Energy storage charging and discharging time sequence optimization scheduling method and system based on revenue maximization

Abstract

The invention provides an energy storage charging and discharging time sequence optimization scheduling method and system based on revenue maximization, and relates to the technical field of power system optimization scheduling, and the method comprises the steps: obtaining price data and system parameters, recognizing a price local extreme point, constructing an envelope line, and stripping an oscillation component to obtain a price trend component; and establishing a corresponding relation between a charge state target value and a time period identifier, enabling the charge state track to converge to the target value step by step, and dynamically correcting the target value and adjusting a price peak value identification method according to real-time feedback data. According to the invention, price fluctuation can be effectively coped, the economic benefit of the energy storage system is improved, and self-adaptive optimization control of the charging and discharging process is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system optimal scheduling, in particular to a storage charging and discharging timing optimization scheduling method and system based on maximum benefit. BACKGROUND

[0002] With the continuous expansion of renewable energy grid-connected scale, the uncertainty and volatility of the power system are increasing, and the storage system plays a key role in power system stability maintenance, demand side response and market price arbitrage as an important regulating means. In the electricity market environment, the storage system can maximize economic benefits and provide peak shaving and frequency modulation auxiliary services for the power grid by reasonably arranging the charging and discharging timing. At present, the storage charging and discharging optimization scheduling technology has become a research hotspot in the field of smart grid and energy internet.

[0003] The traditional optimization scheduling method excessively depends on the accuracy of the electricity price prediction, but the actual electricity market price is influenced by many factors and has strong randomness and volatility, and the prediction deviation is often large, so that the charging and discharging strategy based on the predicted price is difficult to achieve the expected economic benefit. The existing methods mostly do not consider the real-time operation state feedback of the storage system, adopt an open-loop control mode, and cannot timely adjust the state of charge deviation occurring in the actual operation process, lack the necessary closed-loop control mechanism, and reduce the practicability and robustness of the scheduling strategy. When identifying the peak and valley characteristics of the electricity price, the conventional method usually adopts simple threshold judgment or fixed time division, which cannot effectively cope with the complex and variable price fluctuation mode, especially for the electricity price curve with multiple peaks and valleys, it is difficult to accurately identify the best charging and discharging time, thereby affecting the arbitrage effect of the storage system. SUMMARY

[0004] The embodiment of the present application provides a storage charging and discharging timing optimization scheduling method and system based on maximum benefit, which can solve the problems in the prior art.

[0005] In a first aspect, the embodiment of the present application provides a storage charging and discharging timing optimization scheduling method based on maximum benefit, comprising: obtaining power price timing data, state of charge data of the storage system and physical constraint parameters; identifying local extreme points of the power price timing data, constructing an upper envelope line and a lower envelope line of the price based on the local extreme points and performing mean value calculation, iteratively stripping the oscillation component to obtain a change trend component of the power price; identifying a price peak period from the change trend component, and establishing a corresponding relationship between the state of charge target value and the period identifier in combination with the physical constraint parameters; Based on the correspondence and the power boundary constraint of the physical constraint parameter, the state of charge trajectory of the state of charge data gradually converges to the state of charge target value along the time axis, and the charging and discharging power scheduling instruction at each time is obtained; Based on the charging and discharging power scheduling instruction, the energy storage system is controlled to perform charging and discharging actions, and actual state of charge feedback data and actual market price feedback data in the energy storage system execution process are collected in real time; According to the actual state of charge feedback data and the actual market price feedback data, the state of charge deviation and the price prediction deviation at the current time are calculated, the state of charge target value is dynamically modified by using the state of charge deviation, and the identification method of the price peak period is adaptively adjusted by using the price prediction deviation, and the charging and discharging timing optimization scheduling is completed.

[0006] Local extreme points of the power price time series data are identified, the upper envelope line and the lower envelope line of the price are constructed based on the local extreme points, and the mean value is calculated, and the oscillation component is iteratively stripped to obtain the change trend component of the power price, including: The power price time series data is sequentially traversed, the time when the price change direction of adjacent time turns over is taken as a local extreme point, and the local extreme point is divided into a local maximum point set and a local minimum point set; The local maximum point set and the local minimum point set are respectively interpolated and connected on the time axis to construct the upper envelope line and the lower envelope line of the price; the numerical mean value of the upper envelope line and the lower envelope line of the price at each time is calculated to obtain the intermediate trend component of the current iteration period; the power price time series data and the intermediate trend component are subjected to difference operation to obtain the residual component of the current iteration period; The oscillation amplitude of the residual component is calculated, when the oscillation amplitude is higher than a preset oscillation threshold, the residual component is taken as the input data of the next iteration period, and the intermediate trend component of the next iteration period is calculated; the iteration is continued until the oscillation amplitude is lower than the preset oscillation threshold, and the intermediate trend component of the current iteration period is determined as the change trend component of the power price.

[0007] The price peak period is identified from the change trend component, and the correspondence between the state of charge target value and the period identifier is established in combination with the physical constraint parameter, including: The continuous time interval in which the price value exceeds the average price level in the change trend component is identified and marked as a candidate high price period; the candidate high price period is subjected to duration verification, and the period whose duration satisfies the minimum charging and discharging duration requirement of the energy storage system in the physical constraint parameter is determined as the price peak period; setting a maximum state of charge value of the energy storage system in the physical constraint parameter as a state of charge target value corresponding to a starting moment of the price peak period, and assigning a discharging period identifier to the price peak period; for a transition period located between the price peak periods, linearly interpolating the state of charge target values corresponding to adjacent price peak periods to obtain the state of charge target value corresponding to each moment of the transition period, and assigning a transition period identifier to the transition period; summarizing the state of charge target values and period identifiers corresponding to each moment of the price peak period and the transition period, organizing the associated data records, storing the associated data records in chronological order, and forming a corresponding relationship between the state of charge target values and the period identifiers.

[0008] Based on the corresponding relationship and the power boundary constraint of the physical constraint parameter, the state of charge trajectory of the state of charge data gradually converges to the state of charge target value along the time axis, and the charging and discharging power scheduling instruction of each moment is obtained, including: obtaining an actual state of charge value, extracting the state of charge target value corresponding to the current moment and the period identifier from the corresponding relationship, and calculating the state deviation amount of the state of charge target value and the actual state of charge value; According to the state deviation amount and the time interval from the current moment to the next moment, the theoretical charging and discharging power required for the actual state of charge value to converge to the state of charge target value is calculated; obtaining the maximum charging power limit and the maximum discharging power limit of the energy storage system from the physical constraint parameter; performing power boundary constraint processing on the theoretical charging and discharging power, when the absolute value of the theoretical charging and discharging power exceeds the maximum charging power limit or the maximum discharging power limit, the theoretical charging and discharging power is truncated to the corresponding power boundary value to obtain the constrained charging and discharging power of the current moment; the constrained charging and discharging power is used as the charging and discharging power scheduling instruction of the current moment; Based on the constrained charging and discharging power and the time interval from the current moment to the next moment, the predicted state of charge value of the next moment is calculated, and the predicted state of charge value is updated to the state of charge data as the actual state of charge value of the next moment; repeat and execute for subsequent moments until the charging and discharging power scheduling instruction of all moments in the scheduling period is generated.

[0009] and dynamically correcting the state of charge target value by using the state of charge deviation amount, including: Arranging state of charge deviation amounts of each historical moment from a dispatch cycle starting moment to a current moment in time sequence to form a state of charge deviation amount sequence;Calculate the rate of change between adjacent state of charge deviation amounts in the state of charge deviation amount sequence, judge the evolution trend characteristics of the state of charge deviation amount according to the positive and negative signs and the numerical value of the rate of change, determine the correction response intensity level and the response coefficient according to the evolution trend characteristics; Calculate the ratio of the absolute value of the price prediction deviation amount to the historical mean of the price prediction deviation amount in the dispatch cycle to obtain the price fluctuation relative intensity index, perform nonlinear mapping transformation on the price fluctuation relative intensity index, map the price fluctuation relative intensity index to the preset sensitivity coefficient value interval to obtain the price fluctuation sensitivity coefficient; Obtain the response coefficient corresponding to the correction response intensity level, and perform weighted fusion calculation on the response coefficient and the price fluctuation sensitivity coefficient to obtain a comprehensive correction intensity factor;Use the comprehensive correction intensity factor to correct the state of charge deviation amount at the current moment to obtain a state of charge target value correction amplitude;Superimpose the state of charge target value correction amplitude to the state of charge target value corresponding to the current moment to obtain a corrected state of charge target value.

[0010] Meanwhile, the method for adaptively adjusting the identification of the price peak period using the price prediction deviation amount comprises: The identification result of the price peak period is taken as a random variable to be inferred, and the price prediction deviation amount is taken as observation evidence to establish a prior probability distribution of the identification result of the price peak period and calculate a likelihood value;The prior probability distribution and the likelihood value are Bayes fused to obtain a posterior probability distribution;Calculate the relative entropy between the prior probability distribution and the posterior probability distribution; The maximum posterior probability value in the posterior probability distribution is calculated as the confidence value of the identification result of the price peak period;When the confidence value is lower than a preset confidence threshold and the relative entropy exceeds a preset relative entropy threshold, the weight of the prior probability distribution in the Bayes fusion calculation is reduced and the Bayes fusion calculation is re-executed, and a multi-candidate set of the price peak period is constructed based on the updated posterior probability distribution; Calculate the period overlap degree between each candidate price peak period identification result in the multi-candidate set, identify the time points with a period overlap degree lower than the overlap degree threshold as low-confidence price peak periods;Adjust the state of charge target value setting of the low-confidence price peak periods, and update the correspondence between the state of charge target value and the time period identification based on the adjusted state of charge target value setting.

[0011] In a second aspect of the embodiments of the present application, a storage and energy charging and discharging timing optimization scheduling system based on maximum benefit is provided, comprising: The first unit is configured to acquire power price time series data, state of charge data of an energy storage system, and physical constraint parameters; The second unit is configured to identify local extreme points of the power price time series data, construct an upper envelope line and a lower envelope line based on the local extreme points and perform mean value calculation, iteratively strip oscillation components to obtain a variation trend component of the power price, identify a price peak period from the variation trend component, and establish a corresponding relationship between a state of charge target value and a time period identifier in combination with the physical constraint parameters. The third unit is configured to make the state of charge trajectory of the state of charge data gradually converge to the state of charge target value along a time axis based on the corresponding relationship and a power boundary constraint of the physical constraint parameters, and obtain a charging and discharging power scheduling instruction at each time point. The fourth unit is configured to control the energy storage system to perform a charging and discharging action based on the charging and discharging power scheduling instruction, and collect actual state of charge feedback data and actual market price feedback data in a real-time manner during an execution process of the energy storage system. The fifth unit is configured to calculate a state of charge deviation amount and a price prediction deviation amount at a current time point according to the actual state of charge feedback data and the actual market price feedback data, dynamically correct the state of charge target value by using the state of charge deviation amount, simultaneously adaptively adjust an identification method of the price peak period by using the price prediction deviation amount, and complete charging and discharging time series optimization scheduling.

[0012] The third aspect of the embodiment of the application, An electronic device is provided, comprising: a processor; a memory for storing processor-executable instructions; The processor is configured to invoke the instructions stored in the memory to execute the method described above.

[0013] The fourth aspect of the embodiment of the application, A computer-readable storage medium is provided, which stores computer program instructions, and the computer program instructions are executed by a processor to implement the method described above.

[0014] The beneficial effects of the present application are as follows: This invention identifies local extreme points in electricity price time-series data, constructs upper and lower price envelopes for mean calculation, and iteratively removes oscillating components. This effectively obtains the trend components of electricity price changes, avoiding the oversensitivity to random price fluctuations in traditional methods and improving the accuracy of identifying peak price periods. Based on the price trend components, this invention identifies peak price periods and establishes a correspondence between the target state of charge (SOC) value and the time period identifier, making charging and discharging decisions more rational. This effectively avoids the frequent charging and discharging switching problems caused by price fluctuations in traditional methods, extending the lifespan of the energy storage system. Furthermore, this invention employs an optimization method where the SOC trajectory gradually converges to the target value along the time axis. This satisfies the physical constraints of the energy storage system and achieves a smooth transition in charging and discharging power, improving the stability of system operation. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the energy storage charging and discharging timing optimization scheduling method based on maximizing benefits, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram of the price trend component extraction process. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0018] Figure 1 This is a flowchart illustrating the energy storage charging and discharging timing optimization scheduling method based on maximizing returns, as described in an embodiment of the present invention. Figure 1 As shown, the method includes: Acquire time-series data on electricity prices, state-of-charge data of energy storage systems, and physical constraint parameters; Local extreme points of the electricity price time series data are identified, and an upper and lower price envelope are constructed based on the local extreme points and their mean is calculated. Oscillating components are iteratively removed to obtain the trend components of electricity price changes. Price peak periods are identified from the trend components, and a correspondence between the target value of state of charge and the period identifier is established in combination with the physical constraint parameters. Based on the correspondence and the power boundary constraint of the physical constraint parameter, the state of charge trajectory of the state of charge data gradually converges to the state of charge target value along the time axis, and the charging and discharging power scheduling instruction at each time is obtained; Based on the charging and discharging power scheduling instruction, the energy storage system is controlled to perform charging and discharging actions, and actual state of charge feedback data and actual market price feedback data in the energy storage system execution process are collected in real time; According to the actual state of charge feedback data and the actual market price feedback data, the state of charge deviation and the price prediction deviation at the current time are calculated, and the state of charge target value is dynamically modified by using the state of charge deviation, and the identification method of the price peak period is adaptively adjusted by using the price prediction deviation, and the charging and discharging timing optimization scheduling is completed.

[0019] In an optional embodiment, local extreme points of the power price time series data are identified, the upper envelope line and the lower envelope line of the price are constructed based on the local extreme points and the mean value is calculated, and the change trend component of the power price is obtained by iteratively stripping the oscillation component, which includes: The power price time series data is sequentially traversed, the time when the price change direction of adjacent time turns over is taken as a local extreme point, and the local extreme point is divided into a local maximum point set and a local minimum point set; The local maximum point set and the local minimum point set are respectively interpolated and connected on the time axis to construct the upper envelope line and the lower envelope line of the price; the numerical mean value of the upper envelope line and the lower envelope line of the price at each time is calculated to obtain the intermediate trend component of the current iteration period; the power price time series data and the intermediate trend component are subjected to difference operation to obtain the residual component of the current iteration period; The oscillation amplitude of the residual component is calculated, when the oscillation amplitude is higher than a preset oscillation threshold, the residual component is taken as the input data of the next iteration period, and the intermediate trend component of the next iteration period is calculated; the iteration is continued until the oscillation amplitude is lower than the preset oscillation threshold, and the intermediate trend component of the current iteration period is determined as the change trend component of the power price.

[0020] As shown in Figure 2 The method comprises: Obtaining power price time series data, which is from the historical record of the power trading market and contains power price values at different time points. For example, the hourly power price data of a certain regional day-ahead market in a month can be collected to form a time series of 720 data points.

[0021] The acquired power price time series data is traversed in time, local extreme points are identified, and from the second point of the time series data, the current time price is compared with the previous time price to determine the price change direction. Continue to traverse to the third point and subsequent points, and when the price change direction is found to be different from the previous change direction, the previous time is marked as a local extreme point. For example, if the price from the first point to the fourth point shows an upward trend, and the price from the fourth point to the fifth point decreases, then the fourth point is a local maximum point; on the contrary, if the situation changes from a decrease to an increase, then the turning point is a local minimum point.

[0022] In the identification process, all local extreme points are divided into two categories: a local maximum point set and a local minimum point set. For consecutive time points with equal prices, the following processing method can be used: if the consecutive equal points are located between an upward and a downward trend, the last equal point is marked as a local maximum point; if the consecutive equal points are located between a downward and an upward trend, the last equal point is marked as a local minimum point.

[0023] After completing the identification of local extreme points, the local maximum point set and the local minimum point set are respectively interpolated and connected to construct the upper and lower price envelope lines. The interpolation method can use cubic spline interpolation to ensure the smoothness of the connection curve. For example, assuming that the identified local maximum points are located at times t1, t3, t7, and the corresponding price values are p1, p3, p7, then the upper envelope line values at times t2, t4, t5, t6 are obtained by interpolation. Similarly, the lower envelope line is constructed.

[0024] After the envelope lines are constructed, the numerical average of the upper and lower envelope lines at each time is calculated to obtain the intermediate trend component of the current iteration period. The specific calculation method is: for time t, the intermediate trend component m(t) = (upper envelope line value u(t) + lower envelope line value l(t)) / 2.

[0025] The original power price time series data and the calculated intermediate trend component are subjected to difference operation to obtain the residual component of the current iteration period. For time t, the residual component r(t) = original price p(t) - intermediate trend component m(t).

[0026] The oscillation amplitude of the residual component is calculated to determine whether iteration needs to continue. The oscillation amplitude can be measured by the standard deviation of the residual component, that is, the standard deviation value of the residual sequence. The range (maximum value minus minimum value) or average absolute value of the residual component can also be used as a measurement indicator.

[0027] When the oscillation amplitude of the residual component is higher than a preset oscillation threshold, it indicates that the residual still contains significant fluctuation components, and iteration needs to be continued. At this time, the current residual component is taken as the input data of the next iteration period, and the steps of local extreme point identification, envelope line construction, intermediate trend component calculation, and residual component calculation are repeated. The preset oscillation threshold can be set according to the analysis requirements and data characteristics, for example, it can be set to 5% of the standard deviation of the original data.

[0028] The iteration process continues until the oscillation amplitude of the residual component is lower than the preset oscillation threshold, at which time it is considered that the residual does not contain significant fluctuation components, and the intermediate trend component of the current iteration period is determined as the change trend component of the electricity price. The final change trend component represents the main change direction of the electricity price, eliminating the influence of short-term fluctuations.

[0029] The electricity price change trend component obtained by the above method can be used for subsequent electricity market analysis, such as price trend prediction, abnormal price detection, etc. The trend component can reflect the basic change of the market, eliminate the interference of short-term fluctuations, and provide a more reliable reference for decision-making.

[0030] In an optional implementation, identifying a price peak period from the change trend component and establishing a corresponding relationship between the state of charge target value and the period identifier in combination with the physical constraint parameter includes: Identifying a continuous time interval in the change trend component where the price value exceeds the average price level and marking it as a candidate high-price period; performing a continuous duration verification on the candidate high-price period, and determining a period that satisfies the minimum charge and discharge duration requirement of the energy storage system in the physical constraint parameter as a price peak period; Setting the maximum state of charge value of the energy storage system in the physical constraint parameter as the state of charge target value corresponding to the start time of the price peak period, and assigning a discharge period identifier to the price peak period; for a transition period located between the price peak periods, performing linear interpolation on the state of charge target values corresponding to adjacent price peak periods to obtain the state of charge target value corresponding to each time of the transition period, and assigning a transition period identifier to the transition period; Summarizing the state of charge target values and period identifiers corresponding to each time of the price peak period and the transition period, organizing them into associated data records, storing the associated data records in chronological order, and forming the corresponding relationship between the state of charge target value and the period identifier.

[0031] The trend component of the electricity price is analyzed and processed to identify the price peak period. The average price level of the time series price data is calculated, which can be the arithmetic mean of the electricity price at all times within a period, such as a day, a week, or a month. The time series price data is traversed to find all consecutive time points where the price value exceeds the average price level. The time interval formed by these consecutive time points is marked as a candidate high-price period. For example, in the electricity price data of a day, if the electricity price from the 10th hour to the 14th hour is continuously higher than the average electricity price of the day, this period is marked as a candidate high-price period.

[0032] The duration of the candidate high-price period is verified. The minimum charge and discharge duration requirement of the energy storage system is obtained from the physical constraint parameters, which is usually determined by the physical characteristics of the energy storage system, such as some battery energy storage systems require at least half an hour of continuous discharge to ensure high efficiency. The duration of each candidate high-price period is checked in sequence to see if it meets the minimum requirement. If the duration of the candidate high-price period is less than the minimum charge and discharge duration, it is discarded; otherwise, it is confirmed as a price peak period. This can avoid frequent switching of the energy storage system's working state, improving system stability and lifespan.

[0033] After determining the price peak period, the correspondence between the state of charge target value and the period identifier is established. The maximum state of charge value of the energy storage system is obtained from the physical constraint parameters, which represents the maximum energy that the energy storage system can store. This maximum state of charge value is set as the state of charge target value corresponding to the start time of the price peak period. At the same time, the discharge period identifier is assigned to the price peak period, indicating that the energy storage system should perform discharge operation in this period to utilize high electricity prices to generate revenue. For example, if the maximum state of charge value of the energy storage system is 100%, and the 10th to 14th hour is a price peak period, the state of charge target value at the 10th hour is set to 100%, and the discharge period identifier is assigned to the 10th to 14th hour.

[0034] For the period between adjacent price peak periods, it is defined as a transition period. In the transition period, the state of charge target value at each time point is calculated by linear interpolation based on the state of charge target values corresponding to the adjacent price peak periods. The linear interpolation method can be represented as: the state of charge target value at the current time point is equal to the state of charge target value at the end time of the previous price peak period plus the time proportion multiplied by the difference between the state of charge target values at the start time of the adjacent two price peak periods. At the same time, the transition period identifier is assigned to the transition period, indicating that the energy storage system should adjust its charge and discharge behavior according to the actual situation in this period.

[0035] For example, assuming that the 10th hour to the 14th hour and the 18th hour to the 22nd hour are two adjacent price peak periods, the 14th hour to the 18th hour is a transition period. If the state of charge target value at the 14th hour is 60% and the state of charge target value at the 18th hour is 100%, the state of charge target value at the 16th hour (the midpoint of the transition period) is calculated by linear interpolation to be 80%.

[0036] The state of charge target values corresponding to the time points in the price peak period and the transition period and the period identifiers are summarized and organized into association data records. The structure of the association data records can include: a timestamp, a state of charge target value, and a period identifier (a discharge period identifier or a transition period identifier). These association data records are stored in chronological order to form a complete correspondence between the state of charge target values and the period identifiers. These association data records will serve as the basis for subsequent energy storage system scheduling control, guiding the energy storage system to perform corresponding charging and discharging strategies in different periods.

[0037] In this way, the energy storage system can optimize its operation strategy according to the price fluctuation law, maximize economic benefits under the guarantee of system physical constraint conditions, and provide effective peak shaving services for the power grid, realizing efficient utilization of energy storage resources.

[0038] In an optional implementation, based on the power boundary constraint of the corresponding relationship and the physical constraint parameter, the state of charge trajectory of the state of charge data gradually converges to the state of charge target value along the time axis, and the charging and discharging power scheduling instruction at each time point includes: An actual state of charge value is obtained, the state of charge target value corresponding to the current time point and the period identifier are extracted from the corresponding relationship, and a state deviation amount of the state of charge target value and the actual state of charge value is calculated; According to the state deviation amount and the time interval from the current time point to the next time point, a theoretical charging and discharging power required for the actual state of charge value to converge to the state of charge target value is calculated; The maximum charging power limit and the maximum discharging power limit of the energy storage system are obtained from the physical constraint parameter; the theoretical charging and discharging power is subjected to power boundary constraint processing, and when the absolute value of the theoretical charging and discharging power exceeds the maximum charging power limit or the maximum discharging power limit, the theoretical charging and discharging power is truncated to the corresponding power boundary value to obtain the constrained charging and discharging power at the current time point; and the constrained charging and discharging power is taken as the charging and discharging power scheduling instruction at the current time point; Based on the constrained charge-discharge power and the time interval from the current time to the next time, a predicted state of charge value at the next time is calculated, and the predicted state of charge value is updated to the state of charge data as an actual state of charge value at the next time. The iteration is repeated for subsequent times until the charge-discharge power scheduling instructions at all times within the scheduling period are generated.

[0039] An actual state of charge value is obtained, a state of charge target value corresponding to the current time and a time period identifier are extracted from the correspondence relationship, and a state deviation amount of the state of charge target value and the actual state of charge value is calculated. Specifically, the actual state of charge value of the current energy storage unit can be obtained by the battery management system, for example, the measured state of charge at a certain time is 45%. At the same time, according to the pre-established correspondence relationship between the time and the state of charge target value, the state of charge target value corresponding to the current time is extracted, which is assumed to be 50%, and the current time period identifier is determined, such as peak period, valley period or flat period. The state deviation amount is calculated as the target value minus the actual value, and in this example, the deviation amount is equal to 5%.

[0040] According to the state deviation amount and the time interval from the current time to the next time, the theoretical charge-discharge power required for the actual state of charge value to converge to the state of charge target value is calculated. In the specific implementation process, it is assumed that the time interval from the current time to the next time is 15 minutes, and the rated capacity of the energy storage system is 100 kilowatt-hours. If the deviation amount is positive, it means that charging is needed; if the deviation amount is negative, it means that discharging is needed. In the above example, the theoretical charge-discharge power is 20 kilowatts of charging power.

[0041] The maximum charging power limit and the maximum discharging power limit of the energy storage system are obtained from the physical constraint parameters, and the power boundary constraint processing is performed on the theoretical charge-discharge power. For example, the maximum charging power limit of the energy storage system is 30 kilowatts, and the maximum discharging power limit is negative 30 kilowatts. When the absolute value of the theoretical charge-discharge power exceeds the maximum charging power limit or the maximum discharging power limit, the theoretical charge-discharge power is truncated to the corresponding power boundary value to obtain the constrained charge-discharge power at the current time. The specific judgment logic is: when the theoretical power is greater than the maximum charging power limit, the constrained power is equal to the maximum charging power limit; when the theoretical power is less than the maximum discharging power limit, the constrained power is equal to the maximum discharging power limit; otherwise, the constrained power is equal to the theoretical power. In this example, the theoretical charging power 20 kilowatts does not exceed the maximum charging power limit 30 kilowatts, so the constrained charge-discharge power is still 20 kilowatts. The constrained charge-discharge power is taken as the charge-discharge power scheduling instruction at the current time, and is sent to the power control unit of the energy storage system for execution.

[0042] After the power constraint processing of the current time is completed, the predicted state of charge value of the next time is calculated based on the constrained charging and discharging power and the time interval from the current time to the next time, and the predicted state of charge value is updated to the state of charge data as the actual state of charge value of the next time. In the above example, the predicted state of charge value of the next time is 48.5% (45% plus 3.5%). This predicted value will be used as the actual state of charge value of the next time for the power scheduling calculation of the next time.

[0043] The above steps are iteratively performed for subsequent times until the charging and discharging power scheduling instructions for all times in the scheduling period are generated. The scheduling period can be one day, one week, or other time periods, depending on the specific application scenario requirements. Through this state of charge closed-loop control based scheduling method, the energy storage system can achieve smooth convergence of the state of charge according to the preset state of charge target trajectory, while meeting the physical power constraints.

[0044] In actual application scenarios, such as photovoltaic energy storage systems, the state of charge target trajectory that meets the economic requirements can be generated according to the photovoltaic power generation prediction results and the electricity load prediction results, such as charging during the photovoltaic power generation surplus period and discharging during the electricity peak period. The charging and discharging power scheduling realized by the method can make the actual operating state of the energy storage system gradually converge to the expected target, while ensuring that the physical constraints of the equipment are not violated, effectively improving the safety and economy of system operation.

[0045] In addition, when the energy storage system is composed of multiple energy storage units, different state of charge target values can be assigned according to the characteristics and states of each unit to achieve coordinated optimization at the system level. For example, a longer service life of the energy storage unit is assigned a larger charging and discharging power, and the energy storage unit close to retirement is relieved of the burden of charging and discharging, thereby prolonging the service life of the entire energy storage system.

[0046] In an optional embodiment, the dynamic correction of the state of charge target value by the state of charge deviation amount comprises: The state of charge deviation amounts of each historical time from the starting time of the scheduling period to the current time are arranged in time sequence to form a state of charge deviation amount sequence; the change rate between adjacent time state of charge deviation amounts in the state of charge deviation amount sequence is calculated, the evolution trend characteristics of the state of charge deviation amount are judged according to the positive and negative signs and the numerical value of the change rate, and the correction response strength level and response coefficient are determined according to the evolution trend characteristics; The ratio of the absolute value of the price prediction deviation amount to the historical average of the price prediction deviation amount in the scheduling period is calculated to obtain a price fluctuation relative strength index, and the price fluctuation relative strength index is nonlinearly mapped and transformed to map the price fluctuation relative strength index to a preset sensitive coefficient value interval to obtain a price fluctuation sensitive coefficient; The response coefficient corresponding to the correction response intensity level is obtained, the response coefficient is weighted and fused with the price fluctuation sensitivity coefficient to obtain a comprehensive correction intensity factor, and the comprehensive correction intensity factor is used to correct the state of charge deviation at the current time to obtain a state of charge target value correction amplitude.

[0047] The state of charge deviation amounts at each historical time from the dispatch cycle start time to the current time are arranged in time sequence. Assuming that the current time is t and the dispatch cycle start time is t0, the state of charge deviation sequence can be expressed as [ΔSOC(t0), ΔSOC(t0+1),..., ΔSOC(t)], where ΔSOC represents the difference between the actual state of charge and the target state of charge.

[0048] Next, the change rate between adjacent times in the state of charge deviation sequence is calculated. For time i, the change rate can be calculated by (ΔSOC(i) - ΔSOC(i-1)) / Δt, where Δt is the time interval between adjacent times. For example, if sampling is performed once every 5 minutes, Δt is 5 minutes.

[0049] According to the positive and negative signs and the numerical value of the change rate, the evolution trend characteristics of the state of charge deviation are determined. The evolution trend can be divided into the following cases: 1. rapid rise: the change rate is positive and greater than a preset threshold α1; 2. slow rise: the change rate is positive and less than or equal to the preset threshold α1; 3. stable: the change rate is close to zero and the absolute value is less than a preset threshold α2; 4. slow decline: the change rate is negative and the absolute value is less than or equal to a preset threshold α3; 5. rapid decline: the change rate is negative and the absolute value is greater than the preset threshold α3.

[0050] According to the identified evolution trend characteristics, the correction response intensity level and the response coefficient are determined. For example, five intensity levels can be set, corresponding to the five trend characteristics described above. For the rapid rise trend, a larger negative response coefficient should be used; for the rapid decline trend, a larger positive response coefficient should be used; for the stable state, the response coefficient can be close to zero. Specifically, a response coefficient mapping table can be preset, and each trend characteristic can be mapped to a corresponding response coefficient k1.

[0051] At the same time, the ratio of the absolute value of the price prediction deviation to the historical average of the price prediction deviation in the dispatch cycle is calculated. Assuming that the actual price at the current time is P(t) and the predicted price is P'(t), the price prediction deviation is ΔP(t) = P(t) - P'(t). The historical average of the price prediction deviation in the dispatch cycle can be expressed as AvgΔP. The price fluctuation relative intensity index can be calculated as |ΔP(t)| / AvgΔP.

[0052] A nonlinear mapping transformation is performed on the price fluctuation relative strength index, which is mapped to a preset sensitivity coefficient value interval. The sigmoid function can be used for mapping: k2= 1 / (1+e -λ×(|ΔP(t)| / AvgΔP-β) ), where λ and β are preset parameters for adjusting the shape of the mapping curve. Through this mapping, the value range of the price fluctuation sensitivity coefficient k2 is limited to the interval [0, 1].

[0053] The response coefficient k1 corresponding to the corrected response strength level is obtained, and the response coefficient k1 and the price fluctuation sensitivity coefficient k2 are weighted and fused to calculate a comprehensive correction strength factor k. The weighted fusion can be realized by k = w1×k1+ w2×k2, where w1 and w2 are preset weights, and w1+ w2= 1.

[0054] The state of charge target value correction amplitude is obtained by correcting the state of charge deviation at the current time with the comprehensive correction strength factor k. The correction amplitude can be expressed as ΔSOC_adj(t) = k × ΔSOC(t).

[0055] The state of charge target value correction amplitude is added to the state of charge target value corresponding to the current time to obtain the corrected state of charge target value. Assuming that the original target value is SOC_target(t), the corrected target value is SOC_target'(t) =SOC_target(t) + ΔSOC_adj(t).

[0056] Through the above method, the energy storage system can dynamically adjust the state of charge target value according to the real-time state of charge deviation evolution trend and the price prediction deviation during operation, improve the adaptability of the system to market price fluctuations, and ensure that the system operates according to the expected trajectory.

[0057] In an optional implementation, the method for simultaneously adjusting the identification of the price peak period by the price prediction deviation includes: The identification result of the price peak period is taken as a random variable to be inferred, and the price prediction deviation is taken as observation evidence. A prior probability distribution of the identification result of the price peak period is established, and a likelihood value is calculated. The prior probability distribution and the likelihood value are Bayes fused to obtain a posterior probability distribution. The relative entropy between the prior probability distribution and the posterior probability distribution is calculated. The maximum posterior probability value in the posterior probability distribution is calculated as the confidence value of the identification result of the price peak period. When the confidence value is lower than a preset confidence threshold and the relative entropy exceeds a preset relative entropy threshold, the weight of the prior probability distribution in the Bayes fusion calculation is reduced, and the Bayes fusion calculation is re-executed. A multi-candidate set of the price peak period is constructed based on the updated posterior probability distribution. Calculate the time period overlap between each candidate price peak period identification result in the candidate set, and identify the time when the time period overlap is lower than the overlap threshold as a low-confidence price peak period; adjust the state of charge target value for the low-confidence price peak period, and update the correspondence between the state of charge target value and the period identification based on the adjusted state of charge target value.

[0058] The identification result of the price peak period is taken as a random variable to be inferred, and the price prediction deviation is taken as observation evidence to establish a prior probability distribution of the identification result of the price peak period. The price peak period can usually be expressed as a number of time intervals in a day, such as T = {[t1_start, t1_end], [t2_start, t2_end],...}. For each time t, a binary random variable X_t is established to represent whether the time is a peak period, and the prior probability distribution can be calculated according to historical identification results, denoted as P(X_t).

[0059] At the same time, the likelihood value, i.e., the conditional probability P(e_t|X_t) of observing a specific price prediction deviation e_t, is calculated. The price prediction deviation can be obtained by the difference between the actual price and the predicted price. When historical data shows that the prediction deviation of a specific period is large, the reliability of identifying the period as a peak period will decrease.

[0060] The prior probability distribution and the likelihood value are Bayes fused to obtain the posterior probability distribution. According to Bayes' theorem, the posterior probability P(X_t|e_t) can be calculated by multiplying the prior probability P(X_t) and the likelihood P(e_t|X_t), and then dividing by the marginal probability P(e_t), so as to obtain the probability that the time t is a peak period when the price prediction deviation e_t is observed.

[0061] After Bayes fusion, the relative entropy between the prior probability distribution and the posterior probability distribution is calculated to measure the degree of distribution change brought by new information. The relative entropy, also known as KL divergence, can be used to measure the difference between two probability distributions. The larger the relative entropy, the more significant the modification of the observation evidence to the prior judgment.

[0062] At the same time, the maximum posterior probability value in the posterior probability distribution is calculated as the confidence value of the identification result of the price peak period, which reflects the reliability of the current identification result. When the confidence value is lower than a preset confidence threshold (such as 0.75) and the relative entropy exceeds a preset relative entropy threshold (such as 0.3), it means that the current identification result is not reliable enough and needs to be significantly adjusted.

[0063] In this case, the weight of the prior probability distribution in the Bayesian fusion calculation needs to be reduced, and the Bayesian fusion calculation needs to be re-executed. Specifically, a weight coefficient a (0 < a < 1) can be introduced to adjust the influence of the prior probability P(X_t) by a weight. By reducing the influence of the prior probability, the posterior probability is more affected by the current observation evidence, thereby improving the adaptability of the recognition result to the current price fluctuation.

[0064] Based on the updated posterior probability distribution, a multi-candidate set of price peak periods is constructed. All time intervals with posterior probability exceeding a certain threshold (such as 0.5) can be selected as candidate peak periods to form the set T_candidates={[t1_start, t1_end], [t2_start, t2_end],...}. The design of this multi-candidate scheme can reduce the risk brought by a single recognition result.

[0065] The time period overlap between the recognition results of each candidate price peak period in the multi-candidate set is calculated. For any two candidate periods T_i and T_j, the overlap can be calculated by the ratio of the overlapping time length to the total time length. If there is a large difference in the division of a time t in different candidate periods (i.e. low overlap), it indicates that there is uncertainty in the peak judgment at that time.

[0066] Time periods with a time period overlap below an overlap threshold (such as 0.6) are identified as low-confidence price peak periods. These periods are usually near price turning points or areas with large prediction biases, and need special treatment to reduce the risk of energy scheduling.

[0067] Adjust the state of charge target value for low-confidence price peak periods. In traditional methods, different state of charge target values are used for peak and non-peak periods, for example, a lower state of charge is expected in peak periods to discharge for profit, and a higher state of charge is maintained in non-peak periods for future use. For low-confidence periods, an intermediate state of charge target value between the two can be used, or the target value can be set proportionally according to the confidence, thereby reducing the loss caused by false recognition.

[0068] Based on the adjusted state of charge target value setting, update the correspondence between the state of charge target value and the period identification. For example, the period can be divided into "determined peak", "low-confidence peak", "low-confidence non-peak" and "determined non-peak" four categories, and different state of charge target values are set respectively, such as 20%, 40%, 60% and 80%. This fine-grained period division and target value setting can better adapt to the uncertainty brought by price prediction bias.

[0069] Through the above adaptive adjustment process, the energy storage system can dynamically adjust the price peak period identification strategy according to the price prediction deviation, improve the operation robustness and economic benefits in the price fluctuation environment. This method is especially suitable for situations where the electricity price fluctuates sharply or the performance of the price prediction model is unstable, and can effectively reduce the scheduling risk of the energy storage system.

[0070] The embodiment of the application is based on a benefit maximization energy storage charging and discharging timing optimization scheduling system, and the system comprises: A first unit is configured to acquire power price timing data, state of charge data of an energy storage system, and physical constraint parameters; A second unit is configured to identify local extreme points of the power price timing data, construct an upper envelope line and a lower envelope line of the price based on the local extreme points and perform mean value calculation, iteratively strip oscillation components to obtain a change trend component of the power price, identify a price peak period from the change trend component, and establish a corresponding relationship between a state of charge target value and a period identifier in combination with the physical constraint parameters; A third unit is configured to make the state of charge trajectory of the state of charge data gradually converge to the state of charge target value along a time axis based on the corresponding relationship and power boundary constraints of the physical constraint parameters, and obtain charging and discharging power scheduling instructions at each time point; A fourth unit is configured to control the energy storage system to perform charging and discharging actions based on the charging and discharging power scheduling instructions, and acquire actual state of charge feedback data and actual market price feedback data in a real-time manner during the execution of the energy storage system; A fifth unit is configured to calculate a state of charge deviation and a price prediction deviation at a current time point according to the actual state of charge feedback data and the actual market price feedback data, dynamically correct the state of charge target value by using the state of charge deviation, and simultaneously adaptively adjust an identification method of the price peak period by using the price prediction deviation, and complete charging and discharging timing optimization scheduling.

[0071] In a third aspect of the embodiment of the application, an electronic device is provided, comprising: a processor; a memory for storing processor-executable instructions; The processor is configured to invoke the instructions stored in the memory to execute the method described above.

[0072] In a fourth aspect of the embodiment of the application, a computer readable storage medium is provided, which stores computer program instructions, and the computer program instructions are executed by a processor to implement the method described above.

[0073] The present application can be a method, an apparatus, a system, and / or a computer program product. The computer program product can include a computer readable storage medium (or media) having computer readable program instructions thereon for performing various aspects of the present application.

[0074] Finally, it should be noted that the above-described embodiments are merely intended to illustrate the technical solutions of the present application, and are not intended to limit the present application; even though the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or equivalently replace some or all of the technical features thereof; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for optimizing scheduling of energy storage charging and discharging based on maximum revenue, characterized in that, The method comprises: acquiring power price time series data, state of charge data of an energy storage system, and physical constraint parameters; identifying local extreme points of the power price time series data, constructing an upper envelope line and a lower envelope line based on the local extreme points, and performing mean value calculation, iteratively stripping oscillation components, and acquiring a change trend component of the power price; identifying a price peak period from the change trend component, and establishing a corresponding relationship between a state of charge target value and a time period identifier in combination with the physical constraint parameters; based on the corresponding relationship and power boundary constraints of the physical constraint parameters, causing a state of charge trajectory of the state of charge data to gradually converge to the state of charge target value along a time axis, and obtaining a charging and discharging power scheduling instruction at each time; based on the charging and discharging power scheduling instruction, controlling the energy storage system to perform a charging and discharging action, and collecting actual state of charge feedback data and actual market price feedback data in a real-time manner during an execution process of the energy storage system; based on the actual state of charge feedback data and the actual market price feedback data, calculating a state of charge deviation and a price prediction deviation at a current time, and dynamically modifying the state of charge target value by using the state of charge deviation, and simultaneously adaptively adjusting an identification method of the price peak period by using the price prediction deviation, to complete charging and discharging time series optimization scheduling.

2. The method of claim 1, wherein, The method of identifying local extreme points of the power price time series data, constructing an upper envelope line and a lower envelope line based on the local extreme points, and performing mean value calculation, iteratively stripping oscillation components, and acquiring a change trend component of the power price comprises: performing time series traversal on the power price time series data, taking a time when a price change direction of adjacent time points is reversed as a local extreme point, and dividing the local extreme point into a local maximum point set and a local minimum point set; respectively performing interpolation connection on the local maximum point set and the local minimum point set on a time axis, constructing an upper envelope line and a lower envelope line, calculating numerical mean values of the upper envelope line and the lower envelope line at each time, and obtaining an intermediate trend component of a current iteration period; performing difference operation on the power price time series data and the intermediate trend component, and obtaining a residual component of the current iteration period; calculating an oscillation amplitude of the residual component, when the oscillation amplitude is higher than a preset oscillation threshold, taking the residual component as input data of a next iteration period, calculating the intermediate trend component of the next iteration period; and continuously iterating until the oscillation amplitude is lower than the preset oscillation threshold, and determining the intermediate trend component of the current iteration period as the change trend component of the power price.

3. The method of claim 1, wherein, The method of identifying a price peak period from the change trend component, and establishing a corresponding relationship between a state of charge target value and a time period identifier in combination with the physical constraint parameters comprises: identify a continuous time interval in which the price value exceeds the average price level in the change trend component, and mark it as a candidate high-price period; perform duration verification on the candidate high-price period, and determine a period that meets the minimum charging and discharging duration requirement of the energy storage system in the physical constraint parameter as a price peak period; set the maximum state of charge value of the energy storage system in the physical constraint parameter as the state of charge target value corresponding to the start time of the price peak period, and assign a discharging period identifier to the price peak period; for a transition period located between the price peak periods, linearly interpolate the state of charge target values corresponding to adjacent price peak periods to obtain the state of charge target value corresponding to each time of the transition period, and assign a transition period identifier to the transition period; aggregate the state of charge target values and period identifiers corresponding to each time of the price peak periods and the transition periods, organize them into associated data records, store the associated data records in chronological order, and form a corresponding relationship between the state of charge target values and the period identifiers.

4. The method of claim 1, wherein, Based on the corresponding relationship and the power boundary constraint of the physical constraint parameter, the state of charge trajectory of the state of charge data gradually converges to the state of charge target value along the time axis, and the charging and discharging power scheduling instruction of each time is obtained, including: obtain the actual state of charge value, extract the state of charge target value and period identifier corresponding to the current time from the corresponding relationship, and calculate the state deviation between the state of charge target value and the actual state of charge value; According to the state deviation and the time interval from the current time to the next time, calculate the theoretical charging and discharging power required for the actual state of charge value to converge to the state of charge target value; obtain the maximum charging power limit and the maximum discharging power limit of the energy storage system from the physical constraint parameter; perform power boundary constraint processing on the theoretical charging and discharging power, and when the absolute value of the theoretical charging and discharging power exceeds the maximum charging power limit or the maximum discharging power limit, truncate the theoretical charging and discharging power to the corresponding power boundary value to obtain the constrained charging and discharging power at the current time; take the constrained charging and discharging power as the charging and discharging power scheduling instruction at the current time; Based on the constrained charging and discharging power and the time interval from the current time to the next time, calculate the predicted state of charge value at the next time, and update the predicted state of charge value to the state of charge data as the actual state of charge value at the next time; repeat the iteration for subsequent times until the charging and discharging power scheduling instructions for all times in the scheduling period are generated.

5. The method of claim 1, wherein, And dynamically correct the state of charge target value using the state of charge deviation includes: arranging state of charge deviation amounts of each historical time from a dispatch cycle start time to a current time in chronological order to form a state of charge deviation amount sequence; calculating a change rate between state of charge deviation amounts of adjacent times in the state of charge deviation amount sequence, judging an evolution trend feature of the state of charge deviation amount according to a positive and negative sign and a numerical value of the change rate, and determining a correction response intensity level and a response coefficient according to the evolution trend feature; calculating a ratio of an absolute value of the price prediction deviation amount to a historical mean value of price prediction deviation amounts in a dispatch cycle to obtain a price fluctuation relative intensity index, performing nonlinear mapping transformation on the price fluctuation relative intensity index, mapping the price fluctuation relative intensity index to a preset sensitive coefficient value interval to obtain a price fluctuation sensitive coefficient; obtaining a response coefficient corresponding to the correction response intensity level, performing weighted fusion calculation on the response coefficient and the price fluctuation sensitive coefficient to obtain a comprehensive correction intensity factor, correcting the state of charge deviation amount at the current time by using the comprehensive correction intensity factor to obtain a state of charge target value correction amplitude, and superimposing the state of charge target value correction amplitude to a state of charge target value corresponding to the current time to obtain a corrected state of charge target value.

6. The method of claim 1, wherein, Meanwhile, adaptive adjustment of the price peak period identification method by using the price prediction deviation amount comprises: taking an identification result of the price peak period as a random variable to be inferred, taking the price prediction deviation amount as observation evidence, establishing a prior probability distribution of the price peak period identification result, and calculating a likelihood value; performing Bayesian fusion on the prior probability distribution and the likelihood value to obtain a posterior probability distribution; and calculating a relative entropy between the prior probability distribution and the posterior probability distribution; calculating a maximum posterior probability value in the posterior probability distribution as a confidence value of the price peak period identification result; when the confidence value is lower than a preset confidence threshold value and the relative entropy exceeds a preset relative entropy threshold value, reducing a weight of the prior probability distribution in Bayesian fusion calculation and re-executing Bayesian fusion calculation, and constructing a multi-candidate set of the price peak period based on an updated posterior probability distribution; calculating a period overlap degree between each candidate price peak period identification result in the multi-candidate set, identifying a low-confidence price peak period as a time point whose period overlap degree is lower than the overlap degree threshold value, and updating a corresponding relationship between the state of charge target value and the time point based on an adjusted state of charge target value setting.

7. A storage charging and discharging timing optimization scheduling system based on revenue maximization, for implementing the method of any one of claims 1-6, characterized in that, comprises: a first unit configured to acquire power price time series data, state of charge data of an energy storage system, and physical constraint parameters; a second unit configured to identify local extreme points of the power price time series data, construct an upper price envelope line and a lower price envelope line based on the local extreme points, and perform mean value calculation and iterative stripping of oscillation components to obtain a change trend component of the power price; identify a price peak period from the change trend component, and establish a corresponding relationship between a state of charge target value and a time point in combination with the physical constraint parameters. a third unit configured to, based on the correspondence and the power boundary constraint of the physical constraint parameter, gradually converge the state of charge trajectory of the state of charge data to the state of charge target value along a time axis to obtain a charge-discharge power scheduling instruction at each time; a fourth unit configured to control the energy storage system to perform a charge-discharge action based on the charge-discharge power scheduling instruction, and collect actual state of charge feedback data and actual market price feedback data in real time during the execution of the energy storage system; a fifth unit configured to calculate a state of charge deviation and a price prediction deviation at the current time according to the actual state of charge feedback data and the actual market price feedback data, and dynamically correct the state of charge target value by using the state of charge deviation, and simultaneously adaptively adjust the identification method of the price peak period by using the price prediction deviation, to complete the charge-discharge timing optimization scheduling.

8. An electronic device, comprising: comprise: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to execute the method of any one of claims 1 to 6.

9. A computer-readable storage medium having stored thereon computer program instructions, wherein, The computer program instructions, when executed by the processor, implement the method of any one of claims 1 to 6.

Images