic one rather than a static one, helps the transmission system to contribute in ensuring security, stability and reliability of the overall system. It is suggested that, the proper incorporation of FTLI in power system optimization is certainly a better solution for meeting the increase in power demand without the extension of transmission system. Next, the work is to be extended by deriving the sensitivities (gradient) of the system equations with respect to line reactance, so that a correlation can be established between the operation of the power system and the line reactance. These sensitivities are to be used for application in the process of optimizing the system performance.

The authors of this manuscript express their sincere thanks to the Management of Kamaraj College of Engineer-

Gen. Bus No. | Before the outage | After the outage | Cost deviation ($/hr) | ||
---|---|---|---|---|---|

Generation (MW) | Cost ($/hr) | Generation (MW) | Cost ($/hr) | ||

1 | 199.28 | 8915.04 | 130.00 | 9448.23 | 533.20 |

2 | 37.22 | 40.82 | |||

5 | 35.99 | 64.33 | |||

8 | 15.09 | 29.29 | |||

11 | 6.33 | 27.12 | |||

13 | 0 | 1.95 |

Branch No. | Reactance before outage (p.u.) | Reactance after outage (p.u.) | Change in reactance in % | Branch No. | Reactance before outage (p.u.) | Reactance after outage (p.u.) | Change in reactance in % |
---|---|---|---|---|---|---|---|

1 | 0.0575 | 0.0575 | 0.00 | 22 | 0.2185 | 0.1819 | −16.76 |

2 | 0.1652 | 0.1610 | −2.55 | 23 | 0.1292 | 0.1550 | 20.00 |

3 | 0.1737 | 0.2084 | 20.00 | 24 | 0.0680 | 0.0613 | −9.90 |

4 | 0.0379 | 0.0455 | 20.00 | 25 | 0.2090 | 0.1672 | −20.00 |

5 | 0.1983 | 0.1586 | −20.00 | 26 | 0.0845 | 0.1014 | 20.00 |

6 | 0.1763 | 0.2116 | 20.00 | 27 | 0.0749 | 0.0599 | −20.00 |

7 | 0.0414 | 0.0478 | 15.58 | 28 | 0.1499 | 0.1215 | −18.96 |

8 | 0.1160 | 0.1392 | 20.00 | 29 | 0.0236 | 0.0283 | 20.00 |

9 | 0.0820 | 0.0830 | 1.22 | 30 | 0.2020 | 0.1616 | −20.00 |

10 | 0.0420 | 0.0350 | −16.74 | 31 | 0.1790 | 0.2015 | 12.59 |

11 | 0.2080 | 0.2496 | 20.00 | 32 | 0.2700 | 0.3240 | 20.00 |

12 | 0.5560 | 0.6672 | 20.00 | 33 | 0.3292 | 0.3950 | 20.00 |

13 | 0.2080 | 0.1664 | −20.00 | 34 | 0.3800 | 0.3040 | −20.00 |

14 | 0.1100 | 0.1320 | 20.00 | 35 | 0.2087 | 0.2504 | 20.00 |

15 | 0.2560 | 0.2048 | −20.00 | 36 | 0.3960 | 0.3168 | −20.00 |

16 | 0.1400 | 0.1120 | −20.00 | 37 | 0.4153 | 0.3322 | −20.00 |

17 | 0.2559 | 0.2047 | −20.00 | 38 | 0.6027 | 0.4822 | −20.00 |

18 | 0.1304 | 0.1043 | −20.00 | 39 | 0.4533 | 0.3626 | −20.00 |

19 | 0.1987 | 0.1590 | −20.00 | 40 | 0.2000 | 0.1790 | −10.48 |

20 | 0.1997 | 0.2396 | 20.00 | 41 | 0.0599 | 0.0479 | −20.00 |

21 | 0.1923 | 0.1538 | −20.00 | - | - | - | - |

Case | Line that is put out of service | Cost deviation without FTLI (A) $/hr | Cost deviation with FTLI (B) $/hr | Improvement in cost due to FTLI $/hr | Percentage improvement in cost % |
---|---|---|---|---|---|

1 | 1 | 575.34 | 533.20 | 42.14 | 7.3 |

2 | 5 | 169.23 | 111.62 | 57.14 | 34 |

3 | 15 | 37.26 | −5.25 | 42.50 | 114 |

ing & Technology and the authorities of Anna University Regional Campus Madurai for their support to complete this research.

Karuppasamy Muthulakshmi,R.M. Sasiraja,Selvarajan Mukesh Muthu, (2016) The Effective Enhancement of Power System Security by Flexible Transmission Line Impedance with Minimal Rescheduling of Generators. Circuits and Systems,07,381-389. doi: 10.4236/cs.2016.74033