Power Side Risk Assessment of Multi-Energy Microgrids Considering Risk Propagation between Interconnected Energy Networks

: Traditional power systems only contain a single energy type, namely, electrical energy, and involve no interaction with other networks with different energy types, such as gas networks and heat networks. With the rapid development of the Energy Internet, the coupling between various energy types has become increasingly tight, making traditional risk assessment methods no longer suitable for multi-energy microgrids. To this end, this paper proposes a microgrid risk assessment method that considers the impact of multiple interconnected networks with different energy types. First, respectively from the equipment and system levels, a risk transfer integrated energy conversion model is built, depicting the output of equipment under risk conditions and describing the process of risk transfer using energy coupling equipment in the microgrid. Thereafter, from the perspective of the energy ﬂow distribution and considering the microgrid grid energy ﬂow characteristics, a microgrid energy ﬂow distribution model is built, based on which a microgrid risk analysis model that simulates the microgrid risk propagation mechanism is established by introducing risk factors that characterize equipment risk statuses. In addition, based on the system structure and the operational characteristics, a microgrid-oriented risk assessment process is designed. Finally, a numerical simulation conﬁrms that considering the impact of multiple different energy networks to the power side in the risk assessment is necessary.


Introduction
With the further strengthening of energy interconnection, couplings between different energy resources are getting tighter, which makes the traditional power network risk assessment methods no longer suitable for multi-energy systems.As an example, the "8.9"UK blackout in 2019 was caused by cascading failures of offshore wind power, distributed photovoltaic, and gas-to-power conversion equipment [1].Therefore, to ensure the sustainability, reliability, and economy of microgrids, a comprehensive risk assessment of multi-energy microgrids becomes crucial, which makes accurately quantifying the risks faced by multi-energy microgrids an urgent problem.In addition, when assessing the risk of the power grid in a multi-energy microgrid, not only the power grid should be focused on, but also the impact of other interconnected energy networks should be considered for comprehensively assessing the overall risk level of the multi-energy system.
Multi-energy microgrids integrate various energy resources, such as electricity, heat, and natural gas, forming corresponding energy transfer networks and realizing energy generation, conversion, transmission, distribution, storage, and consumption.These different types of energy networks are increasingly connected and coupled as shown in the example in Figure 1.With the increase in energy diversity, the uncertainty faced by the multi-energy system increases correspondingly, and the risk is also transmitted to the integrated power network along with the transmission and conversion of energy.Moreover, with an increasing number of different types of energy resources being connected to the multi-energy microgrid, the uncertainty faced by the entire system increases, which arouses risks that spread along with the transmission and conversion of energy.Specifically, on the one hand, the integration of gas, heat, and other energy resources introduces more equipment, such as gas-to-power equipment, gas-to-heat equipment, and heat-to-power equipment, resulting in additional operational risks due to their operation features and couplings; and on the other hand, the electric network increasingly relies on the supply of natural gas and heat, whose fluctuations would impact to the power side as well.Therefore, the risk assessment of the microgrid considering multi-energy coupling is of great significance to comprehensively evaluate the operation risk of the power grid and ensure its reliable and stable operation.
Energies 2023, 16, x FOR PEER REVIEW 2 of 14 generation, conversion, transmission, distribution, storage, and consumption.These different types of energy networks are increasingly connected and coupled as shown in the example in Figure 1.With the increase in energy diversity, the uncertainty faced by the multi-energy system increases correspondingly, and the risk is also transmitted to the integrated power network along with the transmission and conversion of energy.Moreover, with an increasing number of different types of energy resources being connected to the multi-energy microgrid, the uncertainty faced by the entire system increases, which arouses risks that spread along with the transmission and conversion of energy.Specifically, on the one hand, the integration of gas, heat, and other energy resources introduces more equipment, such as gas-to-power equipment, gas-to-heat equipment, and heat-to-power equipment, resulting in additional operational risks due to their operation features and couplings; and on the other hand, the electric network increasingly relies on the supply of natural gas and heat, whose fluctuations would impact to the power side as well.Therefore, the risk assessment of the microgrid considering multi-energy coupling is of great significance to comprehensively evaluate the operation risk of the power grid and ensure its reliable and stable operation.In recent years, the risk assessment for power grids has been experiencing rapid development.In terms of power system risk assessment methods, a probabilistic power flow that intends to describe the impact of uncertainty factors to the power grid has been extensively studied [2][3][4].Reference [5] proposed a probabilistic multi-energy flow model focusing on power-heat-gas coupled integrated energy systems by introducing the semiinvariant method, and on this basis, an assessment method accompanying with multiple risk indicators under normal operation is proposed.Reference [6], focusing on the multiregional interconnected power grid, built a two-stage joint optimization model of power generation and reserve considering operational risks.Reference [7] analyzed the challenge faced by traditional risk assessment indices and proposed a risk assessment method from the aspects of bus voltage, network loss, and branch flow.Reference [8] proposed an uncertainty-considered assessment method and an index system for microgrids.Moreover, reference [8] developed a risk quantification method to assess the risk of a power shortage under the impact of uncertainty.In [9], the authors proposed a multienergy flow joint model which achieves the decoupling of electrically coupled integrated energy systems.Reference [10] categorized energy systems as power, heat, gas, powergas, and power-heat-gas systems and correspondingly reviewed the state-of-the-art findings in a risk assessment and looked forward to future research directions.
Although risk-assessment-relevant research has been carried out extensively, most of the existing methods focus on traditional power networks.In terms of equipment risk assessments, reference [11] analyzed the outage probability of power equipment considering aging, environment, and operation conditions, which laid the foundation of the power equipment risk assessment.Reference [12] comprehensively considered the impacts of line faults, power flow transfer, hidden faults, and weather factors to access the risk of cascading faults and thereby built a risk-assessment-based coordinated risk control model of cascading faults.As the above references are based more on analyzing the outage probability of equipment, data acquisition becomes the obstacle to ensuring In recent years, the risk assessment for power grids has been experiencing rapid development.In terms of power system risk assessment methods, a probabilistic power flow that intends to describe the impact of uncertainty factors to the power grid has been extensively studied [2][3][4].Reference [5] proposed a probabilistic multi-energy flow model focusing on power-heat-gas coupled integrated energy systems by introducing the semiinvariant method, and on this basis, an assessment method accompanying with multiple risk indicators under normal operation is proposed.Reference [6], focusing on the multiregional interconnected power grid, built a two-stage joint optimization model of power generation and reserve considering operational risks.Reference [7] analyzed the challenge faced by traditional risk assessment indices and proposed a risk assessment method from the aspects of bus voltage, network loss, and branch flow.Reference [8] proposed an uncertainty-considered assessment method and an index system for microgrids.Moreover, reference [8] developed a risk quantification method to assess the risk of a power shortage under the impact of uncertainty.In [9], the authors proposed a multi-energy flow joint model which achieves the decoupling of electrically coupled integrated energy systems.Reference [10] categorized energy systems as power, heat, gas, power-gas, and power-heatgas systems and correspondingly reviewed the state-of-the-art findings in a risk assessment and looked forward to future research directions.
Although risk-assessment-relevant research has been carried out extensively, most of the existing methods focus on traditional power networks.In terms of equipment risk assessments, reference [11] analyzed the outage probability of power equipment considering aging, environment, and operation conditions, which laid the foundation of the power equipment risk assessment.Reference [12] comprehensively considered the impacts of line faults, power flow transfer, hidden faults, and weather factors to access the risk of cascading faults and thereby built a risk-assessment-based coordinated risk control model of cascading faults.As the above references are based more on analyzing the outage probability of equipment, data acquisition becomes the obstacle to ensuring accuracy.On the system level, references [13,14] proposed a risk assessment method that jointly Energies 2023, 16, 7525 3 of 13 considers the usage of electricity, natural gas, and heat to quantify the operational risk of the energy system.Reference [15] proposed a supply demand-based approach focusing on the risk assessment of a power and heating coupled system.Reference [16] represents the uncertainty of natural gas supply caused by faults on the power side and proposed power system risk assessment indices for the power side.References [17][18][19] considered the insolation of hybrid AC-DC microgrids and proposed a static risk assessment method for the isolated hybrid AC-DC microgrids.Although the above risk assessment methods considered the influence of couplings of power, gas, and heat networks from different perspectives, for multi-energy microgrids, the risk propagation from gas and heat networks to the power side is not particularly reflected.In addition, for system-level risk assessments, references [20][21][22] proposed comprehensive power system risk indices, but for microgrids that are interconnected with multiple different types of energy networks, the index system needs to be improved.
Based on the analysis above, this paper focuses on assessing the impact of coupled networks of other energy forms to the power side in multi-energy microgrids, and the proposed method mainly targets areas where renewable energy shows scarcity.This paper establishes an energy conversion model based on risk transfer, respectively, from the equipment level and the system level.Meanwhile, through the analysis of the energy flow, an energy flow distribution model describing the joint operation of power, gas, and heat is built.Risk factors are introduced to consider the risk propagation within the microgrid.Finally, according to the operation characteristics of the multi-energy microgrid, risk indices are designed to quantify the operation risk.

Energy Conversion Model Based Considering Risk Propagation
In a pure microgrid, operation risks mainly come from the equipment outage, voltage deviation, and operational limit violation.By contrast, in a multi-energy microgrid, besides those, the operation risks aroused in the gas network and heating network can be propagated to the power side through energy conversion equipment.Therefore, considering the endogenous risk and the exogenous risk from coupled energy networks, this paper proposes risk orientated energy conversion models on the system level and the equipment level.

Energy Conversion Model of Energy Coupling Equipment
When a failure occurs, the aroused risk will be propagated to the network connected to it through the energy conversion equipment, possibly causing abnormal operation of the equipment in the coupled energy networks.The energy conversion models of individual energy coupling equipment considering risk propagation are modeled in this section.

Gas Turbine
The energy conversion model of the gas turbine is formulated as in Equation (1), where E GT represents the power output of the gas turbine; η GT represents the natural gasto-power efficiency; q is the calorific value of natural gas; V GT G is the of natural gas input; and α, being [0, 1], represents the state of the gas turbine.α < 0.5 means that the equipment is out of service; 0.5 ≤ α < 1 means that the equipment is not in normal operation; and only α = 1 means that the equipment is in normal operation.f 1 (α) represents the risk function and with different system structures, its specific expression varies.

Turbine
The energy conversion model of the turbine is formulated as in Equation ( 2).In Equation ( 2), E T is the turbine power output; η T represents the power generation efficiency; e x,p represents the exergy; V T is the volume flow rate of the working substance; and ρ is the density of the flue gas.f 2 (α) represents the risk function and similarly, with different system structures, its specific expression varies as well.

Combined Heat and Power Equipment
The energy conversion model of the combined heat and power equipment is formulated as in Equations ( 3) and ( 4).E CHP is the power output; and η E is the efficiency of the combined heat and power equipment.Q CHP is the heat output of the combined heat and power equipment; β is the heat collection coefficient, which is generally set as 0.8-0.9;and C is the specific heat capacity at a constant pressure and is usually set as 1-1.2 [19].

Heat Pump
The energy conversion model of the heat pump is formulated as in Equation ( 5), where Q EH is the heat output of the heat pump; E EH is the power consumed by the heat pump; and η EH represents the heat conversion efficiency.

System Level Energy Conversion Model Considering Risk Propagation
In the microgrid, power loads can be supplied by power import and power converted from gas, hydrogen, and heat.Based on the energy conversion models discussed above, for the power side, the system level energy conversion model can be formulated as in Equation (6).
In Equation ( 6), E E−E represents direct power, namely imported power; E G−E represents the power converted from gas by gas turbines; E H−E represents the power converted from hydrogen by hydrogen generators; and E Q−E represents the power converted from heat by steam turbines.ξ E represents the conversion coefficient of electricity to electricity; ξ G represents the conversion coefficient of gas to power; ξ H represents the conversion coefficient of hydrogen to power; and ξ Q represents the conversion coefficient of heat to power.q G represents the calorific value of natural gas; q H represents the calorific value of hydrogen; v G represents the flow rate of natural gas; and ν H represents the flow rate of hydrogen.f E (α), f G (α), f H (α), and f Q (α) are, respectively, risk functions of importing power, gas-to-power conversion, hydrogen-to-power conversion, and heat-to-power conversion.

Energy Flow Distribution Based Risk Analysis
The system operation state change caused by risk-induced equipment outage is indeed reflected as the change of energy flow in the system.The abnormal energy flow that does not meet the operating requirements of the system will generate operational risks and further propagate the risk to the entire system.Therefore, the dynamic effect of the system risk can be understood by analyzing the energy flow change.
For a multi-energy microgrid, the operation of the power side is to distribute the power converted from different energy resources to electrical loads.The power consumed by any load can be considered as composed of the power generated by all power generation resources.Therefore, in this section, from the perspective of loads, the risk of the microgrid is evaluated, and the model can be formulated as in Equation (7).
In Equation ( 7), E l1 to E ln represent the power consumption of different loads; a 1 to a n represent the conversion coefficients of power-to-power of load 1 to n; b 1 to b n represent the energy conversion coefficients of gas-to-power conversion of loads 1 to n; c 1 to c n represent the energy conversion coefficients of hydrogen-to-power conversion of loads 1 to n; and d 1 to d n represent the energy conversion coefficients of heat-to-power conversion of loads 1 to n.
When a risk event happens, the energy flow distribution of the system will change.Therefore, based on Equation (7), by introducing the risk functions to the conversion and distribution of power, gas, and heat, the microgrid risk analysis matrix based on energy flow distribution can be constructed as in Equation (8).f E 1 to f E n represent the risk functions of power-to-power conversion of load 1 to n; f G 1 to f G n are the risk functions of gas-to-power conversion of load 1 to n; f H 1 to f H n are the risk functions of hydrogen-to-power conversion of load 1 to n; and f Q 1 to f Q n are the risk function of heat-to-power conversion of load 1 to n.
With the proposed energy flow distribution based microgrid risk assessment model, on the one hand, the power flow of the power side in normal operation can be analyzed, laying a foundation for the system to dynamically adjust connected energy resources, and on the other hand, it can identify the system risk status with an abnormal energy flow, laying the basis for systemic risk management and control.

Voltage Deviation
The existing voltage deviation risk indices are usually based on the degree of deviation between the actual voltage and the rated value to reflect the severity of emergencies.The shadowing effect, i.e., the cumulative impact of multiple small violations could be greater than the impact of a single severe violation, may appear when using a linear severity function.To this end, the utility theory is used to define the severity function as in Equation ( 9), which can effectively avoid the shadowing effect.In Equation ( 9), R V represents the risk of voltage deviation; P(E) represents the probability of risk events; and V represents nodal voltage (in per unit value).

Branch Flow Limit Violation
The failure of a system component may cause a heavy overload of the branch flow.In this paper, the branch flow limit violation risk of the system is determined by the degree as in Equation (10), where R L represents the risk of branch flow limit violation and L represents the loading rate.

Power Shortage
Failures of power generation equipment may cause insufficient power supply.In this paper, the degree of power shortage is indicated by Equation (11), where L P represents the power supply under normal operation and L P E i represents the actual power supply under risk event i.

Gas Supply Shortage
The index of gas supply shortage is formulated as in Equation ( 12), where i represents the risk event; j represents the total number of risk events; Q P represents the gas supply under normal operation; and Q P E i represents the actual gas supply under risk event i.

Heat Supply Shortage
The risk of a heat supply shortage can be reflected by the outlet temperature of the heating system.With a certain inlet temperature, when the outlet temperature is lower than the threshold, the heat supply is in shortage, and the lower the outlet temperature, the greater the risk of heat supply shortage.The index of heat supply shortage is formulated as in Equation ( 13), where T i represents the outlet temperature under this event, and T 0 represents the lower limit of the outlet temperature.
When a risk event happens, the operation state of the microgrid will change; some units may be overloaded; and nodal voltages may violate the limit.To this end, considering the operation characteristics of the multi-energy microgrid, referring to the rated values, a risk index system that consists of the above five indices is proposed.Based on the "Regulations on Emergency Response and Investigation of Power System Safety Misadventure" issued by the State Council of China, the "Safety Misadventure Investigation Procedures" issued by the State Grid Company of China [20], and reference [19], power grid risks are classified as three levels, as shown in Table 1, and the first-level risk represents the riskiest ones.The risk quantification of the five indices is shown in Table 1.

The Process of Risk Assessment
The flowchart of the risk assessment method is shown in Figure 2.

The Process of Risk Assessment
The flowchart of the risk assessment method is shown in Figure 2.

Case Study
To verify the effectiveness of the proposed risk assessment method, referrin reference [19], the power limit violation, voltage deviation, and power shortage ind

Case Study
To verify the effectiveness of the proposed risk assessment method, referring to reference [19], the power limit violation, voltage deviation, and power shortage indices are used in a simulation that traverses all risk events.Figures 3-5 show the probabilities of the branch flow violation (i.e., the branch power flow exceeds the limit) of three different risk levels after traversing the risk events of the microgrid.
It can be seen from Figures 3-5 that compared with solely considering the operation of the power system, the probabilities of the branch flow limit violation of three different risk levels increase when considering the gas network and the heat network.On the one hand, this shows that after taking into account the coupling of the gas and the heat networks, the risk faced by the power side of a multi-energy microgrid is more severe, which is consistent with the expectation that the multi-energy microgrid faces more risk factors after integrating different energy networks.In addition, the simulation result shows that the risk is greater when only considering the gas network than when only considering the heat network.This is because that the capacity of the natural gas network is higher than that of the heat network in the multi-energy microgrid. of the power system, the probabilities of the branch flow limit violation of three different risk levels increase when considering the gas network and the heat network.On the one hand, this shows that after taking into account the coupling of the gas and the heat networks, the risk faced by the power side of a multi-energy microgrid is more severe, which is consistent with the expectation that the multi-energy microgrid faces more risk factors after integrating different energy networks.In addition, the simulation result shows that the risk is greater when only considering the gas network than when only considering the heat network.This is because that the capacity of the natural gas network is higher than that of the heat network in the multi-energy microgrid.Besides the branch flow, the nodal voltage is also one of the important indicators of the system operation.Its stability is critical to power equipment connected to microgrid.
Figures 6-8 show the probabilities of nodal voltage deviation risks at the three levels obtained after traversing the risk events.It can be seen that similar to the flow limit violation risk, the nodal voltage deviation risk of the multi-energy system becomes more severe when considering the gas network and the heat network.With different risk events, considering the gas network and the heat network leads to a higher probability of nodal voltage deviation in the risk assessment.Besides the branch flow, the nodal voltage is also one of the important indicators of the system operation.Its stability is critical to power equipment connected to the microgrid.
Figures 6-8 show the probabilities of nodal voltage deviation risks at the three levels obtained after traversing the risk events.It can be seen that similar to the flow limit violation risk, the nodal voltage deviation risk of the multi-energy system becomes more severe when considering the gas network and the heat network.With different risk events, considering the gas network and the heat network leads to a higher probability of nodal voltage deviation in the risk assessment.This is because most of the power supplied to the power side of the multi-energy microgrid comes from the energy conversion of natural gas and heat, so the operation of natural gas and thermal energy has an important impact on the operation of the power grid.Therefore, more risks could be propagated from the gas network and heat network to the power network, which leads to a higher probability of nodal voltage deviation in the system.In addition, due to the large capacity of the natural gas network, it has a greater impact on the system.This explains why the risk is greater when only considering the natural gas network than when only considering the heat network.
Figure 9 shows the probability of a power shortage risk of the three levels of the power side.The power supply of the power grid mainly comes from the energy conversion of natural gas, followed by heat and power importation.Therefore, the natural gas supply risk would impact the power shortage risk the most significantly, showing the highest probability of a power shortage risk when considering the natural gas network.This verifies that the risk propagation effect of multiple energy networks has an extremely important impact on the operation of the microgrid, and it cannot be simply ignored when analyzing and evaluating the risks.
The simulation result demonstrates the influence of risk propagation among the multiple energy networks in a multi-energy microgrid.Therefore, when carrying out risk assessment on a multi-energy microgrid, the impact of interconnected energy networks and various indices should be considered.This is because most of the power supplied to the power side of the multi-energy microgrid comes from the energy conversion of natural gas and heat, so the operation of natural gas and thermal energy has an important impact on the operation of the power grid.Therefore, more risks could be propagated from the gas network and heat network to the power network, which leads to a higher probability of nodal voltage deviation in the system.In addition, due to the large capacity of the natural gas network, it has a greater impact on the system.This explains why the risk is greater when only considering the natural gas network than when only considering the heat network.
Figure 9 shows the probability of a power shortage risk of the three levels of the power side.The power supply of the power grid mainly comes from the energy conversion of natural gas, followed by heat and power importation.Therefore, the natural gas supply risk would impact the power shortage risk the most significantly, showing the highest probability of a power shortage risk when considering the natural gas network.This verifies that the risk propagation effect of multiple energy networks has an extremely important impact on the operation of the microgrid, and it cannot be simply ignored when analyzing and evaluating the risks.The simulation result demonstrates the influence of risk propagation among the multiple energy networks in a multi-energy microgrid.Therefore, when carrying out risk assessment on a multi-energy microgrid, the impact of interconnected energy networks and various indices should be considered.

Conclusions
The Energy Internet connects networks with different energy forms, such as power, heat, and gas networks, and realizes the joint operation of them.To this end, this paper focuses on a multi-energy microgrid risk assessment with particular considerations for the impact of interconnected energy networks.
The following conclusions can be drawn: 1. Compared with merely considering the operation of the power side, all levels of line flow violation risks increase when the interaction with the gas network and the heat network is considered.2. The power side nodal voltage violation risk considering the gas network and the heat network is more severe than when only considering the power side.Under different

Conclusions
The Energy Internet connects networks with different energy forms, such as power, heat, and gas networks, and realizes the joint operation of them.To this end, this paper focuses on a multi-energy microgrid risk assessment with particular considerations for the impact of interconnected energy networks.
The following conclusions can be drawn: 1.
Compared with merely considering the operation of the power side, all levels of line flow violation risks increase when the interaction with the gas network and the heat network is considered.

2.
The power side nodal voltage violation risk considering the gas network and the heat network is more severe than when only considering the power side.Under different risk factors, when considering the gas network and the heat network, the probability of nodal voltage violation risk becomes greater.

3.
The risk assessment method proposed in this paper can effectively take the impact of different energy networks into account, and the assessment results are consistent with the actual situation.The risk transfer effect between various energy networks has an extremely important impact on the operation of the multi-energy microgrid, and thus, it is unignorable.
It is worthwhile to mention that on the basis of this work, the influence of renewable energy generation and energy storage systems will be integrated into our future work.

Figure 1 .
Figure 1.The structure of a multi-energy microgrid.

Figure 1 .
Figure 1.The structure of a multi-energy microgrid.

Figure 9 .
Figure 9. Risk probability of power shortage.

Figure 9 .
Figure 9. Risk probability of power shortage.

Table 1 .
Risk indicators and quantitative schemes.