The electrical energy produced must be consumed at the same time, hence the need to achieve a balance between supply and demand. Therefore, the production, transport, and distribution systems together constitute an electricity network. The distribution networks are designed to deliver energy to consumers. Unacceptable voltage drops are observed in the distribution networks of developing countries such as Burkina Faso. A study was carried out on the distribution network of the city of Bobo-Dioulasso in Burkina Faso. It allowed for experimentation with the "Megger MPQ1000" network analyzer to evaluate the quality of the voltage supplied to households. To this end, tests were carried out in a public distribution station and at a few subscribers in the Sarfalao district of the city of Bobo-Dioulasso. These tests were used to assess the percentage of voltage drops. These values, which are higher than 8% of the nominal voltage, are not regulatory. The load curves of the consumers in the district were also drawn. Indeed, the period of the high load is between 19:00 and 23:00 Local Time (LT), while the period of the medium and low load is between 00:00 and 18:00 LT.
Residential photovoltaic (PV) systems connected to the grid are used for selfconsumption. Any surplus production is fed into the grid and contributes to improving the voltage. Several techniques are developed to model their connection. However, studies on methods of injecting energy production into the Low Voltage (LV) network are nowadays a problem. This paper proposes a mathematical model to determine the current to be injected and calculate each node's voltage. The current equation is a recurrence relation with an initial condition. This initial condition is for the case of a single PV system connected to the LV grid. The equation can also be written in matrix form. Similarly, the voltage solution is a recurrence relation. It also has an initial condition for the first node. Both mathematical formulae with the proposed initial conditions are consistent and can be used for the determination of the current and voltage of the different nodes in the grid.
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