Reliability assessment of grid-connected multi-inverter for renewable power generation sector

Purpose – The paper aims to present a grid-connected multi-inverter for solar photovoltaic (PV) systems to enhance reliability indices after selected the placement and level of PV solar. Design/methodology/approach – In this study, the associated probability is calculated based on the solar power generation capacity levels and outages conditions. Then, based on this probability, dependability indices like average energy not supplied (AENS), expected energy not supplied and loss of load expectations (LOLE) are computed, also, another indices have been computed such as (customer average interruption durationindex(CAIDI),systemaverageinterruptionfrequencyindex(SAIFI)andsystemaverageinterruptiondurationindex(SAIDI))addressingbyaffectedcustomerswithdistributionnetworksreliabilityassessment, includingPV.Onthebasisoftheirdependabilityindicesandactivepowerflow,severalPVsolarmodulesinstalledinseveralplacesareanalyzed.Amechanismforassessingtheperformanceofthegrid ’ sintegrationof renewable energy sources is also under investigation. Findings – The findings of this study based on data extracted form a PV power plant connected to the power networksysteminDiyala,Iraq132kV,attemptstoidentifythesystem ’ sweakestpointsinordertoimprovethe system ’ s overall dependability. In addition, enhanced reliability indices are given for measuring solar PV systems performance connected to the grid and reviewed for the benefit of the customers. Originality/value – The main contributions of this study are two methods for determining the reliability of PV generators taking into consideration the system component failure rates and the power electronic component defect rates in a PV system which depend on the power input and the power loss using electrical transient analysis program (ETAP) program.


Introduction
The majority of research in the past and present has focused on the rising of the cost of PV module production and related technological developments (Allan, 2013).
A PV module that transforms solar energy into Direct Current (DC) power and an inverter that transforms DC into AC make up grid-connected PV systems. The utility grid's ability to use PV power has advanced significantly at the same time that global energy consumption is rising. Due to their relatively high cost, few PV systems have been incorporated into the grid (Barakat, Ibrahim, & Elbaset, 2020).

Reliability of grid-tied multi inverter PV
Consequently, highly dependable PV power systems will greatly enhance the output of renewable energy and ensure a greater return on investment.
A grid-connected PV system's grid connection must be implemented by DC-AC converters (inverters), which do this task by transforming the DC from the PV array into a sinusoidal waveform synced with the utility grid (Mudgal, Yadav, & Mahajan, 2019).
Inverters are technology that enables the grid connection of PV systems. Because of the high production capacity of PV modules, both companies and consumers utility is highly concerned about the dependability of PV power systems that are grid-connected (Zhang et al., 2012). Typically, multiple weak points are present in a PV power system (Sayed, El-Shimy, El-Metwally, & Elshahed, 2019), incorporating solar cells and electrical power equipment (Kumar et al., 2020).
When an inverter is reliable, it produces output power that satisfies power quality standards. The inverter might be needed to control the PV module's power output, connected and disconnected with the grid, and monitor and report of the system's health.
Consequently, a significant amount of available research focuses exclusively on evaluating the dependability of critical subsystems, such as the inverter (Martins, 2013).
In contrast, there are comparatively few publications that cover the evaluation of PV system dependability. Based on a system average interruption frequency, duration indices and customer total average interruption duration indices (Hase, Khandelwal, & Kameda, 2020) and (Akhtar, Kirmani, & Jameel, 2021) offered more straightforward system-level models for PV system reliability. Additionally, the usual timeframe for energy delivery was not met.
Other common unavailability indicators include average service unavailability index (ASUI), the complement of average service availability index (ASAI), as well as Mati (assessment of the reliability of large electric power systems). One example of the value-based approach being used to improve distribution reliability is the usage of the feeder indices system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), CAIDI and ASAI ( Cepin, 2011). SAIFI, SAIDI and CAIDI, as well as ASAI, ASUI, energy not supply (ENS) and average energy not supplied, are listed as the most prevalent indices in the distribution system article (Karki et al., 2014).
As indicated by the prevalence of the phrases SAIFI and SAIDI, it is assumed that customer interruptions are linked to reliability. According to sources, ASAI and CAIDI are also widely used, however they can be computed instantly from SAIFI and SAIDI (Roy, Robert, & Allen, 2003).
In Abed and Mhalla (2021), where they used Monte Carlo simulation to determine the effect of inverter failures on the system's overall lifetime, significant advancements to PV reliability modeling are presented. The failure rates of electronic components or it's probabilities in PV systems are treated as constants in older literature.
This study's measurement of the impact of a single medium-or large-sized inverter dedicated on a group of PV panels to measure the failure rates of crucial parts including PV modules, inverters and capacitors using a variety of reliability approaches is consider a noteworthy addition. The suggested strategy makes using of how multi-inverter reliability affects PV system performance and energy output.
The renewable energy resource with the greatest potential in Iraq is solar energy. Numerous nations have successfully installed PV power plants. This article examines the proposed development of a 5 MW PV power plant in the city of Diyala. This substation is located in Diyala, which is in the Middle East, on large-scale PV power plant projects in the 132 kV Iraq network; the site is ideal for installing a solar power plant. For the Diyala network, electrical transient analysis program (ETAP) and MATLAB code have been created to regulate the electrical power distribution and highlight the distribution process's excessive volatility.
The rest of the paper is arranged as follows. Section 2 provides the power flow grid connected PV solar source. Section 3 presents the analysis of load flow. Section 4 describes the reliability modeling of PV inverter. In section 5 we present the reliability indices based PV system. Sections 6 and 7 have flow chart and case study respectively. Section 8 displays the results discussion, and at the end we have section 9 that presents the conclusion of the paper.

Power flow grid connected PV solar source
The operational flexibility of the load distributor is increased by using renewable energy sources. In order to alter the bidirectional power flow in grid-connected hybrid energy systems and produce changeable renewable energy, it can be take the advantage of the adaptive properties of renewable energy sources. The network experiences more minor issues with the operation of grid-connected hybrid energy systems (Shalash et al., 2023). Renewable energy sources may be both used and supplied via the electric system. In this mode of operation, a variety of loads can be supplied by using bidirectional power, power from renewable energy sources and the external grid. New technologies are included into the grid as a part of a new system for better grid electricity regulation (Ibraheem & Abdulraheem, 2021).
We can simplify the system topology of power converters and renewable energy in Figure 1.
For ease and simplicity, we illustrated the renewable energy sources and residential, commercial industrial customers and power converters which are found in distribution system as lumped blocks. Some of loads such as the loads at the top of figure are separating from the load isolation due to its usage for distribution indices.

Load flow analysis
The algorithm of Newton-Raphson (NR) for load flow to analysis the essential findings to estimate the change in the flow of active power (AP) and power losses are executed by ETAP software, Figure 1. Integrating the distribution system with the PV system This algorithm provides a new and powerful technique for calculating the power flow of NR three-phase using the current injection method, also we have written the equations of threephase current injection are in rectangular coordinates. The technique of a sparse and effective matrix technique is applied for investigating the ordering and forward/backward substitution. This method is used to calculate the power flow on real-balanced and unbalanced distribution systems (de Oliveira & Guedes, 2007).
This may be achievable if the solar PV system that is associated with the distribution system generates excess electricity (Hassan, 2022).
Power loss is left out of the equation, the maximum AP is obtained when the resistive of the power transmission line is very small near to zero, that means the power loss can be neglected, because it needs to test distribution indices, and regulated power levels are taken for granted. They are acceptable objects for dependability analysis (Shalash et al., 2014).
The distributed system combined with renewable energy sources operates in the gridconnected PV energy, and the component failure mode of the energy system occurs due to the multiple component failures of the proposed system (Salman, 2015).
Either the generating mode or the off mode may be used by the inverter. Within the current-limiting range, the inverter may operate in one of three main ways: reactive current support, real power support or user-defined PF.
An inverter is regarded as an injector of a continuous current into the network up to the maximum value of the current-limiting curve when it is operating in the current-limiting mode. As a result, it qualifies as a source of continuous current in terms of current volume but not in terms of the current's active and reactive components. One of the three operating modes mentioned above determines how much of the inverter's current is made up of reactive and dynamic components for wind turbine. The user-defined PF was chosen for this work. The reason is that, the ETAP program takes one of the three methods of controlling during operation mode. The current-limiting curve for current is shown in Figure 2.
In this research, the best place for PV generators is seen as the answer to the reactive power (RP) shortage. Our study shows that, even if the PV generator is not a source of RP, positioning it in the network's ideal location may dramatically lower RP demand by reducing RP losses in transmission lines (Shalash & Ahmad, 2013& Wohlgemuth, 2020. The inverter's fault ride-through (FRT) curve is shown in Figure 3. It has many settings for setting the Iq limitations. When the inverter's terminal voltage exceeds Vop, min, the FRT control will not be effective and only works throughout the current-limiting band. Since the following (or absorbing RP) mode is little or never employed in functional short-circuit circumstances, this paper will only cover the leading (or injecting RP) mode (Kaaya et al., 2021). For normal inverters, PV inverters and other types of inverters, the same concepts for continuous current injection with given active and reactive current controls are used.
Contrarily, on-grid solar-PV systems are the greatest choice for rural locations where it is difficult to get power from conventional sources (utility grid). An energy storage device's existence or absence is affected by the load's instantaneous power balancing restriction. Offgrid solar PV systems that power wait-able loads shouldn't use energy storage.
where P gridi 5 0 and Q gridi 5 0 represents the net AP and RP at i-bus, respectively. P PVi and Q PVi represent, at the i-bus, the DG AP and RP, respectively. The discussion of active and reactive load needs P demi and Q demi , respectively. Y i,j the branch entrance between the I and j-buses is shown. The bus voltage at the j-bus is denoted by V j , δ i and δ j specify the respective phase angles of the voltages on the i-bus and j-bus.
(θ i À θ j ) are the branch impedance angle between the i and j busses. The actual power load decreases due to operational and RP shortages is calculated by using the formulas expected energy not served (EENS).

Reliability modeling of PV inverter
IGBT power modules, diodes, firing circuits, DC link capacitors and AC and DC contactors are common components found in three-phase PV inverters. The PV inverter's design was streamlined by eliminating a number of subassemblies. Without respect of the kind of layout, the inverter's overall dependability data is gathered (single-inverter system, string-inverter system or multi-inverter system). Even if these arrangements significantly affect determining something's dependability, the suggested simplification makes sure that a variety of possibilities are gathered and produces a more accurate result (Barakat, Ibrahim, & Elbaset, 2020). As a consequence, a PV inverter lacks parallel redundancy; if one component fails, the whole inverter will also fail. As a result, the PV inverter's dependability may be described as a series network. PV inverter availability, maintenance time and failure rate "λ" are stated as follows: Where are the subscripts, repair times, availability, IGBT, diode and capacitor failure rates, respectively. According to Ibraheem and Abdulraheem (2021), all three indices are dependent on the input voltage, temperature and power flow via the PV inverter. Additionally, as shown in Table 1, the availability of the DC disconnects and AC subpanel may be assessed based on their failure rates and repair times: 5. Reliability indices based PV system (Ahmed, Al-Sulaiman, & Khan, 2022) PV reliability analysis seeks to assess the performance of PV systems and provide reliability indices that help in deciding the best design choice during the planning phase and in devising strategies to get lower operating costs and boost benefits. Two categories of dependability indicesenergy-oriented and time-oriented indices are presented in order to achieve this aims.
The SAIFI shows the frequency of sustained interruptions encountered by the average customer over a set time period, often one year.
C i : is the proportion of clients impacted by each incidence. C T : represents the total number of consumers for which the index is calculated.
SAIDI represents the total duration of interruptions experienced by the typical customer within a predetermined time period.

SAI DI
t i : is the time required to recover from each interruption i. (

3) Customer average interruption duration index (CAIDI).
CAIDI is the typical time needed to resume service.

AGJSR (4) Customer total average interruption duration index (CTAIDI).
The customer total average interruption length index is used to illustrate the entire average length of power outages that customers encountered throughout the reporting period.

CT AI DI
C c : consumers affected by at least one outage throughout the reporting period.
The ASAI indicates the percentage of the reporting period which a customer had access to electricity during it.
T: is the span of time (8,760 or 8,784 h in a leap year).
The AENS index shows the typical amount of energy that wasn't provided to consumers during a certain period of time.
Pi: The amount of work that is often lost due to outages. Ci: implies no energy delivery (interruptions).
The ACCI shows the average amount of energy that consumers who had their power cut off didn't get during a certain time period.
6. Flow chart Figure 4 depicts a flowchart for determining the PV placement, PVsizing and system dependability of the PVs on 47 buses.
(1) Firstly by using ETAP, enter PV properties like solar irradiance and inverter of the electrical distribution system that is used by PV Editor. then calculate the reliability indices by running the power flow and short circuit (SC) limits and after that running the properties of DCcuk inverter such as failure rate.
(2) Before attaching PV, calculate the load active and RP consumption from the annual load curve and SC restrictions.
(3) Add the total required AP of PV generators to the power flow In selection of PV sites it has been found that adding PV generators to a network makes it safer because there will be available AP, Figure A1.
As was said in the part above, properly positioned PV generators may increase dependability greatly by using less RP. RP requirements are reduced via decreased the loss of RP in the network. The PV generators placement is crucial since voltage variations might have an impact on the distant buses. Table 2 illustrates that Q has increased as a result of an increase in the network's RP shortage with a power factor (PF) of 0.85. With a PF of 0.85, the lowest values of P and Q are larger than the case when PV is connected.
The chosen system, which uses a model predictive-based cuk converter and a solar energy system-based 3 phase inverter control, is subjected to a reliability study.   Table 2. power flow after and before PV connected assessed solar-wind energy systems connected to bus 21 and described in Tables 3-5 with capacities ranging from 1 MW to 5 MW. The basic situation, Example 1, is examined without using any additional solar energy gadgets. Table 3 shows the final capacity outage probability for all units, with EENS3 equal to 1,446,433,500 MWh annually. It is estimated that 1 MW will contribute about 2,663 MWh.
Tables 3-5 show the reliability outcomes for the power system with various load percentages. The study's tabular findings demonstrate that incorporating renewable energy sources into the grid increases grid dependability. A solar energy system with a higher rating than Case 1, for instance, can increase the EENS for heavy systems, which increases grid reliability. Figure A1 shows the single line diagram of the diyala network after running power flow by using ETAP.

Result and discussion
The programs evaluated both system indices (SAIFI, SAIDI, CAIDI, ASAI (ASUI), ENS, (ACCI)) and individual load point indices (failure rate, outage length and yearly unavailability). When there is no PV and inverter in the network, the SAIDI equals 379.6419 hours/year, the SAIFI 5 35.8036 interruptions/year and the EENS equals 144643.500 MWh/year. Table 3 displays the reliability indices when PV generators are located at bus stop 12 with a PF below 0.85 and a 10% load change.  Table 5. ALII, ASAI and ASUI after and before PV connected Table 4. CAIDI, SAIFI and SAIDI indices after and before PV connected Table 3. ACCI, EENS and AENS indices after and before PV connected probability distributions for load point changes, as shown in Figure 6. Figure 6 demonstrates that the PV generators at bus 12 are more reliable when the PF is 0.85 since the EENS is lowest in this situation. Even more reliability will be added if more PV generators are added to the network. We can control the PV level instead of conventional load shedding, to modify reliability indices in order to involve the values of interrupted parts of PV level for all customers.
As it appears be in Table 3, the effect of the failure rate on forced outage rate increased remarkably the values of the basic reliability indices.
In Table 3, the reliability indices values (EENS and AENS) may be larger compared to the first values when the bus is not connected to PV, but this does not mean that the performance is better. For example, the large values of ACCI lead to a large number of interruptions that have higher duration.
So this requires studying another indices such as (CAIDI, SAIFI and SAIDI by using eq. (4), (5) and (6) to design the distributed generation such as PV connected to grid, which based on number of customers and interruptions, the results shown in Table 4, the (CAIDI, SAIFI and SAIDI) values of the overall system is increased, therefore, dyala grid reliability is improved. SAIDI growth is higher than SAIFI because of the causes leading to more time of the outages were cleared up based on increased PV level.
In Table 4, a comparison of the commonly used reliability indices CAIDI, SAIFI and SAIDI, which are the main ways to measure the level of reliability, demonstrates the number of customers connected to each load point in the system and the average amount they use. Figure 7 illustrates how several utilities in the Dyala grid compute the fundamental statistics of SAIDI, SAIFI and CAIDI as well as the hr/customer, Year for assessing load point variations. Table 5 compares the widely used reliability indices ALII, ASAI and ASUI using the number and average load of customers connected at each load point in the system by using eq. (8), (9) and (10). These are the most significant measures of dependability.
As illustrated in Figure 8, several utilities in the Dyala grid compute the P.U for analyzing load point changes as well as the fundamental statistics of ASAI, ALII and ASUI. The total performance of the distribution system may be assessed using these extra metrics. Figure 6. ACCI, EENS and AENS after increasing 10% of load

Conclusion
Inverter reliability is a complex issue with many possible failure reasons due to the complexity of the inverter's switching and monitoring processes. In addition to meeting power quality criteria for output power, the inverter may also need to control the output power of the PV module, connect to and disconnect to the grid, read and report status, and keep track of islanding. The evaluations in this paper confirm that the PV levels connection to distribution grids may cause a direct impact reduction of load on reliability indices.
We have studied the impact of RP on the reliability of PV inverters by decreasing active and RP losses. This study's major objective was to boost the Diyala Electric Power (132 kV) Figure 7. SAIDI, SAIFI and CAIDI after increasing 10% of load Figure 8. ASAI, ALII and ASUI after increasing 10% of load grid's efficiency. Utility engineers may use it to determine the optimum network reconfiguration strategy.
The suggested analytical approach for assessing the reliability and performance of the components of PV system has been used with the methodology for power plants in Iraq. The two main contributions, the first is the approach for figuring out the reliability of PV levels that depend on the power loss, and the second takes into account outages conditions of system parts based on the failure rates of power electronic parts in a PV system.