Risk Analysis of Integrated Energy System Based on Security Boundary

In the face of an increasingly diversified energy supply, integrated energy systems (IES) are playing an increasingly important role. The operational risks of complex and diversified IES have also significantly increased. This article proposes an IES risk analysis based on security boundaries. Firstly, using the multi-energy flow equilibrium equation, construct equality constraints for the safety boundary. Then, N-1 safety analysis is conducted on each critical pipeline and equipment using the predicted accident set to obtain safety boundary inequality constraints. By combining the equality and inequality constraints of the safety boundary, the system safety boundary is solved, and the IES risk indicators are determined using the relationship between the operating state points and the safety boundary. Finally, the feasibility and effectiveness of the method were verified by calculating an example of electric heating combined supply.


Introduction
As people's demand for energy becomes increasingly diverse, an integrated energy system (IES) with multiple complementary energy sources has become the future development trend.The equipment of the IES is constantly becoming more complex and diversified, which poses challenges to the operation of IES.
Currently, in terms of IES security risk analysis, Li et al. [1] consider the correlation between wind resources and loads and propose a risk assessment method for wind power generation system lines.Luo and Wang [2] consider the uncertainty of new energy generation and load in microgrids and quantitatively evaluates the probability risk of power shortage.The probability flow taking into account interval characteristics is widely used in characterizing new energy and load uncertainty [3].Liu et al. [4] establishes a risk assessment model for energy price uncertainty, using conditional risk values to quantify the impact of extreme price uncertainty.Jiang et al. [5] propose a new risk index that considers the returns of each operator to comprehensively describe the security risks of a multienergy coupling system and the interests of each operator.Deng et al. [6] propose a new multi-energy probabilistic power flow calculation method to handle a large amount of new energy in the system, providing a basis for risk analysis.Existing research has not yet conducted an IES safety analysis considering N-1 fault conditions.
Based on the current situation, this article proposes an IES risk analysis based on security boundaries.Firstly, using the multi-energy flow equilibrium equation, construct equality constraints for the safety boundary.Then, N-1 safety analysis is conducted on each critical pipeline and equipment using the predicted accident set to obtain safety boundary inequality constraints.By combining the equality and inequality constraints of the safety boundary, the system safety boundary is solved, and the IES risk indicators are determined using the link between the operating state points and the safety boundary.Finally, the feasibility and practicality of the approach were verified by calculating an example of electric heating combined supply.

Multi-energy flow balance constraints for IES
The IES, whether operating under normal or N-1 fault conditions, needs to meet multiple energy flow balance constraints, including electrical energy flow constraints, thermal energy flow constraints, etc.

Electric energy flow equation
The power flow model without considering the three-phase imbalance is: where V i and V j are the voltage amplitudes of nodes i and j, respectively, G ij and B ij are the conductivity and admittance, and θ ij is the phase angle difference of nodes.CHP unit is an efficient, energy-saving, and environmentally friendly electrical and thermal flow coupling equipment widely used in industrial production.Its model can be represented as: where C CHP is the thermoelectric ratio of the CHP unit, and P CHP,h , P CHP,e are thermal and electrical power.

Heat flow equation
The hydraulic model equation of the thermal system is: where A is the network incidence matrix, m is the quantity of heating network pipelines, m q is the inflow load flow of the node, B is the loop incidence matrix, H f is the pressure drop of the pipeline, and K is the pipeline resistance coefficient.
The main equations of the thermal energy balance model are: where Φ is the heat load, T S and T 0 are the water supply temperature and return water temperature, respectively, C p is the specific heat capacity of water, T end and T start are the temperature at the beginning and end of the pipeline, T a is the ambient temperature, L is the length of the pipeline, λ is the heat transfer coefficient, m out and m in are the pipeline flow rates of the outflow and inflow nodes, respectively, and T in and T out are the temperature at the end of the input pipeline and the node mixing temperature, respectively.The GB unit is a key thermal energy equipment that converts chemical energy from fuels such as natural gas into electrical energy through combustion.Its model can be represented as: where β Boiler efficiency, H is the calorific value of the fuel, and m is the mass of fuel consumed by the boiler.Electric boiler is a thermal equipment that converts electrical energy into thermal energy and heats water to pressurized hot water or steam (saturated steam).Its model can be represented as: where α is the efficiency of the electric heating boiler, and P e represents the input electrical power.

IES Security Boundary
The N-1 safety criterion is a significant consideration for planning and operation.It requires that the IES will maintain stable operation except for the fault zone in the event of any independent component failure during operation.
The outlet pipeline of key equipment is used as the observation point for the operational status of the IES, and Figure 1 is used to explain the safety boundary of the IES.In the figure, T represents the transformer, CHP represents the cogeneration unit, HB represents the electric heating equipment, and GB represents the gas boiler.The N-1 faults selected in this article include critical equipment faults (T 1 , T 2 , T 3 , HB, GB, CHP) and critical pipeline faults (L 1 , L 2 , L 3 , L 4 , L 5 , L 6 , L 7 ).

Security boundary of power system
The critical equipment in this IES includes transformers T 1 , T 2 , T 3 , cogeneration unit CHP, and critical pipelines include L 1 , L 2 , L 3 , and L 4 .At the same time, the integration of photovoltaic and wind turbines in the IES can to some extent enhance the system's energy supply capacity.
When transformer T 1 or L 1 malfunctions, its load will be borne by the CHP unit, transformers T 2 , T 3 , photovoltaic, and wind power generation.The security boundary models for T 1 and L 1 are: where C T2 represents the capacity of transformer T 2 , C L2 represents the capacity of line L 2 , C L4 represents the capacity of line L 4 , C e CHP represents the electrical power, C CHP,min represents the minimum thermoelectric ratio, P pv represents the photovoltaic power generation, P w represents the wind power generation power, and L 1 , L 2 , L 3 , L 4 respectively represent the loads carried by lines 1, 2, 3, 4.
When transformer T 2 or L 2 malfunctions, the load it carries will be borne by the CHP unit, transformers T 1 , T 3 , photovoltaic, and wind power generation.The security boundary models for T 2 and L 2 are: where C T1 represents the capacity of transformer T1, and C L1 represents the capacity of line L 1 .
When transformer T 3 or L 3 malfunctions, the load it carries will be borne by the unit, transformers T 2 , T 1 , photovoltaic, and wind power generation.The safety boundary models for T 3 and L 3 are: where C T1 represents the capacity of transformer T 1 , and C L1 represents the capacity of line L 1 .
When the CHP unit or L 2 fails, its load will be borne by transformers T 1 , T 2 , T 3 , photovoltaic, and wind power generation.The safety boundary model for CHP unit and L 4 is:

Thermal system safety boundary
The critical equipment in this IES includes a cogeneration unit CHP, an electric boiler HB, and a gas boiler GB.Key pipelines include L 5 , L 6 , and L 7 .
When the CHP unit or L 5 malfunctions, the heat load it carries will be borne by the electric boiler HB and the gas boiler GB.The safety boundary between CHP unit and pipeline L 5 is: where C HB represents the capacity of the electric boiler HB, C L6 represents the capacity of line L 6 , C GB represents the capacity of the electric boiler GB, and C L7 represents the capacity of line L 7 .When the HB unit or L 6 fails, the heat load it carries will be borne by the CHP unit of the cogeneration plant and the gas boiler GB.The safety boundary between HB unit and pipeline L 6 is:  ), ( ) where C h CHP represents the thermal power of the CHP unit, C CHP,max represents the maximum thermoelectric ratio of the CHP unit, and C L5 represents the capacity of line L 5 .
When the GB unit or L 7 fails, the heat load carried by it will be borne by the CHP unit of the cogeneration plant and the electric boiler HB.The safety boundary between GB unit and pipeline L 7 is: where C HB represents the capacity of the electric boiler HB.

Solution of Security Boundary for IES
The system security boundary point is the maximum energy supply point of IES, which needs to meet both the multi-energy flow equality constraints and the inequality constraints under N-1 conditions.
For such issues, the interior point method has a good effect and can transform the appealing problem into a general form: where L is the power of the critical pipeline, and μ, L represents the relaxation variable vector.The problem is solved using the Lagrange function, and there will not be elaborated.The security boundary is a collection of security boundary points.The appeal solution can only solve one security boundary point.It is necessary to fix other variables and set free variables, so that a series of security boundary point collections can be obtained.

IES risk analysis
The risk of an IES is determined by the distance between the operating state points of the system and the safety boundary.The distance between the operating state point and the safety boundary can be determined by the maximum capacity that can be increased by the pipeline outlet load, which can quantify the safety margin of the system.The safety boundary distance belongs to the closest distance from a point to a surface in Euclidean space.The IES risk can be defined as: where R represents the risk of the IES, r j represents the system risk of the jth energy supply pipeline group, and O represents within the boundary.

Example analysis
This article takes a case study of a certain cogeneration project as an example for analysis.To facilitate analysis and calculation, some lines are simplified.At the same time, the device overload coefficient is set to 1.The equipment parameters are shown in Table 1 According to the analysis in Section 3.1, the output of renewable energy affects the security boundary of the power system.To simplify the analysis, assuming that there is no renewable energy output, the safe boundary of L 1 can be obtained by continuously solving the safe boundary point, which is affected by L 2 , L 3 and L 4 .Its image representation is shown in Figure 2.  Figure 2 shows a four-dimensional image, where the coordinate variables are L 2 , L 3 , and L 4 , and the colored variable is the maximum output of L 1 , which is the safety boundary.According to the analysis in Section 3.1, due to the symmetry of L 1 and L 3 structures, their safety boundaries can be similar to L 1 .Due to its dissimilar structure, L 2 has a safety boundary of: The coordinate variables in Figure 3 are L 1 , L 3 , and L 4 , while the colored variable is the maximum output of L 2 , which is the safety boundary.According to the analysis in Section 3.1, the safety boundary between CHP unit and pipeline L 5 is solved as: After obtaining the safety boundary, the relationship between the operational status points of the IES and the safety boundary is determined to obtain the risk of the IES.Assuming that the IES operates in L (4,4.5,5,3,3,3.2,5.3)state and the renewable energy output is 1 MW, combined with the solved safety boundary model and Section 3.4 analysis, the risk index of the IES can be obtained as: The system needs to make adaptive adjustments for pipelines L 3 , L 5 , L 6 , and L 7 .

Conclusions
This article proposes an IES risk analysis based on safety boundaries for the risk assessment of IES.Based on the expected accident set and the multi-energy flow equilibrium equation, safety boundary inequality constraints and equality constraints are proposed, and the safety boundary is solved using the primal even interior point method.The system operational risk is calculated based on the safety of the operating state points and safety boundaries.Finally, the effectiveness and scientific nature of the above-mentioned method were tested through examples.