Distributed predictive control method and system for alternating-current and direct-current hybrid microgrid
By employing a distributed predictive control method in AC/DC hybrid microgrids, and utilizing data exchange and dynamic consistency observation between devices to construct a predictive model and cost function, the problems of high computational burden and high failure risk in existing technologies are solved, and the overall optimal control of AC/DC hybrid systems is achieved.
Patent Information
- Application Number
- CN202410787273.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-06-18
- Publication Date
- 2026-02-06
AI Technical Summary
Existing microgrid cluster control suffers from problems such as high computational burden, high failure risk, and inability to achieve global optimization in AC/DC hybrid systems, resulting in poor control performance.
A distributed predictive control method for AC/DC hybrid microgrids is adopted. Data is exchanged through communication connections between devices, and a predictive model and cost function are constructed using dynamic consistent observations to achieve distributed control, reduce computational load and avoid single-point failures, and achieve overall optimization of the AC/DC hybrid system.
It achieves distributed control with low computational load and no risk of single point of failure, and can quickly respond to and optimize AC/DC hybrid systems to improve control performance.
Smart Images

Figure CN121485178A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of microgrid control, and particularly relates to a distributed predictive control method and system for AC / DC hybrid microgrids. Background Technology
[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.
[0003] In AC / DC hybrid microgrids, a grid-type equipment cluster is composed of adjustable grid-type devices such as energy storage, new energy power generation units, and flexible loads. Grid-type converters have received widespread attention in recent years due to their capabilities in grid voltage and frequency regulation, damping and inertia support, and passive or weak grid black start. Energy storage, new energy power generation units, and flexible loads are connected to the grid-type converter to form grid-type equipment. Numerous grid-type devices form a grid-type equipment cluster (hereinafter referred to as "cluster"). The microgrid cluster controller provides voltage and frequency references to the cluster in real time, achieving optimal power control while ensuring that the grid voltage and frequency are equal to the given values.
[0004] Microgrid cluster control architectures are divided into two categories: centralized and distributed.
[0005] Centralized control employs a single centralized controller that collects real-time operating status information from all devices in the cluster and transmits this information to a precise system model. Based on the system model, optimization calculations are performed to determine the optimal control commands, which are then distributed to each device in the cluster. This approach requires complete device operating information and a precise system model, and suffers from problems such as high computational burden on large systems and significant risks associated with single-point failures.
[0006] Distributed control employs distributed controllers, meaning each device receives control commands from a separate controller. Traditional distributed control is mainly divided into master-slave control and peer-to-peer control. Master-slave control includes one master controller and several slave controllers. The master controller issues control commands, and the slave controllers track the master controller's commands. Master-slave control also carries the risk of system paralysis due to the failure of the master controller. In peer-to-peer control, each controller has equal status and issues control commands independently. However, the peer controllers in traditional DC microgrids and AC microgrids are designed separately. This means that DC and AC systems can achieve optimal performance individually, but cannot achieve optimal performance for hybrid systems.
[0007] Therefore, existing microgrid cluster control suffers from problems such as high computational burden, high failure risk, and inability to achieve global optimization of AC / DC hybrid systems, resulting in poor control performance. Summary of the Invention
[0008] To overcome the shortcomings of the prior art, this invention provides a distributed predictive control method and system for AC / DC hybrid microgrids. It belongs to peer control and has the advantages of low computational load and no single-point failure risk. Moreover, compared with traditional peer control, it can achieve overall optimization of AC / DC hybrid systems.
[0009] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:
[0010] The first aspect of this invention provides a distributed predictive control method for AC / DC hybrid microgrids.
[0011] A distributed predictive control method for AC / DC hybrid microgrids includes:
[0012] Acquire local values of the device to be controlled and observation values of neighboring devices, which are divided into two types: AC devices and DC devices;
[0013] By using the local values of the device under control and the observation values of neighboring devices, dynamic consistency observation is performed to obtain the observation value formula for the device under control.
[0014] Based on the observed value formula, a prediction model and cost function are constructed;
[0015] With the goal of minimizing cost, the prediction model is optimized and solved to obtain the optimal control variables, which are then used for distributed control of the equipment.
[0016] The local values include the voltage and power of DC equipment and the power of AC equipment, and the observed values include the average DC voltage observation value, the average constant power consumption incremental rate observation value, and the average constant power consumption incremental rate observation value of AC equipment.
[0017] Furthermore, the AC / DC hybrid microgrid includes an AC microgrid and a DC microgrid, each consisting of a number of AC devices and a number of DC devices, which communicate with each other through a communication network.
[0018] Furthermore, the neighboring device is a device that communicates with the device to be controlled, including DC neighboring devices and AC neighboring devices.
[0019] Furthermore, the dynamic consistency observation is divided into two observation methods based on the device type of the device to be controlled:
[0020] If the device to be controlled is a DC device, then the average DC voltage observation value formula is constructed using the average DC voltage observation value of all neighboring DC devices and the voltage of the device to be controlled. The average equal power consumption incremental rate observation value formula is constructed using the average equal power consumption incremental rate observation value of all neighboring devices and the power of the device to be controlled.
[0021] If the device to be controlled is an AC device, then the formula for the average constant power consumption incremental rate is constructed using the average constant power consumption incremental rate observations of all neighboring devices and the power of the device to be controlled.
[0022] Furthermore, the prediction model is divided into two types based on the type of equipment to be controlled;
[0023] The prediction model for the DC equipment is:
[0024]
[0025] Where x(k) represents the value of variable x at time k. R is the setpoint for the second-level control in the droop control at time k. vi U is the droop coefficient. i (k) is a control variable;
[0026] The prediction model for the AC equipment is:
[0027]
[0028] in, This is the setpoint for the second-level control in the droop control at time k.
[0029] Furthermore, the cost function of the DC device is:
[0030]
[0031] in, λ is the reference value for the average voltage. dc These are the weighting coefficients.
[0032] The cost function of the AC device is:
[0033]
[0034] Where, ω * λ is the reference value for the power grid frequency. ac These are the weighting coefficients.
[0035] Furthermore, it also includes: after obtaining the optimal control variables, calculating the voltage reference value of the DC equipment or the frequency reference value of the AC equipment using the corresponding droop control formula according to the equipment type of the equipment to be controlled, for optimal control of the equipment.
[0036] A second aspect of the present invention provides a distributed predictive control system for an AC / DC hybrid microgrid.
[0037] A distributed predictive control system for an AC / DC hybrid microgrid includes:
[0038] The acquisition module is configured to acquire local values of the device to be controlled and observed values of neighboring devices, wherein the devices are divided into two types: AC devices and DC devices;
[0039] The observation module is configured to perform dynamic consistency observation using the local values of the device under control and the observation values of neighboring devices to obtain the observation value formula of the device under control.
[0040] The building module is configured to: build a prediction model and cost function based on the observed value formula;
[0041] The solution module is configured to optimize the prediction model with the goal of minimizing cost, obtain the optimal control variables, and use them for distributed control of the equipment.
[0042] The local values include the voltage and power of DC equipment and the power of AC equipment, and the observed values include the average DC voltage observation value, the average constant power consumption incremental rate observation value, and the average constant power consumption incremental rate observation value of AC equipment.
[0043] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of a distributed predictive control method for an AC / DC hybrid microgrid as described in the first aspect of the present invention.
[0044] The fourth aspect of the present invention provides an electronic device including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of a distributed predictive control method for an AC / DC hybrid microgrid as described in the first aspect of the present invention.
[0045] The above one or more technical solutions have the following beneficial effects:
[0046] This invention utilizes the communication connection between devices in an AC / DC hybrid microgrid to exchange data between adjacent devices, obtaining the average DC voltage observation value, the average incremental rate of equal power consumption observation value, and the average incremental rate of equal power consumption observation value of AC neighbor devices. Through dynamic consistency observation, the data of different types of neighbor devices are fused to obtain the observation formula of the device to be controlled, and then construct the prediction model and cost function of the hybrid system.
[0047] This invention adopts a distributed architecture, which has low computational cost and no risk of single point of failure. Compared with traditional distributed microgrid control, the proposed method can achieve overall optimization of AC / DC hybrid systems and has a fast response speed.
[0048] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0049] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0050] Figure 1 This is a flowchart of the method in the first embodiment.
[0051] Figure 2 This is a diagram of the AC / DC hybrid microgrid structure of the first embodiment.
[0052] Figure 3 This is a control block diagram of the DC microgrid network-type equipment in the first embodiment.
[0053] Figure 4 This is a control block diagram of the first embodiment of the AC microgrid network-type equipment. Detailed Implementation
[0054] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0055] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0056] Example 1
[0057] One embodiment of this disclosure provides a distributed predictive control method for an AC / DC hybrid microgrid. The AC / DC hybrid microgrid includes an AC microgrid and a DC microgrid, each composed of several AC devices and several DC devices, which communicate with each other via a communication network. Figure 1 As shown, it includes the following steps:
[0058] Step S1: Obtain the local value of the device to be controlled and the observation value of the neighboring devices. The devices are divided into two types: AC devices and DC devices.
[0059] The local values include the voltage and power of DC equipment and the power of AC equipment, and the observed values include the average DC voltage observation value, the average constant power consumption incremental rate observation value, and the average constant power consumption incremental rate observation value of AC equipment.
[0060] Furthermore, the neighboring device is a device that communicates with the device to be controlled, including DC neighboring devices and AC neighboring devices.
[0061] Step S2: Using the local values of the device to be controlled and the observation values of neighboring devices, perform dynamic consistency observations to obtain the observation value formula for the device to be controlled.
[0062] Furthermore, the dynamic consistency observation is divided into two observation methods based on the device type of the device to be controlled:
[0063] If the device to be controlled is a DC device, then the average DC voltage observation value formula is constructed using the average DC voltage observation value of all neighboring DC devices and the voltage of the device to be controlled. The average equal power consumption incremental rate observation value formula is constructed using the average equal power consumption incremental rate observation value of all neighboring devices and the power of the device to be controlled.
[0064] If the device to be controlled is an AC device, then the formula for the average constant power consumption incremental rate is constructed using the average constant power consumption incremental rate observations of all neighboring devices and the power of the device to be controlled.
[0065] Step S3: Based on the observed value formula, construct the prediction model and cost function.
[0066] Furthermore, the prediction model is divided into two types based on the type of equipment to be controlled;
[0067] The prediction model for the DC equipment is:
[0068]
[0069] Where x(k) represents the value of variable x at time k. R is the setpoint for the second-level control in the droop control at time k. vi U is the droop coefficient. i (k) is a control variable;
[0070] The prediction model for the AC equipment is:
[0071]
[0072] in, This is the setpoint for the second-level control in the droop control at time k.
[0073] Furthermore, the cost function of the DC device is:
[0074]
[0075] in, λ is the reference value for the average voltage. dc These are the weighting coefficients.
[0076] The cost function of the AC device is:
[0077]
[0078] Where, ω * λ is the reference value for the power grid frequency. ac These are the weighting coefficients.
[0079] Step S4: With the goal of minimizing cost, optimize the prediction model to obtain the optimal control variables, which are then used for distributed control of the equipment.
[0080] Furthermore, it also includes: after obtaining the optimal control variables, calculating the voltage reference value of the DC equipment or the frequency reference value of the AC equipment using the corresponding droop control formula according to the equipment type of the equipment to be controlled, for optimal control of the equipment.
[0081] This embodiment focuses on a cluster of grid-type equipment in a hybrid AC / DC microgrid, consisting of adjustable grid-type devices such as energy storage, new energy power generation units, and flexible loads. It involves two types of equipment: AC microgrid grid-type equipment (i.e., AC equipment) and DC microgrid grid-type equipment (i.e., DC equipment).
[0082] The following section provides a detailed explanation of the implementation process of a distributed predictive control method for an AC / DC hybrid microgrid, focusing on the structure of the AC / DC hybrid microgrid, the control of grid-type equipment in the DC microgrid, and the control of grid-type equipment in the AC microgrid.
[0083] I. AC / DC Hybrid Microgrid Structure
[0084] The AC / DC hybrid microgrid has the following structure: Figure 2 As shown, the system includes two subsystems: an AC microgrid and a DC microgrid. These two subsystems are connected via interconnecting converters to achieve energy exchange. Communication exists between the clusters of the two subsystems. For the i-th device in the AC / DC hybrid system (denoted as device i), the cluster of devices communicating with it is denoted as... Device j (which communicates with device i) ), is defined as a neighbor of device i.
[0085] Specifically, device i's DC device neighbor j sends the average DC voltage observation value to device i via the communication bus. and the observed value of the incremental rate of average consumption Device i's neighbor j sends the average constant power consumption incremental rate observation to device i via the communication bus. This allows us to obtain the observations from neighboring devices.
[0086] II. Control of DC Microgrid Grid-type Equipment
[0087] The control block diagram of DC microgrid network equipment is as follows: Figure 3 As shown, taking DC device i as the controlled object, the process is divided into three steps:
[0088] Step 1: Dynamic Consistency Observation
[0089] Dynamic consistency monitoring of DC grid-type equipment includes average voltage monitoring and equal power incremental rate monitoring.
[0090] The formula for average voltage observation is:
[0091]
[0092] in, The average voltage observations for devices i and j are given by v. i For the DC voltage of device i measured locally, m i As an intermediate variable, For m i The first derivative, a ij N is a positive real number. i A device cluster consisting of devices that communicate with device i, i.e., neighboring devices.
[0093] Because the AC equipment only transmits the average constant loss incremental rate observation value, and not the average DC voltage observation value, therefore, N here... i It is a cluster consisting of all DC device neighbors, excluding AC device neighbors.
[0094] The formula for observing the incremental rate of equal power is:
[0095]
[0096] in, γ represents the observed incremental rate of average constant consumption for equipment i and equipment j, respectively. i For the constant power incremental rate of device i measured locally, q i As an intermediate variable, For q i The first derivative, b ij N is a positive real number. i A device cluster consisting of devices that communicate with device i, i.e., neighboring devices.
[0097] Because both DC and AC equipment transmit observations of the average constant power consumption incremental rate, N here... i It is a cluster consisting of all DC device neighbors and all AC device neighbors.
[0098] The constant power incremental rate γ of device ii The specific calculation formula is as follows:
[0099]
[0100] For the instantaneous power p of local device i i The calculation formula is:
[0101] p i =v id i id +v iq i iq (4)
[0102] Where f is the local equipment consumption cost function, which is defined independently by the grid operator based on parameters such as equipment losses, power generation costs, and carbon emissions; the independent variables are instantaneous power p and v. id v iq i id i iq These represent the local device output voltage V. i Output current i i The d-axis and q-axis components.
[0103] Where f is the local equipment consumption cost function, and the independent variable is the instantaneous power p, which is defined by the grid operator based on parameters such as equipment loss, power generation cost, and carbon emissions.
[0104] Step 2: Distributed predictive control of AC / DC hybrid microgrids
[0105] First, establish a prediction model for DC device i:
[0106]
[0107] Where x(k) represents the value of variable x at time k (the current time). R is the setpoint for the second-level control in the droop control at time k (see step 3). vi U is the droop coefficient. i (k) is a control variable.
[0108] Secondly, construct the cost function:
[0109]
[0110] in, λ is the reference value for the average voltage. dc These are the weighting coefficients (positive real numbers).
[0111] Under the premise of satisfying (5), find the optimal control variable u that minimizes (6). * =u i (k).
[0112] Step 3: DC droop control
[0113] u * Acting on Then, according to the DC droop control formula:
[0114]
[0115] Give the voltage reference value for device i.
[0116] III. Control of AC Microgrid Grid-type Equipment
[0117] The control block diagram of AC microgrid network equipment is as follows: Figure 3 As shown, AC device i is the control pair
[0118] The process of observing elephants involves three steps:
[0119] Step 1: Dynamic Consistency Observation
[0120] Dynamic consistency observation of AC grid-type equipment is conducted using equal power incremental rate observation.
[0121] The formula for observing the incremental rate of equal power is:
[0122]
[0123] in, γ represents the observed incremental rate of average constant consumption for equipment i and equipment j, respectively. i For the constant power incremental rate of device i measured locally, q i As an intermediate variable, For q i The first derivative, b ij N is a positive real number. i A device cluster consisting of devices that communicate with device i, i.e., neighboring devices.
[0124] Because both DC and AC equipment transmit observations of the average constant power consumption incremental rate, N here... i It is a cluster consisting of all DC device neighbors and all AC device neighbors.
[0125] The constant power incremental rate γ of device i i The specific calculation formula is as follows:
[0126]
[0127] For the instantaneous power p of local device i i The calculation formula is:
[0128] p i =vid i id +v iq i iq (10)
[0129] Where f is the local equipment consumption cost function, which is defined independently by the grid operator based on parameters such as equipment losses, power generation costs, and carbon emissions; the independent variables are instantaneous power p and v. id v iq i id i iq These represent the local device output voltage V. i Output current i i The d-axis and q-axis components.
[0130] Step 2: Distributed predictive control of AC / DC hybrid microgrids
[0131] First, establish a prediction model for AC device i:
[0132]
[0133] in, R is the setpoint for the second-level control in the droop control at the current moment (see step 3). vi U is the droop coefficient. i (k) is a control variable.
[0134] Secondly, construct the cost function:
[0135]
[0136] Where, ω * λ is the reference value for the power grid frequency. ac These are the weighting coefficients (positive real numbers).
[0137] Under the premise of satisfying (11), find the optimal control variable u that minimizes (12). * =u i (k).
[0138] Step 3: Controlling sagging
[0139] u * Acting on Then, according to the AC droop control formula:
[0140]
[0141] Give the frequency reference value of device i .
[0142] Example 2
[0143] One embodiment of this disclosure provides a distributed predictive control system for an AC / DC hybrid microgrid, comprising:
[0144] The acquisition module is configured to acquire local values of the device to be controlled and observed values of neighboring devices, wherein the devices are divided into two types: AC devices and DC devices;
[0145] The observation module is configured to perform dynamic consistency observation using the local values of the device under control and the observation values of neighboring devices to obtain the observation value formula of the device under control.
[0146] The building module is configured to: build a prediction model and cost function based on the observed value formula;
[0147] The solution module is configured to optimize the prediction model with the goal of minimizing cost, obtain the optimal control variables, and use them for distributed control of the equipment.
[0148] The local values include the voltage and power of DC equipment and the power of AC equipment, and the observed values include the average DC voltage observation value, the average constant power consumption incremental rate observation value, and the average constant power consumption incremental rate observation value of AC equipment.
[0149] Example 3
[0150] The purpose of this embodiment is to provide a computer-readable storage medium.
[0151] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a distributed predictive control method for an AC / DC hybrid microgrid as described in Embodiment 1 of this disclosure.
[0152] Example 4
[0153] The purpose of this embodiment is to provide an electronic device.
[0154] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in a distributed predictive control method for an AC / DC hybrid microgrid as described in Embodiment 1 of this disclosure.
[0155] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for distributed predictive control of AC / DC hybrid microgrid, characterized in that, The method comprises the following steps: Obtaining local values of a device to be controlled and observation values of neighbor devices, wherein the devices are divided into two types: alternating current devices and direct current devices; Using the local values of the device to be controlled and the observation values of the neighbor devices to perform dynamic consistency observation to obtain an observation value formula of the device to be controlled; Based on the observation value formula, a prediction model and a cost function are constructed; Optimizing and solving the prediction model to obtain optimal control variables for distributed control of the device, with the objective of minimizing the cost; The local values include voltage and power of the direct current devices and power of the alternating current devices, and the observation values include average direct current voltage observation values, average equal consumption micro-increment rate observation values of the direct current devices, and average equal consumption micro-increment rate observation values of the alternating current devices. 2.The AC / DC hybrid microgrid distributed predictive control method of claim 1, wherein, The AC / DC hybrid microgrid comprises an alternating current microgrid and a direct current microgrid, and the alternating current microgrid and the direct current microgrid are respectively composed of a plurality of alternating current devices and a plurality of direct current devices, and the devices communicate with each other through a communication network.
3. The AC / DC hybrid microgrid distributed predictive control method of claim 1, wherein, The neighbor devices are devices that communicate with the device to be controlled, including direct current neighbor devices and alternating current neighbor devices.
4. The AC / DC hybrid microgrid distributed predictive control method of claim 1, wherein, The dynamic consistency observation is divided into two observation modes according to the type of the device to be controlled: If the device to be controlled is a direct current device, an average direct current voltage observation value formula is constructed using the average direct current voltage observation values of all direct current neighbor devices and the voltage of the device to be controlled, and an average equal consumption micro-increment rate observation value formula is constructed using the average equal consumption micro-increment rate observation values of all neighbor devices and the power of the device to be controlled; If the device to be controlled is an alternating current device, an average equal consumption micro-increment rate observation value formula is constructed using the average equal consumption micro-increment rate observation values of all neighbor devices and the power of the device to be controlled.
5. The AC / DC hybrid microgrid distributed predictive control method of claim 1, wherein, The prediction model is divided into two prediction models according to the type of the device to be controlled; The prediction model of the direct current device is: wherein x(k) denotes the value of the variable x at time k, Rk is a given value for the two-layer control in the droop control at time k vi R is a droop coefficient, i (k) is a control variable; The prediction model of the alternating current device is: wherein, is the given value for the two-layer control in the drop control at time k.
6. The AC / DC hybrid microgrid distributed predictive control method of claim 1, wherein, The cost function of the direct current device is: wherein is a reference value for the average voltage, λ dc is a weight coefficient. The cost function of the alternating current device is: where ω * is a reference value of the grid frequency, λ ac is a weight coefficient.
7. The AC / DC hybrid microgrid distributed predictive control method of claim 1, wherein, The method further comprises the following steps: After obtaining the optimal control variables, the voltage reference value of the direct current device or the frequency reference value of the alternating current device is calculated according to the type of the device to be controlled using the corresponding droop control formula, for optimal control of the device.
8. A distributed predictive control system for an AC / DC hybrid microgrid, characterized in that, The method comprises the following steps: An acquisition module is configured to obtain local values of a device to be controlled and observation values of neighbor devices, wherein the devices are divided into two types: alternating current devices and direct current devices; An observation module is configured to use the local values of the device to be controlled and the observation values of the neighbor devices to perform dynamic consistency observation to obtain an observation value formula of the device to be controlled; A construction module is configured to construct a prediction model and a cost function based on the observation value formula; A solving module is configured to optimize and solve the prediction model to obtain optimal control variables for distributed control of the device, with the objective of minimizing the cost; The local values include voltage and power of the direct current devices and power of the alternating current devices, and the observation values include average direct current voltage observation values, average equal consumption micro-increment rate observation values of the direct current devices, and average equal consumption micro-increment rate observation values of the alternating current devices. 9.An electronic device, comprising: a memory for non-transitorily storing computer readable instructions; a processor for executing the computer readable instructions; wherein the computer readable instructions, when executed by the processor, perform the method of any one of claims 1-7.
10. A storage medium characterized by, non-transitorily storing computer readable instructions, wherein the computer readable instructions, when executed by a computer, perform the method of any one of claims 1-7.
