High-Penetration of Renewable Energy into the Grid

1. Introduction

Traditional power networks are characterized by a limited number of centrally situated, high-capacity plants. Many countries are undergoing a swift transition to RE generation [1]. The global energy industry is experiencing a profound revolution propelled by the imperative to address climate change, decrease greenhouse gas emissions, and shift towards sustainable energy sources [2]. One of the primary measures is the enhanced incorporation of RES—specifically wind, solar, and hydropower—into electrical power systems [3]. This transition, also known as the high penetration of RE, has accelerated due to technical innovations, favourable regulations, and decreasing costs of renewable technologies [4]. This transformation offers significant environmental and economic advantages, although it also presents several technological and operational hurdles for grid operators. In contrast to traditional fossil fuel-based generation, renewable energy sources are intrinsically changeable, reliant on meteorological conditions, and regionally distributed [5].These attributes can affect grid stability, reliability, and efficiency if inadequately handled [6].

The research reveals that energy efficiency and RE technologies are fundamental components of the shift, and their synergies are equally significant [4]. RE has the potential to fulfill two-thirds of world energy demand and significantly aid in the reduction of greenhouse gas emissions required to maintain the average global surface temperature increase below 2 °C by 2050 [7]. A growing array of indications suggests a rapid energy transition that may significantly impact energy supply and demand in the forthcoming decades [8].

The shift towards substantial RE integration in power systems is propelled by a confluence of environmental, economic, technical, and policy-related influences [9]. These factors are reshaping the global energy framework and expediting the incorporation of RES such as solar, wind, and hydropower into electrical networks [2]. Presented below is a systematic summary of these major factors in Table 1.

This research examines the KK II Solar PV Plant, which is presumably one of the RE initiatives established under South Africa’s Renewable Energy Independent Power Producer Procurement Programme (REIPPPP) [15]. KK II solar PV is in the Northern Cape, South Africa (many RE projects are situated there due to high solar irradiance). This PV plant has a total installed capacity of 75MW [16]. Secondly, this study uses Metro Wind Van Stadens Wind Farm situated in the Eastern Cape, with an installed capacity of 27 MW, including 9 turbines of 3 MW each [17]. Figure 1(a & b) elegantly illustrates a solar power plant at sunrise, representing the emergence of renewable energy options. Figure 1 (c & d) illustrates the operation of wind energy, wherein these turbines transform kinetic wind energy into electricity, therefore enhancing a cleaner power system.

2. Background Overview

The incorporation of a substantial amount of RE into the power grid signifies a dramatic change in global energy systems [2]. The shift to high penetration of RE in power networks is essential for worldwide initiatives aimed at decarbonizing the energy sector, improving energy security, and fostering sustainability [18]. High-penetration of RE is a scenario in which a substantial percentage—generally 30% or greater—of a grid’s electrical output is derived from renewable sources, including solar, wind, hydropower, and biofuels [19].

2.1. Renewable Grid in South Africa

Renewable Grid Firming in South Africa encompasses a collection of tactics and technology implemented to provide a reliable and stable electrical grid while accommodating the growing integration of variable renewable energy (VRE), including wind and solar sources [20]. As South Africa transitions from a coal-centric energy framework to a cleaner, more sustainable model, grid firming is important owing to the sporadic nature of RES [21]. Figure 2 represents the anticipated power generation composition for South Africa, contrasting data from 2010 with forecasts for 2050 [22].

The long-term approach targets a net-zero power mix by 2050, incorporating wind, solar, hydro, biomass, and maybe nuclear energy [23]. Despite the reliance on fossil fuels, RE has also been on an upward trend, with wind energy contributing significantly [24].

Table 2 indicates that coal continues to be the primary source of power in South Africa due to the country’s large coal reserves; nevertheless, the promotion of RE is essential and cannot be overlooked until coal is exhausted and attention shifts to RES.

2.2. Load Demand Uncertainty

Uncertainty in Load Demand pertains to the unpredictability and variability linked to future power consumption trends [25]. This unpredictability presents difficulties for power system design, operation, and dependability, particularly for the integration of RES and advanced smart grid technology [26]. The concerns associated with RE that must be considered when integrating it into the system are illustrated in Table 3.

Several variables contribute to load demand uncertainties, including weather variations, in which temperature, humidity, and cloud cover have a substantial impact on energy use, notably for heating and cooling [30]. Economic fluctuations, which are Industrial and commercial demand, can be challenging to anticipate [31]. There are two categories of uncertainty in loads: Short-Term Uncertainty, which encompasses variations in demand that occur minutes to days in advance (e.g., weather-induced fluctuations). Long-Term Uncertainty, which encompasses months to years in advance (e.g., demographic shifts, policy changes) [32].

2.3. Grid Reliability

As the proportion of RE in a power system increases substantially, maintaining grid resilience becomes more intricate. This is attributable to the fluctuating and unpredictable characteristics of resources such as solar and wind energy [1]. It is crucial to accurately capture significant transient dynamics that may lead to network failure in actual power grids, as well as the emerging power-balancing and stabilizing characteristics of these interconnected systems [33]. Prediction Uncertainty stemming from erroneous forecasts of renewable energy generation impacts system stabilization and reserve planning [34]. Flexible generation, such as gas turbines or hydroelectric facilities, enables rapid adjustment to mitigate the unpredictability of renewable energy [35].

3. Design and Implementation of RE into the Grid

This section illustrates the integration of RE into the grid, outlining the mathematical methodologies employed in the construction of both wind farms and solar PV plants, aimed at diminishing the reliance on fossil fuels, which adversely impact both the environment and human health.

3.1. Uncertainty of Wind Power

Wind Energy Uncertainty signifies the unpredictable nature of wind energy generation resulting from the variability and limited controllability of wind resources. Unpredictability poses significant challenges for power system design, operation, and reliability, especially with the increasing integration of wind generation. The wind speed follows a Weibull distribution, with the probability density function (PDF) utilized for the wind variations.

$$\mathrm{f}(\mathrm{v})=\left({\displaystyle \frac{\mathrm{k}}{\mathrm{c}}}\right){\left({\displaystyle \frac{\mathrm{v}}{\mathrm{c}}}\right)}^{\mathrm{k}-1}{\mathrm{e}}^{-{\left({\displaystyle \frac{\mathrm{v}}{\mathrm{c}}}\right)}^{\mathrm{k}}}$$

(1)

The scaling index c may be derived from the average wind speed at a certain location, as seen in

$${\mathrm{v}}_{\mathrm{m}}={\displaystyle \underset{0}{\overset{\infty }{\int }}\mathrm{v}\mathrm{f}(\mathrm{v})\mathrm{d}\mathrm{v}=}{\displaystyle \underset{0}{\overset{\infty }{\int }}\left(\frac{2{\mathrm{v}}^2}{{\mathrm{c}}^2}\right)}\exp \left[-{\left({\displaystyle \frac{\mathrm{v}}{\mathrm{c}}}\right)}^2\right]\mathrm{d}\mathrm{v}={\displaystyle \frac{\sqrt{\mathrm{\pi }}}{2}}\mathrm{c}$$

(2)

Take into account the wind velocity, shape factor, and scale factor, referred to as$\mathrm{v}$, $\mathrm{K}$ and$\mathrm{c}$, respectively, where, $\mathrm{k}>0,\mathrm{v}>0$ and $\mathrm{c}>1$ Then, the wind power output can be stated as

$${\mathrm{P}}_{\mathrm{w}}=\left\{\begin{array}{l}0\\ {\mathrm{P}}_{\mathrm{w}}^0(\mathrm{A}+\mathrm{B}\mathrm{v}+\mathrm{C}{\mathrm{v}}^2)\\ {\mathrm{P}}_{\mathrm{w}}^0\\ 0\end{array}\right.\left\{\begin{array}{l}0\le \mathrm{v}\prec {\mathrm{V}}_{\mathrm{c}\mathrm{i}}\\ {\mathrm{V}}_{\mathrm{c}\mathrm{i}}\le \mathrm{v}\prec {\mathrm{V}}_{\mathrm{r}}\\ {\mathrm{V}}_{\mathrm{r}}\le \mathrm{v}\prec {\mathrm{V}}_{\mathrm{co}}\\ \mathrm{v}\ge {\mathrm{V}}_{\mathrm{c}\mathrm{o}}\end{array}\right.$$

(3)

${\mathrm{V}}_{\mathrm{c}\mathrm{i}}$ , ${\mathrm{V}}_{\mathrm{r}}$ and ${\mathrm{V}}_{\mathrm{c}\mathrm{o}}$are recognized as cut-in wind speed, rated wind speed, and cut-out wind speed, respectively. ${\mathrm{P}}_{\mathrm{w}}^0$is the rated power of a wind unit.

The probability of each condition is expressed by the following equation:

$${\mathrm{\pi }}_{\mathrm{s}}^{\mathrm{w}}={\displaystyle \underset{{\mathrm{v}}_{1,\mathrm{s}}}{\overset{{\mathrm{v}}_{2,\mathrm{s}}}{\int }}\mathrm{f}(\mathrm{v})\mathrm{d}\mathrm{v}={\displaystyle \underset{{\mathrm{v}}_{1,\mathrm{s}}}{\overset{{\mathrm{v}}_{2,\mathrm{s}}}{\int }}\left(\frac{2\mathrm{v}}{{\mathrm{c}}^2}\right)}}\exp \left[-{\left({\displaystyle \frac{\mathrm{v}}{\mathrm{c}}}\right)}^2\right]\mathrm{d}\mathrm{v}$$

(4)

Whereby

$${\mathrm{v}}_{\mathrm{s}}={\displaystyle \frac{{\mathrm{v}}_{2,\mathrm{s}}+{\mathrm{v}}_{1,\mathrm{s}}}{2}}$$

(5)

Where ${\mathrm{v}}_{2,\mathrm{s}}$ and ${\mathrm{v}}_{1,\mathrm{s}}$ represent the velocity restrictions in state w.

3.2. Unpredictability in Decentralized Solar Energy

The swift implementation of localized solar energy systems has revolutionized power generation by fostering sustainability and energy autonomy. The intrinsic unpredictability of solar energy generation presents considerable hurdles to grid stability, energy planning, and storage management [36]. Weather unpredictability, seasonal fluctuations, and the geographic distribution of PV systems contribute to inconsistent energy production, complicating precise forecasting [37]. The absence of centralized coordination among several small-scale producers complicates demand-supply equilibrium and grid integration.

The stochastic lighting intensity is the predominant component in solar generation. Numerous studies have shown that the probability density function adheres to the Beta distribution as

$$\mathrm{f}(\mathrm{R})={\displaystyle \frac{\mathrm{\Gamma }(\mathrm{\alpha }+\mathrm{\beta })}{\mathrm{\Gamma }(\mathrm{\alpha })\mathrm{\Gamma }\mathrm{\beta }}}{\left({\displaystyle \frac{\mathrm{R}}{{\mathrm{R}}^{\max }}}\right)}^{\mathrm{\alpha }-1}{\left({\displaystyle \frac{\mathrm{R}}{{\mathrm{R}}^{\max }}}\right)}^{\mathrm{\beta }-1}$$

(6)

Whereby$\mathrm{\Gamma }$stands for Gamma function, $\mathrm{\theta }$ and$\mathrm{\beta }$are the considerations,$\mathrm{R}$is the illumination intensity,${\mathrm{R}}^{\max }$is the maximum value. The communication between the illumination intensity and the output power of a solar unit can be described as

$${\mathrm{P}}_{\mathrm{s}}=\left\{\begin{array}{l}{\mathrm{P}}_{\mathrm{s}}^0\frac{\mathrm{R}}{{\mathrm{R}}_{\mathrm{r}}}\\ {\mathrm{P}}_{\mathrm{s}}^0\end{array}\right.\left\{\begin{array}{l}0\le \mathrm{R}\le {\mathrm{R}}_{\mathrm{r}}\\ \mathrm{R}\succ {\mathrm{R}}_{\mathrm{r}}\end{array}\right.$$

(7)

Where${\mathrm{R}}_{\mathrm{r}}$represents the rated value and ${\mathrm{P}}_{\mathrm{s}}^0$ represents the rated output power of the solar unit.

This study used quasi-dynamic simulation, a modeling method that lies between steady-state and fully dynamic simulations. It illustrates the evolving behavior of a system over time in a simplified, often discontinuous or stepwise manner, rather than continuously recreating every transient characteristic. This method is utilized when extensive dynamic simulations are too resource-demanding or unnecessary, yet steady-state analysis does not sufficiently capture important time-dependent processes

3.3. Available Transfer Capability (ATC) on the Wind Farm

Available Transfer Capability (ATC) indicates the highest supplementary power transfer capacity in the transmission network that may be utilized without breaching system restrictions (including temperature, voltage, and stability constraints) after considering existing commitments. In the context of wind farms, ATC pertains to the extent of supplementary wind-generated electricity that can be integrated into the grid and supplied to load centers. This network utilizes the boundary to ascertain the available transfer capability of the wind farm, excluding the rest of the network, to evaluate losses, earnings, and energy output of the wind farm.

$$\mathrm{A}\mathrm{T}\mathrm{C}=\mathrm{T}\mathrm{T}\mathrm{C}-\mathrm{T}\mathrm{R}\mathrm{M}-\mathrm{C}\mathrm{B}\mathrm{M}-\mathrm{E}\mathrm{T}\mathrm{C}$$

(6)

The total transfer capability (TTC) is less than the transmission reliability margin (TRM), which is lower than the capacity benefit margin (CBM), and is also smaller than the aggregate of existing transmission commitments (ETC). This research did not examine TRM or CBM. Consequently, the ATC may be calculated by deducting the TTC from the ETC.

ATC = TTC − ETC

(7)

Whereby

$$\mathrm{T}\mathrm{T}\mathrm{C}={\displaystyle \sum _{\mathrm{i}\in \sin \mathrm{k}}{\mathrm{P}}_{\mathrm{D}\mathrm{i}}}(\mathrm{\lambda }\max )-{\displaystyle \sum _{\mathrm{i}\in \sin \mathrm{k}}{\mathrm{P}}_{\mathrm{D}\mathrm{i}}^0}$$

(8)

Subjected to

Where B is the set of all buses,${\mathrm{P}}_{\mathrm{G}\mathrm{i}}$is the active power at the generator I, and${\mathrm{P}}_{\mathrm{D}\mathrm{i}}$is the active power demand at the bus $\mathrm{i}$ , ${\mathrm{\theta }}_{\mathrm{i}\mathrm{j}}$is the voltage phase angle between the bus$\mathrm{i}$and $\mathrm{\lambda }$is the scalar parameter.

$${\mathrm{P}}_{\mathrm{G}\mathrm{i}}^{\min }\le {\mathrm{P}}_{\mathrm{G}\mathrm{i}}\le {\mathrm{P}}_{\mathrm{G}\mathrm{i}}^{\max }$$

(9)

$${\mathrm{P}}_{\mathrm{i}\mathrm{j}}\le {\mathrm{P}}_{\mathrm{i}\mathrm{j}}^{\max }$$

(10)

$${\mathrm{P}}_{\mathrm{G}\mathrm{i}}={\mathrm{P}}_{\mathrm{G}\mathrm{i}}^0(1+\mathrm{\lambda }{\mathrm{k}}_{\mathrm{G}\mathrm{i}})$$

(11)

This approach is intended for computing the ATC utilizing Monte Carlo simulations with a sensitivity analysis.

3.4. Design of the Wind Farm and PV Plant

This section discusses the implementation of both the wind farm and solar photovoltaic plant within DIgSILENT PowerFactory software. It outlines the design of wind turbines by including wind speed, the wind power curve, wind power capacity, distribution, and correlation. Furthermore, it indicates the design of the solar PV plant and its load characteristics, offering detailed information on the solar PV plant before its integration into the grid.

Figure 4 illustrates the KK II solar PV plant, with 15 solar PV units, each producing 5 MW, with an apparent power of 7 MVA and a power factor of 0.9, utilizing active power input for energy generation. The solar PV systems are interconnected by an 11kV busbar and a 1km cable. Additionally, a 100MVA step-up transformer with a voltage rating of 11/22kV is employed to elevate the voltage to 22kV in KK II Solar PV, as seen in Figure 4. Figure 3 illustrates the voltage levels more effectively, with a minimum voltage of 16.5kV and a maximum voltage of 345kV.

Figure 5 shows the wind farm integrated into the 39 bus England System, with 11 wind turbines, each rated at 2.778 MVA with a power factor of 0.9. The wind turbines are interconnected via an 11kV busbar and a 1km cable.

Figure 6 illustrates the wind power curve applicable to all wind turbines utilized in this study; it is evident from this curve that the turbines achieve maximum power production at a wind speed of 16 m/s.

The wind power capability curve describes the operational limits of an electrical generator, specifying the restrictions on the active and reactive power it can produce. The circle defines the boundary of all operational locations as seen in Figure 7.

The subsequent characteristics of wind turbines dictate the quantity of wind generated, fluctuating bi-hourly throughout the year. Winds 1 and 8 exhibit identical temporal features as seen in Figure 8, as do winds 3,9 and 10 as shown in (b).

The periodic characteristics of the KK II solar PV Plant exhibit bi-hourly fluctuations throughout the year, resulting in considerable unpredictability in the generated output power, as seen in Figure 9

Figure 10 describes the characteristics assigned to both sources. Figure 10(a) shows the transformed distribution assigned to the wind turbine, incorporating wind speed and the Weibull curve. Figure 10 (b) depicts the allocation of prediction errors among generators and solar PV systems to forecast possible future mistakes. Figure 10(c) illustrates the utilization of the Weibull distribution for wind speed, employing the shape and scale parameters provided in Table 4.

Figure 10(d) illustrates the correlation distribution utilized to establish a relationship among the 11 wind turbines in the wind farm, with the correlation coefficient established at 0.99. A higher coefficient indicates a stronger relationship, with a value of 1 representing a perfect correlation.

4. Discussion and Future Trends

The substantial integration of RE into the power grid is a pivotal aspect of the global energy transition, seeking to diminish reliance on fossil fuels, decrease greenhouse gas emissions, and bolster energy security. Integrating substantial amounts of renewable energy into the current grid infrastructure poses many technological, economic, and regulatory issues. This study used two renewable energy sources, namely solar PV plants and wind farms, to demonstrate the significance of integrating RE into the grid over an extended duration, considering the unpredictable power production associated with the incorporation of RE into the system. This work employs time characteristics linked to the operation of both wind turbines and solar PV plants to regulate power production, as seen in Figure 8 and Figure 9. Initially, both plants provide uniform power, as seen in Figure 11 and Figure 12, which is further illustrated by Figure 13, showing the busbar with consistent voltage magnitude. The quasi-dynamic modelling tool demonstrates that the plants exhibit power variations based on their features over both short and long durations, further elucidated by figures 16, 17, and 18. Furthermore, the research examines the wind farm, initially employing the boundary tool to illustrate the power generated by the wind farm to the broader network. It also analyzes losses, profits, and energy production from the farm through both fundamental and probabilistic studies as shown in Table 5 and Table 6.

Future trends regarding the extensive integration of RE into the grid, emphasizing both technological advancements and structural developments, are anticipated to influence the energy landscape. Enhanced Grid Flexibility and ModernizationSmart Grids necessitate increased use of intelligent technology to regulate the real-time equilibrium of supply and demand. Enhanced forecasting that refined predictive instruments for sun, wind, and load fluctuations. Digitalization refers to the integration of Internet of Things (IoT), Artificial Intelligence (AI), and data analytics to enhance grid operations.

5. Conclusions

This article examines the viability of wind and solar energy as alternatives to traditional energy sources. It demonstrates how high penetration of RE may be integrated into the grid without compromising network stability in both the short and long term, while considering the uncertainties associated with its integration. Furthermore, the ability to determine losses, profits, and energy output from the plant is crucial for economic benefit. The results of this study use quasi-dynamic simulation to demonstrate the operational behaviors of both PV plants and wind farm plants under varying situations for both short-term and long-term scenarios. It employs basic energy analysis and probabilistic analysis in conjunction with Monte Carlo simulation to evaluate losses, profits, and energy.