Feasibility study of an interconnection of electrical energy transmission networks: Case study of 4 countries in Central Africa and Nigeria

 Corresponding author: Romain Platinie KUEDA Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0. Feasibility study of an interconnection of electrical energy transmission networks: Case study of 4 countries in Central Africa and Nigeria Romain Platinie KUEDA *, André YOUMSSI and Ndjiya Ngasop Department of Electrical Engineering, Energy and Automation, National School of Agro-Industrial Sciences (ENSAI), University of Ngaoundere, Cameroon. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 Publication history: Received on 21 April 2025; revised on 04 June 2025; accepted on 06 June 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.23.3.0182 Abstract With the current trend and progress in science, the production of electrical energy can be done in one country and consumed in another. Central Africa is experiencing a paradoxical situation characterized, among other things, by low hydroelectric production, an electrification rate of 13% compared to 90% in North Africa and a very low level of interconnection of its electricity networks. Thus, the interconnection of the networks of the countries of Central Africa and Nigeria will aim not only to facilitate the energy integration of the sub-region but also to reduce the inconvenience caused to the populations of the sub-region. This study focuses on the feasibility of an interconnection between 4 countries in Central Africa (Cameroon, Central African Republic, Chad, DRC) and Nigeria by proposing a multi-terminal high voltage direct current transmission system that we simulated under MATLAB/Simulink software. Keywords: Electric energy; Electric network; Interconnection; High voltage direct current; Power synchronization; Frequency control; Stability and efficiency of HVDC transmission system 1. Introduction The last century has demonstrated that every facet of human development revolves around a healthy and stable energy supply regime. Electricity has become the primary resource needed in human society, for virtually all aspects of societal development, from industry and commercial applications to domestic use. The electric power system serves to generate, transmit and distribute electrical energy to consumers in an efficient, economical and reliable manner. It is made up of production plants, transmission lines and distribution networks [1] . Along the same lines, an electrical interconnection allows electricity to flow between separate networks, or synchronous networks. They can consist of underwater power cables, underground power cables or overhead power lines [11] . The interconnection of electrical networks not only makes it possible to exchange energy between the different power plants in service but also to switch networks in the event of a source failure. It has many advantages such as [12-14] : •Optimization of the exploitation of production park resources and use of available power plants at all times to balance demand and production; •Optimization of savings on operating costs; •The mitigation of frequency and voltage variations resulting from fluctuations in consumption; •Improving the production-consumption adequacy by increasing the interconnection capacity between systems and achieving the energy transition; •Reduction of energy costs; •Optimization of the security, stability and reliability of interconnected networks; •Increase in electricity supply. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 181 In the study of the feasibility of interconnections of alternating electrical energy transmission networks, the basic constraints on the synchronization of frequency and voltage must be observed such that the electrical energy transmission networks must have the same frequency, the same voltage and the same transport angle. The Central Africa sub-region is characterized by a very low level of interconnection, representing a real obstacle to its development. For decades, high-voltage alternating current (HVAC) has been the most conventional method of delivering power. With recent advances in power electronics, high-voltage direct current (HVDC) is an established technology in long-distance power transmission. As a result, it is re-emerging as the best option due to improved system operation and better support for the integration of renewable energy. Due to its flexibility, HVDC technology is able to provide the transmission system with several benefits such as improved transfer capacity, better power flow control, improved transient stability, stability/ improved control and absence of production or absorption of reactive power by the line [2] . Because HVDC electrical power transmission is very attractive, it presents a real problem in terms of its control strategy. This is how many authors have worked on control strategies for HVDC systems with the aim of contributing to improving their performance and stability. In his work, [3] propose the master-slave control strategy for the control of a HVDC system with low reliability because the failure of the “master” converter leads to the total shutdown of the system. To therefore overcome the limits of the master-slave control strategy, [4] and [5] present the voltage drop control strategy where two or more converters are responsible for regulating the voltage in the DC bus and the other converters in the system regulate the power flow. [6] proposed a combined control strategy between the Master Slave Control Strategy (MSCS) and the Voltage Margin Control Strategy (VMCS) with DC voltage oscillations observed due to the MSCS. [7] proposed the power angle control strategy for controlling HVDC systems where it uses the angle and magnitude of the AC voltage at the point of common coupling (PCC) to control the active and reactive power independently. Although the power angle control strategy is interesting and is currently applied in conventional HVAC systems, its major drawback is its inability to limit the currents flowing through the voltage source converter. As a means of circumventing the limit posed by the power angle control strategy, [8] and [2] present the vector control strategy (VCS) having the ability to limit the current flowing through the converter. But the proposed VCS has an inability to connect to weak AC networks because of its phase-locked loop. To therefore deal with the limitations of VCS, [9] and [10] present the power synchronization control strategy (PSCS) where the phase lock loop is replaced by the power synchronization loop. On the other hand, for overall control and for system stability, PSCS does not take into account the frequency control of AC networks. It is in this context that we propose an improvement of the PSCS by adding to the existing control scheme a frequency control strategy for better stability and efficiency of the HVDC transmission system. The main objective of this study is to carry out an interconnection and solve the problem of stability of electric power transmission networks (SEPT) such as the SEPT of the countries of Central Africa and Nigeria by the new energy transport technology electrical in HVDC. Our work will therefore be developed in three parts: • First, we will discuss Modeling of the elements constituting the multi-terminal HVDC system. In this part a complete detail will be given on the power synchronization loop (PSL), the control strategy of the MTDC system and AC voltage control loop. • Secondly, we will present the material and the main analysis tools on the electrical energy transmission networks of the Central African countries mentioned, and Nigeria. • Thirdly, we will present the results and therefore the description of the MTDC system of 5 CA countries and Nigeria as well as the interpretations that we will bring to them. • Finally, all we will have to do is conclude and propose perspectives for future studies to improve this study. 2. Material and methods In this part, we will present the material and the main analysis tools on the electrical energy transmission networks of the Central African countries mentioned and Nigeria. Table 1 shows the description of the electrical energy transmission networks taking into account the production system, voltage level, frequency and the company in charge of the electrical energy transmission on which the implementation of the model is made. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 182 Table 1 Description of electrical energy transmission networks N 0 Network Production Voltage (kV) Frequency (Hz) Company 1 SIN Cameroon Hydroelectricity (74%) Fossil energy (26%) 225 / 90 50 SONATREL 2 NIN Cameroon Hydroelectricity Fossil fuels 110 / 90 50 SONATREL 3 Nigerian Hydroelectricity (18.4%) Fossil energy (81.6%) 330 / 132 50 TCN 4 Chadian Hydroelectricity (0%) Fossil energy (100%) 110 / 15 50 SNE 5 Central African Hydroelectricity (100%) Fossil energy (0%) 225 / 110 / 90 50 ENERCA 6 DRC Hydroelectricity (96%) Fossil energy (4%) 220 / 90 50 SNEL 2.1. Hardware To carry out this study, we will use: • An ordinary Hewlett-Packard HP 110-3800 laptop, Inetl ® Atom™ CPU N455 @1.66GHz 1.67 GHz; 1GB RAM. • MATLAB R2010a data simulation and numerical calculation software. 2.2. Methodology for modeling the elements constituting the multi-terminal HVDC system 2.2.1. Modeling the two-level VSC converter The mathematical model presented here is that proposed by [23] . Figure 1 shows the circuit diagram of the classic VSC, where usl and isl (l = a, b, c) are the AC bus voltages and currents, respectively. Figure 1 Classic VSC topology with 6 valves Let us designate by us_abc , the voltage on the network side and by is_abc , the current leaving the infinite bus. By applying the mesh laws, we obtain the following system of equations: { 𝐿𝑑𝑖𝑠𝑎 𝑑𝑡 =𝑢𝑠𝑎−𝑢𝑐𝑎−𝑅𝑖𝑐𝑎 𝐿𝑑𝑖𝑠𝑏 𝑑𝑡 =𝑢𝑠𝑏−𝑢𝑐𝑏−𝑅𝑖𝑐𝑏 𝐿𝑑𝑖𝑠𝑐 𝑑𝑡 =𝑢𝑠𝑐−𝑢𝑐𝑐−𝑅𝑖𝑐𝑐 …………………… (Eq. 1) Where us_abc : Represents the network voltage; uc_abc : Line voltage After simplification by the Park transformation and according to the instantaneous power theory (the active power at the alternating current side is equal to the power at the DC bus), neglecting the converter reactance resistance and the Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 183 losses of switching, the active and reactive power on the AC side of the VSC and the active power on the DC side can be respectively expressed by: {P=usdi󰇗sd+usqisq Q=usqisd−usdisq Pdc=udc⋅idc …………(Eq. 2) Based on the law of conservation of energy, the active power transferred in the multi-terminal HVDC system must satisfy the following relationship: ∑𝑃=0……………. (Eq. 3) 2.2.2. DC line modeling Depending on the purpose of the study, DC cables can be modeled with the distributed model or with the π-circuit model. The distributed model is suitable for transient analysis, while the π-circuit model is used for slower dynamics. The π-circuit model is chosen and the fast dynamics due to DC cable inductances and converter switching are not considered in this study. Figure 2 shows the DC side of a two-terminal VSC-HVDC system with two cables of opposite voltage level [24] . Figure 2 DC circuit of two-terminal VSC-HVDC system The very simple equations governing this circuit are given by the equation by applying the laws of nodes and meshes: Cdcdudc1 dt =idc1−icc………. (Eq. 4) 𝐶𝑑𝑐𝑑𝑢𝑑𝑐2 𝑑𝑡 =𝑖𝑑𝑐2+𝑖𝑐𝑐………….. (Eq. 5) 𝐿𝑑𝑐𝑑𝑖𝑐𝑐 𝑑𝑡 =𝑢𝑑𝑐1−𝑢𝑑𝑐2−𝑅𝑑𝑐𝑖𝑐𝑐………….. (Eq. 6) One converter in an MTDC system can be connected to a number of other converters ( Figure 3 ). We set the current directions in the DC lines such that the current from converter i to converter j is positive if i is smaller than j. Converter 1 therefore only has incoming currents, and converter n only has outgoing currents. For any other converter i, there are n-1 incoming, and nt outgoing currents. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 184 Figure 3 Node in an MTDC circuit The generalized dynamic equations of any direct current circuit can then be written as follows: 𝐶𝑑𝑐𝑖𝑑𝑢𝑑𝑐𝑖 𝑑𝑡 =𝑖𝑑𝑐𝑖−∑ 𝑖𝑐𝑐𝑖𝑗 𝑛 𝑗=𝑖+1 𝐴𝑣𝑒𝑐 𝑖=1……. (Eq. 7) 𝐶dc𝑖𝑑𝑢dc𝑖 𝑑𝑡 =𝑖dc𝑖+∑ 𝑖−1 𝑗=1𝑖cc𝑗𝑖−∑ 𝑖𝑐𝑐𝑖𝑗 𝐴𝑣𝑒𝑐 𝑖=2,…,𝑛−1 𝑛 𝑗=𝑖+1 ……… (Eq. 8) 𝐶𝑑𝑐𝑖𝑑𝑢𝑑𝑐𝑖 𝑑𝑡 =𝑖𝑑𝑐𝑖+∑ 𝑖−1 𝑗=1𝑖𝑐𝑐𝑗𝑖 𝑎𝑣𝑒𝑐 𝑖=𝑛………. (Eq. 9) 𝐿𝑑𝑐𝑑𝑖𝑐𝑐𝑖𝑗 𝑑𝑡 =𝑢𝑑𝑐𝑖−𝑢𝑑𝑐𝑗−𝑅𝑑𝑐𝑖𝑗𝑖𝐶𝑐𝑖𝑗 ∀𝑗<𝑛,∀𝑖<𝑗……… (Eq. 10) MTDC System Control Strategy The control strategy proposed in this section is a combination of the power synchronization strategy and the frequency control strategy, i.e. a dual control strategy. The overall control structure of the MTDC system is shown in Figure 4: Figure 4 Dual control technique (SCF and SCSP) Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 185 2.2.3. Power synchronization loop (PSL) The power-timing ball is based on equation 11 𝑃=𝑈1𝑈2𝑠𝑖𝑛𝜃 𝑋 𝑄=𝑈12−𝑈1𝑈2𝑐𝑜𝑠𝜃 𝑋……………. (Eq. 11) With: P and Q the active and reactive powers between two nodes θ and X are the phase angle difference and line reactance between the two nodes It maintains synchronism between the VSC and the AC system. This is the active power control loop. The control law is given by equation 12: dΔθ dt =Kp(Pref−P)…………….. (Eq. 12) Where: Pref is the reference for the active power; P is the active power measured at the VSC output; K p is the gain of the controller; Δθ is the controller output which directly provides timing for the VSC so no need for a PLL. 2.2.4. Continuous voltage control loop The PSCS must keep the DC voltage constant to keep the active power flow balanced between the two sides. The control law is given by: Pref=(Kpd+Kid s)(Vdc ref)2−Vdc 2 2………….. (Eq. 13) 2.2.5. AC voltage control loop The function of AC voltage control mode is to keep the point of common coupling (PCC) voltage constant and control the active power to/from the PCC. The control law is given by: ΔV=Ku s(Uref−U)…………. (Eq. 14) Where ∆V gives the change in amplitude of the reference voltage VSC. 2.3. Frequency control loop The frequency control loop has been proposed by several authors [25, 26] and [27] in the literature and all the proposed strategies are based on the same principle, namely: each frequency variation generates a proportional power variation response of the converter. The difference between the works of these authors lies on the overall control of the VSCMTDC system because the basic principle is based on the application of a single VSC converter. The control strategy adopted in this work is the same as that of the above-mentioned authors. Its operating principle is very similar to that of voltage drop. A converter equipped with a frequency drop regulator participates in the frequency regulation of the alternating network to which it is connected and modifies its power reference by following the characteristic line whose slope is 1/ kf where kf corresponds to the frequency drop parameter: ΔPfi∗=1 kfiΔfi………… (Eq. 15) Where: - ΔPfi∗ is the power reference deviation generated by the frequency drop regulator of the ith VSC-HVDC system converter. If ΔPfi∗ positive then we have an injection of power from the DC network to the AC network, negative otherwise. - kfi is the frequency drop parameter of the ith Converter, kfi> 0. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 186 - Δfi is the variation in frequency of the alternating network connected to the ith converter relative to its frequency reference Δfi = fi∗- fi. Based on the PSCS power synchronization loop (Block diagram): ωt=Δθ+ωref………..t (Eq. 16) ωt−ωref t=Δθ Still, according to the power synchronization loop we have: dΔθ dt =Kp(Pref−P)………… (Eq. 17) dΔθ=Kp(Pref −P)dt Δθ=Kp(Pref−P)t By replacing the expression in Eq 2.30, we have: ωt−ωref t=kp( Pref −P) Δω=kp(Pref−P) Δω=kp(ΔPω ∗) Δf=kfΔPf…………….∗ (Eq. 18) Therefore, for the ith converter we have the frequency variation of the AC network to which it is connected by: Δfi=KfiΔpf……………….i ∗ (Eq. 19) kfi is the frequency drop parameter of the ith Converter, Thus, there is a droop relationship between the frequency and the output power of the ith converter, which is the same as that of the primary frequency regulation of a synchronous generator. So, the frequency of VSC station is adjustable, which can synchronize with other AC networks. 3. Results and discussions 3.1. Description of MTDC system of 5 CA countries and Nigeria This section illustrates the behavior of a 6-terminal MTDC system interconnecting six AC networks. The AC networks of the system are the weak (2 < SCR < 3) and very weak (SCR less than 2) AC networks. The converters are controlled using the dual control technique. Figure 5 shows the block diagram of the MTDC system in Simulink. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 187 Figure 5 Block diagram of the MTDC system in Simulink The block diagram of the MTDC system in Simulink presents an interconnection of 6 converters of VSC technology (±100 kV DC) is used to transmit power between 6 AC networks corresponding to the electricity networks of some countries in Central Africa, namely Cameroon (SIN and NIN), Nigeria, Chad, Central African Republic, and Democratic Republic of Congo all with nominal characteristics. In addition to the converters, the VSC station includes the AC side: the step-down and step-up transformers, the AC filters, and the DC side: the capacitors, the DC filters. The rectifiers and inverters are interconnected by cables of different distances (i.e. 2 pi sections). A circuit breaker is used to apply a three-phase ground fault on the AC side of the inverter. Tables 2 and 3 respectively show the initial nominal and reference values of each VSC-MTDC converter station and the lengths (approximate values) of the DC lines. Table 2 Initial and reference values of each station Converter VSC1 VSC2 VSC3 VSC4 VSC6 VSC5 Pn (MW) 388 200 72 60 75 351 Pref (MW) 388 200 72 60 75 351 Qref (MVAR) 0 0 0 0 0 0 Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 188 Table 3 Length of DC lines Line DC1 DC2 DC6 DC4 DC5 DC7 Length (km) 515 700 650 500 720 450 3.2. AC1 network side performance under normal conditions Figure 6 illustrates the performance on the AC1 or SIN Cameroon network side under normal conditions. Figure 6 Performance on the AC1 network side under normal conditions Figure 7 Zoom on the voltage and current of the AC1 network We can observe on the AC1 network or the Southern Interconnected Network of Cameroon that the voltage and current practically stabilize at a time t = 1 s. Just as the measured active and reactive power also stabilize at this time. We can also observe the active power of the AC1 network which is positive, meaning that the SIN network of Cameroon through the VSC1 station injects power into the MTDC network with a value of 1 pu, i.e. its total available injectable power 388 MW in steady state and also a reactive power with a very interesting value of around -0.01 pu. 3.3. Performance on the AC2 network side under normal conditions Figure 8 illustrates the performances on the AC2 side or on the Nigerian network side at the Sakété Town substation under normal operating conditions. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 195 In this simulation to check the reliability of the system, a three-phase fault occurs on the AC2 network at t = 1s, thus causing an imbalance in this AC network for a duration of 0.5s, the fault elimination time. 3.10. AC2 network performance during and after the fault Figure 21 illustrates the AC2 network voltage and current during and after the fault. Figure 21 AC2 network voltage and current during and after the fault We can see from Figure 21 that during the fault, the AC voltage of the VSC2 converter is practically zero, the current passing through it is limited to 1pu thanks to the current limiting loop of the PSCS, and a current peak of one duration of about 0.01s is observed after the fault is cleared and the steady state of the system is reached again. 3.11 AC1 network performance during and after the fault Figure 22 illustrates the AC1 network voltage and current during and after the fault Figure 22 AC1 network voltage and current during and after the fault On the AC1 side, we just open a small variation of around 0.1s during the fault and after eliminating the fault the system resumes its normal operating mode. 3.11. DC side performance of VSC2 station during and after the fault Figure 23 illustrates the pole-to-ground and pole-to-pole DC voltage at the input of the VSC2 station during and after the fault. Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 196 Figure 23 Pole-to-earth and pole-to-pole DC voltage during and after the fault We observe from Figure 23 that the pole-to-pole DC voltage increases by about 1.1pu above the reference voltage because the DC side capacitance is excessively charged and also due to output power losses. One of the loops of the PSCS, more precisely the direct control loop of the direct voltage (in the VSC1 station) attempts to limit the DC voltage to the reference DC voltage. Figure 24 DC power transmitted to the VSC2 station during and after the fault We can observe from figure 24 the continuous power transmitted to the VSC2 station is practically zero and reception continues directly after the fault is cleared. 3.11.1. DC side performance of the VSC3 station during and after the fault Figure 25 illustrates the pole-to-ground and pole-to-pole DC voltage at the VSC3 station output during and after the fault. Figure 25 Pole-to-earth and pole-to-pole DC voltage during and after the fault We observe from Figure 25 a slight increase in the pole-to-pole DC voltage, and also an increase of about 0.1pu in the pole-to-ground DC voltage above the reference voltage range because the DC side capacitance is overloaded as in the Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 197 previous case. The direct voltage control loop installed in the VSC3 station attempts to limit this voltage to its reference voltage. Figure 26 illustrates the DC Power output from the VSC3 station during and after the fault Figure 26 DC power output from the VSC3 station during and after the fault From Figure 26, we observe a power injection of approximately 0.3pu into the AC3 network coming from the surplus stored by the AC1 network during the fault and once the fault is eliminated, it returns to its normal operating position by transmitting its capacity in to other network of the MTDC system. List of abbreviations • AC  Alternating Current • AVC Alternating Current Controller • PSL  Power Synchronization Loop • HVAC  High Voltage Alternating Current • D.C.  Direct Current • GTO  Gate Turn-Off Thyristor • HV  High Voltage • HVAC High Voltage Alternating Current • HVDC High Voltage Direct Current • IGBT Insulated Gate Bipolar Transistor • LCC  Line Commutated Converter • MMC Modular Multi-level Converter • MTDC Multi-terminal Direct Current • PCC  Point of Common Coupling • PLL  Phase Lock Loop • pu Per unit • PWM Pulse Width Modulation • EIN Eastern Interconnected Network • NIN Northern Interconnected Network • SIN Southern Interconnected Network • EETN Electric Energy Transmission Network • PACS Power Angle Control Strategy • VDCS Voltage Drop Control Strategy • FCS  Frequency Control Strategy • MSCS  Master Slave Control Strategy • TMCS Tension Margin Control Strategy • SCR  Short Circuit Ratio • PSCS Power Synchronization Control Strategy • VCS  Vector Control Strategy • TUE  Technical Union of Electricity • VSC  Voltage Source Converter Global Journal of Engineering and Technology Advances, 2025, 23(03), 180-199 198 4. Conclusion The feasibility study of an interconnection of electrical energy transmission networks: Case study of 04 countries of Central Africa and Nigeria had the main objective of carrying out an interconnection and solving the problem of stability of electricity networks. transmission of electrical energy to the countries of Central Africa and Nigeria using the new HVDC electrical energy transmission technology. The results of the simulations obtained confirm the effectiveness of the MTDC system in interconnecting EETN with different parameters. With the model studied, fluctuations or instabilities due to variations in frequency or voltage and faults coming from an AC network of the system like the AC2 network (Nigerian network) that we have simulated are corrected from the MTDC system implemented. place. The implementation of our MTDC system in the sub-region will not only make it possible to avoid energy losses, stability and reliability problems of our EETN but also to reduce as much as possible numerous load shedding, the costs of electricity and promote energy integration. In order to complete this study, it would be interesting to examine the communication aspect of the different terminals for good coordination and efficiency of the proposed MTDC system and also extend the terminals this time with all the countries of Central Africa and Nigeria Compliance with ethical standards Disclosure of conflict of interest No conflict of interest to be disclosed. References [1] J. Machowski, Z. Lubosny, JW Bialek, and JR Bumby, Power system dynamics: stability and control . John Wiley & Sons, 2020. [2] NM Kangwa, C. Venugopal, and IE Davidson, "A review of the performance of VSC-HVDC and MTDC systems," in 2017 IEEE PES PowerAfrica , 2017, pp. 267-273: IEEE. [3] J. Dai, S. Akkari, and M. 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