1. Introduction

Electrical networks supply energy between the production site and the customer site, with a required power, a voltage and frequency. According to the standards, the voltage drop in the network is limited to ± 5%. The power plants of Nouakchott consist of multi-sources that supply several loads, located in seven different places in town making a loop of 33 KV.  It should be noted that the frequency varies continuously. Variations ± 5% of the nominal frequency affect the stability of network and may lead to load shedding.  The voltage level must remain within an authorized range at any point in the network. This will be in all foreseeable production and consumption situations. The proposed goal for this work is to find a solution for load shedding. In this case, we proposed an analysis for both the current and projected production   system. That allows us to meet the domestic demand of the Nouakchott 33 KV network.  This analysis allows us to reach and maintain the voltage profile in stability margin for the network manager. Before that we modelize the electrical network by its transit capabilities. And analysis its simulation results programmed in MATLAB and PSS/E. The growths of distributed renewable generation (solar, wind, etc) are creating challenges for the power grid stability [1-3]. The intermittence problem of these energies makes us always to seek to solve it. To synchronize renewable energy with conventional energy, to make our system more efficient, it requires a delicate control procedure: frequency, phase sequences, phase angles and magnitudes of all the four independent sources should match exactly. A real time monitoring circuitry is necessary which should turn on and off the sources when the loads reach   preset values. Another goal is to optimize Nouakchott power system. The STATCOM device (Static Var Compensator) is a technique for achieving this goal [4, 5]. Per comparison with other types of FACTS (Table 5), STATCOM has been chosen. Thus, to realize predetermined goals, we take the following four steps:

• First step, the single line schematic of the Nouakchott 33 KV loop network is given (Figure 1).
• Secondly, the lines data and voltages (Table 1).

Thirdly generation and load grow are given from 2020 to 2030 years (Tables 2 and 4).

• Thirdly, a mathematical model of power flow equations are solved by Newton Raphson (NR) method, programmed on MATLAB software and PSS/E simulator for two situations (without STATCOM and with STATCOM device) [6-11]. The results of simulations will be following by discussions.
• Last step, a conclusion of the work.

For insertion of the STATCOM device, it is sought a stable power system, even during a disturbance (out limit voltage drop or frequency) to provide the demand power [12, 13]. We notice that FACTS devices are defined by IEEE as “power electronic based controllers and other static equipment which can regulate the power flow and transmission voltage through rapid control action”. Nowadays power system control is based on FACTS devices. STATCOM a shunt connected FACTS device using to rapid voltage and reactive power control, also to reduce harmonics in power system (Table 5). This is realized while keeping constant the frequency to the margin limit of stability and alternators speed rotation also the voltage magnitude in the various network buses [14, 15].

2. Structure of System

2.1.  One line diagram   of Nouakchott Power Grid

The One –line diagram (Figure.1), represents the 33 KV loop (part of the network). The lines data and initials voltage at each bus, the values of generated and load grow are given in Tables 1 and 2 respectively. The system include  eleven(11) transmissions lines,  two renewable plants (one wind power ,one solar plant), two thermal plants and 1 Dual fuel plant)and five(5) loads connected  at buses 2,4,5,6 and 7 respectively. The active and reactive powers generated are given in MW and MVAR respectively. The voltage at each bus (i) is given in KV. The load bus is characterized by its active power P and reactive power Q. Therefore, (P, Q) are specified, while (V) is to be calculated. In this context, it is proposed for the North bus (1), to be a slack bus. Finally, it should also be noted that a bus is numbered (i) and it is connected to (k) other buses such as those shown in Figure 1[16].

Figure 1: Simplified One Line Diagram; of Nouakchott System

      Table 1 present, the active resistances(R), the lines reactances values(X), bus voltage (V), the lengths of each line (L), at each bus (i) connected to the bus (k).

2.2.  Given Data of System

Table 4 are presented the simulation results for PSS/E simulator, case before insertion of STATCOM, we can notice the profile of voltage magnitudes and the voltage angles. The results show that the values of voltage magnitude are below the range of the stability for all system except the slack bus. In blue color the buses were connected the renewable plants (3, 5 and 7 buses).

Table 1: Lines Data and Bus Voltage of Figure 1

Table 2:  Generation Data at 2020 to 2030 Years [16]

Table 3: Load Grow at 2020 to 2030 Years [16]

Table 4: Simulation Results of NR without STATCOM

3. Mathematical Modelisation of STATCOM

The Static Synchronous Compensator (STATCOM) device is a shunt connected FACTS to the buses. It uses the forcing electronic power commutation (GTO, IGBT and IGCT). A STATCOM controls reactive power source can improve the transient stability of systems. This provides voltage support by generating or absorbing reactive power at the point of common

Table 5: Comparison of FACTS systems in terms of technical efficiency [17, 18]

Table 6:  comparison of the two numerical methods NR and GS

coupling without the need of large external or capacitor banks. The basic voltage source converter diagram is shown in Figure 2.

The Table 5 corresponds to the best choice of STATCOM to optimize the system performance.

3.1.  Power Flow Equations of STATCOM Connected to i^th bus

Power flow equation of system with STATCOM connected at bus (i) in Figure 1 and is treated as reactive power source:

Hence P_STCi – is a STATCOM’s active power at bus (i) and Q_STCi – is  a STATCOM’s reactive power at bus (i), Pi – is injected active power at bus (i), Qi – is injected reactive power at bus (i), P_Di – is  active power demand at bus (i) and Q_Di – is  a reactive power demand at  bus (i), P_Gi – is a generator’s active power at bus (i), Q_Gi – is a generator’s reactive power at bus (i).

Equations (1) and (2) represent a case where STATCOM generate reactive power at bus (i) if for reactive power absorption, the signs of Q_STCi will be reversed (positive).

The solution of nonlinear power flow equations (1) and (2) is numerical methods. However, the adopted method in this work is the Newton-Raphson (NR). The specifications of this method, its faster rate of convergence and accuracy, when compared with others methods as Gauss-Seidel (GS), coupled NR, decoupled NR or Gauss method.  We notice this comparison of NR with Gauss Seidel: NR indifferent for choice of slack bus while GS is critical, the resolution of NR with polar coordinates while GS is with rectangular form, the number of iterations is less for NR (4 iterations) compared with GS (16 iterations), with broader systems larger for NR than GS. So the convergence time is lees for GS (0.05 seconds) than NR (0.22 seconds) and the GS resolution is simpler than NR (see Table 6).

In the Table 6 below is given the comparison of the two best numerical methods. These two are important indicators to analyze the quality of the studied network. And also demonstrates the optimal choice of NR method for our work.

3.2.  Modeling of STATCOM

So below is presented the basic schematic and Thevenin’s equivalent circuit of STATCOM respectively, the fundamental frequency operation of the switched mode voltage source inverter and its transformer (Figure 2).

Figure 2: (a) Basic Schematic; (b) Equivalent Circuit [17, 18]

We define STACOM voltage by the equation (3):

Hence V_STC  – is a STATCOM’s voltage, I_STC  – is STATCOM’s current,  Z_SC  – is transformer’s impedance.

The voltages constraints of STATCOM and at bus (i) are given in equation (4)

Where V_STC (min) and V_STC (max) are minimum and maximum STATCOM’s voltages, V_i (min) and V_i (max) are minimum and maximum voltages values at bus (i).

Equation (3) is transformed into a power flow expression for STATCOM and power injected at bus (i) by equations (5) and (6) respectively:

Hence S_STC – is a STATCOM’s apparent power, I*_STC  – is a STATCOM’s complex conjugate current, V*_STC  – is a STATCOM’s complex conjugate voltage, Y*_SC   – is a complex conjugate of short-circuit admittance.

The voltages in rectangular coordinates system are expressed as equations (7) and (8) respectively:

Where e_i – is a active component of voltage at bus (i), f_i  – is a imaginary component of voltage at bus (i), e_STC – is a active component of STATCOM’s voltage, f_STC – is a imaginary component of STATCOM’s voltage.

The STATCOM’s voltage magnitude and angle are expressed as equations (9) and (10) respectively:

The active and reactive power components for the STATCOM and bus (i) on the basis of equations (7) to (10) are respectively expressed by equations (11) to (14):

Where P_STC – is a STATCOM’s active power, Q_STC  – is a STATCOM’s reactive power, G_SC  – is a short-circuit conductance, B_SC – is a short-circuit susceptance.

The Newton-Raphson set of linearized equations for power flow equations (5), (6), (11) and (12) obtained taken into consideration the modeling of shunt-connected STATCOM at bus (i) is given by equation (15):

 The partial derivatives of the Jacobian matrix are defined as following: (expression (16))

4. Simulations Results

 The Table 7 below presents the simulation results of NR with STATCOM. Also presents the best locations at buses.

Table 7: Results of NR with STATCOM

                                                                                                                                                                                                          (16)

Figure 3: (a) Voltage magnitude as a function of bus numbers

Figure 3 (b): Voltage angle as a function of bus numbers

The voltage magnitude and their phase angle before and after insertion of STATCOM are shown in the figure 3(a) and (b) respectively. It demonstrates the improved values at the following buses:  the voltage magnitude for the bus 2 at 0, 80 (value out stability margin) to 0, 97 pu and their angle at -5, 6 to -11, 1 degree. Bus 3 at 0, 93 to 0,99pu and their angle at -1, 8 to -3, 9 degrees. The bus 4 at 0, 75 to 0,95pu and their angle at -7, 3 to -13 degree. The bus 5 at 0, 78 to 1,01pu and their angle at -6, 5 to -14, 1 degree. The bus 6 at 0, 8 to 0,97pu and their angle at -5, 8 to -11, 1 degree. The bus 7 at 0, 83 to 0, 98 pu and their angle at -4, 6 to -9, 8 degrees.

In the Table 8 below is given the simulation results of total power mismatch.

Table 8: Total Power Mismatch

From the Figure 4(a) and (b) below, the power mismatch was reduced at 305, 7 MW to 262, 9 MW for active power losses and 419 MVAR to 360, 3 MVAR for reactive power losses, thereby improving the active power transmission lines.

Figure 4: (a) Active Power Losses;

Figure 4 (b): Reactive Power Losses

Table 9: Reached Tolerance in 4 Iterations

From the Figure.7 so below demonstrates the comparison of the voltage errors variation (a) and the delta angle (b) with and without STATCOM connected to the system as a function of iteration numbers.

Figure 5: (a) Voltage drops function of iterations numbers; (b) Voltage angle function of iterations numbers

5. Conclusions

The simulation results of load flow program on PSS/E Simulator using the NR method have been done.

The main information obtained is the stability exceeding limits at all buses voltage of system except the slack bus (Table 4).

After insertion of STATCOM the voltage for all buses has been improved to the stability limit (Table 7).

The voltages at buses (5, 3 and 7) where connected the renewable plants have improved in limit of stability after insertion of STATCOM

The power mismatch was being reduced after insertion of STATCOM (Table 8).

The novelty is that the studied network presents four different sources in Figure 1. This network undergoes very common load shedding. The cause of these load shedding can be due to the load growth at the nodes. But it can be caused by the presence of clouds or when there is no wind to turn the blades, or non-rainy periods in the Sahel countries. In order to remedy this situation of load shedding, STATCOM has been proposed as a solution.

The STATCOM will replace also the conventional system compensation of reactive power (as shunt capacitor or series capacitor…).

The expected disturbances and the poor power quality problems of the studied power system, at 2030 year, were solved by integration of STATCOM that is able generate or absorb reactive power and maintain the voltage at 1pu. The following areas are proposed or put in mind:

 Other FACTS controller can also be incorporated along the STATCOM and their effect on the system can be studied [17, 18].

Optimal location of STATCOM can be found out using Genetic Algorithm and fuzzy logic.

Economic Assessment of FACTS devices versus other methods can be studied.

Conflict of Interest

The authors of the manuscript declare no conflict of interest.

Acknowledgment

The author likes greatly thank National Electrical Company of Mauritania (SOMELEC) for providing all system data. I also like to thank the General chair of ISAECT2018, Nabil SRIFI, for extended paper to special issue of Advances in Science, Technology and Engineering Systems Journal (ASTESJ) and all reviewers for their corrections and comments.

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42. Ricardo Simões Santos, António João Pina da Costa Feliciano Abreu, Joaquim José Rodrigues Monteiro, "Using Metaheuristics-Based Methods to Provide Sustainable Market Solutions, Suitable to Consumer Needs", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 2, pp. 399–410, 2020. doi: 10.25046/aj050252
43. Hind El Hassani, Nour- Eddine Boutammachte, Sanae El Hassani, "Optimization of Low Temperature Differential Stirling Engine Regenerator Design", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 2, pp. 272–279, 2020. doi: 10.25046/aj050235
44. Nguyen Tuan Anh, Hoang Thang Binh, Tran The Tran, "Optimization of the Stabilizer Bar by Using Total Scores Method", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 1, pp. 431–435, 2020. doi: 10.25046/aj050155
45. Temitayo Olayemi Olowu, Mohamadsaleh Jafari, Arif Sarwat, "A Multi-Objective Voltage Optimization Technique in Distribution Feeders with High Photovoltaic Penetration", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 6, pp. 377–385, 2019. doi: 10.25046/aj040648
46. Mohd Razif Idris, Imad Mokhtar Mosrati, "Optimization of the Electrical Discharge Machining of Powdered Metallurgical High-Speed Steel Alloy using Genetic Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 6, pp. 255–262, 2019. doi: 10.25046/aj040632
47. Jalal Benallal, Lekbir Cherif, Mohamed Chentouf, Mohammed Darmi, Rachid Elgouri, Nabil Hmina, "A New Wire Optimization Approach for Power Reduction in Advanced Technology Nodes", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 6, pp. 140–146, 2019. doi: 10.25046/aj040617
48. Andrei Panteleev, Valentin Panovskiy, "Application of Open-Source Optimization Library “Extremum” to the Synthesis of Feedback Control of a Satellite", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 5, pp. 23–29, 2019. doi: 10.25046/aj040503
49. Houcine Marouani, Amin Sallem, Mondher Chaoui, Pedro Pereira, Nouri Masmoudi, "Multiple-Optimization based-design of RF Integrated Inductors", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 574–584, 2019. doi: 10.25046/aj040468
50. Jaya V. Gaitonde, Rajesh B. Lohani, "Material, Structural Optimization and Analysis of Visible-Range Back-Illuminated OPFET photodetector", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 485–502, 2019. doi: 10.25046/aj040459
51. Dylon Hao Cheng Lam, Jianhui Wong, Yun Seng Lim, Jimmy Chin Yong Hee, "DSTATCOM-Fuel Cell System on Radial Low-voltage Distribution Network for Mitigating Voltage Rise Caused by High Penetration of Photovoltaic Systems", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 285–291, 2019. doi: 10.25046/aj040436
52. Olfa Jedda, Ali Douik, "Optimal Discrete-time Sliding Mode Control for Nonlinear Systems Subject to Input Constraints", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 141–146, 2019. doi: 10.25046/aj040417
53. Uttam S. Satpute, Diwakar R. Joshi, Shruti Gunaga, "Frequency-Based Design of Electric System for Off-shore Wind Power Plant (OWPP)", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 2, pp. 153–161, 2019. doi: 10.25046/aj040220
54. Gabriel Dämmer, Sven Gablenz, Alexander Hildebrandt, Zoltan Major, "Design of an Additively Manufacturable Multi-Material Light-Weight Gripper with integrated Bellows Actuators", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 2, pp. 23–33, 2019. doi: 10.25046/aj040204
55. Nikolay Starostin, Konstantin Mironov, "Strategies of the Level-By-Level Approach to the Minimal Route", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 1, pp. 268–281, 2019. doi: 10.25046/aj040126
56. Hiroyuki Yamamoto, Tomohiro Hayashida, Ichiro Nishizaki, Shinya Sekizaki, "Hypervolume-Based Multi-Objective Reinforcement Learning: Interactive Approach", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 1, pp. 93–100, 2019. doi: 10.25046/aj040110
57. Masahiro Kanazaki, Yusuke Yamada, Masaki Nakamiya, "Multi-Objective Path Optimization of a Satellite for Multiple Active Space Debris Removal Based on a Method for the Travelling Serviceman Problem", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 479–488, 2018. doi: 10.25046/aj030656
58. Chika Yinka-Banjo, Babatunde Opesemowo, "Metaheuristics for Solving Facility Location Optimization Problem in Lagos, Nigeria", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 319–323, 2018. doi: 10.25046/aj030639
59. Mohammad Harun Rashid, Lixin Tao, "Parallelizing Combinatorial Optimization Heuristics with GPUs", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 265–280, 2018. doi: 10.25046/aj030635
60. Wiem Zouari, Ines Alaya, Moncef Tagina, "A Comparative Study of a Hybrid Ant Colony Algorithm MMACS for the Strongly Correlated Knapsack Problem", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 1–22, 2018. doi: 10.25046/aj030601
61. Jamal Al Sadi, "Designing Experiments: 3 Level Full Factorial Design and Variation of Processing Parameters Methods for Polymer Colors", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 5, pp. 109–115, 2018. doi: 10.25046/aj030515
62. Ola Surakhi, Mohammad Khanafseh, Yasser Jaffal, "An enhanced Biometric-based Face Recognition System using Genetic and CRO Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 3, pp. 116–124, 2018. doi: 10.25046/aj030316
63. Mohammad Hossain, Sameer Abufardeh, Sumeet Kumar, "Frameworks for Performing on Cloud Automated Software Testing Using Swarm Intelligence Algorithm: Brief Survey", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 2, pp. 252–256, 2018. doi: 10.25046/aj030229
64. Laud Charles Ochei, Christopher Ifeanyichukwu Ejiofor, "A Model for Optimising the Deployment of Cloud-hosted Application Components for Guaranteeing Multitenancy Isolation", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 2, pp. 174–183, 2018. doi: 10.25046/aj030220
65. An-Ting Cheng, Chun-Yen Chen, Bo-Cheng Lai, Che-Huai Lin, "Software and Hardware Enhancement of Convolutional Neural Networks on GPGPUs", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 2, pp. 28–39, 2018. doi: 10.25046/aj030204
66. Uttara Sawant, Robert Akl, "Adaptive and Non Adaptive LTE Fractional Frequency Reuse Mechanisms Mobility Performance", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 1, pp. 511–520, 2018. doi: 10.25046/aj030162
67. Sahbi Marrouchi, Nesrine Amor, Moez Ben Hessine, Souad Chebbi, "Theoretical Investigation of Combined Use of PSO, Tabu Search and Lagrangian Relaxation methods to solve the Unit Commitment Problem", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 1, pp. 357–365, 2018. doi: 10.25046/aj030144
68. André Richter, Ines Hauer, Martin Wolter, "Algorithms for Technical Integration of Virtual Power Plants into German System Operation", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 1, pp. 135–147, 2018. doi: 10.25046/aj030117
69. Mustafa Saka, Ibrahim Eke, Suleyman Sungur Tezcan, Muslum Cengiz Taplamacioglu, "Analysis of Economic Load Dispatch with a lot of Constraints Using Vortex Search Algorithm", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 6, pp. 151–156, 2017. doi: 10.25046/aj020619
70. Mario Brcic, Nikica Hlupic, Nenad Katanic, "Distributing the computation in combinatorial optimization experiments over the cloud", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 6, pp. 136–144, 2017. doi: 10.25046/aj020617
71. Kornkanok Phoksawat, Massudi Mahmuddin, "Hybrid Ontology-based knowledge with multi-objective optimization model framework for Decision Support System in intercropping", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 3, pp. 1363–1371, 2017. doi: 10.25046/aj0203172
72. Riadh Essaadali, Said Aliouane, Chokri Jebali and Ammar Kouki, "Optimization of Multi-standard Transmitter Architecture Using Single-Double Conversion Technique Used for Rescue Operations", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 3, pp. 73–81, 2017. doi: 10.25046/aj020311