Storage Optimization (r, Q) Strategy under Condition-Based Maintenance of Key Equipment of Coal-Fired Power Units in Carbon Neutrality Era

Abstract

For the safe, stable, and economic operation of thermal power units in new power systems, the condition-based maintenance mode and storage strategy of key equipment and materials for power generation enterprises were selected. According to the storage linkage demand of condition-based maintenance, a Weibull probability density function was used to calculate spare parts demand, and an intelligent storage optimization model with an availability constraint was established. The application cases of spare parts cost and availability of high-value key equipment and low-value key equipment of coal-fired thermal power units were analyzed, respectively, and the influence of different life spans and the number of covered units on the model were expounded. The results show that the cost of spare parts borne by a single unit is greatly reduced via the optimization of an intelligent inventory (r, Q) strategy on the premise that the availability of units is not less than 99.5%.

1. Introduction

In the new power system dominated by photovoltaic, wind power, and other renewable energy sources in the future, due to the intermittent and peak-load regulation characteristics of renewable energy power generation, thermal power units not only undertake more frequent peak shaving, frequency modulation, and other auxiliary services but also face more frequent and more severe supply assurance tasks, which brings great uncertainty and challenges to the operational reliability of thermal power unit equipment [1,2,3,4].

At present, it has become a trend for coal-fired thermal power units to participate in deep peak shaving on a large scale via flexibility retrofitting. Peak shaving operation between 40% and 50% of the rated load has become normal, and deep peak shaving between 20% and 30% of the rated load has also become the focus of technical retrofitting [5,6,7,8,9]. While coal-fired power generation enterprises continue to carry out deep peak shaving and increase revenue from auxiliary peak shaving services, the impact of continuous rapid load fluctuation and low-load operation on power generation equipment cannot be ignored.

Nurkhat, Z., et al. [10] used an optimization model and proposed a combination of quantitative and qualitative approaches, which was used in the data analysis of demand variations and distributions and technical and consumption parameters to provide optimal solutions. Jieping et al. [11] adopted machine learning for benefit prediction, with a good degree of fitting and high accuracy of the model, based on the relevant data of seven power plants adopting CCUS technology in three countries from 2008 to 2022. Nurkhat, Z., et al. [12] analyzed the current state of the problem of electricity forecasting for various subject areas of electricity use, which have been studied in forecasting electricity consumption, taking into account their classification according to the anticipation period.

For the safe, stable, and economic operation of thermal power unit equipment, the service life of unit components can be extended and the probability of failure reduced via optimization schemes such as condition-based maintenance [13,14,15]. However, for key equipment, the power plant also needs to reserve a certain number of spare parts. After the equipment fails, the maintenance can be carried out immediately without waiting for the long processes of bidding, ordering, and delivery, and the downtime of the thermal power units can be greatly reduced. However, due to the high price of this key equipment, unlimited stock will also lead to higher storage costs. Therefore, a reasonable spare parts inventory optimization strategy under advanced maintenance mode can improve the availability of thermal power units and reduce downtime losses and storage costs.

Condition-based maintenance (CBM) is an active optimization maintenance strategy. By monitoring the status of equipment, preventive maintenance is carried out when it shows signs of degradation. In this case, the necessary spare parts are provided from the inventory. However, the equipment may occasionally suffer sudden shocks or malfunctions before showing any signs of deterioration. Out of stock in case of failure will lead to costly downtime.

Inventory theory is one of the important branches of operations research and operation management that focuses on the design of production/inventory systems to minimize costs. In recent years, with the progress of mathematical technology in optimal control, dynamic programming, and network optimization, it has combined the most basic EOQ (economic order quantity) problem, the non-zero lead time EOQ problem, the quantity discount EOQ problem, and the delayed delivery EOQ problem. A series of cross-solutions with inventory theory are proposed.

Kou, Z., et al. [16] considered the constraint of limited maintenance times under the condition of incomplete maintenance and studied the multi-level inventory optimization problem of repairable parts with the scrap process. Zhou, Y., et al. [17] used the time series analysis method to adjust and optimize the enterprise’s demand forecast, obtain shorter order lead times and smaller safety stocks, reduce inventory time, increase inventory turnover, and reduce inventory costs. Pda, B., et al. [18] proposed a state-based critical level spare parts inventory management strategy and established a numerical simulation model. They compared the operating costs under the optimal critical level strategy and the optimal basic inventory strategy, and the results show that the proposed critical level strategy can indeed further reduce the operating costs. Wang, J., et al. [19] studied the joint optimization problem of periodic replacement and inventory control of unrepairable components of the k-out-of-n: F system under different system states. Zhang, J., et al. [20] jointly determined the optimal preventive maintenance and spare parts inventory control strategy via simulation and proved the effectiveness and superiority of the proposed optimization model via numerical experiments.

In order to achieve optimal inventory, the demand for optimization technology is increasingly evident to address the application and challenges of optimization and achieve an optimized design. The goal of optimization is to find the best solution to a problem. The metaheuristic algorithm is one of the most powerful tools for solving optimization problems [21,22,23,24,25].

The spare parts management of domestic power generation enterprises is generally based on the Pareto rule and other methods. They evaluate and classify the spare parts from different perspectives and focus on them to guide the maintenance procurement of power plants [26]. There is a lack of quantitative research on optimal inventory procurement strategies. This paper establishes a cost optimization model under the availability constraint by studying different strategies applicable to the inventory control of power plants, analyzes the cost and availability of spare parts for key equipment of the unit, and provides quantitative reference for maintenance and inventory control of key equipment of a thermal power unit. The technology can also be applied in fields such as optimal coal storage optimization in thermal power plants and position optimization in medium- and long-term power transactions.

2. Key Equipment and Material Methods

In the new power system, with the formation of the national unified power market, according to the market structure mechanism of “medium and long term/spot/auxiliary services,” thermal power enterprises can not only gain profits in the power energy market but also participate in the deep peak shaving and other auxiliary service markets to obtain additional compensation, which has become an important path for the transformation and development of thermal power enterprises [27,28,29,30,31,32].

The frequent and intense deep peak shaving mode of thermal power units has a great impact on the operation and reliability of key equipment. The key equipment is the equipment and components that form a serial relationship with the unit or will cause serious power loss in case of failure. The scope of the key equipment and materials ranges from the pump core package with a higher price to the valve card with a lower price, which are the research objects of this paper.

2.1. Core Package Damage of Feed Water Pump under Peak Shaving Operation

In the new power system, frequent startup and shutdown of feed water pumps caused by peak shaving of thermal power units and long-term low load operation will result in a higher failure probability and reduced life of the feed water pump core package. A certain power plant [31] adopts N200-12.7/535/535 wet cooling units and NK200-12.7/535/535 air cooling units produced by Harbin Turbine Factory (Harbin, China). The feed water pump is a DG750-180 horizontal centrifugal plug-in feed water pump equipped with an FAIB56 imported Weir front pump (Weir Group, Glasgow, UK). The main damage mechanism is shown in Figure 1.

(1) Failure is caused by thermal stress. ① After the feed water pump is out of operation, the heat capacity is much larger than that of the pipeline, so the temperature of the feed water pump body is higher than that of the pipeline before the pump is completely cooled, resulting in thermal stress damage during shutdown. ② During hot startup, the low-temperature water in the pipeline enters the feed pump to generate thermal shock, which causes thermal stress in the pump body. ③ During the load increase in the unit, the water pressure and temperature at the outlet of the deaerator increase accordingly, and the high-temperature water flows into the low-temperature pump body to cause thermal shock, which generates pressure stress on the surface of the impeller and the inner wall of the pump casing, leading to life loss and damage to the core package of the feedwater pump.

(2) Failure is caused by a low load. Under the new power system, the coal power unit, as the peak-shaving power supply, often operates under low load for a long time. At this time, ① the operation of the feed water pump at low flow will cause cavitation damage, vibration, and damage at the back of the impeller. ② At low flow rate, the feed pump will generate eddy current at the impeller inlet, which will endanger the safe operation of the feed pump.

(3) Failure is due to thermal deflection. ① After peak shaving and shutdown, restart when the deflection is not eliminated. ② The pump is not fully warmed up during normal startup.

2.2. Control Card Failure under Peak Shaving Operation

The control card of the instrument control system is the nerve center of the coal-fired power plant, and the failure rate is relatively high. Especially in the peak shaving operation mode, the output coil of the control card acts more frequently, accelerating the aging of the electronic device. Common failure modes include open electrodes, dendritic growth, short circuits, faulty soldering, and failure to act. Once the electronic control card for important components such as the turbine control valve fails, the whole thermal power unit will be shut down.

Therefore, in order to ensure the safe and stable operation of thermal power units, a certain number of spare parts will be prepared. The number of spare parts will affect the repair time of the failed equipment and the availability of the system. If the number of spare parts on the key control card cannot be reasonably configured, it will directly affect the reliability and economy of the peak-shaving operation of the thermal power plant.

Most of the I/O modules in the key I/C system of coal-fired power plants adopt the redundancy allocation principle. According to the requirements of a single failure criterion, for redundant equipment, the operation of the whole unit cannot be affected due to the failure of one of the pieces of equipment. Therefore, the impact of common causes of failure of similar control cards on the operation of the whole unit shall be considered.

Long-term experience in power plant safety analysis shows that CCF (Common Cause Failures) is one of the main causes of system failure and equipment unavailability and one of the main sources of system risk. Therefore, CCF is an important factor that must be considered in the reliability and safety analysis of the system. If the effect of CCF is not properly considered, the reliability and safety model will get overly optimistic results [32].

CCF, ${\mathsf{\lambda }}_{\mathrm{C}}$, and non-CCF (single random failure) ${\mathsf{\lambda }}_{\mathrm{N}}$ parameters were shown in Formulas (1) and (2).

$${\mathsf{\lambda }}_{\mathrm{C}}=\mathsf{\beta }\times \mathsf{\lambda }$$

(1)

$${\mathsf{\lambda }}_{\mathrm{N}}=(1-\mathsf{\beta })\times \mathsf{\lambda }$$

(2)

$\mathsf{\lambda }$ is a failure rate. If the redundant I/O modules of the control card are installed on the same card, they are set with channel physical isolation, which is the same in design. The estimated value of the factor $\mathsf{\beta }$ is 0.032 [32].

3. Storage Strategy

For power plants, the storage of necessary spare parts plays an important role in system maintenance and effective operation. However, the storage of a large number of spare parts will increase the storage cost and occupy a large amount of funds. In addition, the long-term storage of spare parts is easy to rust or become invalid and can only be left idle or scrapped, increasing the operating costs of enterprises.

Therefore, on the basis of ensuring safety in production, it is of great practical significance to adopt appropriate inventory strategies to optimize resource allocation, reduce the total amount of inventory funds, and improve the capital turnover rate, which will increase the profits of power plants. The storage strategy of spare parts generally has the following four basic types: periodic order $(\mathrm{t},\mathrm{S})$ storage strategy, continuous inventory $(\mathrm{s},\mathrm{S})$ storage strategy, periodic order (t, Q) storage strategy, and continuous inventory $(\mathrm{r},\mathrm{Q})$ warehousing strategy.

In addition to the above four basic strategies, there are also hybrid warehousing strategies such as $(\mathrm{t},\mathrm{r},\mathrm{Q})$, $(\mathrm{t},\mathrm{s},\mathrm{S})$, etc. Practice has proven that the application of these storage strategies can effectively manage the inventory, but it is also necessary to select and use spare parts according to their characteristics, needs, storage conditions, and other aspects.

For low-value consumables such as general spare parts of a single unit lay, small valves, instrument pipelines, etc., if the shortage cost is low and if the inventory cost is higher than the value of the spare parts, the $\left(\mathrm{t},\mathrm{Q}\right),$ $(\mathrm{t},\mathrm{S})$ strategy of periodic inventory is preferred. If the inventory cost is lower than the value of the spare parts, the $(\mathrm{s},\mathrm{S})$ strategy of continuous inventory is preferred.

The research object of this paper is mainly aimed at the spare parts of the key equipment of coal-fired thermal power units, including not only the important components such as the feedwater pump assembly, core package, and gearbox with high unit prices but also the key devices such as DEH valve servo card and safety level instrument with low unit prices that will affect the normal operation of the unit. For the key equipment of such units, the continuous inventory $(\mathrm{r},\mathrm{Q})$ storage strategy is generally adopted. With the promotion and application of intelligent warehousing in power generation enterprises, it is more convenient to monitor and count the inventory level, and it also provides the basic conditions for continuous counting for the application of $(\mathrm{r},\mathrm{Q})$ storage strategy.

As shown in Figure 2, $\mathrm{r}$ is the reorder point, and the inventory level y is monitored continuously. If $\mathrm{y}\le \mathrm{r}$, an order is issued to the supplier; after the order lead time ${\mathrm{T}}_{\mathrm{L}}$, the goods arrive, and each order quantity is Q.

4. Condition-Based Maintenance and Reliability Model

As shown in Figure 3, the condition-based maintenance of key equipment in the power plant conducts in-depth diagnosis and analysis based on the monitored online status of the equipment, interacts with the operators by HMI, and then decides the maintenance plan of the equipment. Via linkage with the intelligent storage system, the maintenance event is initiated to repair the equipment in service. At the same time, the intelligent storage system orders replenishment from the equipment manufacturer to deal with the occurrence of the next maintenance event. The online status of running equipment can also be systematically fed back to the equipment manufacturer. The manufacturer can not only further improve the equipment quality, but also further support the status diagnosis and analysis based on the equipment status by providing means and methods for the optimization of maintenance plans and storage strategies.

The failure of the key equipment of the generator set, especially electromechanical products or components, is generally described by Weibull distribution [33,34]; its probability density function can be expressed as:

$$\mathrm{f}\left(\mathrm{t}\right)=\frac{\mathrm{m}}{\mathsf{\eta }}{\left(\frac{\mathrm{t}}{\mathsf{\eta }}\right)}^{\mathrm{m}-1}\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\left(\frac{\mathrm{t}}{\mathsf{\eta }}\right)}^{\mathrm{m}}\right]$$

(3)

where $\mathrm{m}$ is the shape parameter, $\mathsf{\eta }$ is the scale parameter (characteristic life), and $\mathrm{t}$ is the component running time. Within the design life $\mathrm{T}$ of the unit, the average annual failure probability of a single component is:

$$\mathsf{\lambda }=\frac{{\int }_0^{\mathrm{T}}\mathrm{f}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}}{\mathrm{T}}$$

(4)

According to Formula (3), the expectation for the working time of a single component is:

$${\mathrm{T}}_{\mathrm{N}}=\mathrm{E}\left(\mathrm{t}\right)={\int }_0^{\mathrm{\infty }}\mathrm{t}\mathrm{f}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}$$

(5)

Under the infinite inventory condition ($\mathrm{r}=\mathrm{\infty }$), if the key equipment fails, the storage system can provide infinite and sufficient spare parts. The replacement cycle of a single component is:

$${\mathrm{T}}_{\mathrm{\infty }}={\mathrm{T}}_{\mathrm{m}}+{\int }_0^{\mathrm{\infty }}\mathrm{t}\mathrm{f}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}$$

(6)

where ${\mathrm{T}}_{\mathrm{m}}$ is the time taken for fault maintenance, mainly including the time for the shutdown fault diagnosis of the operating equipment, installation, deployment, and commissioning of spare parts.

Under the zero inventory condition ($\mathrm{r}=0$), the order can be started only after the failure of key equipment and the order lead time ${\mathrm{T}}_{\mathrm{L}}$. The maintenance shall be carried out after arrival, so the replacement cycle of a single component is:

$${\mathrm{T}}_0={\mathrm{T}}_{\mathrm{m}}+{\mathrm{T}}_{\mathrm{L}}+{\int }_0^{\mathrm{\infty }}\mathrm{t}\mathrm{f}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}$$

(7)

5. Optimization Modeling

The main purpose of $\left(\mathrm{r},\mathrm{Q}\right)$ storage strategy optimization under the condition of limited inventory of condition-based maintenance is to achieve the lowest annual cost $\mathrm{L}(\mathrm{r},\mathrm{Q})$ for key spare parts of a single unit on the basis of ensuring the availability of the key equipment of the unit. $\mathrm{L}(\mathrm{r},\mathrm{Q})$ cost mainly includes the purchase cost of key spare parts ${\mathrm{L}}_1$. Shortage cost ${\mathrm{L}}_2$ and inventory maintenance cost ${\mathrm{L}}_3$.

5.1. Modeling of Annual Purchase Cost of Key Spare Parts for a Single Unit

Acquisition cost ${\mathrm{L}}_1$ was mainly from the original value or unit price of the single spare parts of the key equipment ${\mathrm{c}}_1$ and the total purchase cost ${\mathrm{c}}_2$ of single spare parts inquiry, bidding, transportation, etc. It can be calculated by Equation (8).

$${\mathrm{L}}_1=\mathsf{\lambda }\left(\frac{{\mathrm{Q}{\mathrm{c}}_1+\mathrm{c}}_2}{\mathrm{N}}\right)$$

(8)

5.2. Modeling of Annual Shortage Cost of Key Spare Parts of a Single Unit

5.2.1. Modeling of Downtime Expectation Caused by Spare Parts Shortage

After the failure of the key equipment of the thermal power unit, it may be out of stock due to the existence of an order lead time. Literature [35] deduced the downtime caused by the shortage of spare parts within the order lead time.

The probability of a single component failure within the order lead time can be calculated by Equation (9):

$${\mathsf{\lambda }}_{\mathrm{L}}=\mathsf{\lambda }{\mathrm{T}}_{\mathrm{L}}$$

(9)

For the number of failures of key components of $\mathrm{N}$ thermal power units covered by intelligent storage within the lead time of ordering, $\mathrm{X}$ follows a binomial distribution and is recorded as $\mathrm{X}~\mathrm{B}(\mathrm{N},{\mathsf{\lambda }}_{\mathrm{L}})$. Then the probability of k failures of key components of N thermal power units in the order lead time is:

$$\mathrm{P}(\mathrm{X}=\mathrm{k})={\mathrm{C}}_{\mathrm{N}}^{\mathrm{k}}{\mathsf{\lambda }}_{\mathrm{L}}^{\mathrm{k}}{(1-{\mathsf{\lambda }}_{\mathrm{L}})}^{\mathrm{N}-\mathrm{k}}$$

(10)

It is assumed that the time interval of k failures of key components of the unit in lead time ${\mathrm{T}}_{\mathrm{L}}$ is the same. Under the continuous inventory $(\mathrm{r},\mathrm{Q})$ strategy, if $\mathrm{k}<\mathrm{r}+1$, there will be no shortage of spare parts and waiting for spare parts, so the downtime is zero. If $\mathrm{k}\ge \mathrm{r}+1$, that is, the fault after the $\mathrm{r}$ time (excluding the $\mathrm{r}$ time) can only be repaired after the arrival of spare parts. Therefore, the total downtime for waiting for spare parts caused by k failures in order lead time ${\mathrm{T}}_{\mathrm{L}}$ is:

$$\mathrm{g}\left(\mathrm{k}\right)=\sum _{\mathrm{j}=\mathrm{r}+1}^{\mathrm{k}}\frac{\mathrm{k}-(\mathrm{j}-1)}{\mathrm{k}}{\mathrm{T}}_{\mathrm{L}}, \mathrm{k}\ge \mathrm{r}+1$$

(11)

According to Formulas (10) and (11), the total downtime of all units covered by intelligent storage due to the shortage of spare parts is expected to be:

$${\mathrm{T}}_{\mathrm{s}}\left(\mathrm{r}\right)=\sum _{\mathrm{k}=0}^{\mathrm{N}}\mathrm{P}(\mathrm{X}=\mathrm{k})·\mathrm{g}\left(\mathrm{k}\right)$$

(12)

5.2.2. Modeling of Downtime Cost Caused by Shortage of Spare Parts

Shortage cost is ${\mathrm{L}}_2$. Under the condition of limited inventory, the outage power loss caused by waiting for the arrival of spare parts after the failure of the key equipment of the unit can be calculated by Equation (13).

$${\mathrm{L}}_2=\frac{{\mathrm{T}}_{\mathrm{s}}\left(\mathrm{r}\right)}{\mathrm{N}{\mathrm{T}}_{\mathrm{p}}}\left[{\mathrm{n}}_{\mathrm{H}}({\mathrm{p}}_{\mathrm{r}}-{\mathrm{c}}_3)\mathrm{P}\right]$$

(13)

${\mathrm{n}}_{\mathrm{H}}$ is the average annual utilization hours of thermal power units, which depends on the local power supply and demand level, the installed proportion of renewable energy power generation, the role of units in the regional power grid, and other factors; ${\mathrm{p}}_{\mathrm{r}}$ is the local benchmark grid price; ${\mathrm{c}}_3$ is the cost of electricity per kilowatt hour, which is mainly composed of fuel cost, employment cost, maintenance cost, etc. Among them, fuel cost is the decisive factor, which is closely related to the supply and demand of the fuel market, fuel transportation, etc. $\mathrm{P}$ is the installed capacity of the unit.

5.3. Modeling of Key Spare Parts Inventory Maintenance Cost for a Single Unit

Inventory maintenance cost ${\mathrm{L}}_3$ mainly refers to various costs related to holding inventory, and the most important is the cost of capital occupation. The inventory consumption shall be considered simultaneously. The annual inventory maintenance cost of each unit can be calculated by Formula (14).

$${\mathrm{L}}_3=\left\{\begin{array}{c}\frac{{\mathrm{c}}_4}{\mathrm{N}}·\frac{{\left(\mathrm{Q} + \mathrm{r} - \mathsf{\lambda }\mathrm{N}{\mathrm{T}}_{\mathrm{L}}\right)}^2}{2\mathrm{Q}} 0\le \mathrm{r}\le \mathsf{\lambda }\mathrm{N}{\mathrm{T}}_{\mathrm{L}}\\ \frac{{\mathrm{c}}_4}{\mathrm{N}}·\frac{\mathrm{Q} + 2\mathrm{r} - 2\mathsf{\lambda }\mathrm{N}{\mathrm{T}}_{\mathrm{L}}}{2} \mathrm{r}\le \mathsf{\lambda }\mathrm{N}{\mathrm{T}}_{\mathrm{L}} \end{array}\right.$$

(14)

${\mathrm{c}}_4$ is the annual inventory maintenance cost of single key spare parts.

5.4. Modeling of Availability of Key Equipment

Under the condition of the limited inventory continuous counting $(\mathrm{r},\mathrm{Q})$ strategy, the availability rate of the key equipment of the unit is calculated using the statistical data such as the design life of N units, the expectation of normal working hours, and the expectation of out of stock time within the order lead time [35]:

$$\mathrm{A}\left(\mathrm{r},\mathrm{Q}\right)=\frac{{\mathsf{\alpha }}_1\mathrm{N}{\mathrm{T}}_{\mathrm{N}}-{\mathrm{k}\mathsf{\alpha }}_2{\mathrm{T}}_{\mathrm{s}}\left(\mathrm{r}\right)}{\mathrm{N}\mathrm{T}}$$

(15)

where $\mathrm{t}{\mathsf{\alpha }}_1=\mathrm{T}/{\mathrm{T}}_{\mathrm{\infty }}$ is the ratio of the design life of key components to the replacement cycle under unlimited inventory. ${\mathsf{\alpha }}_2={\mathrm{T}}_{\mathrm{\infty }}/{\mathrm{T}}_{\mathrm{p}}$ is the ratio of the design life to the spare parts ordering cycle. ${\mathrm{T}}_{\mathrm{p}}=\mathrm{Q}/\left(\mathsf{\lambda }\mathrm{N}\right)$ is the ordering cycle of spare parts.

5.5. Cost Optimization Modeling

According to the sub-item calculation of Equation above, set the annual cost of the key spare parts of a single unit as the lowest objective function and take the relationship between the ordering point and the ordering quantity, the availability of components within the allowable range, etc. as constraints to obtain the optimization model under the $(\mathrm{r},\mathrm{Q})$ storage strategy of the key equipment of thermal power units:

$$\min \mathrm{L}\left(\mathrm{r},\mathrm{Q}\right)={\mathrm{L}}_1+{\mathrm{L}}_2+{\mathrm{L}}_3$$

$$\begin{array}{c}\mathrm{s}.\mathrm{t}.\mathrm{A}(\mathrm{r},\mathrm{Q})\ge 99.5\%\\ \mathrm{r}\ge 0\\ \mathrm{Q}>\mathsf{\lambda }\mathrm{N}{\mathrm{T}}_{\mathrm{L}}\end{array}$$

(16)

5.6. System Design and Implementation

With the continuous promotion of the new power system, the positioning of thermal power units has changed from the original base-load power supply to the regulated power supply. Frequent and intense load tracking has significantly increased the failure rate of key equipment. The profit source of the power plant has also expanded from the original electricity revenue to the auxiliary service revenue. The utilization hours of power generation have also changed significantly with the promotion of the carbon target. The current optimal control model cannot adapt to the current electricity and auxiliary service market boundary changes. This paper designs a set of spare parts inventory strategy optimization methods and systems for key equipment in thermal power plants, as shown in Figure 4. Adaptive intelligent methods and systems, which include electricity price forecast, life trend prediction, etc., are used to achieve cost optimization $(\mathrm{r},\mathrm{Q})$ procurement strategies with changing boundaries using the following steps:

Step S0: The program is started, and the interface status between the detection system and the equipment reliability platform, power market platform, warehousing, and other systems is ready.

Step S1: Predict equipment characteristic life trends under the new power system. Read the historical failure data of the equipment reliability system, and predict the characteristic life trends of the equipment in the new power system. The steps are as follows:

S1.1: Read the annual historical data on the characteristic life of the key equipment of the reliability system.

S1.2: Time series prediction: The PROPHET algorithm is used for supervised learning of historical data to obtain the training model.

S1.3: Use the training model to predict the characteristic life of the equipment in the next year $\mathsf{\eta }(\mathrm{t}+1)$.

S1.4: Calculate the average failure rate of key equipment from the current year to the end of unit life $\mathsf{\lambda }$.

Step S2: Calculate the purchase cost of spare parts. The scale parameter of the next year, namely characteristic life $\mathsf{\eta }\left(\mathrm{t}+1\right),$ is substituted into the Weibull distribution formula. Then the next year’s failure rate $\mathsf{\lambda }$ is calculated according to Formula (2). Finally, calculate the annual spare parts purchase cost ${\mathrm{L}}_1$ of key equipment for a single unit according to Formula (6).

Step S3: Electricity market forecast: Predict the average value of annual operating hours, kilowatt-hour revenue, kilowatt-hour cost, and other parameters from the current year to the end of unit design. The method for predicting the average value of annual operating hours, kilowatt-hour revenue, kilowatt-hour cost, and other parameters from the current year to the end of unit design is as follows:

S3.1: Collect relevant historical data on annual operating hours, benchmark price, ancillary service income, and electricity cost of the power plant.

S3.2: The PROPHET machine learning algorithm is used for supervised learning, and the training models of annual operating hours, benchmark price, ancillary service income, and electricity cost are obtained, respectively.

S3.3: Use the training model to forecast the annual operating hours, benchmark price, ancillary service income, and electricity cost from the current year to the end of unit design.

S3.4: Calculate the mean value of the following parameters from the current year to the end of the unit life: annual operating hour mean value ${\mathrm{n}}_{\mathrm{H}}$; average annual benchmark price ${\mathrm{p}}_0$; average annual ancillary service income ${\mathrm{U}}_0$; average annual electricity cost ${\mathrm{c}}_3$.

S3.5: Calculation of the annual converted electricity price: ${\mathrm{p}}_{\mathrm{r}}=\frac{{\mathrm{p}}_0{\mathrm{n}}_{\mathrm{H}}\mathrm{P}+{\mathrm{U}}_0}{\mathrm{W}{\mathrm{n}}_{\mathrm{H}}\mathrm{P}}$.

P is the installed capacity of the unit.

Step 4: Calculate the shortage cost of spare parts. Calculation is according to the characteristic life predicted in Step 1 and the annual converted electricity price forecast of the electricity market considering the ancillary service market income in Step 3 and according to the calculation formula in Section 5.2, the outage loss caused by waiting for the arrival of spare parts after the failure of the key equipment of the computer group, that is, the annual cost of spare parts shortage ${\mathrm{L}}_2$.

Step S5: Calculate the inventory maintenance cost of spare parts according to the annual characteristic life prediction in Step 1 and the method in Section 5.3.

Step S6: Calculate the annual cost of key spare parts for a single unit: $\mathrm{L}\left(\mathrm{r},\mathrm{Q}\right)={\mathrm{L}}_1+{\mathrm{L}}_2+{\mathrm{L}}_3$.

Step 7: Find the best $({\mathrm{r}}^{\mathrm{*}},{\mathrm{Q}}^{\mathrm{*}})$.

Step 8: Judge whether the inventory level y is less than ${\mathrm{r}}^{\mathrm{*}}$. If it is less than ${\mathrm{r}}^{\mathrm{*}}$, push it to the ERP system. If it is greater than ${\mathrm{r}}^{\mathrm{*}}$, continue inventory counting.

Step 9: The ERP system initiates the purchase demand according to the inventory results of the warehouse system, and the purchase quantity of key equipment is ${\mathrm{Q}}^{\mathrm{*}}$.

Step 10: The program ends and enters the next cycle.

6. Example Analysis

A thermal power unit is a series system composed of typical key equipment. According to the above modeling formula, this paper will focus on the optimal control strategy of key high value spare parts and key low value spare parts that affect the operation of a thermal power unit. In the specific scenario selected, the intelligent storage system covers 4 coal-fired supercritical units with an installed capacity of P = 600 MW and a design life of T = 30 years.

According to the prediction of the local power market of units, the average annual utilization hours are ${\mathrm{n}}_{\mathrm{H}}=5500$ h, the converted electricity price considering the revenue and marginal cost of auxiliary services such as peak-shaving is ${\mathrm{p}}_{\mathrm{r}}=0.45 \mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{k}\mathrm{W}\mathrm{h}$, and the electricity cost ${\mathrm{c}}_3=0.2 \mathrm{y}\mathrm{u}\mathrm{a}\mathrm{n}/\mathrm{k}\mathrm{W}\mathrm{h}$.

6.1. Inventory Strategy Analysis of Key High-Value Spare Parts

Taking the core package of a feed water pump as an example, each unit is equipped with one 100% capacity steam feed water pump. The relevant initial parameters of the steam feed pump are as follows: unit price of spare parts ${\mathrm{c}}_1$ = 2,800,000 yuan/set, procurement cost ${\mathrm{c}}_2$ = 20,000 yuan/set, inventory maintenance cost ${\mathrm{c}}_4$ = 15,000 yuan/(set·a), failure maintenance time ${\mathrm{T}}_{\mathrm{m}}$ = 90 days, and order lead time ${\mathrm{T}}_{\mathrm{L}}$ = 150 days. Failure probability density function of feed pump: Weibull shape parameter $\mathrm{m}$ = 1.04; Weibull scale parameter $\mathsf{\eta }$ = 50.

Substitute the above parameters into the optimization model Formula (14), optimize and analyze the continuous inventory (r, Q) strategy, and get the annual cost curve of the spare parts of a single unit under different ordering points r to Q-L. The results are shown in Figure 5. The best warehousing strategy is to reorder when the spare parts inventory is lower than the ordering point (1 unit). The order quantity is 1 unit each time. Under this strategy, the annual cost of the spare parts borne by each unit is at least 142,500 yuan. Compared with the order quantity of a single machine with zero inventory, the annual cost decreased by 9.69% and the availability rate increased by 0.01%. The cost is 66.77% lower than the highest ordering strategy, and the unit availability remains above 99.5% with no significant change.

With the promotion of the power market, thermal power units participate in more peak-shaving auxiliary services. According to the failure mechanism of the feed water pump core package, assuming that the characteristic life of the spare parts decreases year by year, the optimal algorithm is substituted to find the best advantage, as shown in

Table 1. Influence of the life of feed water pump core package on the optimal (r, Q) model.

Characteristic Life (Years)	$\mathbf{Optimal} (\mathbf{r},\mathbf{Q})$	Minimum Cost	Availability
10	(1, 1)	7.68	0.9952
5	(1, 1)	14.26	0.9967
4	(1, 1)	17.48	0.9972

. Although the best advantage of the inventory strategy has not changed and the unit availability has not changed much, the annual spare parts cost of the feed water pump core package under the optimal strategy has significantly increased.

When the power plant implements condition-based maintenance, condition monitoring and regular maintenance are improved. Working status data can be fed back to the manufacturer. Orders in advance can be realized via more accurate predictive maintenance and intelligent early warning measures. As shown in

Table 2. Influence of condition-based maintenance on the optimal (r, Q) model of feed water pump.

Order Lead Time (Day)	$\mathbf{Optimal} (\mathbf{r},\mathbf{Q})$	Minimum Cost	Availability
150	(1, 1)	14.26	0.9967
90	(0, 1)	14.18	0.9957
60	(0, 1)	14.17	0.9979

, the order lead time ${\mathrm{T}}_{\mathrm{L}}$ can be greatly shortened, and the optimal strategy point has moved from (1, 1) to (0, 1); that is, the optimal strategy under condition-based maintenance is zero inventory, which will reduce the annual spare parts cost.

Therefore, with the shortening of order lead time caused by condition-based maintenance, the storage system no longer needed to prepare goods, and the system availability also increased from 99.67% to 99.79%. The spare parts optimization cost of a single unit was also further reduced.

With the expansion of the unit or the Federal Reserve’s joint reserve of spare parts of the same model, the number of units covered increased, which makes the cost of spare parts borne by a single unit decrease rapidly, as shown in

Table 3. Influence of the quantities of thermal power units covered on the cost and availability of spare parts for feed water pump core package.

Quantities of Thermal Power Units Covered	$\mathbf{Optimal} (\mathbf{r},\mathbf{Q})$	Minimum Cost	Availability
N = 4	(1, 1)	14.26	0.9952
N = 6	(1, 1)	9.51	0.9921
N = 10	(1, 1)	5.71	0.9920

. However, the availability did not decrease significantly.

6.2. Inventory Strategy Analysis of Key Low Value Spare Parts

Taking the DEH servo control card as an example, the failure of the DEH system servo control card caused the sudden full closure of the high-pressure control valve, resulting in shutdown. The continuous inventory $(\mathrm{r},\mathrm{Q})$ strategy is optimized and analyzed. The relevant parameters of the DEH servo control card are as follows: unit price of spare parts ${\mathrm{c}}_1$ = 10,000 yuan/set; procurement cost ${\mathrm{c}}_2$ = 200 yuan/set; inventory maintenance cost ${\mathrm{c}}_4$ = 200 yuan/(set a); failure maintenance time ${\mathrm{T}}_{\mathrm{m}}$ = 3 days; order lead time ${\mathrm{T}}_{\mathrm{L}}$ = 90 days. Failure probability density function of feed pump: Weibull shape parameter m = 1.05; Weibull scale parameter $\mathsf{\eta }$ = 20.

Similarly, the above parameters are substituted into Equation (14), and the annual cost curve of the spare parts of a single unit in space (r, Q) is obtained for L, as shown in Figure 6. The best warehousing strategy is to reorder when the spare parts inventory of the servo control card is lower than the ordering point (2 units). The quantity of each order is 1 unit. Under this strategy, the annual cost of the spare parts borne by each unit is the lowest, at only 245 yuan. The unit price of the spare parts is low, but if the stock is not prepared, the loss of downtime caused by out of stock is huge, especially in the context of the current thermal power unit undertaking the peak shaving power supply. The probability of servo card failure is further improved, so the cost of the zero inventory strategy is generally high. The annual spare parts cost of a single unit under the (r = 0, Q = 1) strategy is up to RMB 9994, 40 times the cost of the optimal ordering point, and the availability rate is 0.02% lower than the best. When r > 2, with the increase in the spare parts scale, the cost will rise slightly, but the unit availability will not change.

Table 4. Influence of DEH valve servo card life on the optimal model.

Life of Servo Card (Years)	$\mathbf{Optimal} (\mathbf{r},\mathbf{Q})$	Minimum Cost	Availability
20	(1, 1)	0.0130	0.9998
15	(1, 1)	0.0161	0.9997
10	(2, 1)	0.0245	0.9996

shows the best advantages, optimal cost, and corresponding unit availability level of the DEH valve servo card under different service lives. In view of the increasing flexibility adjustment tasks currently undertaken by thermal power units, which have a negative impact on the service life of the DEH servo card, the unit condition maintenance can further improve the service life of DEH servo cards by strengthening status monitoring, regular maintenance, and feeding back the working status data to the manufacturer. The change in service life will inevitably change the optimal storage strategy. For example, as the service life decreases, the optimal (r, Q) point moves in the direction of increasing stock, the cost of spare parts also increases, and the availability level decreases.

The quantities of thermal power units covered by the intelligent storage also have a great impact on the cost of spare parts for DEH servo control cards. As shown in

Table 5. Influence of the quantities of thermal power units covered on the spare parts cost of DEH servo control card.

Quantities of Thermal Power Units	$\mathbf{Optimal} (\mathbf{r},\mathbf{Q})$	Minimum Cost	Availability
N = 4	(2, 1)	0.0245	0.9996
N = 6	(2, 1)	0.0164	0.9996
N = 10	(2, 1)	0.0098	0.9996

, with the increase in the number of units covered, the optimal ordering point has not been moved, and the cost of spare parts borne by a single unit has decreased significantly without changing the availability level. This shows that the Federal Reserve’s joint reserve strategy for the same type of spare parts and intelligent warehousing can significantly reduce the cost of spare parts without reducing the availability of the unit.

7. Conclusions

This article studies the condition-based maintenance mode, key equipment, and spare parts of coal-fired power plants and proposes an optimization strategy for the inventory cost of coal-fired power plants and an intelligent warehousing system under the condition-based maintenance mode. The main conclusions are as follows:

(1) On the premise of not affecting system availability, there is still significant optimization space for the inventory cost of thermal power units. ① For the implementation of inventory optimization for key high-value spare parts (core packages of feedwater pumps in thermal power units), the cost was reduced by 66.77% compared to the highest ordering strategy, and the unit availability remained above 99.5%. ② For key low-value spare parts (DEH valve servo cards), inventory optimization is implemented, and the optimal order point cost is only 1/40 of the zero inventory order point cost.

(2) For any type of critical spare part, the number of thermal power units covered by the intelligent warehousing system has a significant impact on reducing inventory costs. During the process of increasing the number of units covered from 4 to 10, the optimal inventory costs of key high- and low-value spare parts are reduced by 60%. Therefore, the Federal Reserve’s joint reserve between intelligent warehouses has a significant effect on reducing inventory costs.

(3) The increasing flexibility regulation tasks currently undertaken by thermal power units have had a negative impact on the lifespan of key components of the units. It is necessary to adopt equipment predictive diagnosis and early warning methods and, if necessary, make advance orders.

This optimization strategy and system basically meet the needs of power generation enterprises in terms of condition-based maintenance and inventory management. However, as power plants are a very complex system, the following aspects of the paper still need to be further studied:

(1) In terms of spare parts consumption calculation, this paper adopts the reliability prediction scheme to predict faults according to the shape and distribution of the Weibull curve, which is persuasive. However, the current unit generally does not operate in its design state, and the demand curve for some key components is bound to change. In the future, neural network correction of the curve according to the actual operating parameters of the unit can be considered to bring the inventory control strategy closer to the actual situation of the current unit operation.

(2) The more thermal power units covered by the intelligent storage system, the lower the cost of spare parts. However, the factors that need to be considered, such as spare parts scheduling mechanisms and cost-sharing between power plants, are not reflected in the model in this paper. In order to promote the cross-plant application of the system, research and modeling in this area need to be strengthened.

(3) Given the complexity of thermal power units, in addition to the key equipment of the reliability series system studied in this article, the storage control strategy for these spare parts is also crucial for reducing management costs due to the large proportion of non-critical equipment that partially affects the power generation of the units.

(4) In the future, a new type of power system dominated by new energy will inevitably require thermal power units to undertake more peak shaving and frequency regulation tasks. It is necessary to further study the optimization, maintenance mode, and storage strategy of units, support thermal power units to better play a flexible role, further increase the proportion of new energy in the power grid, and reduce the carbon emissions level of the power system.