Offshore Electrical-Oil Production Coupling System Reliability Analysis

The role played by offshore oil resources in energy supply is becoming more and more important, and the normal operation of oil production system on offshore oil platforms requires the reliable operation of the electric power system as a prerequisite; the failure of the components in the oil production system may lead to a large-scale production shutdown, and cause the related electrical components to shut down, making the power system ineffective in a certain range. In this paper, a coupled system model of the electric power system and production system of an offshore oil platform based on massively parallel computing is proposed. By analysing the connection between the oil production system and the electric power system, the coupled system model is established and the load data are calculated. Meanwhile, the reliability model of the coupling components is established based on the fault data, and the electric-related reliability index and the production-related reliability index of the coupling system are proposed. The broad-first search (BFS) algorithm was used to determine whether the coupling nodes were powered, and the depth-first search (DFS) algorithm was used to determine the connectivity of the coupling system. In addition, a minimum load-shedding model based on the integrated fault degree is proposed to reduce the load shedding of the coupled system.


Introduction
On offshore oil platforms as the base of operations for offshore oil extraction, processing, and transportation processes, ensuring the reliability of their power and oil coupling systems is an important guarantee for offshore oil operations.In actual production, how accurately assessing the reliability of the coupling system of power and oil production is important to achieve the normal operation of the offshore platform.
Most of the current reliability studies of electric power and other multi-platforms have conducted their reliability studies by establishing coupled systems.[1] and [2] regionalized the generation, transmission, and distribution system and assessed the reliability of the electric power system of offshore oil platforms in a system-wide context.[3] studied the effect of extreme weather on the coupled electricgas system to make the reliability index assessment closer to the real value under severe weather.[4] established a load-shedding model and analysed the impact of demand response on the reliability of integrated energy systems.[5] combines wind power hydrogen production with local hydrogen storage tanks and fuel cells to participate in a day-ahead economic dispatch, bringing better environmental friendliness and economy to the system.In [6], a minimum cut load model with actions according to load classes is proposed, and a model simplification method for minimum cost flow is proposed to improve the rationality of the interconnected power system structure in offshore oil fields.
This paper conducts targeted research on the coupled system of oil production for offshore power interconnection.Based on the fault data, a reliability model of the coupled components is established and the electric class-related reliability index and the production-related reliability index of the coupled system are proposed.The reliability of the coupled system is evaluated using an improved nonsequential Monte Carlo method.During the single sampling of the system, the BFS is used to determine whether the coupling nodes are powered, and the DFS is used to determine the coupling system connectivity.In addition, a minimum load cut model based on the integrated fault degree is proposed to reduce the load cut of the coupled electrical power-oil production energy system.

Structural Model of Offshore Power-Oil Coupled System
Offshore oil platforms are mainly divided into Central Platform (CEP) and Wellhead Platform (WHP).According to the power supply requirements, the central platform is generally equipped with a small power station structure and a certain number of turbine generators of the same type to supply power [7], which is required to meet not only its load demand but also the load demand of sub-platforms in the region.
In this paper, the structure of the oil production system is simplified, and each component of the production system is directly connected to the power system after simplification.The platform power distribution system mainly supplies power to the components of this platform coupling system, and the connection relationship between a WHP and the power distribution system is shown in Figure 1.

Stability assessment process of electro-oil coupled system
To assess the reliability of a coupled system, the state j of the power system must first be evaluated to determine the connectivity of the coupled nodes before further evaluation.We chose a non-sequential Monte Carlo method for sampling component states based on a state sampling approach, where model components are classified into normal and fault states, or numbers in the range [0,1] for normal, fault, and repair states.To quickly traverse each node of the attributed topology one by one, a vertical topdown traversal method using DFS was chosen.
After each oil platform and power system state sampling, the connectivity of each node of the coupled system is judged on the premise that the end nodes of the distribution system are connected, and then whether there is a branch connection in the production process of the coupled system.First, the connectivity of the end nodes of the distribution system is judged by BFS, and then the connectivity is judged by DFS, and if it is connected, the production process can continue, otherwise, it returns to the previous node for traversal.

Electricity-related reliability indicators of offshore power and oil coupling system
After establishing the reliability model of the coupled components, the system-related reliability indexes are proposed from two aspects, namely, electricity and oil production, according to the characteristics of the coupled system itself and the operation mode different from that of the electric power system.
The specific evaluation indicators are as follows: 1) The probability of production load curtailments (PPLC) represents the probability that the production process will be affected by the removal of its component load in a coupled system.The calculation formula is as follows: =1 () where is the set of system states in which load state i generates a cut production load quantity; is the number of occurrences of state j; is the total number of samples sampled for load state i; is the duration of load state i; is the total time of each load state; is the number of production load states.
2) The expected number of production load curtailments (ENPLC), in units of times/year, refers to the number of times the state of the system with (without) cut production load is transferred to the state of the system without (with) cut production load.The calculation formula is as follows: where is the total number of transfer rates leaving the cut production load state j; is the k-th transfer rate of the component leaving the coupled system cut production load state j.
3) Expected duration of production load curtailments (EDPLC), in h/a, indicates the duration of time per year that the component load is removed from the coupled system and is calculated as follows: ×8760 EDPLC = PPLC .
(3) 4) Expected probability of coupled system failure (EPCSF), which indicates the annual probability of failure of the coupled system, is calculated as follows: =1 ( ) where i F is the set of coupled system fault states at the i-th load state.5) Expected time of coupled system failure (ETCSF), in h/a, indicates the duration of failure of the coupled system per year and is calculated as follows: =1 ( ) where j T is the sustained failure time of the coupled system state j.
6) Expected Production Energy Not Supplied (EPENS), in MWh/a, indicates the expected value of the coupled system being supplied with insufficient production power and is calculated as follows: =1 () where j C is the amount of cut production load corresponding to system state j.

Oil production-related reliability indicators of offshore power and oil coupling system
Such indicators are designed to evaluate the number of further losses caused by the impact on the entire production process.IOP Publishing doi:10.1088/1742-6596/2592/1/0120344 1) Probability of Invalid Production Energy Supplied (PIPES) is used to evaluate the probability that a coupled system will supply invalid electrical energy in one year.The calculation formula is as follows: =1 ( ) where A is the amount of supply inefficient production load corresponding to system state j.
2) Crude Oil Production Loss (COPL) in m3/a, which is used to measure the average annual production system oil reduction due to coupled system failure.The calculation formula is as follows: where i S is the set of all coupled system failures leading to production reduction states; i P is the crude oil production reduction corresponding to the unified state i; i T is the duration of system state i.
3) Diesel Fuel Production Loss (DFPL) in m3/a, which is used to measure the average annual production system oil reduction caused by coupled system failures.The calculation formula is as follows: where i D is the diesel reduction rate corresponding to system state i.

Integrated Fault Degree-Based Load Cutting Model
After each determination of the system state, a tidal current calculation is required to determine if the line is overloaded, and a load-shedding operation is required.In this subsection, the optimal loadshedding model is proposed and a method adapted to the tide calculation of offshore oil platforms is selected.

Regional proximity cut load model
The components used in offshore oil platforms have a total of three states, and the three-state model includes normal operation state, fault state, and maintenance state.The non-sequential Monte Carlo sampling method often requires multiple simulations of many system states, for each of which fault analysis and load cut evaluation are performed.In these fault states, the original system structure may have undergone minor changes, such as a busbar fault that prevents some loads from being supplied, or in more severe fault states, the system may have been disconnected, forming an "island" structure without power.
Based on the relevance to the production process, the components are divided into 21 levels of production load and 10 levels of power system load.The importance of the load decreases with the increase of the critical level.The principle of load removal is that no smaller level load shall be removed until the removal of a larger level load is completed.

DC sensitivity analysis
Since the non-sequential Monte Carlo method requires many systems states to be simulated, each nonrepetitive state requires a tide calculation to determine whether to cut the load or not, so the DC tide method is less computationally intensive and faster.The DC current-based load-shedding model can be described as follows: The overall objective is to minimize the amount of cut load and the objective function: The constraints include two formula constraints, the tidal formula constraint, the active power balance constraint, and some inequality constraints, the load cut constraint, the line tidal constraint, and the generator output constraint.
In addition, to quantitatively describe the importance of each load point in the production process and to consider the impact of faults on the production system and the power system, the concept of comprehensive failure degree (CFD) is proposed in this paper, and the constraints on the degree of faults are added.The specific calculation formula is shown below: where n S is the set of nodes ranked from smallest to largest integrated fault degree; i CFD P is the amount of node load with integrated fault degree I; i ELL is the load level of the busbar power system to which load i is connected.

Example of calculation
Offshore oil platforms are now mostly supplied in the form of a network [8].In this paper, an offshore oil platform group is used as an example for analysis, which consists of three central platforms and eight wellhead platforms, and the specific location distribution and network schematic are shown in Figure 2.

Analysis of calculation results
To make the estimation more accurate when performing the calculation of the arithmetic example, the coupled system is calculated with 30, 000 samples, the reliability assessment index is shown in Table 1, and the variance convergence graph is shown in Figure 3.In terms of failure probability, the power system failure probability is 1.45 times higher than the coupled system failure probability, and in terms of failure time, the power system failure time accounts for 50.48% and the coupled system failure time is 49.52%.The power system failure time is overwhelmingly composed of transmission system failure time, while most transmission system failures, although they will cause its directly connected sub-platform coupling system to be affected, only a very few transmission failures will only cause the interconnected system to decouple into several parts without causing coupling system failure, so the coupling system failure time is only slightly smaller than the power system failure time.
2) Comparison of load shedding indicators: In terms of the number of load shedding, the load-shedding of the power system is only slightly more than that of the coupled system, and once the transmission system cuts load, it is more likely to cause the overall load shedding of the wellhead platform connected to it, and thus its coupled system has a load shedding situation.In terms of load-cutting time, the power system load-cutting time is 1.34 times longer than the coupled system load-cutting time.For the coupled system, its load is not cut due to the backward order of cut, and at the same time, the gap between the two types of systems in terms of cut load time is more obvious due to the long repair time of the interconnected submarine cable.
3) Comparison of power shortage expectation: The table shows that the expected value of power shortage in the power system is 3.45 times higher than the expected value of power shortage in the coupled system.Since the load reduction model based on the integrated fault level prioritizes the removal of unproductive loads, it makes the proportion of coupled system power losses smaller than its load volume proportion by about 9%.4) Analysis of other coupled system reliability indicators: The crude oil daily production and diesel daily production data of each offshore oil platform were statistically derived, and the production-related reliability indexes of each offshore oil platform coupling system were sampled and calculated for a total of 30, 000 times, and the production-related reliability indexes of each platform were obtained as shown in  The amount of oil loss from each platform is positively correlated with its oil production, but on this basis, it is the structure of the coupled system and the weakness of its connected distribution system links that affect the final loss value.

Conclusion
To study the mutual influence relationship between the reliability of the electric power system and the reliability of the production system of an offshore oil platform, a coupled system model is established in this paper, taking the electric power system and the production system of an offshore oil platform as the research object; the reliability of the coupled electric power-oil production system is evaluated by using the improved non-sequential Monte Carlo method.
The actual failure data was used to establish the coupled component reliability model.In the system state assessment, the BFS algorithm is used to determine whether the coupling components are reliably supplied, and the DFS algorithm is applied to determine the production process connectivity.The production fault degree is considered based on the regional proximity cut load model, and a comprehensive fault degree index is proposed to comprehensively judge the importance of the load, which reduces the amount of load removal in the coupled system.

Figure 1Coupled system structure connection diagram
Figure 1Coupled system structure connection diagram

P
is cut production load quantity for load i ; D N is the set of load nodes; i  is the production importance level of load i .

Figure 2
Figure 2 Offshore oil platform network diagram B is the nodal derivative matrix;  is the nodal voltage phase angle vector; 0

Table 1
System electrical-related reliability index results Convergence diagram of the variance of the coupled system reliability index Further analysis of the reliability indicators in the table yielded the following results: 1) Comparison of failure indicators:

Table 2
Production-related reliability indicators for each platform