Distribution network risk assessment with distributed generation impact based on non-sequential Monte Carlo method

At present, the development of renewable energy distributed generation is fast, and the distribution network is facing significant challenges. Unlike traditional fossil fuels, new energy generation is characterized by significant volatility caused by uncertain factors like environmental and meteorological conditions. This paper presents a risk assessment index system that utilizes the non-sequential Monte Carlo method to tackle the given issue. The system comprises two assessments: voltage limit risk and reliability index assessment. Through the application of the Monte Carlo method, a comparative analysis of the results with alternative calculation approaches is conducted. Subsequently, these findings are utilized to evaluate the effectiveness of two commonly employed protection strategies.


Introduction
At present, the smart grid, which is marked by the intelligent distribution network, has been widely studied, and in the context of future smart distribution networks, a crucial role is played by the safe and reliable integration of distributed power sources like wind power and photovoltaic generation.When numerous distributed power sources are interconnected with the grid, they serve as a backup electricity supply during system failures, ensuring uninterrupted power supply to users.Simultaneously, this integration transforms the distribution network structure, evolving it into a multi-power system, which introduces potential challenges and risks to the operation and control of the distribution network, diverging from the conventional radial distribution network model.A risk assessment method is proposed for intelligent substations based on Markov models [1].Firstly, a Markov model is used to model devices with the same hardware structure and functionality, to achieve state evaluation of secondary devices.The aim is to minimize the security risk and total operating cost of the receiving power grid, and an optimization model for the receiving power grid operation is constructed considering security risk assessment [2].The effectiveness of the proposed optimization model for the receiving power grid operation considering security risk assessment is verified through numerical simulation.A first-second coupled multiple-fault model was established [3].Then, Latin hypercube sampling is applied to realize the rapid generation of the initial fault set, and then risk indicators such as system load loss, node voltage out of limit, branch power flow out of limit, etc. are evaluated.However, these schemes have less consideration for distributed power sources, and due to the distinctive attributes of distributed power sources, they cannot be entirely treated as conventional backup power sources when it comes to reliability and risk assessment.Consequently, the current reliability and risk assessment approaches for distribution networks face challenges in their applicability [4].As a result, there is a need to investigate novel reliability and risk assessment techniques tailored to the unique environment characterized by the integration of distributed power sources in distribution networks.

Adaptive current quick-break protection strategy
The core concept behind adaptive current quick-break protection is to enhance the responsiveness of the protection system by dynamically calculating the system equivalent impedance (Zs) and fault type coefficient (Kd) based on the current operation mode and fault type of the power grid.This real-time computation allows for the determination of the short circuit current at the end of the line, and the online settings are adjusted accordingly to avoid this specific current value.The ultimate goal is to optimize the protection device's adaptability to different operational scenarios, leading to an overall improvement in protection performance [5].
In the given formula, the reliability coefficients, denoted by rel K ϒ , can be assigned values within the range of 1.2 to 1.3.Kd is also a constant.Es can be determined using the pre-set or accurately calculated value of Es=Ud+IdZs.Here, Ud represents the voltage measured after the fault, Id denotes the current measured after the fault, and ZL represents the impedance between the protection device and the fault point.
The protection range of adaptive current quick-break protection is that although a is not a constant and decreases with the increase of Zs, independent of Kd, it can make the protection in the optimal state under the corresponding operating mode.For the successful implementation of adaptive protection, continuous real-time monitoring of power system parameters becomes essential.It enables the swift acquisition of fault type and system impedance Zs information precisely at the moment of fault occurrence.Subsequently, the protection device's setting value is calculated using Formula (1) based on the current operating mode.This calculated value is then compared with the actual short-circuit current to make a decisive determination on whether the protection should trigger the tripping action.

Wide area protection strategy
Through the utilization of measurement and communication systems, comprehensive data from multiple points within the power system can be gathered, enabling the swift, dependable, and precise removal of faults [6].Additionally, following the resolution of the fault, this approach facilitates the determination of alterations in network structure, power flow distribution direction, and overall operational stability, and corresponding control measures can be taken.This system that simultaneously realizes relay protection and automatic device functions is called a wide area protection system.Traditional protection only needs to analyze a single component, and the primary objective is to guarantee fault isolation within the system by effectively utilizing the tripping and closing switches integrated into the system components.These switches play a crucial role in swiftly disconnecting faulty components from the system and restoring them once the fault has been resolved.The interconnectivity between each component is relatively small, and it does not take into account the operating conditions of non-fault areas or the problems caused by the action of this component on non-fault areas.Wide area protection, by measuring various electrical information at all points within the system, can quickly locate faults [7], receive operational data from the entire system, and perform state estimation and safety assessment analysis on the system from the highest point, avoiding the occurrence of large-scale power outages.In wide-area protection, intelligent electronic devices (IEDs) play an indispensable role.Their main functions include communication and liaison, responsible for exchanging information with the main station and peer-to-peer communication with other IEDs in the same area.Based on their information and receiving information from other IEDs through the communication system, they can jointly formulate protection strategies.
The architecture of the wide area protection system is widely used as a distributed structure, which does not require centralized control and only retains the communication interface region decision unit (RDU) between the IED and the substation main control device to upload information [8].

Non-sequential monte carlo method
Currently, the main methods of power grid risk assessment are an analytical method and the Monte Carlo simulation method [9].Due to the different mathematical ideas of these two methods, their specific calculation methods and implementation steps are very different.However, with the widespread integration of distributed power sources, the uncertainty of risk has greatly increased [10], making the Monte Carlo simulation more widely used.The non-sequential Monte Carlo simulation method does not extract the element states according to the time sequence but uses the probability of each element in the state to determine the state, so it is also called the state sampling method [11].The steps are as follows: (1) Randomly and uniformly generate n numbers U on [0,1].
(2) Components in the system can be categorized into two distinct states: operational and failure.The state of an individual component remains unaffected by the states of other components, and it is determined by the following equation: The formula includes FORi, which stands for the forced outage rate of component i, representing the probability of a component being unavailable.In the case of a derating operation state, as observed in distributed power sources like photovoltaic and wind power, the component can experience derating.Under such circumstances, the state of component i is determined by the following equation: a tn 2 ( ) ( 0) in the formula, PDRi refers to the probability of component i in the derated state.
(3) Use the state combination of all elements to form the system state (assuming that the system contains N elements).The system state is an N-dimensional vector, which becomes the state vector of the system, as shown in the following formula: (4) The system state is represented by a state vector, X, where X=0 indicates that all elements are operational, and the system is functioning.Conversely, when X=1, it signifies the occurrence of at least one component failure, rendering the entire system in a failed state.(5) It is important to estimate the risk indicators when the system is in a failed state.Try to increase smoking as much as possible.The number of samples and the frequency of sampling can be regarded as unbiased estimates of probability, as shown in the following equation: in the formula: M is the number of samples, and m(s) is the number of times the system states occur.The distinct feature of the non-sequential Monte Carlo simulation method lies in its independence of the system size concerning the sampling number, provided that specific accuracy requirements are met, which can get rid of the constraints of the grid size on the calculation amount and accuracy.

Establishment and calculation of risk assessment indicators for distribution networks
3.2.1.Risk assessment indicators for voltage exceeding limits at distribution network nodes.The study of the impact of distributed power generation on the voltage of the distribution network primarily focuses on voltage exceeding the limit as the most critical indicator [12].The integration of distributed power sources can lead to voltage fluctuations within the distribution network, potentially resulting in voltage surpassing the upper or lower limit.An excessive voltage upper limit can jeopardize the insulation of equipment, while a lower limit breach can cause voltage support loss, increase energy loss during transmission, and pose threats to power grid safety and stability.In severe scenarios, there may be a risk of varying degrees and areas of power outages.Consequently, it becomes essential to establish an indicator for node voltage exceeding the limit, and the risk assessment indicators for this aspect include: v m a x (() S e v () , () S e v () ) in the formula, Pr is the calculation formula for the probability of node voltage exceeding the limit: Vi represents the voltage amplitude of node i, Vmax and Vmin represent the upper and lower limits of node voltage of 1.05 and 0.95, respectively, and F(V) represents the voltage accumulation function.
Sev (Vi) represents the severity indicator of the risk of node voltage exceeding the limit, as follows:

Reliability risk assessment indicators for distribution networks.The risk assessment indicators
proposed in this article not only include voltage limit exceeding indicators but also include load reduction probability PLC, expected short supply power EDNS, and variance coefficient of EDNS β, and these three reliability risk assessment indicators.Combined with the non-sequential Monte Carlo simulation method, the reliability risk assessment index system is established.
In the context of the non-sequential Monte Carlo method, P(s) denotes the frequency calculation of state s in the sampling process.The set of failure states for the i-th level load level in the NL level load model is represented by Fi.Ti signifies the duration of the i-level load in hours, while T corresponds to the total duration of the load in hours.NL stands for the number of stages used for load classification.
(2) Expected demand not supplied EDNS. in the formula, C(s) represents the load reduction rate at state s.The unit of EDNS is megawatts (MW).This indicator represents the average value of load reduction power caused by insufficient power generation capacity or grid failures, scheduling restrictions, and other factors within a certain period.
(3) Expected variance coefficient of EDNS with insufficient power supply β.The coefficient of variance is a relative indicator, where variance represents the degree of fluctuation in an absolute quantity, while the coefficient of variance represents the degree of fluctuation in a relative quantity.This indicator has been selected as the convergence criterion for the sampling process.

Example analysis
Taking the IEEE33 bus distribution network as the research object, the Monte Carlo simulation method is used to calculate the risk assessment.During simulation, first, connect photovoltaic power at Node 7 and wind power at Node 15, and calculate the voltage risk value of the relevant nodes.Subsequently, the risk indicators are computed upon the integration of distributed power sources.A comparative analysis is performed to assess the strengths and weaknesses of the three methods.Finally, an evaluation of the protection strategies for connecting two distributed power sources to the distribution network is presented.

Risk assessment of node voltage exceeding the limit
In Figure 1, photovoltaic power generation is integrated into Node 7, while wind power generation is connected to Node 15.The capacity of the photovoltaic power is 2000 kW, and its solar-cell efficiency is 14%.For the beta distribution of light intensity, the shape parameter a is 2.47, and the parameter β is 2.4, with the sunlight time spanning from 6 to 18 o'clock.The wind power is 2000 kW, with a rated wind speed set at 10 m/s, and the size and shape parameters are c=2.11and k=11.678,respectively.According to Formulas (6) to (10), the risk value of voltage exceeding the limit for each node can be obtained.Choose to calculate a representative risk value at noon.As shown in Figure 2, the largest ones are Node 7 and Node 15, as Node 7 is relatively advanced and the connected photovoltaic system has the highest output at 12, which increases the risk of exceeding the upper limit of voltage.This confirms that the connection of distributed power sources has a significant impact on the risk value of node voltage, proving the effectiveness of this indicator.

Reliability risk assessment indicators
The distribution network system connected with distributed power sources, as depicted in Figure 1, undergoes the application of three different methods: the importance sampling method (Method 1), the equal dispersion sampling method (Method 2), and the Monte Carlo method (Method 0).By employing these methods, the reliability risk assessment index values of the distribution network are computed and compared.The results are summarized in Table 1.For the two protection strategies, it can be seen that the EDNS variance coefficient for wide area protection β Maintaining at a relatively low level, lower than adaptive current quick-break protection, confirms that the reliability of wide area protection is significantly stronger than that of current quickbreak protection.This is due to the special protection mechanism of wide area protection and the calculation deviation caused by current quick-break protection for distributed power supply access.The results demonstrate the feasibility and effectiveness of the evaluation system proposed in this article.

Summary
In this paper, a distribution network risk assessment index system based on non-sequential Monte Carlo calculation is proposed, which includes node voltage out of limit, load reduction probability PLC, expected power failure EDNS, and EDNS variance coefficient β.A distribution network risk assessment index system with equal indicators.Incorporating specific calculation examples, this study applied the Monte Carlo algorithm, importance sampling method, and equal dispersion sampling method for computation and comparison.The risk assessment encompassed four aspects: node voltage exceeding the limit, PLC, EDNS, and EDNS variance coefficient β.The results obtained from the three methods were juxtaposed, illustrating the superiority of the non-sequential Monte Carlo simulation method over the other two approaches in terms of result accuracy, sample reduction, and operational efficiency.The fact that the reliability of wide area protection is significantly stronger than that of current quick-break protection further demonstrates the rapidity, effectiveness, and practicality of the risk assessment method and risk assessment indicators proposed in this article.

Figure 2 .
Figure 2. Risk value diagram of node voltage exceeding the limit.According to Formulas (6) to(10), the risk value of voltage exceeding the limit for each node can be obtained.Choose to calculate a representative risk value at noon.As shown in Figure2, the largest ones are Node 7 and Node 15, as Node 7 is relatively advanced and the connected photovoltaic system has the highest output at 12, which increases the risk of exceeding the upper limit of voltage.This confirms that the connection of distributed power sources has a significant impact on the risk value of node voltage, proving the effectiveness of this indicator.