The Impact of Hybrid Power Generations on a Power System's Voltage Stability

The issue of voltage stability has become a primary topic of concern in the electric utility industry, as electric power utilities today face many difficulties due to the increasing complexity of their operations and organizational structures [1]. Voltage instability has also attracted attention recently. Competitive bidding and poor generation scheduling cause voltage instability in an unregulated power market. Thus, many electrical utilities and academics have focused on static voltage stability system studies to reduce or eliminate voltage instability. Static voltage stability with continuation power flow (CPF) studies and optimization methods are used to determine the system voltage stability margin or load margin (LM) [2]. Facilities and academics create programs using these methods of study. Load flow calculations, including forecast and corrector phases, are solved using CPF. Based on an objective function and constraint, the optimization solves equations for necessary conditions, where breakdown voltages and excessively high or low voltages affect several sizeable interconnected power systems [3].

Transmission line load, insufficient local reactive supply, and long-distance power charging cause these voltage problems. Voltage breakdown is a significant voltage instability caused by a power system voltage drop under load [4]. This causes the voltage on the power system buses to decrease slowly and rapidly during a voltage breakdown. If they are located in low-voltage locations, small generator tripping can increase the transmission network's reactive power losses, leading to severe voltage drops and stability problems [5]. Voltage stability is a local phenomenon affected by load characteristics, "Voltage stability refers to the ability of a power system to maintain a constant voltage on all buses in the system after being perturbed from a certain initial operating condition", according to the IEEE/CIGRE joint working group study [6]. There are numerous approaches to voltage stability analysis, including static and dynamic voltage stability assessments. The voltage stability analysis approach can be chosen according to the microgrid stability mechanism. Static analysis methodologies use static operational parameters of micro grids to discover the primary elements influencing voltage stability. Static analysis methodologies solely address the static functioning of micro grid systems, with the real-time variable differential equation set to zero. Static analysis methodologies are currently mostly based on load flow assessments, such as P-V, V-Q, and V-Q sensitivity analysis. Dynamic voltage stability analysis methods are useful for analyzing voltage collapse and measuring the effect of a control approach. Dynamic analysis methods are related to transient analyses of power systems, which use a set of differential equations to model the systems. Most dynamic voltage stability studies still rely on the system's static operational characteristics due to the slow dynamic influence on stability [7]. These disturbances can be processed and controlled in many ways to improve voltage stability and rebalance the system, such as reactive power control with the use of flexible alternating current transmission system (FACTS) equipment, such as STATCOM, D STATCOM, UPQC, and so on, these will be instrumental in controlling the power and its quality [8, 9]. The majority of renewable energy sources (RES) technologies are intermittent due to their reliance on climatic conditions, fluctuating environmental factors, and/or time limitations. This leads to demand generation imbalances, which have a detrimental impact on the voltage and frequency of the power grid, hence compromising its stability due to a shortage of generation units that can supply reserve power. Furthermore, the inertia constant of modern power systems is reduced since the renewable energy sources (RESs) are disconnected from the alternating current (AC) grid through the use of power converters. Thus, under normal circumstances, RESs are unable to engage in frequency regulation alongside traditional generation sources [10, 11].

Variable-speed wind turbines do better as they grow. The ability of a variable wind turbine to operate at varying wind speeds and the isolation of the power electronic device from the mechanical and electrical parts of a wind power plant are significant factors, as mechanical unpredictability does not affect the electrical or grid side of wind power. Variable-speed wind power systems use double-feed induction generators and fully rated-transformers. Reactive wind power injection increases system voltage and load ability [12, 13]. Wind power plants can meet load demand and improve voltage stability. However, power injection and its unpredictable features may increase the difficulties of power system operation and control [14-16].

The integration of wind power plants requires the stability of the energy system [16, 17]. Photovoltaic sources generate intermittent electricity because clouds, fog, rain, dust storms, etc., affect solar radiation and temperature, and there is no night solar energy, so grid injection will be intermittent with high photovoltaic penetration. Cloud cover can significantly reduce the photovoltaic system's output, which affects generation [18]. Voltage stability, the ability of the grid for a power system to maintain stable voltages throughout the grid after a grid disturbance occurs under nominal operation, is a serious challenge with the high penetration of intermittent PV power sources. To ensure the power grid's reliability with increasing penetration of intermittent power sources such as solar PV systems, the voltage stability of the electrical grid needs to be evaluated [19-21].

Previous research has predominantly focused on utilizing FACTS devices and individual hybrid energy systems to enhance voltage stability. In contrast, this study individually examines the impact of hybrid energy systems on voltage stability. As a collective group. this study also uses a genetic algorithm to find the optimal size and location of capacitor banks in a hybrid system.

This paper proposes and represents the IEEE 42 bus system using the ETAP program. Voltage stability analysis was done, and the weakest regions were identified using P-V and Q-V curves. Most voltage security estimates use those curves. Power-flow solutions generate those curves to calculate a power system's loading margin [22]. The V-Q sensitivity method is also used to identify the weakest regions where the power flow Jacobian matrix is essential to the V-Q sensitivity. In complicated power systems, it can predict voltage instability [23, 24]. After identifying the weakest regions, DG, SPVA, WT, and HES, Cb are added individually to different locations in these weakest regions to improve the voltage stability in this work. The results compare the effect of adding these systems with traditional devices, such as Cb, to improve voltage stability.

V-Q sensitivity evaluates the relationship between voltage change and reactive power change, and is one of the main methods used to analyse voltage stability [29]. The eigenvalues relate to a voltage and reactive power change type that can provide a relative measure of voltage instability [30]. The participation factor values can be used to identify the system's weakest bus [31]. The power voltage equations for a linearized steady-state system are as follows:

$\left[\begin{array}{l}\Delta P \\ \Delta Q\end{array}\right]=\left[\begin{array}{ll}J_{p \delta} & J_{p V} \\ J_{q \delta} & J_{q V}\end{array}\right]\left[\begin{array}{l}\Delta \delta \\ \Delta V\end{array}\right]$                        （1）

where: $\Delta \mathrm{P}=$ Incremental change in bus real power, $\Delta \mathrm{Q}=$ Incremental change in bus reactive power, $\Delta \delta=$ Incremental change in bus voltage angle and $\Delta \mathrm{V}=$ the incremental change in bus voltage. The Jacobian matrix in (1) is identical to the Jacobian matrix used when the power flow equations are solved using the Newton-Raphson technique when the standard power flow model is utilized for voltage stability analysis [30].

$P$ and $Q$ both have an impact on system voltage stability. However, hold $\mathrm{P}$ at a constant value at each operational point and assess voltage stability by considering the incremental relationship between $\mathrm{Q}$ and $\mathrm{V}$. Based on these arguments, the expression (1) if $\Delta \mathrm{P}=0$, gives:

$\left[\begin{array}{c}0 \\ \Delta Q\end{array}\right]=\left[\begin{array}{ll}J_{p \delta} & J_{p V} \\ J_{q \delta} & J_{q V}\end{array}\right]\left[\begin{array}{c}\Delta \delta \\ \Delta V\end{array}\right]$             (2)

$\Delta Q=\left(-J_{q \delta} \cdot J_{p \delta}^{-1} \cdot J_{p V}+J_{q V}\right) \cdot \Delta V=J_R \cdot \Delta V$             (3)

$J_R=J_{q V}-J_{q \delta} \cdot J_{p \delta}^{-1} \cdot J_{p V}$                    (4)

$J_R$ is the system's reduced Jacobian matrix (2). It is the linearized relationship between $\Delta V$ and $\Delta Q$.

The system is voltage stable if the smallest eigenvalue of J_R is more significant than zero. The critical mode's left and right eigenvectors can determine bus participation factors. Critical buses in the connected power network have high participation factors [32].

It is essential to use J_Rto carry out voltage stability analysis. The V-Q sensitivity at the bus is the diagonal element. This is the slope of the QV curve at a specific operating point. The following criteria are used in V-Q sensitivity studies to determine the impact of reactive power on voltages [33].

The V-Q sensitivity value is the normalized ∂V/∂Q component in the reduced V-Q Jacobian matrix. The normalization is based on the system buses' most significant ∂V/∂Q component. This method involves using a reduced Jacobian matrix, system modes, and the participation factor of each load bus. The technique is used to determine the minimum eigenvalue and the associated eigenvectors of the reduced Jacobian matrix of the power system. The eeigenvalues are linked to a mode encompassing voltage and reactive power fluctuations. A system is deemed voltage stable if all its voltage eigenvalues are positive. If any of the eigenvalues is negative, the system is said to be voltage unstable, as demonstrated below [33]:

1. Positive V-Q sensitivity suggests system stability.
2. Negative V-Q sensitivity suggests system instability.
3. Low sensitivity indicates more stability.
4.  A system with a sensitivity of 0 is entirely stable.
5. The system operates at the stability limit threshold if the sensitivity is infinite.

3.2 P-V curve

The P-V curves are often used to characterize system-stable operating zones. Moreover, it provides sufficient data on active power margin and voltage magnitude due to different disturbances. The p-v curve provides data about the system's operation zones. At the same time, v-q sensitivity identifies the weak bus so it can describe the two methods as complementary to each other. A circuit model can describe a power system, where generators are the source and loads are the sink. To generate the $\mathrm{P}-\mathrm{V}$ curve depicted in Figure 3, the power transfer between the source and sink is increased. The voltage on a specific bus is determined by the absolute power transferred, line reactance, and load power factor. As the load increases, the voltage falls and approaches a critical threshold; any further increase in load causes system instability. Consider a basic system consisting of a power source with voltage $\mathrm{E} \angle \delta$ and a load at voltage $\mathrm{V} \angle 0$ fed by an infinite bus transmission system [34]. The active and reactive powers are obtained by Eqs. (5) and (6) when the transmission line resistance is neglected [22,35].

$P=\frac{E V}{X} \operatorname{Sin} \delta$                         (5)

$Q=\frac{E V}{X} \operatorname{Cos} \delta-\frac{V^2}{X}$                       (6)

P-V curves illustrate the correlation between the load inside a specific region and the bus voltage at various power factors.

Where $\tan \varphi=\frac{Q}{P}$. Since this study does not consider the load angle, it can be eliminated. Let $p=\frac{P X}{E^2}, q=\frac{Q X}{E^2}$ and $v=$ $\frac{V}{E}$. Normalizing Eqs. (5) and (6) using short circuit power.

$S=\frac{E^2}{X}$                          (7)

$p=v \operatorname{Sin} \delta$                           (8)

$q=v \operatorname{Cos} \delta-v^2$                      (9)

3.png

Figure 3. Receiving end voltage vs real power loading curve [35]

Real power loss, cost, and voltage stability index have more priority among power objectives. Several methods can be used to inject (add) electrical energy into the power system to solve the voltage instability problem and reduce the total losses. But, these methods can't be applied directly using any type, value, or location.

In this work, A capacitor bank (Cb) is used for the reactive power compensation, in addition to solar photovoltaic array (SPVA), wind turbines (WTs), distributed generators (DGs), and hybrid energy system (HES) are used as energy source systems (ESS) for the weakest regions of the proposed system (IEEE- 42 bus) to improve the voltage stability. Two stability indexes are used to determine the optimal placement of supported Cb and ESS: V-Q sensitivity and P-V curves, which are employed to identify the weakest regions within the power system based on voltage stability analysis, which gives the five weakest regions in the system.

The results demonstrate that HES outperforms others in terms of increasing the P margin and lowering active power losses. The results showed that the best locations for addition are WR4 and WR5, which resulted in the lowest total losses and the greatest increase in power margin for all WRs, while the worst position for addition is WR2, which resulted in an increase in total losses and a decrease in power margin for other regions.

On the other hand, the optimal value of the injection power of 5 MW gives good results when compared with the injection power that is equal to the load power, which provides more P margin and large voltage incremental for the injection bus but on the same time limited effect on the other bus with increasing in the system overall loss. The proposed methodology is certainly limited with the utility decision-makers, which can resize and relocate the inserting number of SPVA, WT, and DG.