Modeling of reliability of power supply systems with autonomous energy source

The methodology for calculating the reliability of power supply systems with autonomous and mixed energy sources has been considered. Autonomous sources are widely used in industrial power supply systems as primary, backup or emergency sources. The functioning and interchangeability of these systems has features that affect the reliability of power supply. The proposed methodology is based on the method of semi-Markov random processes and can be used for comparative analysis of the reliability of options for power supply systems. The methodology has been brought to software implementation and is accompanied by an example of calculating the reliability of the power supply system for stationary marine oil production platforms.


Introduction
Objects of production, transportation and refining of oil and gas are complex continuous production, which put increased requirements for the reliability of power supply [1][2][3][4]. Autonomous power plants of own needs (PPPON) based on diesel or gas turbine units are used to power consumers of electricity in oil and gas industries. Depending on the number and type of PPPON units used, the conditions for their parallel operation with centralized power supply sources, various options for power supply systems with autonomous power supplies can be used. For a comparative analysis of the reliability of options for power supply systems, a technology based on the mathematical method of semi-Markov random processes is proposed [5][6][7][8].

The methodology for modeling and calculating the reliability of power supply system
Includes the following steps [2,6,7]: • Formation of the space and graph of the state of the system; • Mathematical description of the space and graph of the state of the system; • Determination of indicators of system reliability. Formation of the space and graph of the state of the system.
When performing this stage, for power supply systems it is necessary to take into account the working, standby and repair conditions of power supplies and system connections, i.e. power lines, connecting distribution devices of 6 (10) kV technological installations to which generators of autonomous power sources are connected. Along with structural redundancy, characterized by a reserve of generating capacities and backup links, power supply systems also have a temporary reserve [4,7,10]. Temporary redundancy consists in the fact that consumers allow a short interruption in power supply. A break in the power supply during the operation of the automatic switch-on reserve (ASOR) does not stop the process and not considered as failure. Along with failures of elements (sources, lines) and failures in the operation of the reserve input, it is necessary to take into account the possibility of system failures, which may be due to interruptions in the supply of fuel to generating electrical units and the failure of relay protection of power supply systems Failures of system elements occur with the intensity year; / 1 , . The probabilities of events make it possible to "sift" the flow of failures and recoveries [9,11]. In case of unsuccessful ABP, the operator carries ,... , , In the formation of states, it is necessary to take into account the main states and neglect the secondary ones. It is accepted that the combination of independent failures of more than three main elements of the system is impossible [3,5]. A subset of nonfunctional states can be divided into a number of levels, ranked by the energy deficit in the system.

Mathematical description of the space and graph of state of the system.
Initially, the process is described by the matrix   The Gauss method is used to solve the system of equations.

Determination of system reliability indicators
Calculation of the reliability of power supply to consumers comes to the determination of reliability indicators. A set of reliability indicators includes: year , During scheduled preventive repairs (SPR) of the main elements of the system, i.e. units of power plants and system connections, the level of redundancy of the system decreases, which reduces its reliability during the specified period. The evolution of the system during SPR corresponds to its own graph of states and transitions, which allows to calculate the reliability indicators of the system in the corresponding period. The resulting reliability indicator of the system is calculated as a weighted average, taking into account the value of the corresponding indicator and the duration (hour) of the system during the year in normal and repair situations.
Reliability calculation algorithms are implemented in the RELIABILITY program, using which calculations were performed in the example below.

An example of calculating the reliability indicators of the power supply system of a platform of compressor station of the marine oil production
The compressor station of power plant consists of three units with a rated power of 2800 kW each. In normal mode, two units operate at a combined tire system, loaded at 50%; the third unit is in reserve. In addition to the power plant units, a backup source for the compressor station is communication with the power supply system of the central platform (CPU). Communication throughput is 1600 kW.
In case of failure of the power plant unit (intensity 1  ), it turns off and the standby unit automatically turns on. In case of unsuccessful ABP, part of the load is disconnected by the automatic unloading system. The graph of states and transitions of the power supply system of the compressor station in the normal mode is shown in Fig. 1. The states of the system in the normal mode are shown in Table 1. Fig. 2. shows the data input interface.

Conclusion
A method for calculating the reliability of power supply systems with autonomous power supplies is proposed, which is developed based on analysis of the features of power supply for oil and gas industry objects and allowing more reasonably choosing options for power supply of industrial complexes during their design and reconstruction. The technology was created on the basis of semi-Markov random processes, brought to a software implementation and is effective for rapid assessment of the reliability of systems with autonomous power sources.