Energy supply reliability assessment of the integrated energy system considering complementary and optimal operation during failure

Integrated energy system (IES) is an effective solution for energy and environment prob-lems. In view of the difﬁculty of traditional reliability assessment methods to reasonably and effectively assess the reliability of the IES, an energy supply reliability assessment method based on sequential Monte Carlo simulation is proposed in this study. The optimal operation of the system is realised by mobilising the multi-energy complementary characteristics during device failure. The reliability of the system under three different operation objectives is compared and analysed. Three new reliability indices are proposed, which take into account the supply of multiple energy loads and the differences among different energy. Finally, through the analysis of energy supply reliability under different objectives, the reasonability of the proposed indices and the ﬂexible scheduling of energy ﬂow under different objectives are veriﬁed; therefore, the IES can realise adaptive and targeted operation strategy during device failure. Also, the inﬂuence of different device faults on the system’s energy supply reliability is ranked, which is of great signiﬁcance to ﬁnd the weak parts of the system and provide a reference for the system to improve energy supply reliability.


INTRODUCTION
Traditionally, gas and electrical systems operate independently, which limits the efficiency of the overall energy system. The integrated energy system (IES), coupling different types of energy technologies, is an effective solution to improve energy efficiency [1][2][3][4]. A representative IES architecture is introduced in [1], and the interdependencies and interactions in the IES are discussed in [2]. Cheng et al. [3] proposed a novel concept of IES cyber-physical systems. Hu et al. [4] improved the energy efficiency of IES through the proposed 'exergy efficiency'. Compared to the traditional independent planning and operation of each energy system, IES realises the coordination and optimisation of the production, distribution, conversion, storage, and consumption of multiple energy sources. Therefore, it can be regarded as the physical carrier of the Energy Internet [5,6]. However, the energy coupling of the IES is complex and the energy characteristics are different, making its reliability assessment more complicated than the traditional energy system. Therefore, there is an urgent need to carry out research on the reliability assessment methods of IES to provide a more scientific and reasonable decision reference for planning, construction, and safe operation. As a key technology in the operation and planning process, the research on reliability assessment methods has been widely conducted. The reliability assessment can be summarised as the following three basic steps [7]: Obtaining the random state of the system; analysing and evaluating the random state; calculating the system reliability indices. In order to obtain the random state of the system, two main methods [8,9] are adopted in the previous studies: The analytical method and the Monte Carlo method. The analytical method has a clear physical concept and high model accuracy, but it is difficult to deal with the random failure and simulate the actual large-scale system operation [10]. Monte Carlo method belongs to statistical experimental methods. Compared to analytical methods, it can simulate the random variation characteristics of the system and also obtain the probability distribution of some variables of interest, but it often takes a long time to obtain high accuracy [11,12]. Since the failure occurrence and the failure device are uncertain in the IES, the Monte Carlo method is more suitable for the evaluation of the IES. To analyse and evaluate the random state, failure model and effectiveness analysis (FMEA) is widely used by traversing the impact of device fault on load in the system. Moeiniaghtaie et al. [13] used the FMEA method to evaluate the electrical supply reliability of distribution network, and Che et al. [14] and Xu et al. [15] applied the same method for the reliability assessment of microgrids with distributed energy resource. However, there are few studies about the impact of device fault on the energy supply of the IES. Chaudry et al. [16] proposed the objective operation function of the system aiming at minimising the total operational costs based on a reliability assessment model of the combined GB gas and electricity network (EN) during the device failure. Qadrdan et al. [17] built a Monte Carlo model of the combined gas and EN and minimised the combined costs. These two studies realised the calculation of electricity and gas losses, but they do not consider the cooling and the heating, ignoring the diversity of loads. In the process of calculating system reliability indices, most of the existing reliability indices are only used for single energy systems with traditional reliability indices. Oh et al. [18] used the indices to evaluate the reliability of the electrical system considering wind generators. Shan et al. [19] proposed the structural and functional indices to evaluate dynamic reliability of heating networks. However, few reliability indices have been proposed specifically to evaluate the IESs. Mohammad-Hossein et al. [20] considered the dynamic characteristics of the heating load and uses 'unavailability' as the reliability indicator of IES. Zhe et al. [21] proposed a new approach based on hierarchical decoupling optimisation and uses the probability of load curtailments to assess the reliability of IES. In addition, the current reliability indices of IES are mainly based on electrical systems, and research studies on the reliability index of cooling and heating system have rarely been conducted [22,23]. Moreover, Liu et al. [24], proposed an operational reliability assessment method for an electricity-gas integrated energy distribution feeder with traditional reliability indices such as system average interruption frequency index and expected energy not supplied (EENS). Yang et al. [25] proposed an analytical method that can incorporate the uncertainty of the natural gas pipeline network system into the reliability assessment of IES, and it uses the loss of load probability, loss of load expectation and EENS as the reliability evaluation indices. The main contributions of this study are as follows: 1. In order to make full use of the complementary characteristics of various energy sources, a mathematical model for the optimal operation of the IES during the failure period is established, and three optimal operation objectives are proposed. The three different operation objectives are proposed based on different perspectives to minimise the user's energy loss, to minimise the economic loss of the energy supply station, and to obtain the best energy supply indices, respectively. So the operation state can be optimised during failure based on the model established in the study. Three new indices are proposed to evaluate the reliability of the IES system collectively, considering the cooling, heating and electricity supply at the same time, and the energy value differences among the three types of energy are taken into account. The index system established in this study is more suitable for the evaluation of the energy supply reliability of the IES. 3. The rest of the study is organised as follows. An IES with multiple energy supply stations is constructed in Section 2. The structure of the system and the key devices inside are introduced. To take the advantage of the multienergy complementary characteristics of IES, a mathematical model with three operational objectives during the device failure period is established in Section 3, which optimises the output of remaining devices and realises the optimal scheduling of energy flow. In Section 4, an energy reliability assessment method for IES is proposed, including specific reliability assessment processes and the detailed reliability indices; in Section 5, simulations are performed to verify the effectiveness of the proposed method and indices.

2.1
Inter-station and intra-station structure of energy supply stations IES with multiple energy supply stations has been used to replace the existing model of traditional energy systems that divides production and supply, which realises the centralised coordination of resources. The structure of the IES constructed in this study is shown in Figure 1. The system realises the exchange of various energy sources such as cooling, heating, electricity and gas. During the normal operation, the system can meet the load demands, including cooling, heating and electricity. In Figure 1, the EN and the gas network (GN) are connected to energy supply stations. The inter-station connection network is built to achieve energy interaction among different stations. It includes the electrical connection network (ECN) and the thermal connection network (TCN), which achieves the energy interaction of the cooling and heating systems. The gas required by the energy supply station can only be supplied through the GN, and there is no gas connection network among stations. Each energy supply station is responsible for supplying energy to cooling, heating and electricity demands in their respective areas.
The internal structure of the energy supply station is shown in Figure 2, where the system is comprised of energy input, conversion, output, and so forth. Energy is converted through the gas turbine (GT), the electric boiler (EB), the electric refrigerator (ER), the absorption chiller (AC), the gas boiler (GB) and other devices in the system. This figure can clearly show the energy flow and conversion inside the system, as well as the connection of devices. To simplify the analysis, all load nodes in the downstream network are collectively equivalent to cooling, heating and electricity load nodes as shown in Figure 2.

Mathematical model of devices
In this study, the sequential Monte Carlo method is used to simulate the system timing state over a time span, and then to evaluate the reliability of the energy supply when a device fails. When failures happen, the specific energy flow path, energy conversion mode and energy balance in the system are reflected by input and output of devices. Therefore, in this section, the mathematical model of each device in the system is established to determine its input and output during the failure, further to judge the system's ability to supply various types of loads and evaluate the system's energy supply reliability.

Gas turbine
GTs consume natural gas to convert energy into electricity while conveying the waste heat into the heating system. It is a key device for achieving gas-electricity coupling and gas-heat coupling, and the model is expressed as where P e GT ,t and P h GT ,t , respectively, represent the electrical power and the heat power output of the GT at time t; V GT ,t denotes the amount of natural gas input of the GT; L NG is the calorific value of natural gas, which is taken as 9.78J/kg in this study; EGT and HGT , respectively, represent the gas-electricity and gas-heat conversion efficiencies of the GT; Δt is the time step.

Electric boiler
EBs are essential electricity-heat coupling devices, and its model is given as follows: where P h EB,t represents the heat power output of the EB at time t; P e EB,t represents the electrical power consumed by the EB at time t; EB denotes the electricity-heat conversion efficiency; LOSS represents the heat loss at time t, which is assumed to be zero in this study.

Gas boiler
GBs are the key devices of gas-heat coupling, which is modelled as where P h GB,t represents the heat power output of the GB at time t; V GB,t represents the natural gas consumption of the GB; GB represents the heating efficiency of the GB.

Electric refrigerator
ERs convert electrical energy for cooling energy, and its model is where P c ER,t represents the cooling power output of the ER; ER represents the refrigeration coefficient of the ER; P e ER,t represents the electrical power input of the ER.

Absorption chiller
ACs are used to convert heat energy for cooling energy, which is typically modelled as where P c AC ,t represents the cooling power output of the AC at time t; C AC represents the refrigeration coefficient; P h AC ,t represents the heat power input of the AC at time t. The energy conversion efficiency of the device is shown in Table 4 of the Appendix, and the failure rate and repair time of devices is shown in Table 6 of the Appendix.

Multi-energy complementary characteristic of IES
When failure happens, the system will be forced to lose load if energy source spare is not enough, and thus reliability is challenged. IES couples several types of energy, and for specific user demands, there are many ways of energy supply. The essence of multi-energy complementarity of IES lies in making full use of the convertibility among different types of energy and cooptimising all parts of the system. In the IES, when the energy supply is insufficient, the other energy suppliers will compensate it through energy conversion devices, which is equivalent to increasing the system's spare. When a device of the system fails, the corresponding load demands cannot be met. However, if the other energy suppliers with the same kind of energy have a large spare capacity, the load can still be satisfied. If other devices are not enough to provide spare at this time, the load will be at the risk of being removed. Under such circumstance, IES can take the advantage of multi-energy complementarity, so that it can change 'the form of energy loss' according to the operational objectives. For example, in the heating season, users have relatively more heat energy demand, and the loss of heating supply will cause greater impacts to users. If the heat energy supply is inadequate, the EB can be put into operation at full power, so that changing 'the form of energy loss' can be realised. Even if it will result in tight electrical supply and lead to cut off some electrical loads, it guarantees the supply of more important loads for users in the system, making the user's loss smaller.

3.2
The complementary and optimal operation during failure and its mathematic mode The followings are the three different operation objective functions and constraints, and the complementary and optimal operation during a failure is achieved under this model.
Operation objective functions: e,t P e loss,t Δt + where f 1 is based on the user's perspective with minimising the user's energy loss; e,t , c,t , h,t are important factors of electricity, cooling and heating load, and they are dynamically changed over time according to the user's requirement, for example, in the heating season, h,t is larger, while e,t and c,t are smaller. f 2 is to minimise the economic losses of energy supply station from the perspective of energy supply station; e,t , c,t , h,t , are the energy price for each type of load; and the prices of various types of energy is shown in Table 5 of the Appendix. f 3 is to obtain the best reliability indices; e , c , h are 'energy value coefficients', which are first proposed in this study. As there are great differences in cooling, heating and electricity energy, the amount of energy utilisation and transformation for different types of energy is also different, so this concept is proposed to unify the available value of different energies. e , c , h , respectively, represent the available value of electricity, cooling and heating energies. T is the total simulation time, P e loss,t , P c loss,t , P h loss,t respectively, represent the energy loss of electricity, cooling and heating load at time t.
The three different operation objective functions are put forward standing, respectively, in the angle of users, energy supply stations and social benefits. They are used to minimise the user's energy loss, minimise the economic loss of the energy supply station and obtain the best energy supply indices, respectively. One of the three objectives will be chosen to optimise the operating state during failure, and which optimisation objective is chosen depends on actual demands and the decision-makers. Such as if the maker is the owner of the energy supply station, the second objective may be chosen to minimise the energy station loss.
Equality constraints: 3. Cooling power balance 4. Natural gas balance P g GN ,t = P GT ,t + P GB,t (13) where P e EN ,t , P g GN ,t represent the power input from the EN and the GN at time t; P e ECN ,t , P e DG ,t , respectively, represent the electricity power from inter-station connection network and the output of distributed generations; P h TCN ,t , P c TCN ,t represent the heating and the cooling powers of the TCN; P e D,t , P h D,t ,P c D,t , respectively, represent electricity, heating and cooling loads at time t; P GT ,t and P GB,t represent the natural gas consumed by GTs and GBs, respectively.
Inequality constraints: 2. Device output constraints 3. Output constraints of distributed generation 4. Transmission power limitation of the connection network 5. Constraints on load loss where i represents the type of loads, including electricity, cooling, and heating loads, P e,max EN ,t , P g,max GN ,t represent maximum input from EN and GN; P i j ,t represents the output power of the device j; P i,max j ,t is its maximum limit value, which is determined by the construction capacity and conversion efficiency; P max WT ,t represents the upper output limit of the distributed wind turbine, which is obtained based on the wind turbine construction capacity and real-time wind speed; P max PV ,t is similarly obtained; P i,max ECN ∕TCN ,t is the transmission limit of the connection network, and when it is positive, it indicates that energy flows into the energy supply station, and when it is negative, it indicates that energy flows out of the energy supply station.

Reliability indices
The traditional reliability assessment gives the reliability index of single energy systems, which cannot evaluate the overall reliability of IES. Therefore, this study proposes the following three new indices from different perspectives to improve the shortcomings of traditional reliability indices.

Average annual energy loss (AAEL)
It expresses the AAEL (MWh/a) due to device fault, which is defined as follows: where AAEL e ,AAEL h and AAEL c are energy loss of electricity, heating and cooling supply; N is the number of years for simulation; X t is the random state of the system at time t, F AAEL (X t ) is the experimental function defined as

Insufficient energy supply probability (IESP)
It represents the probability (%) of an insufficient energy supply event, which is defined as follows: where IES P e , IES P h and IES P c are the probability of insufficient electricity/heating/cooling supply, respectively, F IESP represents the experimental function, and it is defined as System has no load loss in state X t 1 System has load loss in state X t (32)

Insufficient energy supply time (IEST)
It indicates the time of insufficient energy supply throughout the year (h/a) due to device fault, and its calculation formula is

Sequential Monte Carlo reliability assessment process used in IES
Usually, IES is a large-scale system with a great number of devices. The failure device and failure occurrence in the system are uncertain. Since the traditional analytical methods are not suitable for large-scale systems and are difficult to reflect the timing characteristics, sequential Monte Carlo method is used to simulate the state sequence of the system over a long time span and can more effectively reflect the operation state of IES. We can easily get the operation state data of all devices through the Monte Carlo method, so we can get the optimal operation strategy based on the data. Thus, the Monte Carlo method is used in this study to evaluate the energy supply reliability of IES. The following assumptions are made for IES constructed in Section 2 of this study: The fault among devices is The output of wind power generation and photovoltaic power generation independent of each other and do not affect each other, which means the system will not have chain faults; all devices in the system can be repaired, and they have only two states: Normal operation and the fault states. It is assumed that the normal operation time of the device (the time to fault (TTF)) and the repair time of the device (the time to repair (TTR)) are both subject to an exponential distribution.
The process of reliability assessment is shown in Figure 3, which can be divided into the following steps: Step 1: Enter initial data, which mainly includes the fault rate and the repair time of each device, the device  capacity, the parameters of distributed generators and load data.
Step 2: Select one of the three operation objective functions mentioned above and perform the Monte Carlo simulation.
Step 3: Calculate the TTF of each device, select the device with the smallest TTF as the faulty device, and use this smallest time as the normal operation time of the system, then calculate the fault duration time (TTR) of the faulty device.
Step 4: During the failure, fully mobilise the multi-energy complementary characteristic and optimise the output of each device according to the operation objective, and then use the Grobi solver to obtain the loss of electricity, heating and cooling.
Step 5: Accumulate the simulation time, if the simulation time is less than 8760 h, return to step 3, otherwise go to step 6. Step 6: Perform N times of simulations and obtain the average annual reliability index of the system by averaging the N sample years.

The introduction of the case
The system structure of the study case is as shown in Figure 1.
There are three energy supply stations, and the ECN is built between stations 1 and 2 and between stations 2 and 3, while the TCN is only built between station 1 and 2. The capacity of the devices in power stations are shown in Tables 7, 8    The photovoltaic power generation is built in stations 1 and 3, and its installed capacity is 3000 and 5000 kW, respectively, the wind power generation is built in station 2 and the installed capacity is 4000 kW. The output curves of photovoltaic power and wind power generations of each energy supply station are shown in Figure 4.

System reliability indices analysis under different operation objectives
Based on the proposed reliability assessment method and the complementary and optimal operation during device failure, the simulation results are illustrated in Table 1.
The case verifies that IES can provide differential reliability guarantee for loads of different importance. As shown in Table 1, both cooling and heating energy loss are more than the electrical energy loss because the optimal operation objective 1 established in this study is based on the user's perspective to minimise the user's energy loss. From the perspective of energy use, electrical energy can be converted into cooling and heating energies, and continue to supply cooling and heating loads, while   cooling and heating energies cannot be reversed into electrical energy. Therefore, in the process of the complementary optimisation of cooling, heating and electricity, to minimise the loss of user, the optimisation result will reduce the electrical energy loss.  Also, the above results give the indices of each single energy system and IES and there is no significant difference between the cooling and heating indices since the user demand characteristics of heating and cooling load are relatively similar when measured in one year. It is found that the energy supply reliability of the system cannot be evaluated only by a single system index of the cooling, heating and electricity. The proposed AAEL takes the differences of energy sources into account, and it is more optimistic and reasonable than just adding up the reliability indices of each energy system because when the energy loss with a lower quality accounts for a large proportion, the index has revised the available value of different energy according to the 'energy value coefficient', which makes a more sensitive and reasonable response. IESP and IEST no longer only consider a single type of energy supply reliability, it simultaneously considers the reliability of the three types of energy supply for cooling, heating and electricity, and any type of energy loss is counted as a lack of energy in IES. In this way, the reliability indices are more suitable for evaluating IES that can supply multiple types of energy.  Tables 2 and 3, we can see that the change in AAEL is more obvious in both the single energy system indices and IES indices, while the change in IESP and IEST is relatively small. This is because AAEL is closely related to the amount of load loss, and this is exactly the variable that needs to be optimised by mobilising the multi-energy complementary characteristics of IES during the device failure. Therefore, different objective functions will cause larger numerical differences in AAEL. According to the definition of the other two indices, they mainly depend on the inherent fault rate and the repair time of devices. To a certain extent, these two indices mainly focus on reflecting the reliability to supply loads from the device itself. At the same time, it can be found that when the optimal operation is performed under different objectives, the reliability indices of the system are also different. Therefore, after mobilising the multi-energy complementary characteristics of the system for the optimal operation, the system has the ability to adjust the output of the remaining devices and actively select and change 'the form of load loss', making the entire system operation more conducive to the reliability of energy supply under different objectives, which fully reflects multi-energy complementary characteristics of IES and its ability to flexibly schedule the energy flows.

5.3
The difference of different device fault on system reliability In order to explore the difference of different device faults on the system's energy supply reliability, six hypothetical scenarios for comparative analysis are studied in this section. Each scenario considers the fault of only one of the following devices: GT, GB, RB, ER, AC and the inter-station connection network. This section uses 'AAEL' as an example to compare the system reliability in the above six scenarios.
As shown in Figures 5 and 6, among all devices inside the energy supply station, the fault of different devices has a different impact on system reliability. The GT has the greatest impact on the reliability of the system's energy supply, while the fault of the inter-station connection network has the smallest impact. The impact of each device on the reliability of energy supply can be arranged in order as GT > GB > EB > ER > AC > interstation connection network. Although the inter-station connection network can optimise scheduling resources to improve the overall energy supply reliability of the system to a certain extent, considering its limited transmission capacity, it cannot take the main responsibility of energy supply; therefore, the fault of the inter-station connection network is not enough to cause a great The load of transition season fluctuation in energy supply reliability of the system. When the GT fails, it will affect the supply of three types of energy; the specific operation mode, the output of each device and the load loss of energy are determined by the complementary and optimal operation model described in this study. Further, the GT directly supplies electricity and heating energies, and the supply of cooling energy needs to be converted by the AC; therefore, the impact on the electricity and heating supplies is a direct impact, and the impact on the supply of cooling is an indirect impact, and it is expressed on a quantified level such that AAEL e and AAEL h are larger, though AAEL c is smaller. The above results and analysis can be used as an important reference for identifying weak links in the system, and can also provide a theoretical basis for formulating strengthening measures and improve the reliability of IES.

CONCLUSION
In this study, we propose a mathematical model for the optimal operation of cooling, heating and electricity in the IES during failure. Additionally, three new indices are proposed to evaluate the reliability of IES collectively. Through the case analysis, the following conclusions can be drawn: First, IES can flexibly schedule energy flow under different objectives to realise adaptive and targeted operational strategies, which can reflect the multi-energy advantages of IES. Second, the new reliability index proposed in this study is more reasonable and optimistic. It is suitable for IES that combines several types of energy together. Also, the variation of the three reliability indices under different operation objectives is explained in detail in the case studies. Finally, the fault scenarios of different devices are assumed and the influence of different device on the energy supply reliability of the system is ranked, which is of great significance to find the weak parts of the system and provide a reference for the system to develop measures to improve the reliability of the system.