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On the other side, the IEEE Working Group on FACTS defines the SVC as a generator that is capable of generating or absorbing reactive power variable reactive current capability when connected in parallel with a load—hence the desired parameters such as voltage can be controlled. It consists of a thyristor-controlled reactor in an arm with a capacitor in the opposite arm.

Varying the phase angle, a continuous range of reactive power variation can be achieved. The main drawbacks of this setting are the production of low-order harmonics and high losses while working in the inductive region.

AT-UCR , 99, SVC model and its corresponding V—I characteristic. Figure 4.

Artificial Intelligence-Based Techniques : Artificial intelligence AI is a human-made system that possess some of the important characteristics of life. Optimization-Based Methods : Nonlinear programming, Integer and Mixed-integer programming, and Dynamic programming techniques all belong to this category. Sensitivity-Based Methods : Minimum singular value decomposition and eigenvalue analysis fall into this category.

Q—V modal analysis is used to check the stability of the system, and the weakest buses are identified using the eigenvalues and the participation factors. For voltage below 46 kV, Range A corresponds to the ideal or optimal voltage limits, whereas Range B is acceptable but not desirable. For voltage above 46 kV, the two ranges, namely normal operating and emergency condition, are defined. After compensation, all voltage limits in the network are rechecked.

If the compensated voltage violates its permissible values, the above processes are repeated again. The IEEE bus test system is used for case studies. The numerical data were taken primarily from Ref. Power Systems Test Case Archive. Power flow test cases: 14 bus. The test network with its bus labels is shown in Figure 6. Figure 6. The system under study. IEEE 14 bus system.

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This enables solving large systems. On the other side, this method may present some computing and time challenges in a system comprising thousands of buses. It becomes financially impractical to place a FACTS compensator at each bus to maintain voltage magnitude at its desired level. Generally, to overcome this challenge, a network is divided into different regions called pilot nodes. These pilot nodes represent the voltage in these regions. Hence, the presented flowchart can be applied to maintain voltage within tight tolerances at these nodes. First, simulation results are presented without reactive power compensation, and the results are examined in detail.

The first study performed is solving the power flow using the full Newton-Raphson algorithm, with reactive power limits of the system taken into consideration. The results of the uncompensated system are given in Table 2. Results of the uncompensated load flow. Initially, Bus 2 was set as a PV bus with voltage being 1. However, after the load flow, the voltage is 1. Hence, it can be concluded that there is a lack of reactive power support at the generator of Bus 2. The negative sign of reactive power injection at Bus 8 reflects the ability of the DFIG to absorb reactive power. Additionally, the voltage level is below 0.

Bus 14 has the lowest voltage followed by bus 10 and bus This occurs as they are far from generation and suffer from the voltage drop across transformers and transmission lines. The second study performed was Q—V modal analysis. The results are given in Table 3. All the eigenvalues of the reduced Jacobian matrix are positive with no imaginary part indicating that the system is stable. Thus the bus having the highest participation factor associated with this eigenvalue is the weakest bus.

From Table 3 , it can be seen that the smallest eigenvalue is number 5 0. Hence, Bus 14 is the weakest bus. Modal analysis results. The third study performed was the V—P curve analysis using the continuation power flow. It is used to obtain the voltage profile at each bus with the generation limits taken into consideration. The results for the PV buses are shown in Figure 7 , and the results for the buses associated with the lowest eigenvalues are shown in Figure 8.

Lec-36 Voltage Stability-Part-2

It can be observed that Bus 14 has the lowest voltage at the SNB point and ultimately collapsed to zero. At Bus 2, the voltage profile is not constant as the generator is already operating at its upper reactive limit.

V-P curves for the PV buses. Moreover, Figure 9 shows the different voltage magnitudes at the saddle node bifurcation point. This represents the lowest voltage at each bus before voltage collapse. Once more, it can be seen that Bus 14 has the lowest voltage magnitude. Voltage magnitudes profile at the bifurcation point. Figure 9. The reactive power required to bring the voltage within limits is calculated using the flowchart shown in Figure 5.

Two iterations are required to bring the voltage within limits. The first iteration places a compensator at Bus The system is rechecked for voltage stability. Consequently, the second iteration places a compensator at Bus Rechecking the system for voltage stability, the target voltage has been achieved with the two compensators. The voltage magnitudes at each iteration are given in Table 4. Consequently, the power flow results after compensation is shown in Table 5. Voltage magnitude at each iteration. The V—P curve analysis is used to check the new loadability limit of the system using the CPF, without any voltage limits.

The new critical loading parameter is 2.

Jasmon, The developed EP engine could be beneficial for solving other optimization problems. Published online: 15 Sep It can be concluded that EP technique is a better optimization technique as compared to AIS in searching the optimum value of reactive power loading at a single or multi-load. Table 3.

This represents an increase of Hence, providing reactive power compensation will increase the loadability of the system. This is particularly important where the system operator wants to defer investment in assets but increase capacity of transmission lines.

The load flow results give basic data required to specify the normal operating condition of the compensators. However, during the planning, the level to which the system will be stretched must be taken into consideration. The result is depicted in Table 6. It can be observed that during normal operation, the system can be loaded up to 1. Similarly, Bus 11 is the first bus to attend the voltage limits in case of the contingency operating condition. V-P curves for compensation for buses 4 to 7. Table 6. Buses attaining their voltage limits with variations of load parameters.

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When this loadability limit is reached, a load flow is performed again to obtain the reactive power limit of the compensators. Their specifications are given in Table 7. Additionally, for the compensated system, the real power loss decreases by The huge decrease of the reactive power loss is that it is being supplied locally at Bus 14 and Bus Hence, it does not have to be transmitted via power lines and thus no losses.

Compensators specifications. Other parameters that need to be specified are the desired switching technology and permissible active power losses.

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The response time and type of response maximum overshoot and settling time determines the time required by the compensators to bring voltage to its pre-disturbed condition, or to a new stable operating point. These can be obtained by performing a dynamic simulation. Loss of line is simulated at a time t equals 20 seconds.

Their performance is analyzed, and their limits have not been exceeded. Hence, it can be concluded that both compensators have the same voltage support capability when they are operating within their limits. This corresponds to the linear region of the V—I characteristic of theses devices. The voltage profile at bus 03 is analyzed again, as shown in Figure Figure When the SVC operates at its low reactive power limit, it behaves as a fixed shunt reactance, and the amount of reactive power it can provide or sink depends on the voltage of its bus.

Theoretically, the reactive power output at the limits is proportional to the square of this voltage.

It can provide a constant reactive current at its limit. A comparison of the indices regarding to sensitivities, and calculation time has been done. The results show that the performances of these indices are corresponding to one another regarding to voltage stability of the power system. All indices were found falling between 0 and 1 in their intended range. When the system is stable, these indices are closed 0.

When the system is in critical condition with regard to voltage instability, the indices moved towards closed to 1, but at different levels of convergence to 1. Hsu, C.

Chung, K. Neural Comput. Al-Shammari, E.