The city of Kinshasa is currently supplied with electricity from the Inga and Zongo hydroelectric power stations in Central Kongo ( Figure 1 ). Table 1 shows that even supplied by two central there is a huge lack of energy in Kinshasa. Energy is transported from the production centers to Kinshasa by [25] :

A 220 kV double-circuit line between Inga and Kinshasa, 262 km long, operated without n-1 safety.

A 132 kV Zongo-Badiadingi line, 59 km long, with a transit capacity of 90 MW operated without n-1 security.

A 70 kV Zongo-Gombe line, 80 km long, with a transit capacity of 23 MW, operated without security n-1. The energy situation in the city of Kinshasa is shown in Table 1 below.

The main causes of load shedding in the Kinshasa distribution network and the energy deficit in the city of Kinshasa are due to the following reasons [26] - [28] .

While the installations are being rehabilitated, the logical outcome of this situation is to rotate load shedding among certain installations to protect them and ensure a fair distribution of electrical energy [29] [30] .

The documentary approach involved reviewing existing records and documents related to electricity consumption and load shedding in Kinshasa. This included historical data from SNEL, reports on electricity distribution, and previous studies on load profiles and energy management in Central Africa. This approach provided a foundational understanding of the current state of electricity supply and demand, as well as the factors contributing to load shedding.

For our study, the energy was measured every hour or half hour, depending on the accuracy required which is the case in the various substations and sub-stations of the Société Nationale d’Électrique (SNEL).

The main objective is to evaluate SNEL’s network feeders in the city of Kinshasa to help it achieve its economic and social plan. However, our approach consisted of identifying the SNEL/Kinshasa branches, including Regional Management East (DKE), Regional Management North (DKN), Regional Management West (DKO), Regional Management Centre (DKC), and Regional Management South (DKS). These five directions/areas formed the basis of our survey.

The 30 days of November were divided into three groups, as follows:

The Direction Regional Sud (DKS) is part of the Department de Distribution de Kinshasa (DDK). It is located in the commune of Limete, at 12^th Street Industrial. It manages 5 sub-stations and 1 substation ( Figure 1 ): Liminga substation, Lemba substation, Campus substation, Kingabwa substation, and Limete substation.

The mean (average) is calculated by summing all the data points and dividing by the number of data points as follows [31] [32] :

$Mean\left(\mu \right)\frac{{{\displaystyle \sum }}_{=1}^{in}{x}_i}{n}$(1)

The standard deviation measures the variation or dispersion in a set of values. The mathematical Formula [33] [34] :

$\text{Standard Deviation}\left(\sigma \right)=\sqrt{\frac{{{\displaystyle \sum }}_{=1}^{in}{\left(x_i-\mu \right)}^2}{n-1}}$(2)

The median is the middle value of a dataset when it is ordered in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers.

Quartiles divide the data into four equal parts. The first quartile (Q₁) is the 25^th percentile, the second quartile (Q₂) is the median, and the third quartile (Q₃) is the 75^th percentile [31] [33] [34] .

The IQR is the range between the first quartile (Q₁) and the third quartile (Q₃). The mathematical expression is [31] [32] :

$I_{QR}=Q_3-Q_1$(3)

a) Objective

To determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

b) Steps

(1) Assumptions Check

The samples are independent.

The data in each group are normally distributed.

Homogeneity of variances.

(2) Hypotheses

Null hypothesis (H₀): All group means are equal.

Alternative hypothesis (H₁): At least one group mean is different.

(3) ANOVA Test

Calculate the between-group variability (sum of squares between).

Calculate the within-group variability (sum of squares within).

Compute the F-statistic.

Compare the F-statistic to the critical value from the F-distribution table to determine the p-value.

(4) Decision:

If p-value < alpha level (commonly 0.05), reject the null hypothesis.

a) Objective

To compare the means of two groups and determine if they are significantly different from each other.

b) Steps

(1) Assumptions Check

The samples are independent.

The data in each group are normally distributed.

The variances of the two groups are equal (for a two-sample t-test).

(2) Hypotheses

Null hypothesis (H0): The means of the two groups are equal.

Alternative hypothesis (H1): The means of the two groups are different.

(3) T-Test Calculation

Calculate the t-statistic and p-value [32] .

$t=\frac{\left(\overline{X_1}-\overline{X2}\right)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$(4)

(4) Decision

If p-value < alpha level (commonly 0.05), reject the null hypothesis.

Neglecting the contribution of harmonics, a power factor equal to $\cos \phi =0.8$ was considered. The total power lost (Pp) during load shedding for each of the substation feeders is calculated as follows:

1) Calculation of the arithmetic mean for each working day with load shedding. The formula 5 is the average which corresponds to the power loss for the day with only one load shedding and is given by the following expression:

$p=\frac{{{\displaystyle \sum }}_{i=1}^{24}Pi}{n}$(5)

where Pp is the power loss due to load shedding, Pi is active power per hour, and n = 24.

1) For a day with several load-shedding events, add up these averages. To determine the total power lost for that day.

2) Add up the power losses for each working day of the month, which corresponds to the total power loss for the feeder.

The load-shedding ratio (formula 6) is the ratio between the power in hours without load-shedding and the power in hours with load-shedding. It will enable us to classify the different feeders in order of priority.

$Ratio=\frac{{{\displaystyle \sum }}^{\text{}}\text{load-shedding power per hour}}{{{\displaystyle \sum }}^{\text{}}\text{power without load shedding per hour}}$(6)

The load-shedding power is the average power for the whole day, or what would be delivered on average if there were no load-shedding (Pp).

The power without load shedding corresponds to the power delivered without any interruption (normal).

The Table 2 below presents the sales tariffs of electricity by the National Society in charge of electricity, which is:

Two main sets of indices are used to characterize voltage continuity: 1) “system” indices and 2) “connection point” indices (connection point of a neighboring network or a generation or consumption installation). The “system” indices provide more global information, making it possible to characterize the system as a whole or a subset of it. The IEEE has defined a series of indices of both types [35] [36] :

$SAIDI=\frac{\text{the sum of all customer interruption duration}}{\text{and total number of customers served}}$(7)

$SAIFI=\frac{\text{total number of interruptions per customer}}{\text{and total number of customers served}}$(8)

$CAIDI=\frac{\frac{\text{the sum of all customer interruption duration}}{\text{total number of customers served}}}{\frac{\text{number of interruptions per customer}}{\text{total number of customers served}}}=\frac{SAIDI}{SAIFI}$(9)

The load factor for a feeder is the ratio between the rated power and the maximum power. It is given by the relationship below.

${\delta }_i=\frac{S_{i,n}\left[MVA\right]}{S_{i,\max }\left[MVA\right]}$(10)

where ${\delta }_i$ represents the feeder i factor, $S_{i,n}$ is the feeder i power rating, and $S_{i,\max }$ is the feeder i maximum power.

MATLAB software was employed for the analysis and visualization of the collected data. This software provided a robust platform for performing complex analyses and ensuring accurate results, which were essential for developing strategies to mitigate load shedding in Kinshasa.

Figures 2-3 show the power averages for days with load shedding, days without load shedding, and weekends without load shedding for the various feeders in the southern distribution direction.

Figure 4 represents the probability of occurrence of load shedding and no load shedding.

Figure 5 and Table 3 show the results of the ANOVA test used to compare load shedding and non-load shedding.

To confirm the results on the disparity between load shedding and non-load shedding, we added the t-student test shown in Figure 6 .

Analyzing the first two figures, we see that load shedding is a major factor in the distribution of electrical energy.

There is a high probability density of load shedding in the city of Kinshasa, as shown in the figure Based on the information in the table above, since the p-value (Prob > F) is extremely small, less than 0.00000000000000000001, we can conclude that there is a statistically significant difference between the means of the three groups (days with load shedding, days without load shedding, and weekends without load shedding).

This indicates that it is implausible that the observed differences in the group means could have occurred by chance, and we can reject the null hypothesis that there is no difference between the group means. The key features from the t-student test figure are:

The red curve represents the t-student PDF for the “Days with load shedding” scenario. This curve appears to be centered around a t-statistic value close to 0, indicating that the mean difference between the two groups (days with vs. without load shedding) is not statistically significant. The blue curve represents the t-student PDF for the “Days without load shedding” scenario. This curve is also centered around 0, similar to the red point. The green curve represents the t-student PDF for the “Weekends without load shedding” scenario. This curve appears to be shifted to the right, indicating a larger t-statistic value compared to the other two scenarios. The dashed vertical line represents the critical cutoff value for the t-student distribution. This cutoff value is likely used to determine statistical significance, with values beyond the cutoff considered statistically significant.

Overall, this figure suggests that there is no statistically significant difference between the “Days with load shedding” and “Days without load shedding” scenarios, as their t-statistic values are close to 0. However, the “Weekends without load shedding” scenario appears to have a larger t-statistic value, potentially indicating a significant difference compared to the other two scenarios.

The SAIDI, SAIFI, and CAIDI indices: For our system (DKS), the various corresponding indices are shown in Table 4 below. The customers represent the various feeders of the major DKS substations, namely: Limete, Kingabwa, and Lemba. These indices give:

Limete substation feeder load factor: Table 5 shows the load factor for the various feeders at the Limete substation.

Our calculations demonstrate that the load-shedding ratio shows that a significant amount of energy is lost throughout the various load-shedding activities. According to the calculations above, nearly $ 23,4 08,984 was lost due to load shedding in November 2022 alone. This is a common practice that should only be used in extreme emergencies, but it has become commonplace in the operation of our electricity network.

The load factors as seen in Table 5 are above 100%, which means that our feeders are operating almost at overload.

Launch pilot programs in select areas to test the effectiveness of the designed programs.

launch public awareness campaigns on energy-efficient technologies and practices.

Develop and implement incentive programs for adopting energy-efficient appliances.

Monitor energy consumption patterns and adjust initiatives as necessary.

Develop policies to promote distributed energy resources like solar panels and small generators.

Implement incentives for the adoption of distributed generation technologies.

Integrate distributed generation into the grid and monitor its impact.

Assess available smart grid technologies and real-time monitoring systems.

Implement pilot projects in select areas to test these technologies.

Develop educational materials on load shedding and energy conservation.

Launch campaigns to educate consumers on the importance of reducing peak demand.

Maintain ongoing engagement with consumers through regular updates and workshops.

Review existing policies and regulations related to grid reliability and infrastructure investment.

Develop new policies that support grid reliability and infrastructure investment.

Implement new policies and continuously monitor their impact on grid performance.

Collect and analyze load profiles to identify trends and issues.

Adjust mitigation strategies based on updated load profiles.

Continuously monitor load profiles and make necessary adjustments to strategies.

Implementation of advanced forecasting models, smart grid technologies, and distributed generation systems is technically feasible and aligns with global best practices.

While the initial investment for infrastructure upgrades and technology implementation is significant, the long-term economic benefits outweigh the costs. Reducing load shedding will enhance economic productivity, reduce financial losses, and attract investments. Funding can be sourced from government budgets, international donors, and private sector investments.

The phased approach ensures manageable implementation and minimal disruption to current operations. Pilot projects will help refine strategies and address potential operational challenges before full-scale rollout.

Public awareness campaigns and consumer engagement will ensure community support for the initiatives. Educating consumers on the benefits of reduced load shedding and energy efficiency will enhance acceptance and cooperation.

Promoting energy-efficient technologies and distributed generation (e.g., solar panels, waste to energy) supports environmental sustainability. These initiatives will reduce greenhouse gas emissions and reliance on fossil fuels.