Modeling of static var compensator-high voltage direct current to provide power and improve voltage profile

Received Apr 14, 2021 Revised Jun 15, 2021 Accepted Jun 27, 2021 Transmission lines react to an unexpected increase in power, and if these power changes are not controlled, some lines will become overloaded on certain routes. Flexible alternating current transmission system (FACTS) devices can change the voltage range and phase angle and thus control the power flow. This paper presents suitable mathematical modeling of FACTS devices including static var compensator (SVC) as a parallel compensator and high voltage direct current (HVDC) bonding. A comprehensive modeling of SVC and HVDC bonding in the form of simultaneous applications for power flow is also performed, and the effects of compensations are compared. The comprehensive model obtained was implemented on the 5-bus test system in MATLAB software using the Newton-Raphson method, revealed that generators have to produce more power. Also, the addition of these devices stabilizes the voltage and controls active and reactive power in the network.


INTRODUCTION
The use of flexible alternating current transmission system (FACTS) and high-voltage direct current (HVDC) equipments are considered by designers of electrical transmission networks due to the increased demand for transmission networks, the creation of long transmission line routes, long distance of production centers from consumption centers, accumulation of energy resources in specific places and wide distribution of consumption centers [1]- [8]. This equipment can control both active and reactive power simultaneously, regulate voltage range and reduce power flow on overloaded lines by creating the desired voltage level [9]-

RESEARCH METHOD 2.1. Modeling of FACTS devices
The general model of FACTS devices when used in series on the network as Figure 1 is formulated in the manner [28].
The model of the parallel application of FACTS devices is as Figure 2 [28].
In these equations, S, P, Q and I are the apparent power, active and reactive powers, and line current, respectively. Power control by FACTS devices according to the power as shown in (7) [34].

SVC modeling
In this paper, SVC is modeled as an ideal reactive power source injected into bus A. Static VAR compensator can continuously generate reactive power compensation by operating in inductive and capacitive modes. Static VAR compensator model and structure are specified in Figure 3 [55]. The role of SVC is to keep the voltage in the bus constant, which is done by injecting power into the bus [30]. In modeling, we considered SVC as a parallel variable susceptance as Figure 3 [9], [30], [55].
The power absorbed or injected into the bass is as (9) [21], [24]. The HVDC system is conveniently modeled with two voltage sources along with an equation that states the active power condition. With the introduction of HVDC, the range of transmission power increased (from below 1000 W to 3 to 4 GW) [56]. High-voltage alternative current (HVAC) design and construction are not economical for long distances, but using HVDC improves the cost and transmission of high voltages [57]. In the system HVDC and FACTS devices, due to less insulation and resistance DC less than AC, fewer losses [58], the need for two conductors in the system and as a result of the volume and space of the less to install, reduce of the thickness and cross-section of the cable in a certain power, use of the ground as a return wire, it has lower costs than HVAC, which in Figure 4, we see the difference in costs based on references [59], [60]. Moreover, the HVDC is able to improve stability of inter-connected HVAC by modulating power in response to small/large disturbances [61]. The DC terminals will always be more expensive than AC terminals simply because they have to have the components to transform DC voltage as well as convert the DC to AC. But the DC voltage conversion and circuit breakers have been dropping in price, the break-even price continues to drop. The HVDC model in power flow studies is as Figure 5 [23], [24], [62].

Total AC Cost
For both HVDC components connected by a DC cable [9], [23].

Comprehensive SVC-HVDC modeling for power flow
Due to the limitations of transmission lines and the advantages of using FACTS devices as parallel and series compensators in the network, also, for connecting the power grid and taking into account the advantages of HVDC lines, establishing HVDC connections as a complement to AC systems is essential. In this paper, a comprehensive model for modeling SVC and HVDC devices was used as Figure 6. Then, the Newton-Raphson power flow on the final model was applied. According to the Figure 6, an SVC is used as a parallel compensator and an HVDC as a link. where: = − 2 (33) where Va, Vb, V1, V2, ϴa, ϴb, δ1, and δ2 are the voltage and angles of the bus a, b, and HVDC link, respectively. B1, B2 and BSVC are susceptance for the rectifier, inverter and SVC, respectively. G1 and G2 are the side conductance of the rectifier and inverter, respectively. P1, P2, Pa, Pb are the active powers of rectifier and inverter, buses a, and b, respectively. Finally, Qa, Qb, QSVC, Q1, and Q2 are the reactive powers for a, and b buses, the SVC reactive power and the rectifier and inverter sides of the model, respectively. In (29) to (37) we see that the hybrid model is effective in active and reactive powers related to buses and lines. For example, in (30) B3 is used which is a combination of SVC and HVDC. These show a comprehensive hybrid model that can be generalized to larger networks, and this model can also be used in load flow and stability analysis, etc. To solve the Newton-Raphson power flow (38)- (44). The Newton-Raphson method is scientifically efficient due to quadratic convergence and high convergence velocity, which is obtained by extending the Taylor series [63]- [67].
The matrix [J] is the Jacobin matrix obtained by the partial derivatives of each function as shown in (29)-(37) relative to the variables: Where in the above relations , 1 , 2 , 3 , 4 are the Jacobin matrix and its components and f(x) are the function of state variables and x are state variables in load flow equations and we have: Since the active power is set at the end of the rectifier in the HVDC line and the voltage range at bus b is kept constant, the equations of active and reactive power of the inverter are additional [9].

RESULTS AND DISCUSSION
We applied the model obtained in the previous section on a 5-bus test system according to Figure 7, where all the information about the buses and lines and the whole network was extracted from reference [38]. The information required for the test system is provided in Appendix. First, power flow was without adding FACTS devices, and then in this network, we added the SVC and HVDC devices individually to the network and observed the results. Finally, based on the SVC-HVDC model obtained in the previous section of this paper, all the both devices were added to the system and the results were recorded. In this paper, the focus was on load flow in buses on which the devices have a direct effect, such as buses 3 and 4 (Lake and Main), although they affect the whole network.  Figure 8, which shows voltage changes in the presence of various FACTS devices, the voltage state for stabilization at 1p.u. is presented. Using SVC, was better than the mode without FACTS devices and the mode of using HVDC, and in buses 3 and 4, it was 1p.u. closer. But the best state and voltage stabilization occurred in the case that the SVC-HVDC combination was used. Also, compared to the different references in Figure 9, the SVC-HVDC model hasd the best state of recovery and voltage stabilization. The best state for voltage improvement was the mode of using SVC in reference [9]. In all diagrams and figures, PG1, PG2, P3-4 and P4-3 are the active powers produced by the North and South generators, and the active powers are between buses 3 and 4, respectively. In addition, QG1, QG2, Q3-4 and Q4-3 are the reactive powers generated by the North and South generators, and the reactive powers are between buses 3 and 4, respectively. By applying Newton-Raphson load flow in the final model and different models in Figure 10 and Figure 11 (by keeping the output of the South generator constant at 40 MW), an increase in active and reactive power between the buses used by the devices is noted, which is the best way to use SVC-HVDC. It is the most efficient model in compensating active and reactive power. In the final hybrid model, the generators are forced to produce more power, which is more costly for the system and is among the disadvantages of the system. By comparing load flow in the models used in this paper and the different references in Figure 12 and Figure 13, we see a further spike in active and reactive power, which indicates the efficiency of the proposed SVC-HVDC hybrid model in the network. Comparing this model with the references in Figure 12 and Figure 13, it can be concluded that good compensation is obtained for the system. Besides, an increase in active and reactive power between the buses and lines, and at the same time, voltage stabilization in the Main and Lake Buses in this SVC-HVDC model were obtained. However, this paper examined a comprehensive model for the simultaneous effects of all the two types of devices for power flow and controlled the active and reactive power simultaneously, which had not been done in any of the previous studies [9], [23]- [25], [29]- [31], [33], [34], [40], [52], [54], [57], [68]- [70].

CONCLUSION
In this paper, models for the use of different flexible alternating current transmission system (FACTS) devices were presented, and finally a hybrid model including static var compensator (SVC) as a parallel compensator and high voltage direct current (HVDC) link was modeled for simultaneous use in a 5-bus network and Newton-Raphson load flow. According to the results, the installation of several types of FACTS devices simultaneously with SVC-HVDC, by increasing the flexibility of the power network to achieve better results, improved the voltage profile and compensation to increase the active and reactive power in the network. In this model, we observed an increase in the power generation of generators, which increases the production cost in the network and is one of the disadvantages of the model. The results showed that the proposed method had good performance. This study obtained a suitable hybrid model for load flow studies that can be generalized to larger networks and this model can be used in stability discussion studies and other power system studies. Future studies are needed to examine the optimal load flow of this model and optimal placement of these devices in the network. The information required for the test system in Figure 6 and the range of selected parameters for the equipment is as: Where BSVC0, BLO, BHi, V0 and QSVC0 are the initial values and upper and lower limits of the susceptance, the initial voltage and range of change of reactive power values in SVC, respectively. Also, V1', V2', VLO and VHi are the initial voltage values on the rectifier and inverter side and their change amplitude, respectively. PHVDC0 the range of change of active power values is HVDC. The rest of the information related to buses, lines and generator information is available in reference [38].