An intelligent smoothing method for grid-connected controller

Abstract

The present invention discloses an intelligent smoothing method for a grid-connected controller, which relates to the field of controller smoothing technology, including real-time collection of grid data, cleaning and feature extraction of the collected data; constructing a prediction model, predicting the future grid state based on real-time grid data, formulating a smoothing strategy using a control model MPC based on the prediction result, executing controller smoothing operations, and real-time monitoring of the adjusted grid data for evaluation; and recording and storing all data. The present invention collects grid data in real time, constructs a prediction model to predict the future grid state, and uses the control model MPC to formulate a control strategy, which can respond to various situations that may occur in the grid in advance, and achieve more efficient and reliable grid operation management. The optimized control strategy not only reduces energy waste, but also improves the grid's adaptability to renewable energy and the sustainability of the overall environment.

Description

Technical Field

[0001] The invention relates to the technical field of controller smoothing, and in particular to an intelligent smoothing method for a grid-connected controller. Background Art

[0002] With the widespread application of renewable energy, the stable operation of the power grid faces unprecedented challenges. As a key technology connecting renewable energy and traditional power grids, the performance of the grid-connected controller directly affects the safety and efficiency of the entire power system. In traditional power systems, the regulation of the power grid usually relies on the central control system to adjust large generators. This method is not efficient when dealing with the high volatility and uncertainty of distributed generation and renewable energy. The development of intelligent grid-connected controller technology, especially the use of real-time data acquisition and advanced data analysis technology, has provided new solutions for the smooth operation of the power grid, including real-time monitoring of each node of the power grid through high-speed photoelectric sensors and current sensors, and the use of advanced synchronization technology Network Time Protocol NTP to ensure the timing consistency of data.

[0003] Although the existing intelligent smoothing methods have made some progress, there are still some obvious shortcomings. The data collection and processing in the existing technology often cannot be carried out in real time, which limits the response speed and accuracy of the control strategy. The existing prediction models and control algorithms often lack sufficient adaptability and flexibility, and it is difficult to effectively respond to rapidly changing grid conditions and complex power demands. Summary of the invention

[0004] In view of the problems existing in the above-mentioned existing intelligent smoothing method of the grid-connected controller, the present invention is proposed.

[0005] Therefore, the problem to be solved by the present invention is that data collection and processing in the prior art often cannot be performed in real time, which limits the response speed and accuracy of the control strategy. The existing prediction models and control algorithms often lack sufficient adaptability and flexibility, making it difficult to effectively respond to rapidly changing grid conditions and complex power demands.

[0006] To solve the above technical problems, the present invention provides the following technical solutions: an intelligent smoothing method for a grid-connected controller, which includes collecting grid data in real time, cleaning and extracting features from the collected data; building a prediction model to predict the future grid state based on the real-time grid data, formulating a smoothing strategy based on the prediction results using a control model MPC, executing controller smoothing operations, and monitoring the adjusted grid data in real time for evaluation; and recording and storing all data.

[0007] As a preferred solution of the intelligent smoothing method of the grid-connected controller of the present invention, wherein: the real-time collection of grid data refers to installing photoelectric sensors and current sensors at the entrance and exit of the grid substation, load connection points and renewable energy access points to collect grid current, voltage, frequency and temperature data in real time;

[0008] The Network Time Protocol (NTP) is used to synchronize the time of power grid data.

[0009] As a preferred solution of the intelligent smoothing method of the grid-connected controller of the present invention, wherein: the cleaning and feature extraction of the collected data refers to filling the missing data points with the average value of the adjacent points;

[0010] A standard deviation-based method was used to identify outliers. If a data point was beyond three standard deviations of the mean, it was considered an outlier and was removed.

[0011] The collected data were analyzed using wavelet transform;

[0012] Extract features from the results of wavelet transform analysis;

[0013] Convert the extracted features into feature vectors.

[0014] The construction of the prediction model to predict the future power grid state based on the real-time power grid data refers to using a convolutional neural network (CNN) to construct a power grid state prediction model, including an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer;

[0015] Normalize the feature vector v and convert it into feature map f in , and set the format of the convolutional neural network CNN input to the feature map f in form;

[0016] The feature map f in Input into the grid status prediction model;

[0017] Use convolutional layers to extract local features from feature vector data;

[0018] The pooling layer uses the maximum pooling operation to reduce the feature dimension;

[0019] The output of the pooling layer is classified through a fully connected layer;

[0020] The fully connected layer outputs the prediction result y through the output layer to obtain the predicted future state of the power grid;

[0021] The historical power grid data is used to train the model, and the cross-validation method is used to optimize the model parameters to obtain the prediction model.

[0022] The use of the control model MPC to formulate a smoothing strategy based on the prediction result refers to providing N according to the prediction result yp The grid state prediction of each time synchronization includes the grid state y at time k k ;

[0023] The grid state y k Input the control model MPC to get the output;

[0024] Define the control input u k and control constraints, the constraint range is [-50,50]MW, and the control target y is set ref,f ;

[0025] Use MPC to optimize control actions;

[0026] Define the control input sequence and update the control input u through iteration k In each step, the solver is used to calculate the control input that minimizes the error according to the optimization model, and the iteration is continued until the preset convergence condition is reached. After the final iteration, the optimal control input u is obtained. k , and converted into actual grid-connected controller operation instructions to build a control smoothing strategy.

[0027] The execution controller smooth operation refers to sending the control strategy to the corresponding execution device through the integrated automation system SCADA system;

[0028] The time synchronization of control data is performed at each control node to implement specific controller smoothing operation commands.

[0029] The real-time monitoring and evaluation of the adjusted power grid data refers to re-collecting real-time data from the SCADA system and sensors;

[0030] Use synchronization technology to synchronize the collected data time and pre-process the collected real-time data;

[0031] Evaluate the actual operation status of the power grid through the collected real-time data, statistical analysis and power grid status prediction model;

[0032] Based on the results of the performance evaluation, data analysis tools are used to analyze the deviations in the control strategy, adjust the parameters of the control model, and modify the weight factor λ.

[0033] As a preferred solution of the intelligent smoothing method of the grid-connected controller described in the present invention, the recording and storage of all data refers to recording sensor equipment data, preprocessing data, feature vectors, prediction model outputs, control decisions and operation data, system performance evaluation data, communication and instruction data, as well as adjustment coefficients and parameters, and using the distributed database system Apache Cassandra for storage.

[0034] A computer device comprises: a memory and a processor; the memory stores a computer program, and the processor implements the steps of the above-mentioned grid-connected controller intelligent smoothing method when executing the computer program.

[0035] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned intelligent smoothing method of a grid-connected controller.

[0036] The beneficial effects of the present invention are as follows: the present invention collects power grid data in real time, constructs a prediction model to predict the future power grid state, and uses the control model MPC to formulate a control strategy, so as to be able to respond in advance to various situations that may occur in the power grid and achieve more efficient and reliable power grid operation management. The optimized control strategy not only reduces energy waste, but also improves the adaptability of the power grid to renewable energy and the sustainability of the overall environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0038] Figure 1 It is a flow chart of the intelligent smoothing method of the grid-connected controller.

[0039] Figure 2 It is a structural diagram of the intelligent smoothing method of the grid-connected controller. DETAILED DESCRIPTION

[0040] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0041] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0042] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor is it a separate or selective embodiment that is mutually exclusive with other embodiments.

[0043] Example 1

[0044] Reference Figure 1 and Figure 2 , which is the first embodiment of the present invention, and which provides an intelligent smoothing method for a grid-connected controller, the intelligent smoothing method for a grid-connected controller comprising:

[0045] S1. Collect power grid data in real time, and clean and extract features from the collected data;

[0046] Specifically, real-time collection of grid data refers to installing photoelectric sensors and current sensors at the entrances and exits of grid substations, load connection points, and renewable energy access points to collect grid current, voltage, frequency, and temperature data in real time;

[0047] The Network Time Protocol (NTP) is used to synchronize the time of power grid data.

[0048] By collecting sensor data in real time, it is possible to instantly identify possible problems in the power grid, such as overload, abnormal frequency or equipment overheating, which helps to adjust the control strategy in time, prevent accidents and ensure the safety and stability of power grid operation. Sensors installed at renewable energy access points can monitor the output of these energy sources in real time, and optimize the distribution and use of energy in combination with the overall needs and status of the power grid. The collected real-time data can be used to support more complex data analysis and prediction models. Real-time data collection synchronized by NTP can more accurately locate the time and location of the fault, making the fault response more rapid and accurate. It is crucial to quickly restore the normal operation of the power grid and minimize the impact of the fault.

[0049] Furthermore, cleaning and extracting features from the collected data means filling the missing data points with the average value of the adjacent points;

[0050] A standard deviation-based method was used to identify outliers. If a data point was beyond three standard deviations of the mean, it was considered an outlier and was removed.

[0051] The collected data is analyzed using wavelet transform, and the formula is:

[0052]

[0053] Where x(t) is the collected data, ψ is the wavelet function, a is the scale parameter, b is the displacement parameter, W(a,b) is the transformation result, and t is the time variable;

[0054] The features are extracted from the results of wavelet transform analysis. The formula is:

[0055] E=∫|W(a,b)| 2 ab

[0056] P = max(W(a,b)|)

[0057]

[0058] Where E is the energy density, P is the spectrum peak, C is the spectrum center, r i For the displacement b i The modulus of the wavelet transform under , H is the total number of data points; , the energy-weighted average frequency, provides the center frequency information of the signal energy distribution;

[0059] The extracted features are converted into feature vectors using the formula:

[0060] v=[E,P,C]

[0061] Where v is the eigenvector.

[0062] Through precise data cleaning and advanced feature extraction methods, the accuracy of grid status monitoring and future behavior prediction can be significantly improved, which is conducive to timely adjustment and optimization of grid operation. Accurate data analysis and feature extraction can not only improve the operating conditions of the grid, but also optimize energy distribution and load management by predicting future grid behavior, which can greatly improve the operating efficiency of the grid, reduce energy waste, and increase the utilization rate of renewable energy. By integrating advanced signal processing technology wavelet transform and machine learning models, the present invention can support more complex and efficient grid management strategies, including prediction-based load adjustment, automatic fault detection and response, and optimized maintenance and operation decisions.

[0063] S2, build a prediction model to predict the future grid state based on real-time grid data, use the control model MPC to formulate a smoothing strategy based on the prediction results, perform controller smoothing operations, and monitor the adjusted grid data in real time for evaluation;

[0064] Specifically, building a prediction model to predict the future power grid state based on real-time power grid data refers to using a convolutional neural network (CNN) to build a power grid state prediction model, including an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer;

[0065] Normalize the feature vector v and convert it into feature map f in , and set the format of the convolutional neural network CNN input to the feature map f in form;

[0066] The feature map f in Input into the grid status prediction model;

[0067] Use the convolutional layer to extract local features in the feature vector data. The formula is:

[0068] f out =ReLU(BatchNorm(W c *f in +dc ))

[0069] where f out and f in is the feature map of the output and input of the convolutional layer, W c is the weight of the convolution kernel, d c is the bias term, * is the convolution operation, and BatchNorm is batch normalization;

[0070] The pooling layer uses the maximum pooling operation to reduce the feature dimension;

[0071] The output of the pooling layer is classified through the fully connected layer, the formula is:

[0072] y=σ(W j X+d j )

[0073] Where y is the prediction result of the network, X is the output of the pooling layer, σ is the activation function, and W j is the weight of the fully connected layer, d j is the bias term of the fully connected layer;

[0074] The fully connected layer outputs the prediction result y through the output layer to obtain the predicted future state of the power grid;

[0075] The historical power grid data is used to train the model, and the cross-validation method is used to optimize the model parameters to obtain the prediction model.

[0076] Using CNN for feature extraction and pattern recognition can significantly improve the accuracy of grid status prediction, which is crucial for real-time grid management and prevention of grid failures. Accurate prediction can help grid operators allocate resources more efficiently and optimize energy consumption, especially with the increasing use of renewable energy, to ensure stable and efficient grid operation. By continuously monitoring the grid status and predicting potential problem areas, CNN models can help operators take measures in advance to prevent failures, reduce power outages and related economic losses, and promote the development of grid automation and intelligence.

[0077] Furthermore, the smoothing strategy is formulated based on the prediction result using the control model MPC, which means providing N according to the prediction result y. p The grid state prediction of each time synchronization includes the grid state y at time k k ;

[0078] The grid state y k Input the control model MPC to get the output;

[0079] Define the control input u k and control constraints, the constraint range is [-50,50]MW, and the control target y is set ref,f,The additional power adjustment at time k is made by starting the backup power supply and adjusting the output of the main generator sets. The target power demand at time step k is obtained based on historical data and weather forecast prediction;

[0080] Use MPC to optimize control actions, minimize the difference between the future predicted state and the target state, and control the smoothness of the operation. The formula is:

[0081]

[0082] Among them U * is the error, y k is the predicted state of the power grid at time k, r k is the target state at time k, u k is the control input at time k, λ is the weight factor, N s is the forecast time range, N g The time frame for control;

[0083] Define the control input sequence and update the control input u through iteration k In each step, the solver is used to calculate the control input that minimizes the error according to the optimization model. The iteration continues until the preset convergence condition is reached or the calculation of all time steps is completed. After the final iteration, the optimal control input u is obtained. k , and converted into actual grid-connected controller operation instructions to build a control smoothing strategy.

[0084] u k Refers to the control action that the grid controller needs to perform within a specific time k, according to the input u k Formulate specific control strategies and convert the quantified control strategies into control commands that can be automatically recognized and executed by the grid-connected controller. *In minimizing the difference between the future predicted state and the target state, while taking into account the cost of the control input, reflecting the intention to make the grid state as close to the target state as possible and the control action as smooth as possible, using MPC to formulate control strategies based on real-time data and prediction results can significantly improve the response speed and flexibility of the grid. The strategy allows grid operators to respond in advance and optimize the performance of the grid, especially in the case of large demand fluctuations or unstable renewable energy output. By setting the constraint range of the control input, it can ensure that the grid operates under safe and effective conditions. This control not only helps to avoid excessive load, but also prevents equipment damage caused by extreme operations. MPC ensures the smoothness and efficiency of grid operation by minimizing the difference between control actions and target states. The optimization of control strategies takes into account a variety of factors, including energy costs, system safety, environmental impact and reliability, and converts the optimal control actions calculated by MPC into actual operating instructions. As the grid state and external conditions change, MPC can dynamically adjust the control strategy to respond to changes in the market, climate and demand. This flexibility is difficult to achieve with traditional control methods. It provides a powerful tool for modern grid management to adapt to rapidly changing energy landscapes.

[0085] Furthermore, the smooth operation of the execution controller refers to sending the control strategy to the corresponding execution device through the integrated automation system SCADA system;

[0086] The time synchronization of control data is performed at each control node to implement specific controller smoothing operation commands.

[0087] Using the SCADA system to execute control strategies can significantly improve the accuracy and reliability of power grid operations. The automated system reduces problems caused by human operational errors and ensures the stable operation of the power grid. The real-time monitoring function of the SCADA system enables power grid operators to instantly detect any anomalies or faults in the system and respond quickly, which not only improves the security of the power grid but also reduces potential economic losses. Through precise time synchronization and automated control execution, power grid managers can more effectively dispatch energy and optimize the balance between power supply and demand. Optimization helps to improve energy utilization efficiency, reduce operating costs, and support the integration of sustainable energy. The present invention supports the development of smart grid technology and provides strong technical support for future power grid technologies such as demand response, distributed generation, and power quality management through high automation and precise control.

[0088] Specifically, real-time monitoring of adjusted power grid data for evaluation refers to re-collecting real-time data from SCADA systems and sensors;

[0089] Use synchronization technology to synchronize the collected data time and pre-process the collected real-time data;

[0090] Evaluate the actual operation status of the power grid through the collected real-time data, statistical analysis and power grid status prediction model:

[0091]

[0092] Among them, p is the result of the pre-evaluation, T is the total number of time points in the evaluation period, is the prediction result, y q for actual results;

[0093] Based on the results of the performance evaluation, data analysis tools are used to analyze the deviations in the control strategy, adjust the parameters of the control model, and modify the weight factor λ.

[0094] Use data analysis tools and data visualization tools to analyze the deviations in the control strategy in detail, compare the predicted values ​​with the actual values ​​graphically, identify areas or time points with large deviations, and explore possible causes of the deviations. According to the results of performance evaluation and deviation analysis, adjust the parameters of the control model and modify the weight factor λ of the model. Use SCADA systems and sensors to collect data in real time so that grid operators can instantly obtain grid status and respond quickly to potential problems. Data synchronization ensures that all data points are aligned in time to avoid analysis errors caused by time misalignment. Preprocessing further cleans up the data and improves the accuracy of the analysis. Statistical methods and machine learning models can be used to deeply understand the meaning of grid data, identify patterns and trends, and predict grid behavior. According to the results of performance evaluation, the parameters of the control model can be adjusted, such as modifying the weight factor, to optimize the response and stability of the grid.

[0095] S3, record and store all data;

[0096] Furthermore, recording and storing all data means recording sensor device data, preprocessing data, feature vectors, prediction model outputs, control decisions and operation data, system performance evaluation data, communication and instruction data, and adjustment coefficients and parameters, and storing them using the distributed database system Apache Cassandra.

[0097] By systematically storing and managing various types of data on the power grid, the present invention can support more complex data analysis and machine learning applications, and provide data support for the intelligent management of the power grid. With efficient data processing and storage capabilities, operators can monitor the performance of the power grid in real time and make rapid data-based decisions, thereby improving the response speed and operating efficiency of the power grid. Systematically collecting and analyzing power grid data can help identify operational problems and potential improvement points, thereby optimizing control strategies and operation and maintenance plans.

[0098] Example 2

[0099] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0100] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0101] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0102] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

Claims

1. An intelligent smoothing method for a grid-connected controller, characterized in that: include, Collect power grid data in real time, clean and extract features from the collected data; Build a prediction model to predict the future grid state based on real-time grid data, use the control model MPC to formulate a smoothing strategy based on the prediction results, perform controller smoothing operations, and monitor the adjusted grid data in real time for evaluation; Record and store all data; The real-time collection of grid data refers to installing photoelectric sensors and current sensors at the entrances and exits of grid substations, load connection points and renewable energy access points to collect grid current, voltage, frequency and temperature data in real time; Use the Network Time Protocol (NTP) to synchronize the power grid data; The cleaning and feature extraction of the collected data refers to filling the missing data points with the average value of the adjacent points; A standard deviation-based method was used to identify outliers. If a data point was beyond three standard deviations of the mean, it was considered an outlier and was removed. The collected data were analyzed using wavelet transform; Extract features from the results of wavelet transform analysis; Convert the extracted features into feature vectors; The construction of the prediction model to predict the future power grid state based on the real-time power grid data refers to using a convolutional neural network (CNN) to construct a power grid state prediction model, including an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer; Normalize the feature vector and convert it into a feature map , and set the format of the convolutional neural network CNN input to the feature map form; The feature map Input into the grid status prediction model; Use convolutional layers to extract local features from feature vector data; The pooling layer uses the maximum pooling operation to reduce the feature dimension; The output of the pooling layer is classified through a fully connected layer; The fully connected layer outputs the prediction results through the output layer to obtain the predicted future power grid state; Use historical power grid data to train the model and use cross-validation method to optimize model parameters to obtain a prediction model; The use of the control model MPC to formulate a smoothing strategy based on the prediction results refers to providing The grid state prediction of time synchronization includes the grid state at time k ; The grid status Input the control model MPC to get the output; Defining Control Inputs and control constraints, the constraint range is [−50,50] MW, and the control target is set ; Use MPC to optimize control actions; Define the control input sequence and update the control input through iteration In each step, the solver is used to calculate the control input that minimizes the error according to the optimization model, and the iteration continues until the preset convergence condition is reached. After the final iteration, the optimal control input is obtained. , and convert it into actual grid-connected controller operation instructions to build a control smoothing strategy; The execution controller smooth operation refers to sending the control strategy to the corresponding execution device through the integrated automation system SCADA system; Implement specific controller smoothing operation commands by performing time synchronization of control data at each control node; The real-time monitoring and evaluation of the adjusted power grid data refers to re-collecting real-time data from the SCADA system and sensors; Use synchronization technology to synchronize the collected data time and pre-process the collected real-time data; Evaluate the actual operation status of the power grid through the collected real-time data, statistical analysis and power grid status prediction model; Based on the results of the performance evaluation, use data analysis tools to analyze the deviations in the control strategy, adjust the parameters of the control model, and modify the weighting factors .

2. The intelligent smoothing method of the grid-connected controller according to claim 1, characterized in that: The recording and storing of all data refers to recording sensor device data, preprocessing data, feature vectors, prediction model outputs, control decisions and operation data, system performance evaluation data, communication and instruction data, and adjustment coefficients and parameters, and storing them using the distributed database system Apache Cassandra.

3. A computer device comprising: Memory and processor; The memory stores a computer program, characterized in that: when the processor executes the computer program, the steps of the intelligent smoothing method of the grid-connected controller described in any one of claims 1 to 2 are implemented.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the intelligent smoothing method of the grid-connected controller according to any one of claims 1 to 2 are implemented.

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