IEWS system reliability evaluation method considering multi-state model of water system equipment

Abstract

The invention belongs to the technical field of electricity-water integrated system evaluation, and particularly relates to an IEWS system reliability evaluation method considering a water system equipment multi-state model, which comprises the following steps: S1, constructing an IEWS simulation model; s2, performing MCMC sampling to obtain the state of each element in each hour every day within a preset simulation age limit; s3, enabling Y to be equal to 1; s4, solving an optimal load reduction model by using the state of each element in each hour of each day in the Yth year and combining an IEWS element reliability model to obtain load reduction data in each hour of each day in the Yth year; s5, calculating an energy supply shortage expectation variance coefficient, and if the energy supply shortage expectation variance coefficient is smaller than a preset threshold value, turning to S6; if not, judging whether Y reaches a preset value or not, if so, turning to S6, and if not, updating Y to enable Y to be equal to Y + 1 and returning to S3; s6, calculating a reliability evaluation index; and S7, performing reliability evaluation by using the reliability evaluation index. According to the method, the influence of intermediate fault states such as leakage on electricity-water bidirectional coupling can be accurately quantified, and large-scale IEWS operation risk dynamic assessment is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of integrated electricity-water system evaluation, and in particular relates to an IEWS system reliability evaluation method considering a multi-state model of water system equipment. Background Art

[0002] As the global energy transition accelerates, renewable energy, represented by wind power and photovoltaics, is replacing traditional fossil fuels on a large scale, driving the construction of integrated energy systems with a high proportion of renewable energy. These new systems feature a complex array of equipment and demanding operating environments. Combined with risks such as human error, natural disasters, and equipment failure, these systems pose significant challenges to their safe and reliable operation, directly impacting normal social production and life. It is noteworthy that the water system, a critical energy consumer within the power system (accounting for approximately 10% to 20% of total electricity consumption), is deeply coupled and interdependent with the power system. The power system drives the water system, which in turn provides water resources for critical processes, including power plant cooling. This tight coupling has given rise to a new paradigm for integrated electricity-water systems (IEWS). Exploiting electricity-water synergies is crucial for ensuring the sustainable development of energy and water resources and improving the overall reliability of IEWS.

[0003] However, reliability issues with IEWS are becoming increasingly prominent. On the one hand, the large-scale integration of renewable energy sources has significantly increased uncertainty on both the source and load sides of the power system, placing enormous pressure on the reliability of these new power systems. A typical case involves a widespread power outage in a state in the United States caused by the integration of wind and solar power, impacting over 400,000 customers. On the other hand, water systems themselves face significant reliability issues, particularly leakage in water supply pipelines. Globally, pipeline leakage rates in developed countries range from approximately 15% to 24%, while in developing countries, the rate is as high as 25% to 45%. Pipeline failures not only waste precious water resources but also force water pumps to operate at high loads for extended periods (power increases can reach 1%-4%), further increasing operational pressure on the power system. Of particular concern is the fact that the high degree of coupling in IEWS can amplify the cascading effects of single system failures. When the power system encounters a disaster (such as the snowstorm in D state, USA, which caused 4.5 million users to lose power), the failure will quickly spread to the water supply system (the incident caused 13 million people to face a water crisis); conversely, water system failure (such as equipment failure in areas relying on seawater desalination, which caused a sharp drop in water production or a surge in water demand) may cause a surge in electricity demand for large load units such as seawater desalination plants (energy consumption of about 3.5-4.5kWh / m 3) could threaten the cooling water supply of thermal power plants, ultimately negatively impacting power system reliability. As the proportion of energy consumed by water systems continues to rise and their coupling deepens, accurate IEWS reliability assessment and capacity expansion planning are crucial to maintaining their safe and stable operation. Therefore, focusing on issues such as surges in water system power consumption and increased grid burden from equipment failures, developing IEWS reliability assessment methods that account for the impact of multi-state water system failures has become an urgent need to improve system resilience and economic efficiency. However, existing IEWS reliability assessments have significant limitations: current models typically simplify water supply pipelines into two states: "normal" and "faulty," completely ignoring the critical intermediate state of "leakage."

[0004] This simplification stems from three core difficulties. Modeling complexity: The leakage state is neither a complete failure nor a significant reduction in efficiency, requiring the construction of a nonlinear multi-state model to characterize its gradual failure characteristics. Difficulty in quantifying the coupling effect: Pipeline leakage leads to increased power consumption of water pumps, requiring the establishment of a water pressure-flow-power consumption coupling model to accurately calculate the additional pressure on the power system. Heavy computational burden: The multi-state model causes the system state space to explode, making it difficult for traditional enumeration methods to meet the needs of real-time reliability assessment.

[0005] The above limitations make it impossible for existing assessments to capture the chain reaction of leakage on the power system (such as insufficient grid backup capacity and increased operating costs), ultimately overestimating the actual reliability level of IEWS, concealing potential operational risks, and misleading system planning decisions.

[0006] Therefore, how to break through the limitations of the "normal-fault" two-state model, build a multi-state reliability model for water system equipment, accurately quantify the impact of intermediate fault states such as leakage on the bidirectional coupling of electricity and water, and develop an efficient solution algorithm to realize the dynamic assessment of large-scale IEWS operation risks, so as to obtain reliability indicators that conform to engineering reality to guide accurate decision-making, has become an urgent problem to be solved. Summary of the Invention

[0007] To address the shortcomings of the above-mentioned existing technologies, the present invention provides an IEWS system reliability assessment method that considers a multi-state model of water system equipment. This method can break through the limitations of the "normal-fault" two-state model, construct a multi-state reliability model for water system equipment, accurately quantify the impact of intermediate fault states such as leakage on the bidirectional coupling of electricity and water, and develop an efficient solution algorithm to realize dynamic assessment of large-scale IEWS operation risks.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0009] The IEWS system reliability assessment method considering the multi-state model of water system equipment includes the following steps:

[0010] S1. Construct an IEWS simulation model for calculating various operating data according to the status of each component; the IEWS simulation model includes a water system simulation model and an electrical system simulation model;

[0011] S2. Obtain the status of each component at each hour of each day within the preset simulation period through Markov Chain Monte Carlo (MCMC) sampling;

[0012] S3. Initialize the simulation life coefficient, set Y = 1;

[0013] S4. Using the component status at each hour of each day in year Y, combined with the IEWS component reliability model, solve a preset optimal load reduction model to obtain load reduction data for each hour of each day in year Y; the optimal load reduction model aims to minimize the sum of the wind curtailment penalty cost and the IEWS electricity and water load reduction penalty costs; the load reduction data includes the load reduction status and the optimal load reduction amount;

[0014] S5. Based on the obtained load reduction data for each hour of each day in year Y, calculate the expected variance coefficient ε of the energy shortage. If ε is less than the preset threshold, proceed to S6. If not, determine whether Y has reached the preset value. If so, proceed to S6. If not, update Y to set Y = Y + 1 and return to S3.

[0015] S6. Calculate a reliability evaluation index based on the currently obtained load reduction data for each hour of each day in year Y; the reliability evaluation index includes an expected value of load undersupply and a probability of load undersupply;

[0016] S7. Use reliability evaluation indicators to conduct reliability evaluation.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] 1. Accurately quantify the impact of intermediate fault states in water systems. By constructing a multi-state model of the desalination plant (normal operation / inefficiency / fault) and the water supply network (normal / leakage / fault), intermediate states such as leakage and inefficiency are introduced into IEWS reliability assessment for the first time. This model breaks through the limitations of the traditional "normal-fault" two-state model and accurately captures the characteristics of gradual faults, such as high-power operation of water pumps caused by pipeline leakage and a sharp increase in energy consumption caused by desalination plant inefficiency, thus avoiding overestimation of system reliability due to simplified modeling.

[0019] 2. Revealing the cascading transmission mechanism of bidirectional power-water faults. By synergistically optimizing wind curtailment penalty costs and power / water load reduction costs within an optimal load reduction model, this method dynamically reflects the impact of water system faults (e.g., leaks that increase pump power consumption) on power system reserve capacity, as well as the countervailing effects of power outages on water supply capacity. This overcomes the existing method's neglect of the coupling path of "water system faults → increased power system operating pressure → decreased power reliability," achieving the first closed-loop quantification of bidirectional power-water fault propagation.

[0020] 3. Efficiently solve large-scale state space problems. Using MCMC sampling to generate equipment state sequences, combined with a variance convergence criterion (the expected variance coefficient of the energy shortage) to dynamically control the simulation lifespan, significantly reducing computational complexity. This avoids the state combination explosion problem caused by multi-state models and enables long-term operational risk assessment of large-scale IEWS while ensuring accuracy.

[0021] 4. Generate practical reliability indicators for engineering projects. By iteratively converging load reduction data, the expected value of undersupply (EENS) and probability (LOLP) are calculated, forming a quantitative basis to directly guide system planning. These indicators accurately reflect the cumulative impact of intermediate conditions such as water system leaks on overall reliability, providing data support for expansion site selection and pipeline maintenance priority setting.

[0022] In summary, this method transcends the limitations of the "normal-fault" two-state model to construct a multi-state reliability model for water system equipment. This model accurately quantifies the impact of intermediate fault states, such as leakage, on the bidirectional coupling of electricity and water. Furthermore, an efficient solution algorithm is developed to dynamically assess the operational risk of large-scale IEWS, thereby obtaining reliability indicators that meet engineering requirements and guide accurate decision-making. This method achieves systematic innovation in modeling depth, coupling mechanism analysis, and computational efficiency, providing key technical support for the coordinated security of energy-water resources in regions with high hydropower dependence.

[0023] Preferably, the water system simulation model is a multi-state model of a seawater desalination plant, which is used to determine the current state according to the component state and calculate the corresponding operating data. The state of the seawater desalination plant includes a normal operating state, an inefficient operating state and a fault state. In the multi-state model of the seawater desalination plant, the water pump operation constraints are:

[0024]

[0025] Where: and They represent the water pump power, water flow rate and head at time t respectively; ρ is the density of seawater; g is the acceleration of gravity; η in is the water intake pump efficiency; The working status of the water pump is a 0-1 variable, 1 means running; q in,min is the lower limit of water intake per unit time of the water intake pump, qin,max The upper limit of water intake per unit time of the water intake pump; assuming that the pump head remains constant;

[0026] The reverse osmosis device consists of a high-pressure pump and a reverse osmosis unit. The operating constraints of the reverse osmosis unit are:

[0027]

[0028] Where: are the water inlet and outlet of the reverse osmosis unit respectively; p r,t Reverse osmosis unit working pressure; K r 、A r and Δπ are the permeability coefficient, permeation area and transmembrane osmotic pressure difference of the osmotic membrane respectively; R is the reverse osmosis recovery rate; is the power consumed by the reverse osmosis unit; a r 、b r is the high-pressure pump power coefficient; is the feed water concentration; is the minimum net transmembrane pressure of the osmotic membrane unit, is the maximum value of the net transmembrane pressure of the osmotic membrane unit; φ r,t is the operating state of the permeation unit, which is a 0-1 variable and the operating state is 1;

[0029] The reverse osmosis device has r reverse osmosis units, and the operating constraints of the reverse osmosis device are:

[0030]

[0031] Where: Respectively represent the total water inflow and total water outflow of the reverse osmosis device; It represents the total power consumed by the high-pressure pump and the booster pump; β represents the ratio of the amount of pretreated seawater to the amount of feed water;

[0032] The water storage facilities include clean water tanks and product water tanks, and the operating constraints are:

[0033]

[0034] Where: are the water storage capacity of the clean water tank and the product water tank at time t; A CWP 、A PRP are the bottom areas of the clean water pool and the product water pool respectively; h CWP,max 、h PRP,max They are the maximum capacity of the clean water tank and the product water tank, h CWP,min 、h PRP,min They are the minimum water storage capacity of the clean water tank and the product water tank respectively.

[0035] This setup accurately depicts the gradual failure characteristics of water systems. By using constraints such as flow limits and transmembrane pressure differential ranges, the model explicitly defines "inefficient states" (e.g., pump flow drops to the lower limit but does not fail, or reverse osmosis membrane pressure differential is abnormal) for the first time, breaking through the simplistic limitations of the traditional "normal-failure" two-state model. Compared with existing technologies, it addresses the problem of energy consumption surges (e.g., high-power operation of pumps) caused by existing methods ignoring intermediate states such as pipeline leakage and equipment aging, thus avoiding distortion in reliability assessments.

[0036] 2. Quantify the energy flow transfer mechanism of electricity-water coupling. Reverse osmosis energy consumption equation Directly linked to the power system, it dynamically reflects the cascading impact of water system status changes on grid load. This reveals the transmission path from "pipeline leakage → increased water pump power consumption → insufficient grid backup capacity," providing a physical basis for load reduction decisions.

[0037] 3. Supports dynamic reliability assessment at multiple time scales. The water tank state equation simulates the cumulative impact of fault duration on water supply capacity, supporting risk assessments from hourly to annual levels. Compared to static models, this model effectively captures the gradual risk of "equipment inefficiency → insufficient water storage capacity → water supply shortage," improving the accuracy of long-term reliability predictions.

[0038] 4. Optimize system-level collaborative control capabilities. By integrating unit-level (reverse osmosis membrane) and system-level (water storage) constraints, coupled boundary conditions are provided for the optimal load reduction model (step S4), achieving collaborative optimization of electricity and water load reduction. This ensures that even in the event of equipment inefficiency or failure, the system can still minimize penalty costs by dynamically adjusting water and electricity loads (e.g., avoiding blind load shedding).

[0039] Preferably, when judging the state of the seawater desalination plant, if a component in the component 1 fails, the seawater desalination plant is in a fault state; the components in the component 1 include a water intake pump, a high-pressure pump, a clear water tank, a product water tank, and post-processing link components;

[0040] If only components in Components 2 to 5 fail, the desalination plant will be in an inefficient operating state. Components in Component 2 include pretreatment components; components in Component 3 include additional pumps and energy recovery devices; component failures in Component 4 include aging and scaling of the reverse osmosis membrane; and component failures in Component 5 include failure of the reverse osmosis membrane.

[0041] Otherwise, the desalination plant is in normal operation;

[0042] The operating status and operating model of the reverse osmosis desalination plant are shown in the following table:

[0043]

[0044]

[0045] In the table, U means no fault, D means fault; RO,t represents the operating state variable of the reverse osmosis desalination plant at time t, s RO,t =1,2,...,17; Indicates that the reverse osmosis desalination plant is in state s RO,t Power consumption P RO and water production from desalination plants The functional relationship between For desalination plants in s RO,t The proportion of power consumption increase in the state;

[0046] The state transition probability matrix between the states of the seawater desalination plant is as follows:

[0047]

[0048] Each element in the matrix represents the transition probability between states;

[0049] Assume that the desalination plant is in operation state s at time t RO,t =k, k∈{1,2,...,17}; then based on the MCMC method [generate a random number p∈[0,1], the operating state s of the desalination plant at time t+1 is obtained according to the following formula RO,t+1 :

[0050]

[0051] This setting can 1. Accurately capture the characteristics of gradual faults. Through 15 inefficient states, detailed modeling of the nonlinear effects of intermediate faults such as reverse osmosis membrane aging / scaling on energy consumption (such as RP x The proposed method addresses this gap by quantifying the increase in energy consumption (a coefficient that quantifies the increase in energy consumption), accurately reflecting equipment performance degradation. Traditional "normal-fault" two-state models fail to describe the gradual increase in energy consumption caused by membrane aging (e.g., pumps operating at high power to compensate for reduced flow), leading to overestimation of system reliability.

[0052] 2. Quantifying the energy consumption dynamics of electricity-water coupling. Multi-state energy consumption formulas are embedded in the IEWS simulation to dynamically calculate the impact of water system state changes on the power load (e.g., increased power consumption under inefficient conditions), providing input for the load shedding model. Existing methods ignore the cascading stress (e.g., insufficient backup capacity) that inefficient conditions (e.g., component 2-5 failures) can impose on the grid. This method, for the first time, achieves closed-loop modeling of bidirectional electricity-water energy consumption transmission.

[0053] 3. Supports efficient, large-scale risk assessment. The MCMC state transition mechanism, combined with probabilistic sampling, avoids the computational explosion associated with fully enumerating all 17 state combinations, enabling simulation of long-term states (from hours to years). While traditional static models require numerous assumptions to simplify intermediate states, this method significantly reduces computational complexity while maintaining comparable accuracy, making it suitable for the dynamic assessment needs of IEWS.

[0054] 4. Enhanced reliability adaptability. The state transition matrix parameterizes failure and repair rates, simulating real-world conditions (such as scheduled maintenance of reverse osmosis membranes). The resulting reliability metrics are more closely aligned with engineering practice. Existing models ignore gradual state transitions, resulting in inaccurate predictions of long-term risks (such as power outages caused by cumulative energy consumption increases). This approach can guide targeted maintenance strategies.

[0055] Preferably, the water system simulation model includes a multi-state model of the water supply network, which is used to determine the current state according to the component state and calculate the corresponding operating data. The state of the water supply network includes a normal working state, a leakage state and a fault state.

[0056] When the multi-state model of the water supply network determines the current state, the leakage state of the water supply network includes small hole leakage and hole leakage, and the fault state includes rupture. The operating state of the water supply pipeline is shown in the following table:

[0057]

[0058] s L,t represents the operating state variable of the water supply pipeline at time t, s L,t =1,2,3,4; Indicates that the water supply pipeline is in state s L,t Lower leakage q Lj Pipeline fault displacement The functional relationship between

[0059] The state transition probability matrix between the states of the water supply pipeline is as follows:

[0060]

[0061] Among them, λ 0,1 ,λ 0,2 and λ 0,3 Respectively represent the transition rates between the normal state and the pinhole leakage, hole leakage and rupture states; λ 1,3 and λ 2,3 They represent the conversion rates of the pinhole leakage state and the hole leakage state to the damage state; μ 2,0 and μ 3,0 Represents the repair rate of holes, leakage and damage;

[0062] Assume that the water supply pipeline is in state s at time t L,t=k, k∈{1,2,3,4}; then based on MCMC, a random number p∈[0,1] is generated, and the operating state s of the water supply pipeline at time t+1 can be obtained according to the following formula L,t+1 :

[0063]

[0064] This setup accurately quantifies the cascading impact of progressive leakage. Four states (normal, small holes, holes, and ruptures) are associated with leakage functions f1 through f4, enabling differentiated modeling of small hole and hole leakage for the first time, accurately calculating water loss at different leakage levels. Traditional "normal-rupture" two-state models ignore small hole leakage, leading to underestimation of long-term water waste and increased pump power consumption; this model fills this gap.

[0065] 2. Revealing the hidden impact of leakage on the power system. Dynamically calculating pipeline pressure loss using leakage functions f2-f3 and correlating it with the additional power consumption required by pumps to compensate for flow (e.g., additional pumps are needed to maintain water pressure when a small hole leaks), provides input for assessing power system reserve capacity. Existing methods only account for the impact of pipeline ruptures (f4) and fail to capture the hidden burden on the power grid caused by long-term small hole leakage (e.g., the $39 billion annual loss in South Africa).

[0066] 3. Simulate the real leakage evolution and repair process. The transfer matrix includes the deterioration path of "small hole → hole → rupture" (λ 1,3 ,λ 2,3 ) and the “hole / crack→normal” repair path (μ 2,0 and μ 3,0 ) to support long-term risk assessment of pipeline aging and maintenance strategies. This model addresses the limitations of traditional models that treat leakage as a transient event and quantifies the cumulative impact of progressive failures on IEWS reliability (e.g., a 1%-4% increase in annual power consumption due to persistent leakage).

[0067] 4. Efficiently simulate large-scale pipeline network states. MCMC sampling combined with a probability cumulative function compresses the combinatorial space of four states N (N is the number of pipelines) to a linear computational complexity, avoiding the failure of enumeration methods. Traditional methods, ignoring state transitions, cannot predict the chain reaction from "small hole leakage to system failure." This method supports dynamic simulations over several years.

[0068] Preferably, the water supply pipe is in state s L,t Lower leakage q Lj Pipeline fault displacement Functional relationship between Obtained by the following calculation formula:

[0069] Node balance under normal operation:

[0070] AQP =Q N ;

[0071] Where: Q P =[q Pj ] is an m×1 vector, each element of which represents the water flow rate transported in the pipeline; Q N =[q Nj ] is an n×1 vector, each element represents the water demand of a node; A=[a ij ] is an n×m incidence matrix, whose element a ij It can take three values: 0, 1 and -1; a ij =0 means that node j is not the endpoint of pipe i, and no water in pipe i flows into or out of node j; a ij =1 means the water in pipe i flows out of node j; a ij = -1 means that the water in pipe i flows into node j; m and n are the number of pipes and nodes in the water system respectively;

[0072] Node balance in steady-state leakage:

[0073] AQ P =Q N +Q L ;

[0074] Where: Q L =[q Lj ] is an n×1 vector, each element of which represents the leakage flow of a node;

[0075] The steady-state leakage refers to leakage in the pipeline while the temperature and density of the water in the pipeline remain unchanged;

[0076] Point leakage calculation model:

[0077]

[0078] Where: q Lj is the leakage flow rate of the leakage point, μ is the flow coefficient, σ is the leakage coefficient considering the obstruction of soil and filler to water flow, A Lj is the leakage area at the leakage point, H Lj Point water head for leakage;

[0079]

[0080] Where: R is the critical displacement of pipeline leakage, D is the pipeline diameter, A is the pipeline cross-sectional area, and S is the displacement of the pipeline after the pipeline failure;

[0081] Pipeline leakage flow calculation formula:

[0082]

[0083] Where H1 and H2 are the water heads at the two end points of the leaking pipe; α is the leakage coefficient that takes into account the obstruction of soil and filler to water flow.

[0084] This setup accurately quantifies leakage status. Using the displacement threshold R and the gradient interval [R, R + A / (πD)], leakage is first classified into three levels: "no leakage," "gradual leakage," and "complete rupture," and correlated with physical displacement (such as foundation settlement).

[0085] Compared with existing technologies: Traditional models only use binary judgment (leakage / no leakage) and cannot distinguish between small hole leakage and rupture. This model fills the gap.

[0086] 2. Reveal the cascading effects of leakage on hydropower systems. The leakage flow formula couples the soil resistance coefficient σ with the pipe network head H to quantify the surge in pump power consumption caused by increased leakage (e.g., the need to add additional pumping stations to maintain pipe network pressure). This addresses the current approach's neglect of the transmission path from small pore leakage to water pressure drop to high-power pump compensation to insufficient grid backup, thus avoiding the hidden risk of $39 billion in annual losses, as seen in the South African case.

[0087] 3. Supports real-world impact assessment of pipeline network topology. The association matrix A defines the node-pipeline topology relationship and, combined with the differences in hydraulic heads H1 and H2, dynamically calculates the diffusion effect of leaks at different locations (e.g., leaks at the end of a pipeline network have a wider impact). While traditional homogenized models cannot locate highly sensitive areas, this method accurately guides pipeline maintenance priorities (e.g., prioritizing repairs in high-head areas).

[0088] 4. Engineering practicality by coupling environmental and equipment parameters. The soil coefficient σ modifies flow, and pipe diameter D and cross-sectional area A are factored into leakage area calculations, improving the model's adaptability to complex operating conditions (e.g., faster seepage in sandy soils). This model is also adaptable to high leakage rates (25%-45%) in developing countries, providing a basis for customized leakage control strategies.

[0089] Preferably, the objective function of the optimal load shedding model is:

[0090]

[0091] Where, To reduce the load of power transmission system, is the wind power curtailment, Reduce water system water energy load; c en Penalty cost for load shedding per unit of the transmission system, c wc is the penalty cost per unit of wind curtailment, c Wm is the penalty cost of unit load reduction in the water system; n is the total number of nodes in the transmission system, N w is the set of wind turbine grid-connected nodes, N Wmis the total number of nodes in the water network; T is the scheduling period; subscripts i, w, Wm and t represent node i, node w, node Wm and time t respectively.

[0092] This setup 1. Quantifies the cascading economic losses of power-water failures. By integrating water system load shedding penalties with power load shedding into a unified framework, it is possible to economically quantify the cascading losses of both systems caused by pipeline leaks for the first time. Example: Pipeline leak → Increased water pump power consumption → Insufficient grid backup → Urgent load → ΔD EDS Cost; at the same time, leakage forces water supply to be cut → ΔD WDS Cost. Traditional methods only consider load reduction in a single system, ignoring the cross-system cost transmission of "leakage-power consumption-load reduction".

[0093] 2. Balancing renewable energy consumption and system reliability. Through wind curtailment penalties, dynamic decisions are made regarding the trade-off between curtailing wind power to maintain supply and reducing load. When pipeline inefficiencies (such as leaks) cause a surge in pump power consumption, appropriate wind curtailment is permitted to maintain the hydropower baseload and avoid system collapse. Existing technologies optimize wind curtailment and hydropower load independently, making it easy for coupled failures to cause dual power outages.

[0094] 3. Drive engineering decisions based on multi-state models. The objective function directly receives the output of the multi-state model of the water system (e.g., when a leak occurs, Wm For example, when the model detects that a pipeline is in a "hole leakage" state (q Lj ↑→Pump power consumption↑), the optimizer will give priority to reducing high c Wm Node load, rather than blindly cutting off the grid load. It can guide the maintenance priority of the pipeline network (such as repairing c Wm leak point with high value).

[0095] 4. Support the accurate generation of reliability indicators and output the optimal load reduction as input for steps S5-S6, ensuring that indicators such as EENS (Expected Energy Shortage) reflect real economic priorities. In existing technologies, the equal load reduction strategy causes indicators to deviate from actual user losses.

[0096] Preferably, the constraints of the optimal load shedding model include power system constraints, which include:

[0097] Node power balance constraints:

[0098]

[0099] Where, P i,t is the transmission system node power, represents the predicted value of wind power, is the predicted value of conventional power load, is the power consumed by the desalination plant, and They represent the collection of thermal power units, wind farms, and water systems connected to the transmission system node n, is the set of transmission system nodes, variable θ n,t and θ m,t represents the node phase angle, B n,m It represents the susceptance of line nm;

[0100] Thermal power unit ramp constraints:

[0101]

[0102] Where, φ i,t is the state of generator set i at time t, R i is the climbing rate, Ω T Assemble for thermal power units; Respectively represent the minimum and maximum output power of the generator;

[0103] Output power constraints of thermal power generating units:

[0104]

[0105] Wind power curtailment constraints:

[0106]

[0107] Where, Ω W Assemble for wind farms;

[0108] Power line flow constraints:

[0109]

[0110] Where S n,m is the upper limit of line transmission capacity, Δ E A collection of power transmission lines;

[0111] Phase angle constraint of equilibrium node:

[0112] θ ref,t =0;

[0113] Where θ ref,t =0 is the equilibrium node phase angle.

[0114] This setup can 1. quantify the chain reaction of water system failures on the power grid. Dynamically responding to multi-state models of desalination plants (e.g., increased energy consumption in inefficient states) accurately transmits water equipment failures to grid nodes. Compared to existing technologies, traditional models treat water loads as fixed values ​​and fail to capture the real-time pressure on the grid caused by a surge in pump power consumption (e.g., 1%-4% additional power consumption) caused by leaks.

[0115] 2. Enhance system resilience under fluctuations in renewable energy. Ramp-up constraints are linked to the unit status database (normal / faulty), dynamically limiting the thermal power regulation capacity during faults. Wind curtailment constraints provide decision-making space for the choice between ensuring water supply and ensuring consumption. When pipeline leaks cause a sharp increase in water pump power consumption, wind curtailment is prioritized to ensure minimum hydropower supply and avoid "double water and power outages."

[0116] 3. Block the spread of topological risks from coupled faults. Power flow constraints limit local overloads caused by leakage or desalination plant failures, preventing single water equipment failures from triggering cascading grid trips. For example, if a hole leak (state 3) causes a 30% increase in power consumption for a group of water pumps in a certain area, without this constraint, the safety of the line would be misjudged.

[0117] 4. Support collaborative decision-making of multi-state models. All constraints receive multi-state outputs of the water system (such as φi,t corresponding to the state of the seawater desalination plant), driving the load reduction model to accurately allocate electricity / water shortages. When the pipeline network breaks (fault state), the load of the node with high economic cost is automatically reduced ( load shedding (users with large load values) rather than evenly shedding the load.

[0118] Preferably, the constraints of the optimal load shedding model include hydraulic system constraints, which include:

[0119] Total water head constraints at water network nodes:

[0120]

[0121] Where, and Represents water network node W m The total water head, water flow pressure and position head, ρ and g are the density of water and gravitational acceleration, Λ W Represents a collection of water network nodes;

[0122] Head loss along the pipeline:

[0123]

[0124] Where, denote the hydraulic heads at the end nodes of pipe mn, Indicates the water flow through the pipe. is the pipe head loss coefficient, Δ W Represents a collection of water network pipes;

[0125] Pipeline flow constraints:

[0126]

[0127] Where, Respectively represent the maximum and minimum values ​​of pipeline flow;

[0128] Pump constraints:

[0129]

[0130] Where, Respectively represent water pump P m The head gain and flow rate through the pump, For the water pump assembly, Indicates the head coefficient of the pump, Respectively represent the maximum and minimum water flow through the pump, φ Pm,t is the state 0-1 variable of the water pump, and takes 1 in normal state;

[0131] Reservoir constraints:

[0132]

[0133] Where, and W Wm,t Respectively represent the water reservoir W at time t m Inflow, outflow and storage capacity, μ W represent the cross-sectional area of ​​the reservoir and the water loss rate, respectively. They represent the maximum water storage capacity and the minimum required water storage capacity of the reservoir, respectively; Δt represents the scheduling time step; φ Tm,t is the state 0-1 variable of the reservoir, and takes 1 in normal state; Represents a collection of reservoirs;

[0134] Valve Constraints:

[0135]

[0136] Where, φ Vmn,t is the valve state 0-1 variable, the normal state is 1; M is a constant with a preset value, and The minimum and maximum allowable flow rates when a valve is installed in the pipeline. A collection of valves;

[0137] Node balance constraints:

[0138]

[0139] Where, and They are water network nodes W k Water load, inflow and outflow at time t, q LWmn,tis the leakage amount of the pipeline when there is a fault in pipeline mn;

[0140] Pump power constraints:

[0141]

[0142] Water network power constraints:

[0143]

[0144] Where, Indicates water pump P m The power consumed at time t, η is the working efficiency of the pump.

[0145] This setup accurately quantifies the cascading losses caused by leakage on the hydropower system. The head loss equation dynamically calculates the pipe network pressure loss caused by leakage, and when coupled with the pump power consumption equation, accurately translates this into grid load increments. Traditional models ignore the quadratic relationship between leakage and head loss (e.g., a 20% drop in pressure from a small orifice leak results in a 15% increase in pump power consumption), thus underestimating the burden on the grid.

[0146] 2. Simulate the buffering effect of storage and transportation facilities on failures. The reservoir equation is combined with the leakage rate μ W , quantify the cumulative impact of fault duration (e.g., the duration of water reservoir support after a rupture fault). This can guide the priority maintenance of high μ W Regional pipeline network to reduce risks.

[0147] 3. Supports bidirectional, safe, and coordinated control of electricity and water. Total power consumption constraints provide input to the grid balance equation, enabling a second-by-second response to the "water system failure → sudden change in electricity load → load reduction decision" model. Traditional methods use fixed water load factors and are unable to respond to the real-time risk of a sudden surge in power consumption in a water pump fleet during a snowstorm.

[0148] Preferably, the expected value of load supply shortage includes the expected value of power load loss EENS, the expected value of water shortage EWNS, the expected value of leakage EWL and the comprehensive loss due to supply shortage; the probability of load supply shortage includes the probability of power load loss LOELP, the probability of water load reduction LOWLP and the probability of leakage PWL.

[0149] With this setup, the indicator system decouples the three major risk dimensions of "leakage", "water shortage" and "power shortage", and for the first time achieves a panoramic assessment of gradual failures in the electricity-water integrated system, providing a feasible quantitative benchmark for pipeline network transformation and new energy consumption strategy formulation in highly coupled areas.

[0150] Preferably, the power load loss probability LOELP is:

[0151]

[0152] Where, N is the state variable of the system load reduction at time t in year y. If it is 1, it means there is load reduction, and if it is 0, it means there is no load reduction. y is the simulation years;

[0153] The expected value of power loss load EENS is:

[0154]

[0155] Where, is the load reduction at the transmission system node i at time t in year y;

[0156] The water load reduction probability LOWLP is:

[0157]

[0158] Where, is the state variable of the system water load reduction at time t in year y. If it is 1, it means there is water load reduction, and if it is 0, it means there is no water load reduction.

[0159] The expected value of water shortage EWNS is:

[0160]

[0161] Where, is the water load reduction at the water network node Wm at time t in year y;

[0162] The leakage probability PWL is:

[0163]

[0164] Where, is the state variable indicating whether there is pipe leakage in the water system at time t in year y. If it is 1, it means there is pipe leakage, and if it is 0, it means there is no pipe leakage;

[0165] The expected value of leakage EWL is:

[0166]

[0167] Where, is the leakage loss at the water network pipe mn at time t in year y;

[0168] The comprehensive loss due to supply shortage is:

[0169] C ENS =c p EENS+c w EWNS+c l EWL;

[0170] Where cp 、c w 、c l They represent the penalty costs of electricity, water and pipeline leakage respectively. EENS, EWNS and EWL represent the expected values ​​of electricity load, water load and water leakage respectively.

[0171] This setup breaks through the limitations of binary failure metrics. The Probability of Loss (PWL) and Expected Loss (EWL) metrics, for the first time, incorporate leakage as an independent risk dimension, accurately quantifying the long-term impact of small-pore leakage (not complete rupture) in pipelines. Traditional reliability metrics (such as SAIDI) only count complete failures, neglecting the progressive losses caused by leakage.

[0172] 2. Reveal the hidden transmission paths of hydropower failures. The correlation mechanism between EWL and EENS is as follows: pipeline leakage (high EWL) → surge in pump power consumption → insufficient grid backup → increased EENS; leakage and water shortage (high EWL) → increased desalination plant supply → sharp increase in power load → worsening LEOLP. This indicator chain can make explicit the cascading risk of "small leaks → major power outages" (e.g., the Texas snowstorm).

[0173] 3. Drive accurate maintenance decisions and economic scheduling. Spatial positioning: EWL can be decomposed into specific pipelines (mn) to identify high leakage sensitive areas (such as 25%-45% leakage rate areas in developing countries). Economic priority: C ENS Indicator c l Assign weights to leakage costs to guide priority repair of high-c l EWL pipelines (such as water supply hub areas) can avoid resource mismatches caused by equalized maintenance and improve the effectiveness of pipeline network reconstruction.

[0174] 4. Quantify the engineering benefits of multi-state models. State variables Directly responding to the multi-state output of the water supply network (small holes, holes, and ruptures) ensures that the indicator truly reflects the cumulative risk of "inefficient operation." Existing assessments ignore intermediate states and fail to capture the hidden costs of "hole leakage for three years → 4% additional water pump power consumption → delayed grid expansion." BRIEF DESCRIPTION OF THE DRAWINGS

[0175] In order to make the purpose, technical solutions and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0176] Figure 1 Flowchart of this method;

[0177] Figure 2 This is a process flow chart of a reverse osmosis seawater desalination plant in Example 1;

[0178] Figure 3The multi-state Markov model of the reverse osmosis desalination plant in Example 1;

[0179] Figure 4 The water supply pipe leaking in Example 1;

[0180] Figure 5 The multi-state Markov model of the water supply pipeline in Example 1;

[0181] Figure 6 The two-state Markov model of the water tank (or water box) and the valve in Example 1;

[0182] Figure 7 This is the A calculation system based on the 6-node power transmission system and the 21-node water system in Example 2;

[0183] Figure 8 The typical daily curve of wind farm output and conventional electric load in Example 2;

[0184] Figure 9 The electricity price for the water system in Example 2;

[0185] Figure 10 This is a schematic diagram of the energy consumption of the water pump and the seawater desalination plant in Example 2;

[0186] Figure 11 Schematic diagram of electrical load reduction at each moment under different fault conditions of the reverse osmosis desalination plant in Example 2;

[0187] Figure 12 Schematic diagram of pipeline leakage at each moment under different states of the reverse osmosis desalination plant in Example 2;

[0188] Figure 13 Schematic diagram of comprehensive energy loss due to shortage of water supply with different unit water load reduction penalty costs in Example 2. DETAILED DESCRIPTION

[0189] The following is a further detailed description through specific implementation methods:

[0190] Example 1

[0191] like Figure 1 As shown, this embodiment discloses an IEWS system reliability evaluation method considering a multi-state model of water system equipment, including the following steps:

[0192] S1. Construct an IEWS simulation model for calculating various operating data according to the status of each component; the IEWS simulation model includes a water system simulation model and an electrical system simulation model.

[0193] Specifically, the water system simulation model includes a multi-state model for a desalination plant, which determines the current state based on component status and calculates corresponding operating data. The desalination plant states include normal operation, inefficient operation, and fault conditions. A multi-state model for a water supply network, which determines the current state based on component status and calculates corresponding operating data. The water supply network states include normal operation, leakage, and fault conditions. Regarding the multi-state model for a desalination plant that considers inefficient operation.

[0194] The power system simulation model uses the principle of node power balance to construct a linearized power flow model, transforming the nonlinear AC power flow problem into a linear problem through reasonable assumptions. The DC power flow is based on the following key assumptions:

[0195] 1. Constant voltage amplitude: V i ≈V j ≈1.0pu (the per-unit value of all node voltage amplitudes is approximately 1);

[0196] 2. Small phase angle difference: θ ij =θ i -θ j Very small sinθ ij ≈θ ij ,cosθ ij ≈1;

[0197] 3. Ignore branch resistance (R< <X):

[0198] 4. Ignore ground admittance and ground charging capacitance: B sh ≈0

[0199] In the above formula, V i and V j Denotes the voltage amplitude of node i and node j respectively, θ i and θ j Represents the voltage phase angle of node i and node j (unit: radian), R ij Indicates the resistance parameter of the branch (line or transformer), X ij Represents the reactance parameter of the branch, G ij represents the real part of the branch admittance, B ij represents the imaginary part of the branch admittance, B sh It represents the shunt admittance of the node to ground.

[0200] Based on the active power equation of AC power flow, substitute Using the small angle approximation, the final DC equation is:

[0201]

[0202] The matrix form is as follows:

[0203] P = B′θ; where:

[0204]

[0205] Where: P represents the node injected active power vector (n×1), B′ represents the node admittance matrix (n×n), and θ represents the node voltage phase angle vector (n×1).

[0206] In this embodiment, the seawater desalination plant is modeled by taking the reverse osmosis desalination method as an example. The process flow of the reverse osmosis desalination method is as follows: Figure 2 shown.

[0207] Assuming that the water intake pump head remains constant, the operating constraints are:

[0208]

[0209] Where: and They represent the water pump power, water flow rate and head at time t respectively; ρ is the density of seawater; g is the acceleration of gravity; η in is the water intake pump efficiency; The working status of the water pump is a 0-1 variable (1 means running); q in,min is the lower limit of water intake per unit time of the water intake pump, q in,max The upper limit of water intake per unit time of the water intake pump.

[0210] The reverse osmosis device is composed of a high-pressure pump and several reverse osmosis units. The water inlet, water outlet and power consumption of the reverse osmosis unit satisfy formula (2):

[0211]

[0212] Where: are the water inlet and outlet of the reverse osmosis unit respectively; is the power consumed by the reverse osmosis unit; p r,t Reverse osmosis unit working pressure; K r , A r and Δπ are the permeability coefficient, permeability area and transmembrane osmotic pressure difference of the permeable membrane respectively; a r 、b r is the high-pressure pump power coefficient, is the feed water concentration; R is the reverse osmosis recovery rate. is the minimum net transmembrane pressure of the osmotic membrane unit, is the maximum value of the net transmembrane pressure of the osmotic membrane unit; φ r,t It is the operating status of the permeation unit, which is a 0-1 variable (the operating status is 1).

[0213] Assuming that the reverse osmosis device has r reverse osmosis units, the total water inlet and outlet of the reverse osmosis device, and the power consumed by the high-pressure pump and the booster pump satisfy the following relationship:

[0214]

[0215] Where: as well as They represent the total water inlet and outlet of the reverse osmosis device, as well as the total power consumed by the high-pressure pump and the booster pump; β refers to the ratio of the pretreated seawater volume to the feed water volume.

[0216] The clean water tank and product water tank are both water storage facilities, and their operation constraints are as follows:

[0217]

[0218] Where: are the water storage capacity of the clean water tank and the product water tank at time t, A CWP 、A PRP are the bottom areas of the clean water pool and the product water pool respectively; h CWP,max 、h PRP,max They are the maximum capacity of the clean water tank and the product water tank, h CWP,min 、h PRP,min They are the minimum water storage capacity of the clean water tank and the product water tank respectively.

[0219] When all components are operating normally, the desalination plant is in normal operation, and the output of desalinated water and the power consumed are determined by equations (1) to (4). If the water intake pump fails, the desalination plant will not be able to operate normally without feed water; if the clear water tank fails, it will not be able to store pretreated feed water, and the RO equipment will not be able to desalinate seawater without feed water; the RO equipment uses a semipermeable membrane, which allows water molecules to pass through while inhibiting the passage of dissolved salt molecules larger than water molecules. Therefore, the feed water before the membrane has a higher salinity than the permeate water after the membrane; if the high-pressure pump fails and cannot pressurize the water, the osmotic pressure will force the permeate water to flow through the membrane back to the feed water side, and the RO equipment will not operate normally; if the product water tank fails, the desalination plant will not be able to produce water, which is equivalent to a direct failure. Therefore, when the above components (referred to as component 1) fail, the desalination plant will enter a fault shutdown state. If the pretreatment link fails, the seawater cannot be flocculated, precipitated, filtered, and other treatments. The concentration of seawater entering the reverse osmosis device will be higher than that of the treated seawater. The greater the concentration difference on both sides of the osmotic membrane, the greater Δπ will be. The difference between the working pressure of the reverse osmosis membrane unit and the membrane osmotic pressure difference (p r,t -Δπ) is smaller, as can be seen from formula (2), it will lead to a decrease in the desalinated water flow through the osmosis unit. The smaller the desalination unit is, the lower the efficiency of the operation and the higher the feed seawater concentration. Will increase, resulting in the high pressure pump power consumption Therefore, when the above-mentioned component (referred to as component 2) fails, the desalination plant will enter an inefficient operation state. If the booster pump fails, the reverse osmosis recovery rate R decreases, which will cause the desalinated water flow through the osmosis device to When the above-mentioned component (denoted as component 3) fails, the desalination plant will enter an inefficient operation state. In the reverse osmosis device, as the reverse osmosis membrane increases in service time, the reverse osmosis membrane will age, scale, and other phenomena, and the permeation efficiency will decrease, which will lead to the permeation coefficient K r The desalination plant is operating inefficiently. Reverse osmosis unit aging and scaling, denoted as component 4, can cause the desalination plant to operate inefficiently. Furthermore, due to the excessive pressure differential across the reverse osmosis unit, the reverse osmosis unit can fail, reducing the number of effective reverse osmosis units, r. Therefore, reverse osmosis unit failure, denoted as component 5, can lead to inefficient operation. This is shown in Table 1.

[0220] Table 1 Equipment and fault status corresponding to components 1-5 of the reverse osmosis desalination plant

[0221]

[0222] Based on the failure mechanism analysis of the reverse osmosis desalination plant, this section establishes its multi-state Markov model, such as Figure 3 As shown in the model, λ RO,1-5 、μ RO,1-5 They are the transfer rates of the reverse osmosis desalination plant respectively; "1U, 2U, 3U, 4D, 5D" respectively indicate that components 1, 2, and 3 are in normal working conditions, and components 4 and 5 are in fault conditions.

[0223] according to Figure 3 The operating status of the reverse osmosis desalination plant can be divided as shown in Table 2.

[0224] Table 2 Operation status of reverse osmosis desalination plant

[0225]

[0226] Define the operating state variable of the reverse osmosis desalination plant at time t as s RO,t , s RO,t =1,2,...,17; Indicates that the reverse osmosis desalination plant is in state s RO,t Power consumption P RO and water production from desalination plants The functional relationship between them can be obtained according to formula (1)-formula (4): For desalination plants in s RO,t The percentage of power consumption increase in this state.

[0227] The state transition probability matrix between the states of the desalination plant is established as shown in formula (5), and each element in the matrix represents the transition probability between the states. Assume that the desalination plant is in the operating state s at time t RO,t =k,k∈{1,2,...,17}. Based on MCMC method

[13] Generate a random number p∈[0,1], and according to formula (6), the operating status s of the desalination plant at time t+1 can be obtained RO,t+1 .

[0228]

[0229] On the multi-state model of water supply pipeline considering pipeline leakage.

[0230] The reliable operation of the system infrastructure is the key to ensuring the uninterrupted supply of clean water. Among these infrastructures, pipeline leakage is a major factor affecting the normal operation of the water network. Figure 4 shown.

[0231] Generally, the node balance of the water system under normal operation is shown in formula (7):

[0232] AQ P =Q N (7)

[0233] Where: Q P =[q Pj ](m 3 / s) is an m×1 vector, each element of which represents the water flow rate transported in the pipeline; Q N =[q Nj ](m 3 / s) is an n×1 vector, each element of which represents the water demand of a node; A=[a ij ] is an n×m incidence matrix, whose element a ij It can take three values: 0, 1 and -1. ij = 0 means that node j is not the endpoint of pipe i, that is, no water in pipe i flows into or out of node j, a ij = 1 means that the water in pipe i flows out of node j and a ij = -1 means that the water in pipe i flows into node j. Here, m and n are the number of pipes and nodes in the water system, respectively.

[0234] When a water supply pipeline leaks due to a fault, assuming that the water temperature and density in the pipeline remain unchanged, the leakage process is steady-state leakage, that is, after the leakage occurs, it takes a short time to reach steady-state leakage. Equation (7) will be modified to Equation (8):

[0235] AQ P =Q N +Q L (8)

[0236] Where: Q L =[q Lj ](m 3 / s) is an n×1 vector, and each element represents the leakage flow of a node. Based on the leakage flow theory of water pipe network, the following point leakage model is proposed, as shown in formula (9):

[0237]

[0238] Where: H Lj (m) is the water head at the leakage point, μ is the flow coefficient, σ is the leakage coefficient considering the obstruction of soil and filler to water flow, q Lj is the leakage flow rate at the leakage point, A Lj (m 2 ) is the leakage area at the leakage point, and is calculated as shown in formula (10):

[0239]

[0240] R(m) is the critical displacement of pipeline leakage, that is, when the leakage displacement reaches R, the fault point begins to leak. Due to the randomness of pipeline characteristics and construction, R is a random variable. D(m) is the diameter of the pipeline, A(m 2 ) is the cross-sectional area of ​​the pipeline, and S (m) is the displacement of the pipeline after a failure. It is related to the degree of pipeline deformation or rupture, pipeline size, and material elastic modulus. Because pipeline size and material elastic modulus vary little, the randomness of S primarily comes from the randomness of pipeline deformation or rupture, making it a random variable.

[0241] The leakage model above gives the leakage flow rate at the leakage point. For pipelines with multiple leakage points, an accurate method is to calculate the leakage flow rate at each leakage point, which is a function of the head at each leakage point. Pipeline leakage generally occurs at the joints of the connecting pipes. Therefore, it can be assumed that the number of leakage points is equal to the number of joints in the water pipe network, as shown in formula (11), where H Lj The water head of the water pipe network joint.

[0242]

[0243] However, since the length of a single pipe segment is usually between 4m and 6m, the number of joints in the water pipe network is huge. In order to simplify the calculation, some researchers use the virtual node method to assume that all pipeline leakage is leaking from the midpoint of the pipeline, as shown in formula (12), where H Mj is the water head at the midpoint. Although the number of nodes added is greatly reduced compared to the exact method, adding m nodes still complicates the water system and the topology of the water system must be rebuilt.

[0244]

[0245] In order to avoid reconstructing the topology of the water system and simplify the calculation, some researchers assumed that the leakage of the pipeline comes from its two ends, and assumed that the water head H Lj Equal to the average water head at the two endpoints, the calculation efficiency is significantly improved compared to the virtual intercept method, and the leakage loss results are close. Usually, the manufacturing, construction and surrounding soil of the pipeline are almost the same. Therefore, it can be assumed that R at all fault points of the same pipeline is exactly the same. Considering that the pipelines in the urban water system are not very long, generally shorter than 1000m, it can be assumed that S is the sum of the pipeline displacements at all fault points. Therefore, the leakage flow of the pipeline is shown in formula (13):

[0246]

[0247] Where: H1 and H2 are the water heads at the two end points of the leaking pipe; α is the leakage coefficient that takes into account the obstruction of soil and filler to water flow.

[0248] Existing research generally uses a two-state reliability assessment model for water pipeline networks: normal operating state and fault state. However, the magnitude of leakage displacement in water supply pipelines is random, and they may be in a variety of operating states, including normal, small hole leakage, hole leakage, and rupture. The assumption is that the normal operating state of water supply pipelines can transition between other operating states, while the fault state can only transition to the normal operating state. This means that when a leak is detected, personnel will be promptly dispatched to restore normal operation and prevent further deterioration of the pipeline.

[0249] In this embodiment, it is assumed that only one state change occurs within the sampling time interval Δt (1h), and based on the failure mechanism analysis of the water supply pipeline, a multi-state Markov model of the water supply pipeline is established, such as Figure 5 As shown. 0,1 ,λ 0,2 and λ 0,3 They represent the transfer rates between the normal state of the water supply pipeline and the states of small hole leakage, hole leakage and rupture, respectively, and λ 1,3 and λ 2,3 They represent the transition rates from the pinhole leakage state and the hole leakage state to the damage state, λ 0,1 μ2,0 and μ 3,0 Represents the water supply pipeline repair rate.

[0250] according to Figure 5 The operating status of the water supply pipeline can be divided as shown in Table 3. The operating status variable of the water supply pipeline at time t is defined as s L,t , s L,t =1,2,3,4; Indicates that the water supply pipeline is in state s L,t Lower leakage q Lj Pipeline fault displacement The functional relationship between them can be obtained according to formulas (7)-(13).

[0251] Table 3 Operation status of water supply pipeline

[0252]

[0253] according to Figure 5 As shown, the state transition probability matrix between the states of the water supply pipeline is established as shown in formula (14). Assume that the water supply pipeline is in state s at time t L,t =k,k∈{1,2,3,4}. Based on MCMC

[13] Generate a random number p∈[0,1], and according to formula (15), the operating state s of the water supply pipeline at time t+1 can be obtained L,t+1 .

[0254]

[0255] Two-state Markov model of reservoir and valve

[0256] The water reservoir (or water tank) is mainly used to store and provide water, and the valve is mainly used to control the direction of water flow. In this embodiment, a classic two-state model is adopted, such as Figure 6 As shown, λ tank 、μ tank is the transfer rate between two states of the reservoir (or tank).

[0257] S2. Obtain the status of each component at each hour of each day within the preset simulation period through Markov Chain Monte Carlo (MCMC) sampling;

[0258] S3. Initialize the simulation life coefficient, set Y = 1;

[0259] S4. Using the component status at each hour of each day in year Y, combined with the IEWS component reliability model, a preset optimal load reduction model is solved to obtain load reduction data for each hour of each day in year Y. The optimal load reduction model aims to minimize the sum of the wind curtailment penalty cost and the IEWS electricity and water load reduction penalty costs. The load reduction data includes the load reduction status and the optimal load reduction amount.

[0260] On the Optimal Load Shedding Model

[0261] With the goal of minimizing the sum of the penalty costs for wind curtailment and the penalty costs for electricity and water load reduction in IEWS, and taking into account the power flow constraints of the transmission system and the operating constraints of water network equipment, an IEWS optimal load reduction model considering water-energy coupling was established to simulate the system operation status and the shortage of electricity, water energy and other loads under fault conditions.

[0262] The objective function is shown in formula (16):

[0263]

[0264] Where, To reduce the load of power transmission system, is the wind power curtailment, Reduce water system water energy load; c en Penalty cost for load shedding per unit of the transmission system, c wc is the penalty cost per unit of wind curtailment, c Wm is the penalty cost of unit load reduction in the water system; n is the total number of nodes in the transmission system, N w is the set of wind turbine grid-connected nodes, N Wm is the total number of nodes in the water network; T is the scheduling period. The subscripts i, w, Wm, and t represent node i, node w, node Wm, and time t, respectively.

[0265] Power system constraints

[0266] The linearized DC power flow is used to simulate the power flow constraints of the transmission system, as follows:

[0267]

[0268] In formula (17), P i,t is the transmission system node power, represents the predicted value of wind power, is the predicted value of conventional power load, is the power consumed by the desalination plant, and They represent the collection of thermal power units, wind farms, and water systems connected to the transmission system node n, is the set of transmission system nodes, variable θ n,tand θ m,t represents the node phase angle, B n,m represents the susceptance of line nm. In formula (18), φ i,t is the state of generator set i at time t, R i is the climbing rate, Ω T is the set of thermal power units. In formula (19), Respectively represent the minimum and maximum output power of the generator. In formula (20), Ω W is the wind farm set. In formula (21), S n,m is the upper limit of line transmission capacity, Δ E is the set of power transmission lines. In formula (22), θ ref,t =0 is the equilibrium node phase angle.

[0269] Formula (17) is the node power balance constraint, formula (18) is the thermal power unit ramp constraint, formula (19) is the thermal power unit output power constraint, formula (20) is the wind power curtailment constraint, formula (21) is the power line flow constraint, and formula (22) is the phase angle constraint of the balance node.

[0270] Water system constraints

[0271] In addition to the desalination plant constraints (1)-(15), the water system constraints also include pipe equations, pump equations, node flow balance equations, and conventional constraints such as water network head and flow upper and lower limit constraints. The specific modeling is as follows:

[0272]

[0273]

[0274] In formula (23), and Represents water network node W m The total water head, water flow pressure and position head, ρ and g are the density of water and gravitational acceleration, Λ W represents the water network node set. In formula (24), denote the hydraulic heads at the end nodes of pipe mn, Indicates the water flow through the pipe. is the pipe head loss coefficient, Δ W represents the set of water network pipes, in formula (25), Represent the maximum and minimum values ​​of pipeline flow respectively. In formula (26) and (27), Respectively represent water pump P m The head gain and flow rate through the pump, For the water pump assembly, Indicates the head coefficient of the pump, Respectively represent the maximum and minimum water flow through the pump, φ Pm,t is the state 0-1 variable of the water pump (1 in normal state). In formulas (28)-(30), and W Wm,t Respectively represent the water reservoir W at time t m Inflow, outflow and storage capacity, μ W represent the cross-sectional area of ​​the reservoir and the water loss rate, respectively. They represent the maximum water storage capacity and the minimum required water storage capacity of the reservoir, Δt represents the scheduling time step, φ Tm,t is the state 0-1 variable of the reservoir (normal state is 1), represents the collection of water reservoirs. In formulas (31) and (32), φ Vmn,t is the valve state 0-1 variable (normal state is 1), M is a very large constant, and The minimum and maximum allowable flow rates when a valve is installed in the pipeline. is the set of valves. In formula (33), and They are water network nodes W k Water load, inflow and outflow at time t, q LWmn,t is the leakage of the pipeline when there is a fault in pipeline mn. In formula (34), Indicates water pump P m The power consumed at time t, η is the working efficiency of the pump.

[0275] Formula (23) represents the total head constraint of the water network node, and formula (24) represents the head loss along the pipeline (using the Darcy-Weisbach equation

[16] ), Equation (25) represents the pipeline flow constraint, Equations (26) and (27) are the modeling of the water pump, Equations (28)-(30) are the reservoir constraints, Equations (31) and (32) are the valve constraints, Equation (33) is the node balance constraint, Equation (34) is the water pump power constraint, and Equation (35) represents the water network power constraint.

[0276] Solution

[0277] In this method, the optimal load reduction model is a typical nonlinear mixed integer programming problem.

[17] The nonlinear constraints (24), (26) and (34) are linearized to transform the optimal load reduction model into a mixed integer linear programming problem, which is solved using the commercial Gurobi software.

[0278] S5. Based on the load reduction data obtained for each hour of each day in year Y, calculate the expected variance coefficient ε of the energy shortage according to the following formula:

[0279]

[0280] Where, is the system energy shortage variance, EENS is the expected value of the total power loss load of the system, and EENS i It represents the expected value of total power loss load in the system under the i-th state.

[0281] If ε is less than the preset threshold, go to S6; if not, determine whether Y has reached the preset value. If so, go to S6; if not, update Y to make Y=Y+1 and return to S3;

[0282] S6. Calculate reliability evaluation indicators based on the currently obtained load reduction data for each hour of each day in year Y; the reliability evaluation indicators include the expected value of load supply shortage and the probability of load supply shortage.

[0283] While power system reliability indicators are relatively mature, there is still a lack of reliability assessment indicators that reflect the continuous water supply capacity and leakage. To this end, this method expands on the power system reliability assessment indicators and characterizes the reliability level of IEWS from the perspectives of the expected value and probability of load undersupply.

[0284] (1) Loss of Electricity Load Probability (LOELP)

[0285]

[0286] Where, N is the state variable of the system load reduction at time t in year y. If it is 1, it means there is load reduction, and if it is 0, it means there is no load reduction. y The simulation period.

[0287] (2) Expected Energy Not Supplied (EENS)

[0288]

[0289] Where, is the load reduction at the transmission system node i at time t in year y.

[0290] (3) Loss of Water Load Probability (LOWLP)

[0291]

[0292] Where, It is the state variable of the system water load reduction at time t in year y. If it is 1, it means there is water load reduction, and if it is 0, it means there is no water load reduction.

[0293] (4) Expected Water Not Supplied (EWNS)

[0294]

[0295] Where, is the water load reduction at the water network node Wm at time t in year y.

[0296] (5) Probability of Water Leakage (PWL)

[0297]

[0298] Where, It is the state variable indicating whether there is pipe leakage in the water system at time t in year y. If it is 1, it means there is pipe leakage, and if it is 0, it means there is no pipe leakage.

[0299] (6) Expected Water Leakage (EWL)

[0300]

[0301] Where q LWmn,yt is the leakage loss at the water network pipe mn at time t in year y.

[0302] (7) Comprehensive Loss of Energy Not Supply (CLENS).

[0303] C ENS =c p EENS+c w EWNS+c l EWL(42)

[0304] Where c p 、c w 、c l They represent the penalty costs of electricity, water and pipeline leakage respectively. EENS, EWNS and EWL represent the expected values ​​of electricity load, water load and water leakage respectively.

[0305] S7. Use reliability evaluation indicators to conduct reliability evaluation.

[0306] Compared to existing technologies, this method can accurately quantify the impact of intermediate fault states in water systems. By constructing a multi-state model of the desalination plant (normal operation / inefficiency / fault) and the water supply network (normal / leakage / fault), this method, for the first time, incorporates intermediate states such as leakage and inefficiency into IEWS reliability assessment. This method overcomes the limitations of the traditional "normal-fault" two-state model and accurately captures the characteristics of gradual faults, such as pipeline leakage causing high-power operation of water pumps and a sharp increase in energy consumption due to desalination plant inefficiency, thus avoiding overestimation of system reliability due to simplified modeling. It also reveals the cascading transmission mechanism of bidirectional power-water faults. By synergistically optimizing the wind curtailment penalty cost and power / water load reduction costs within an optimal load reduction model, it dynamically reflects the squeeze effect of water system faults (such as increased pump power consumption due to leakage) on power system reserve capacity, as well as the counter-effect of power outages on water supply capacity. This method overcomes the existing method's neglect of the coupling path from "water system fault → increased power system operating pressure → decreased power reliability," achieving the first closed-loop quantification of bidirectional power-water fault propagation. Furthermore, this method can efficiently solve large-scale state-space problems. MCMC sampling is used to generate equipment state sequences, and the variance convergence criterion (the expected variance coefficient of the energy shortage) is combined to dynamically control the simulation lifespan, significantly reducing computational complexity. This avoids the problem of state combination explosion caused by multi-state models and enables long-term operational risk assessment of large-scale IEWS while ensuring accuracy. It can also generate practical reliability indicators for engineering applications. By iteratively converging load reduction data, the expected value of undersupply (EENS) and probability (LOLP) are calculated, forming a quantitative basis that directly guides system planning. The indicators can accurately reflect the cumulative impact of intermediate states such as water system leaks on overall reliability, providing data support for expansion site selection and pipeline maintenance priority setting.

[0307] This method transcends the limitations of the "normal-fault" two-state model to construct a multi-state reliability model for water system equipment. It accurately quantifies the impact of intermediate fault states, such as leakage, on the bidirectional coupling of electricity and water. It also develops an efficient solution algorithm for dynamic assessment of large-scale IEWS operational risks, thereby obtaining reliability indicators that meet engineering requirements and guide accurate decision-making. This method achieves systematic innovation in modeling depth, coupling mechanism analysis, and computational efficiency, providing key technical support for the coordinated security of energy and water resources in regions with high hydropower dependence.

[0308] Example 2

[0309] In order to help those skilled in the art better understand the effect of this method, the following example is given.

[0310] The simulation analysis is conducted based on two IEWS, namely a 6-node power transmission system and a 21-node water system, and an IEEE-30-node power transmission system and a 36-node water system. First, for the test system A (6-node power transmission system and 21-node water system), different water network pipeline and desalination plant reliability models are used to conduct reliability evaluation to illustrate the advantages of the proposed multi-state reliability evaluation method based on water network equipment. Its grid structure is as follows Figure 7 As shown. Then, simulation analysis is carried out on the B measurement system (IEEE-30 node transmission system and 40 pipe water system) to verify the adaptability of the proposed model and reliability assessment method to different IEWS. In order to improve the calculation efficiency, the modified typical daily curve is used to represent the annual level. The typical daily curves of wind farm output and conventional power load are shown as follows: Figure 8 shown.

[0311] The wind farm and thermal power plant have installed capacities of 800 MW and 400 MW, respectively, and the thermal power plant ramp rate is 20 MW / min. The parameters of the desalination plant operation model and related pump parameters are shown in Table 4, and the reliability parameters of each device are shown in Table 5.

[0312] Table 4 Water system equipment operating parameters

[0313]

[0314] Table 5 Reliability parameters of equipment

[0315]

[0316] The electricity price for water system is Figure 9 The unit cost of load reduction for electric load is RMB 500 / (MWh), and the unit cost of wind curtailment is set at RMB 100 / (MWh). Considering that the average energy consumption of the water system including the desalination plant is about 16kWh / m 3 According to the load reduction cost of electric load, the unit load reduction cost of water load is set to 8 yuan / kg.

[0317] Simulation analysis of case A

[0318] IEWS optimization results considering water network equipment failure

[0319] Three scenarios are set up to illustrate the impact of water network equipment failure on the coupled operation of IEWS.

[0320] Case 1: Assume that the water network, reverse osmosis desalination plant, water tanks and valves are all normal.

[0321] Case 2: Assuming that the reverse osmosis desalination plant, water tanks, and valves are operating normally, a leakage occurs in the water supply pipeline I21 between 1:00 and 10:00 and is repaired at 11:00. The leakage is caused by a hole with a diameter of 10 mm.

[0322] Case 3: Assume that the water pipe network, water tanks, and valves are operating normally, but component 3 of the reverse osmosis desalination plant fails and is operating inefficiently.

[0323] Figure 10 The figure shows the energy consumption of the water pumps and desalination plant under three scenarios. As can be seen from the figure, the power consumption of the water pumps and desalination plant in Case 2 is higher than that in Case 1 from 1:00 AM to 10:00 AM. This shows that when there is a leak in the pipeline, the water pump's power consumption increases significantly to meet user water demand as much as possible. At the same time, the desalination plant's increased freshwater production also increases its power consumption. In other words, compared to normal conditions, a leak in the water supply pipeline causes the water system to consume more electricity overall. In Case 3, the water pump's power consumption is the same as in Case 1, but because the desalination plant is operating inefficiently, producing the same quality of freshwater consumes more electricity. Therefore, the desalination plant's power consumption in Case 3 is significantly higher than in Cases 1 and 2.

[0324] Figure 11 and Figure 12 The figures represent the load reduction and pipeline leakage of the IEWS, respectively, when the reverse osmosis desalination plant meets user water demand under multiple fault conditions, assuming a failure of generator set G1, based on Case 2. Since load reduction did not occur between 1:00 AM and 5:00 PM or 12:00 PM, the figure shows the load reduction from 5:00 PM to 11:00 PM.

[0325] During normal operation of a reverse osmosis desalination plant, the failure of generator unit G1 resulted in a total load reduction of 194.16 MW in the transmission system. When the desalination plant encountered different component failures, the impact on the transmission system load was as follows: Component 2 failure affected the pretreatment process, including seawater flocculation, sedimentation, and filtration, resulting in a total load reduction of 211.39 MW. Component 3 failure, specifically the booster pump failure, reduced the reverse osmosis recovery rate, increasing the total load reduction to 280.17 MW. Component 4 failure reduced the efficiency of the reverse osmosis unit due to aging or scaling, resulting in a load reduction of 205.47 MW. Component 5 failure caused the reverse osmosis membrane to fail, resulting in a load reduction of 214.16 MW. These data indicate that different component failures in a reverse osmosis desalination plant have varying degrees of impact on transmission system reliability, with component 3 failure having the most severe impact. Furthermore, when the desalination plant operates inefficiently, there are periods of load reduction, and these load reductions are higher than those during normal operation.

[0326] Figure 12 The figure shows the pipeline leakage at each moment under different states of the reverse osmosis desalination plant. Since the pipeline leakage was repaired from 11:00 to 24:00, the figure shows the pipeline leakage from 1:00 to 10:00. As shown in Table 5, when the reverse osmosis desalination plant is operating normally, the total pipeline leakage is 4575.91m 3 , and when it is in an inefficient operating state, the total leakage of the pipeline will increase.

[0327] System reliability analysis

[0328] For Example A, the following four methods are used for simulation analysis to illustrate the advantages of the multi-state model of water network equipment proposed in this method.

[0329] Method 1: Use the two-state model of water network pipelines and the two-state model of seawater desalination plant.

[0330] Method 2: Using the two-state model of the water network pipeline and the multi-state model of the seawater desalination plant proposed in this method.

[0331] Method 3: Use the multi-state model of water network pipelines and the two-state model of seawater desalination plant proposed in this method.

[0332] Method 4: Use the multi-state model of water network pipelines and the multi-state model of seawater desalination plant proposed in this method.

[0333] The reliability evaluation indicators of Example A calculated by the four methods are shown in Table 6.

[0334] Table 6 Reliability evaluation indicators of Example A

[0335]

[0336] In the table, LOELP and EENS are the probability of electric energy load loss and the expected value of power shortage, respectively; LOWLP and EWNS are the probability of water load reduction and the expected value of water shortage, respectively; PWL and EWL are the probability of water leakage and the expected value of water leakage, respectively.

[0337] Table 6 shows that Method 2's LOELP, EENS, PWL, and EWL all increase compared to Method 1, while LOWLP and EWNS decrease. This is because Method 1 only considers the states of either complete normal operation or complete shutdown of all water network equipment, while Method 2 fully accounts for the multi-state operating characteristics of reverse osmosis desalination plants. Compared to normal operation, the desalination plant in Method 2 consumes more electricity when operating in an inefficient state to meet user water demand. This increases the operating pressure on the transmission system, resulting in reduced transmission system reliability. For the water system, in Method 1, the desalination plant cannot supply water to the water system normally after a direct failure, resulting in a decrease in the water flow rate of the water supply pipeline, and the leakage of the faulty pipeline will be reduced. However, in Method 2, when the desalination plant is inefficiently operating, it can still supply water to the water system, resulting in an increase in the water leakage of the faulty pipeline. Therefore, compared with Method 1, the probability of pipeline water leakage and the expected value of pipeline water leakage in Method 2 will increase, that is, PWL and EWL will increase. But at the same time, the overall reliability of the water system will be improved to a certain extent. Therefore, compared with Method 1, the LOWLP and EWNS of Method 2 will decrease.

[0338] Method 3's LOELP, EENS, LOWLP, EWNS, PWL, and EWL all increase compared to Method 1. This is because Method 3 considers a multi-state pipeline operation model, as opposed to Method 1. Compared to a normal state, when a pipeline is leaking, the pump's power consumption increases significantly to meet user water demand. This increases the overall power consumption of the water system, increasing the operating pressure on the transmission system and reducing its reliability. Furthermore, compared to a fault state, pipeline leakage is difficult to detect and the maintenance cost is relatively high. This can lead to delays in timely pipeline repairs, resulting in more severe leakage and reduced water system reliability.

[0339] Compared to Method 1, Method 4 shows a significant decrease in the reliability of the power system, while the reliability of the water system improves. Both the probability and expected value of pipeline leakage increase. This indicates that the two-state model of the water supply pipeline and reverse osmosis desalination plant overestimates the reliability of the power system in the IEWS. Furthermore, ignoring pipeline leakage will fail to accurately simulate the operation of the water system.

[0340] Compared to Method 2, Method 4 shows increases in LOELP, EENS, PWL, and EWL. This is because Method 4 considers the multi-state reliability model of the pipeline. To meet user needs, when a pipeline leaks, the pumps must operate at high power, which increases the operating pressure of the power system and reduces its reliability. Therefore, considering only the multi-state reliability model of the reverse osmosis desalination plant and ignoring the presence of pipeline leaks will still overestimate the reliability of the power system.

[0341] Compared to Method 3, Method 4 shows increases in LEOLP, EENS, PWL, and EWL. This is because Method 4 considers the multi-state reliability model of the reverse osmosis desalination plant. The results show that when the reverse osmosis desalination plant operates inefficiently, the electricity consumed to produce the same quality of water increases, placing operational pressure on the power system and increasing pipeline leakage in the water system. This shows that only considering the two-state model of the water supply pipeline while ignoring the inefficient operation of the reverse osmosis desalination plant will overestimate the reliability of the power supply system. Therefore, it is necessary to consider the multi-state reliability models of both the reverse osmosis desalination plant and the water supply pipeline simultaneously.

[0342] In summary, the multi-state reliability model of the water pipeline network and reverse osmosis desalination plant proposed in this method can fully consider the leakage in the water supply pipeline and the power load reduction caused by the inefficient operation of the desalination plant, avoiding overestimation of the reliability level of the transmission system when the IEWS is jointly operated.

[0343] Analysis of the impact of water load reduction penalty costs

[0344] According to the system reliability analysis, when the unit water load reduction penalty cost C W 8 yuan / m 3 When C is used, the system will give priority to reducing the electric load to ensure the reliable supply of water load, thereby reducing the total energy loss. W Comprehensive energy loss due to system shortage C ENS The impact of 8 yuan / m 3 As the base value, Method 4 is used to evaluate different C W C ENS , the calculation results are as follows Figure 13 shown.

[0345] from Figure 13 It can be seen that when c w When the value is lower than the base value, if a power line or other equipment failure occurs, the system will choose to reduce the water load as much as possible to reduce the reduction of the electric load, thereby reducing C ENS With the c w Gradually reduced, the reliability level of electric load slightly improved, C ENS Continuously decreasing. When c w When the value is higher than the base value, and the desalination plant is in an inefficient operating state, the system will choose to reduce the power load as much as possible to ensure the reliability of water supply, thereby reducing the total load reduction penalty cost. w gradually increases, the reliability level of electric load gradually decreases, C ENS It is also increasing.

[0346] Simulation analysis of case B

[0347] To further verify the adaptability of the model and reliability assessment method proposed in this paper, the reliability assessment of Case B was performed using the four methods set in the system reliability analysis. The simulation results are shown in Table 7.

[0348] Table 7 Reliability evaluation indicators of Example B

[0349]

[0350] As shown in Table 7, compared with method 1, method 4 has better LOELP, EENS, and C ENS All of them increase, while LOWLP and EWNS decrease. In summary, the simulation conclusions are consistent with the system reliability analysis.

[0351] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the technical solutions. Those skilled in the art should understand that modifications or equivalent replacements of the technical solutions of the present invention that do not depart from the purpose and scope of the technical solutions of the present invention should be included in the scope of the claims of the present invention.

Claims

1. The IEWS system reliability evaluation method considering the multi-state model of water system equipment is characterized by: The following steps are involved: S1. Construct an IEWS simulation model for calculating various operating data according to the status of each component; the IEWS simulation model includes a water system simulation model and an electrical system simulation model; S2. Obtain the status of each component at each hour of each day within the preset simulation period through Markov Chain Monte Carlo (MCMC) sampling; S3. Initialize the simulation life coefficient, set Y = 1; S4. Using the component status at each hour of each day in year Y, combined with the IEWS component reliability model, solve a preset optimal load reduction model to obtain load reduction data for each hour of each day in year Y; the optimal load reduction model aims to minimize the sum of the wind curtailment penalty cost and the IEWS electricity and water load reduction penalty costs; the load reduction data includes the load reduction status and the optimal load reduction amount; S5. Based on the obtained load reduction data for each hour of each day in year Y, calculate the expected variance coefficient ε of the energy shortage. If ε is less than the preset threshold, proceed to S6. If not, determine whether Y has reached the preset value. If so, proceed to S6. If not, update Y to set Y = Y + 1 and return to S3. S6. Calculate a reliability evaluation index based on the currently obtained load reduction data for each hour of each day in year Y; the reliability evaluation index includes an expected value of load undersupply and a probability of load undersupply; S7. Use reliability evaluation indicators to conduct reliability evaluation.

2. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 1 is characterized in that: The multi-state model of the seawater desalination plant of the water system simulation model is used to determine the current state according to the component state and calculate the corresponding operating data. The state of the seawater desalination plant includes normal operating state, inefficient operating state and fault state; In the multi-state model of the seawater desalination plant, the pump operation constraints are: Where: and They represent the water pump power, water flow rate and head at time t respectively; ρ is the density of seawater; g is the acceleration of gravity; η in is the water intake pump efficiency; The working status of the water pump is a 0-1 variable, 1 means running; q in,min is the lower limit of water intake per unit time of the water intake pump, q in,max The upper limit of water intake per unit time of the water intake pump; assuming that the pump head remains constant; The reverse osmosis device consists of a high-pressure pump and a reverse osmosis unit. The operating constraints of the reverse osmosis unit are: Where: are the water inlet and outlet of the reverse osmosis unit respectively; p r,t Reverse osmosis unit working pressure; K r 、A r and Δπ are the permeability coefficient, permeability area and transmembrane osmotic pressure difference of the membrane respectively; R is the reverse osmosis recovery rate; is the power consumed by the reverse osmosis unit; a r 、b r is the high-pressure pump power coefficient; is the feed water concentration; is the minimum net transmembrane pressure of the osmotic membrane unit, is the maximum value of the net transmembrane pressure of the osmotic membrane unit; φ r,t is the operating state of the permeation unit, which is a 0-1 variable and the operating state is 1; The reverse osmosis device has r reverse osmosis units, and the operating constraints of the reverse osmosis device are: Where: Respectively represent the total water inflow and total water outflow of the reverse osmosis device; It represents the total power consumed by the high-pressure pump and the booster pump; β represents the ratio of the amount of pretreated seawater to the amount of feed water; The water storage facilities include clean water tanks and product water tanks, and the operating constraints are: Where: are the water storage capacity of the clean water tank and the product water tank at time t; A CWP 、A PRP are the bottom areas of the clean water pool and the product water pool respectively; h CWP,max 、h PRP,max They are the maximum capacity of the clean water tank and the product water tank, h CWP,min 、h PRP,min They are the minimum water storage capacity of the clean water tank and the product water tank respectively.

3. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 2 is characterized in that: When judging the status of the seawater desalination plant, if a component in component 1 fails, the seawater desalination plant is in a faulty state; the components in component 1 include the water intake pump, high-pressure pump, clear water tank, product water tank, and post-processing link components; If only components in Components 2 to 5 fail, the desalination plant will be in an inefficient operating state. Components in Component 2 include pretreatment components; components in Component 3 include additional pumps and energy recovery devices; component failures in Component 4 include aging and scaling of the reverse osmosis membrane; and component failures in Component 5 include failure of the reverse osmosis membrane. Otherwise, the desalination plant is in normal operation; The operating status and operating model of the reverse osmosis desalination plant are shown in the following table: In the table, U indicates no fault, and D indicates fault; RO,t represents the operating state variable of the reverse osmosis desalination plant at time t, s RO,t =1,2,...,17; Indicates that the reverse osmosis desalination plant is in state s RO,t Power consumption P RO and water production from desalination plants The functional relationship between For desalination plants in s RO,t The proportion of power consumption increase in the state; The state transition probability matrix between the states of the seawater desalination plant is as follows: Each element in the matrix represents the transition probability between states; Assume that the desalination plant is in operation state s at time t RO,t =k, k∈{1,2,...,17}; then based on the MCMC method [generate a random number p∈[0,1], the operating state s of the desalination plant at time t+1 is obtained according to the following formula RO,t+1 :

4. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 3 is characterized by: The water system simulation model includes a multi-state model of the water supply network, which is used to determine the current state based on the component status and calculate the corresponding operating data. The status of the water supply network includes normal working state, leakage state and fault state; When the multi-state model of the water supply network determines the current state, the leakage state of the water supply network includes small hole leakage and hole leakage, and the fault state includes rupture. The operating state of the water supply pipeline is shown in the following table: s L,t represents the operating state variable of the water supply pipeline at time t, s L,t =1,2,3,4; Indicates that the water supply pipeline is in state s L,t Lower leakage Pipeline fault displacement The functional relationship between The state transition probability matrix between the states of the water supply pipeline is as follows: Among them, λ 0,1 ,λ 0,2 and λ 0,3 Respectively represent the transition rates between the normal state and the pinhole leakage, hole leakage and rupture states; λ 1,3 and λ 2,3 They represent the conversion rates of the pinhole leakage state and the hole leakage state to the damage state; μ 2,0 and μ 3,0 Represents the repair rate of holes, leakage and damage; Assume that the water supply pipeline is in state s at time t L,t =k, k∈{1,2,3,4}; then based on MCMC, a random number p∈[0,1] is generated, and the operating state s of the water supply pipeline at time t+1 can be obtained according to the following formula L,t+1 :

5. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 4 is characterized in that: The water supply pipeline is in state s L,t Lower leakage Pipeline fault displacement Functional relationship between Obtained through the following calculation formula: Node balance under normal operating conditions: AQ P =Q N ; Where: is an m×1 vector, each element of which represents the water flow rate transported in the pipe; It is an n×1 vector, each element represents the water demand of a node; A=[a ij ] is an n×m incidence matrix, whose element a ij It can take three values: 0, 1 and -1; a ij =0 means that node j is not the endpoint of pipe i, and no water in pipe i flows into or out of node j; a ij =1 means the water in pipe i flows out of node j; a ij = -1 means that the water in pipe i flows into node j; m and n are the number of pipes and nodes in the water system respectively; Node balance in steady-state leakage: AQ P =Q N +Q L ; Where: It is an n×1 vector, each element represents the leakage flow of the node; The steady-state leakage refers to leakage in the pipeline while the temperature and density of the water in the pipeline remain unchanged; Point leakage calculation model: Where: is the leakage flow rate of the leakage point, μ is the flow coefficient, and σ is the leakage coefficient considering the obstruction of soil and filler to water flow. is the leakage area at the leakage point, Point water head for leakage; Where: R is the critical displacement of pipeline leakage, D is the pipeline diameter, A is the pipeline cross-sectional area, and S is the displacement of the pipeline after the pipeline failure; Pipeline leakage flow calculation formula: Where H1 and H2 are the water heads at the two end points of the leaking pipe; α is the leakage coefficient that takes into account the obstruction of soil and filler to water flow.

6. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 5 is characterized in that: The objective function of the optimal load reduction model is: Where, To reduce the load of power transmission system, is the wind power curtailment, Reduce water load for water system; c en Penalty cost for load shedding per unit of the transmission system, c wc is the penalty cost for unit wind curtailment, Penalty costs for load reduction for water system units; n is the total number of nodes in the transmission system, N w is the set of wind turbine grid-connected nodes, is the total number of nodes in the water network; T is the scheduling period; the subscripts i, w, Wm and t represent node i, node w, node Wm and time, respectively. t .

7. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 6 is characterized in that: The constraints of the optimal load shedding model include power system constraints, which include: Node power balance constraints: Where, P i,t is the transmission system node power, represents the predicted value of wind power, is the predicted value of conventional power load, is the power consumed by the desalination plant, and They represent the collection of thermal power units, wind farms, and water systems connected to the transmission system node n, is the set of transmission system nodes, variable θ n,t and θ m,t represents the node phase angle, B n,m It represents the susceptance of the line nm; Thermal power unit ramp constraints: Where, φ i,t is the state of generator set i at time t, R i is the climbing rate, Ω T is the collection of thermal power units; P i gmin 、P i gmax Respectively represent the minimum and maximum output power of the generator; Output power constraints of thermal power generating units: P i gmin f i,t ≤P i,t ≤P i gmax f i,t , Wind power curtailment constraints: Where, Ω W Assemble for wind farms; Power line flow constraints: -S n,m ≤B n,m (i n,t -θ m,t )≤S n,m , Where S n,m is the upper limit of line transmission capacity, Δ E A collection of power transmission lines; Phase angle constraint of equilibrium node: i ref,t =0; Where θ ref,t =0 is the equilibrium node phase angle.

8. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 7 is characterized in that: The constraints of the optimal load shedding model include hydraulic system constraints, which include: Total water head constraints at water network nodes: Where, and Represents water network node W m The total head, flow pressure and position head, ρ and g are the density of water and gravitational acceleration, Λ W Represents a collection of water network nodes; Head loss along the pipeline: Where, denote the hydraulic heads at the end nodes of pipe mn, Indicates the water flow through the pipe. is the pipe head loss coefficient, Δ W Represents a collection of water network pipes; Pipeline flow constraints: Where, Respectively represent the maximum and minimum values ​​of pipeline flow; Pump constraints: Where, Respectively represent water pump P m The head gain and flow rate through the pump, For water pump assembly, Indicates the head coefficient of the pump, Respectively represent the maximum and minimum water flow through the pump, φ Pm,t is the state 0-1 variable of the water pump, and takes 1 in normal state; Reservoir constraints: Where, and Respectively represent the water reservoir W at time t m Inflow, outflow and storage capacity, μ W represent the cross-sectional area of ​​the reservoir and the water loss rate, respectively. They represent the maximum water storage capacity and the minimum required water storage capacity of the reservoir, respectively; Δt represents the scheduling time step; φ Tm,t is the state 0-1 variable of the reservoir, and takes 1 in normal state; Represents a collection of reservoirs; Valve Constraints: Where, φ Vmn,t is the valve state 0-1 variable, the normal state is 1; M is a constant with a preset value, and The minimum and maximum allowable flow rates when a valve is installed in the pipeline. A collection of valves; Node balance constraints: Where, and They are water network nodes W k Water load, inflow and outflow at time t, is the leakage amount of the pipeline when there is a fault in pipeline mn; Pump power constraints: Water network power constraints: Where, Indicates water pump P m The power consumed at time t, η is the working efficiency of the pump.

9. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 8, characterized in that: The expected value of load supply shortage includes the expected value of power loss load EENS, the expected value of water shortage EWNS, the expected value of leakage EWL and the comprehensive loss due to supply shortage; the probability of load supply shortage includes the probability of power loss load LOELP, the probability of water load reduction LOWLP and the probability of leakage PWL.

10. The IEWS system reliability assessment method considering a multi-state model of water system equipment according to claim 9, characterized in that: The power load loss probability LOELP is: Where, N is the state variable of the system load reduction at time t in year y. If it is 1, it means there is load reduction, and if it is 0, it means there is no load reduction. y is the simulation years; The expected value of power loss load EENS is: Where, is the load reduction at the transmission system node i at time t in year y; The water load reduction probability LOWLP is: Where, is the state variable of the system water load reduction at time t in year y. If it is 1, it means there is water load reduction, and if it is 0, it means there is no water load reduction. The expected value of water shortage EWNS is: Where, is the water load reduction at the water network node Wm at time t in year y; The leakage probability PWL is: Where, is the state variable indicating whether there is pipe leakage in the water system at time t in year y. If it is 1, it means there is pipe leakage, and if it is 0, it means there is no pipe leakage; The expected value of leakage EWL is: Where q LWmn,yt is the leakage loss at the water network pipe mn at time t in year y; The comprehensive loss due to supply shortage is: C ENS =c p ONCE+c w EWNS+c l EWL; Where c p 、c w 、c l They represent the penalty costs of electricity, water and pipeline leakage respectively. EENS, EWNS and EWL represent the expected values ​​of electricity load, water load and water leakage respectively.

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