Dynamic photovoltaic module parameter identification method based on reinforced differential evolution algorithm
By optimizing the parameters of the fractional-order dynamic photovoltaic model using a differential evolution algorithm based on reinforcement learning, the problems of slow convergence speed and low accuracy in existing technologies are solved, and a more efficient parameter identification effect is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- DONGHUA UNIV
- Filing Date
- 2026-02-12
- Publication Date
- 2026-06-09
AI Technical Summary
Existing dynamic photovoltaic model parameter identification algorithms suffer from slow convergence speed and low accuracy, especially for fractional-order dynamic photovoltaic models. Hybrid algorithms still fall short in improving this aspect.
A reinforcement learning-based differential evolution algorithm is adopted. By constructing a population Q-table and using a Softmax strategy to select mutation strategies, combined with binary crossover operations, the parameters of the fractional-order dynamic photovoltaic model are optimized to achieve accurate parameter identification.
It improves the accuracy and convergence speed of fractional photovoltaic model parameter identification, demonstrating excellent parameter accuracy, convergence speed and average relative error index, and provides an effective parameter identification scheme.
Smart Images
Figure CN122174931A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of solar photovoltaic cell and photovoltaic power generation array detection technology, specifically involving a dynamic photovoltaic module parameter identification method based on enhanced differential evolution algorithm. Background Technology
[0002] In recent years, the extensive development of fossil fuels has highlighted their non-renewable nature and volatile prices, suggesting they will eventually be depleted. Therefore, the development of renewable energy sources has gained increasing attention. Solar energy, as a significant renewable energy source, possesses immense development potential and value. To ensure photovoltaic (PV) systems operate at maximum available power and improve the quality of energy supply from PV modules, it is necessary to construct accurate and effective models and precisely identify their parameters to optimize and control the PV model.
[0003] In all recorded systems, static PV models such as the single-diode model (SDM) and the dual-diode model (DDM) have been widely used in many fields due to their simple structure and ease of modeling. However, static models do not consider sudden changes and switching operations of load elements, as well as interactions with the external environment. Therefore, dynamic PV models have been introduced as the most accurate and effective models to address the aforementioned shortcomings of static PV models. Among them, fractional-order dynamic PV models introduce fractional calculus theory on the basis of integer-order dynamic PV models, enhancing their efficiency and flexibility. Therefore, they have become a new trend in handling the dynamic behavior of PV models. However, their more complex parameters compared to static models also pose a significant challenge for practical applications.
[0004] There are relatively few intelligent optimization algorithms proposed for parameter identification of dynamic photovoltaic models. Some swarm intelligence algorithms for static photovoltaic models generally face problems such as getting trapped in local optima and slow convergence when dealing with dynamic photovoltaic models. In order to combine the strengths and compensate for the weaknesses, some hybrid algorithms have been proposed, such as the proposed chaotic ensemble particle swarm optimization algorithm. These algorithms have achieved good results to a certain extent, but the convergence speed and accuracy still need to be improved.
[0005] Therefore, it is necessary to propose a fractional-order dynamic photovoltaic model parameter identification method based on an improved differential evolution algorithm, which can balance convergence speed and global search, thereby further improving the accuracy of dynamic photovoltaic model parameters. Summary of the Invention
[0006] The purpose of this invention is to address the shortcomings of low accuracy and slow convergence in existing technologies by providing a dynamic photovoltaic module parameter identification method based on an enhanced differential evolution algorithm.
[0007] To address the aforementioned technical problems, this invention provides a dynamic photovoltaic module parameter identification method based on an enhanced differential evolution algorithm, comprising the following steps:
[0008] S1: Based on the fractional-order dynamic photovoltaic equivalent circuit model and load current function, define the parameter range and construct the objective function;
[0009] S2: Randomly search within the defined parameter range to establish a parent population. Based on the parent population and the objective function, calculate the objective function value for each individual in the population, establish an objective function value vector, and sort the parent population according to the magnitude of the objective function values to obtain the optimal parameters of the parent population;
[0010] S3: Set the initial state, action, and next state for each individual, and establish the population Q-table;
[0011] S4: Using the Softmax strategy, based on the Q value of each individual, one of the four mutation strategies is selected as the mutation strategy for the corresponding individual. A binary crossover strategy is used to perform mutation and crossover operations on the corresponding individual.
[0012] S5: Calculate the objective function value of the experimental vector, select whether to retain the original vector or replace it with the experimental vector based on the comparison result of the objective function value, and decide the size of the reward value and the next state value based on the superiority or inferiority of the comparison result; construct a new parent population based on the replaced vector group, and sort to obtain the optimal parameters of the new parent population.
[0013] S6: Calculate the new Q value based on the current state value, action value, next state value, and reward value of each individual in the population, and update the Q table;
[0014] S7: Repeat steps S4-S6 until the maximum number of objective function calculations is reached, and use the output parameter vector as the parameter vector of the optimized fractional-order dynamic photovoltaic model.
[0015] Compared with the prior art, the advantages of the present invention are as follows:
[0016] 1. A parameter identification method combining reinforcement learning and multi-policy differential evolution is proposed. By establishing a population Q-table, defining state values, corresponding actions, and four policies, a Q-learning framework is constructed. A Softmax policy is used to instill a tendency in individuals to choose actions with higher probabilities. The policy corresponding to the selected action is then used as the mutation policy for differential evolution. Finally, based on the result of the selection operation, the reward value and the next state value are returned to update the Q-table. This effectively improves the parameter identification accuracy of fractional photovoltaic models.
[0017] 2. The selection of multiple strategies in this algorithm is obtained through interactive learning between the algorithm and the selection results of the previous generation, without relying on manual settings. It shows excellent results in terms of parameter accuracy, convergence speed, and average relative error, and provides an effective solution to the parameter identification problem of fractional photovoltaic models. Attached Figure Description
[0018] To more clearly illustrate the method provided by this invention, the accompanying drawings required to describe this invention are briefly explained below, wherein the objective function for all algorithm optimizations is the objective function set by this invention.
[0019] Figure 1 The flowchart shows the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided by the present invention.
[0020] Figure 2 The equivalent circuit diagram of the fractional-order dynamic photovoltaic model for the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided by this invention.
[0021] Figure 3 This is a diagram illustrating the reinforcement learning principle of the dynamic photovoltaic module parameter identification method based on the reinforcement differential evolution algorithm provided by this invention.
[0022] Figure 4 A schematic diagram of the fitting curve based on It, which is the load current test data of the connected photovoltaic module and the fractional-order dynamic photovoltaic model simulation data obtained by this invention.
[0023] Figure 5 This diagram illustrates a comparison of the average relative error of the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided by this invention with other advanced algorithms.
[0024] Figure 6 The mean square error box plots of the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided by this invention, which were run independently 20 times with other advanced algorithms.
[0025] Figure 7 The diagram shows the convergence curves of the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided by this invention and other advanced algorithms. Detailed Implementation
[0026] The present invention will be further described and illustrated below with reference to specific embodiments.
[0027] like Figure 1 As shown, this invention provides a method for dynamic photovoltaic module parameter identification based on an enhanced differential evolution algorithm. It includes the following steps:
[0028] S1: Based on the fractional-order dynamic photovoltaic equivalent circuit model and load current function, define the parameter range and construct the objective function.
[0029] On the original dynamic experimental dataset, the current of repeated timestamps is deduplicated by averaging, uniform time points are generated with a fixed step size, and the current value is calculated by linear interpolation to construct the test dataset.
[0030] like Figure 2 The figure shows the equivalent circuit diagram of a fractional-order dynamic photovoltaic model. It consists of an equivalent voltage source, a series resistor, a load resistor, a capacitor branch resistor, a fractional capacitor, and a fractional inductor. Its load current-voltage relationship can be represented in the S-domain, and the specific formula is as follows:
[0031] (1)
[0032]
[0033] The fractional-order dynamic photovoltaic model contains five parameters to be identified, namely: ,in For load current, Open-circuit voltage for photovoltaic modules For series resistance, For load resistance, For the capacitor branch resistance, and These are fractional capacitors and fractional inductors, respectively. and These are the fractional orders of the capacitor and the inductor, respectively. For the complex frequency domain operator after the Laplace transform of the time-domain system, These are intermediate variables, and their values are the elements at corresponding positions in the two matrices.
[0034] The specific parameter range of the load current function is as follows:
[0035]
[0036] The objective function is the mean square error of the difference between the measured current and the predicted current, and the specific formula is as follows:
[0037] (2)
[0038] Where N is the number of measurement points. For the i-th measured current, for The unit step response at the i-th time point.
[0039] S2: Randomly search within the defined parameter range to establish a parent population. Based on the parent population and the objective function, calculate the objective function value for each individual in the population, establish an objective function value vector, and sort the parent population according to the magnitude of the objective function values to obtain the optimal parameters of the parent population. Specifically, this includes the following sub-steps:
[0040] S2.1: Initialization parameters, specifically including the maximum number of evaluations Max_NFE, the upper bound vector UB and lower bound vector LB of the load current function, the population size Np, the dimension of the parameter vector D, the number of evaluations NFE, the crossover factor CR, the mutation factor F, and the discount factor γ;
[0041] S2.2: Randomly generate a population of size Np within UB and LB, where each individual is a D-dimensional vector, serving as the parent population. The formula for establishing this population is as follows:
[0042]
[0043] (3)
[0044] in, The first generation of the parent population Individual, Indicates the first The first individual One parameter, It is a random number generated in [0,1].
[0045] S2.3: Calculate the objective function value for each individual in the parent population. Update the NFE value once for each calculation, i.e., NFE = NFE + 1.
[0046] S2.4: Sort the parent population according to the size of the objective function value, find the individual with the smallest objective function value, and set it as the current generation's best individual.
[0047] S3: Set the initial state, initial action, and initial next state for each individual, and establish the population Q table.
[0048] The specific steps are as follows: Define the state set for each individual. and action set The system consists of two states, representing that the search results of the offspring are better than those of the parents and worse than those of the parents, respectively. Four actions correspond to four mutation strategies. Arrays are created and initialized for the state values, action values, reward values, and next state values of all individuals. Finally, the population Q-table is initialized. The population Q-table contains the Q-tables of all individuals in the population in their order of appearance.
[0049] S4: Using the Softmax strategy, based on the Q-value of each individual, select one of the four mutation strategies as the mutation strategy for the corresponding individual. Then, using a binary crossover strategy, perform mutation and crossover operations on the corresponding individual. This includes the following sub-steps:
[0050] S4.1: Set the dynamically decaying learning rate The learning rate update formula is:
[0051] (4)
[0052] S4.2: Extract the Q-table for each individual from the population Q-table, and use the Softmax strategy to convert the Q-value into the probability of the individual choosing an action from the action set A. The Softmax strategy is as follows:
[0053] (5)
[0054] in Indicates that the individual is in Status Adoption The Q-value of an action, where M is the number of selectable actions. This refers to the temperature parameter.
[0055] S4.3: Based on the action probabilities obtained in S4.1, establish an action sample space, and randomly select one of them as an independent individual action. The four actions of an individual correspond to four mutation strategies, including a generalized learning strategy, a transitional learning strategy, an elite learning strategy, and an elite-guided strategy. The correspondence between individual action values and mutation strategies is as follows:
[0056] (6)
[0057] in For the four actions in action set A, For the number of iterations, for Randomly selected distinct integers, As a scale factor, Individuals are randomly selected from the top ten individuals in terms of fitness value in the population. This is the individual with the best fitness value in the current generation.
[0058] S4.4: A re-initialization method is used to process the boundaries of each individual, that is, to check whether the parameters in the individual vector exceed the upper and lower limits of the parameters. If they do, a random value within the parameter range is reassigned. The specific method is as follows:
[0059] (7)
[0060] in For the first Generation 1 The first mutant individual Dimensional parameters, and The first The lower and upper bounds of the dimension parameter.
[0061] S4.4: Perform a binary crossover operation on each individual in the population to generate an experimental population. The method is as follows:
[0062] (8)
[0063] in In order to be in Intra-selected cross factor, In order to be in Randomly selected intersection points.
[0064] S5: Calculate the objective function value of the experimental vector. Based on the comparison results of the objective function values, choose to retain the original vector or replace it with the experimental vector, and determine the return reward value and the next state value based on the comparison results. Construct a new parent population based on the replaced vector group, and sort them to obtain the optimal parameters of the new parent population. Specifically, this includes the following sub-steps:
[0065] S5.1: Calculate the objective function value for each individual in the experimental population. Update the NFE value once for each calculation, i.e., NFE = NFE + 1.
[0066] S5.2: Perform a selection operation on each individual in the population. Specifically, if the objective function value of the trial vector is lower than the objective function value of the corresponding original vector, then replace the original vector with the trial vector, set the reward value to 1, and set the next state value to... If the objective function value of the experimental vector is higher than the objective function value of the corresponding original vector, then the original vector is retained, the reward value is set to 0, and the next state value is set to... .in The selection method for the next generation of the population is represented as follows:
[0067] (9)
[0068]
[0069] S6: Calculate a new Q value based on each individual's current state value, action value, next state value, and reward value in the population, and update the Q table. The specific calculation formula is as follows:
[0070] (10)
[0071] in, and They represent individuals in Perform an action in a state The original Q value and the updated Q value at that time, For learning rate, Indicates the reward value. Indicates the discount factor. This represents the maximum Q value among all actions in the next state.
[0072] In each individual's Q-table, the Q-value at the corresponding position is updated using the method described above, while the Q-values at other positions remain unchanged. For the population at the end of the update process, the current state of each individual is replaced with its next state.
[0073] S7: Repeat Steps 4-6 until the maximum number of objective function calculations is reached. Use the output parameter vector as the parameter vector of the optimized fractional-order dynamic photovoltaic model. Specifically, determine if the number of function evaluations has reached the set maximum number of evaluations. If not, use the population from the previous step as the parent population and execute the next iteration. If it has reached the maximum number of evaluations, obtain the optimal parameter vector based on the objective function value and output it as the parameter vector of the optimized fractional-order dynamic photovoltaic model.
[0074] Figure 3 This diagram illustrates the reinforcement learning principle of the dynamic photovoltaic module parameter identification method based on the reinforcement differential evolution algorithm provided in this invention. It shows that the current individual first determines its action based on the state and reward passed down from the previous generation, and then obtains new states and rewards through interaction with the environment, which are then passed on to the next generation.
[0075] Figure 4 The load current test data of the connected photovoltaic module is fitted with the simulation data of the fractional-order dynamic photovoltaic model obtained by this invention based on It. Here, QLSDE represents this method. It can be seen that the curve constructed by the parameters calculated by this method closely matches the data in the test set, proving that this method has strong parameter identification capabilities.
[0076] Figure 5 This paper compares the average relative error of the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided in this invention with other advanced algorithms. In this paper, QLSDE represents the proposed method, DE represents the differential evolution algorithm, GA represents the genetic algorithm, SEDE represents the adaptive ensemble differential evolution algorithm, IJAYA represents the improved hybrid frog-leaping algorithm, ALTDE represents the hybrid adaptive teaching differential evolution algorithm, and HCLPSO represents the heterogeneous integrated learning particle swarm optimization algorithm. It can be seen that compared with other algorithms, the proposed method obtains the smallest average relative error, proving its excellent performance in terms of convergence accuracy.
[0077] Figure 6Box plots show the mean square error (MSE) of the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided in this invention, run independently 20 times with other advanced algorithms. Here, QLSDE represents the proposed method, DE represents the differential evolution algorithm, GA represents the genetic algorithm, SEDE represents the adaptive ensemble differential evolution algorithm, IJAYA represents the improved hybrid frog-leaping algorithm, ALTDE represents the hybrid adaptive teaching differential evolution algorithm, and HCLPSO represents the heterogeneous integrated learning particle swarm optimization algorithm. It can be seen that compared to other algorithms, the proposed method yields highly concentrated computational results with minimal computational error, demonstrating excellent convergence stability.
[0078] Figure 7 The convergence curves of the dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm provided in this invention are compared with those of other advanced algorithms. Here, QLSDE represents the proposed method, DE represents the differential evolution algorithm, GA represents the genetic algorithm, SEDE represents the adaptive ensemble differential evolution algorithm, IJAYA represents the improved hybrid frog-leaping algorithm, ALTDE represents the hybrid adaptive teaching differential evolution algorithm, and HCLPSO represents the heterogeneous integrated learning particle swarm optimization algorithm. It can be seen that compared with other algorithms, this method exhibits excellent overall performance in both convergence speed and convergence accuracy.
[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for identifying dynamic photovoltaic module parameters based on a reinforced differential evolution algorithm, characterized in that... Includes the following steps: S1: Based on the fractional-order dynamic photovoltaic equivalent circuit model and load current function, define the parameter range and construct the objective function; S2: Randomly search within the defined parameter range to establish a parent population. Based on the parent population and the objective function, calculate the objective function value for each individual in the population, establish an objective function value vector, and sort the parent population according to the magnitude of the objective function values to obtain the optimal parameters of the parent population; S3: Set the initial state, action, and next state for each individual, and establish the population Q-table; S4: Using the Softmax strategy, based on the Q value of each individual, one of the four mutation strategies is selected as the mutation strategy for the corresponding individual. A binary crossover strategy is used to perform mutation and crossover operations on the corresponding individual. S5: Calculate the objective function value of the experimental vector, select whether to retain the original vector or replace it with the experimental vector based on the comparison result of the objective function value, and decide the size of the return reward value and the next state value based on the comparison result; construct a new parent population based on the replaced vector group, and sort to obtain the optimal parameters of the new parent population; S6: Calculate the new Q value based on the current state value, action value, next state value, and reward value of each individual in the population, and update the Q table; S7: Repeat steps S4-S6 until the maximum number of objective function calculations is reached, and use the output parameter vector as the parameter vector of the optimized fractional-order dynamic photovoltaic model.
2. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 1, characterized in that, On the original dynamic experimental dataset, the current of repeated timestamps is deduplicated by averaging, uniform time points are generated with a fixed step size, and the current value is calculated by linear interpolation to construct the test dataset.
3. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 1, characterized in that, In S1 above, the load current-voltage relationship of the fractional-order dynamic photovoltaic model is represented in the S-domain, and the specific formula is as follows: (1) ； The fractional-order dynamic photovoltaic model contains five parameters to be identified, namely: ,in For load current, Open-circuit voltage for photovoltaic modules For series resistance, For load resistance, For the capacitor branch resistance, and These are fractional capacitors and fractional inductors, respectively. and These are the fractional orders of the capacitor and the inductor, respectively. For the complex frequency domain operator after the Laplace transform of the time-domain system, These are intermediate variables, and their values are the elements at corresponding positions in the two matrices; The specific parameter range of the load current function is as follows: ； The objective function is the mean square error of the difference between the measured current and the predicted current, and the specific formula is as follows: (2) Where N is the number of measurement points. For the i-th measured current, for The unit step response at the i-th time point.
4. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 3, characterized in that, The specific process of step S2 is as follows: S2.1: Initialization parameters, specifically including the maximum number of evaluations Max_NFE, the upper bound vector UB and lower bound vector LB of the load current function, the population size Np, the dimension of the parameter vector D, the number of evaluations NFE, the crossover factor CR, the mutation factor F, and the discount factor γ; S2.2: Randomly generate a population of size Np within UB and LB, where each individual is a D-dimensional vector, serving as the parent population. The formula is as follows: ； (3) in, The first generation of the parent population Individual, Indicates the first The first individual One parameter, It is a random number generated in [0,1]. S2.3: Calculate the objective function value for each individual in the parent population. Update the NFE value once for each calculation, i.e., NFE = NFE + 1. S2.4: Sort the parent population according to the size of the objective function value, find the individual with the smallest objective function value, and set it as the current generation's best individual.
5. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 4, characterized in that, The specific process of step S3 is as follows: Define the state set for each individual. and action set The two states represent that the search results of the offspring are better than those of the parents and that the search results of the offspring are worse than those of the parents, respectively. The four actions correspond to four mutation strategies. The state values, action values, reward values and next state values of all individuals are created into arrays and initialized. Finally, the population Q-table is initialized. The population Q-table contains the Q-tables of all individuals in the population in the order they are in the population.
6. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 5, characterized in that, The specific process of step S4 is as follows: S4.1: Set the dynamically decaying learning rate The learning rate update formula is: (4) S4.2: Extract the Q-table for each individual from the population Q-table, and use the Softmax strategy to convert the Q-value into the probability of the individual choosing an action from the action set A. The Softmax strategy is as follows: (5) in Indicates that the individual is in Status Adoption The Q-value of an action, where M is the number of selectable actions. For temperature parameters; S4.3: Based on the action probabilities obtained in S4.1, establish an action sample space, and randomly select one of them as an independent individual action; the four actions of an individual correspond to four mutation strategies, including a generalized learning strategy, a transitional learning strategy, an elite learning strategy, and an elite-guided strategy; the correspondence between individual action values and mutation strategies is as follows: (6) in Let A contain four actions, and t be the number of iterations. for Randomly selected distinct integers, As a scale factor, Individuals are randomly selected from the top ten individuals in terms of fitness value in the population. The individual with the best fitness value in the current generation; S4.4: A re-initialization method is used to process the boundaries of each individual, that is, to check whether the parameters in the individual vector exceed the upper and lower limits of the parameters. If they do, a random value within the parameter range is reassigned. The specific method is as follows: (7) in For the first Generation 1 The 1st mutant individual Dimensional parameters, and The first Lower and upper bounds of the dimensional parameter; S4.5: Perform a binary crossover operation on each individual in the population to generate an experimental population. The method is as follows: (8) in In order to be in Intra-selected cross factor, In order to be in Randomly selected intersection points.
7. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 6, characterized in that, The specific process of step S5 is as follows: S5.1: Calculate the objective function value for each individual in the experimental population. Update the NFE value once for each calculation, i.e., NFE = NFE + 1. S5.2: Perform a selection operation on each individual in the population. Specifically, if the objective function value of the trial vector is lower than the objective function value of the corresponding original vector, then replace the original vector with the trial vector, set the reward value to 1, and set the next state value to... If the objective function value of the experimental vector is higher than the objective function value of the corresponding original vector, then the original vector is retained, the reward value is set to 0, and the next state value is set to... ; (9) ； in For the next generation of the species.
8. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 7, characterized in that, In step S6, a new Q value is obtained based on the current state value, action value, next state value, and reward value of each individual in the population. The specific process is as follows: (10) in, and They represent individuals in Perform an action in a state The original Q value and the updated Q value at that time, For learning rate, Indicates the reward value. Indicates the discount factor. This represents the maximum Q-value among all actions in the next state; In each individual's Q-table, the Q-value at the corresponding position is updated using the above method, while the Q-values at other positions remain unchanged; for the population after the update is complete, the current state of each individual is replaced with the next state of that individual.
9. The dynamic photovoltaic module parameter identification method based on the enhanced differential evolution algorithm according to claim 8, characterized in that, The specific process of step S7 is as follows: determine whether the number of evaluations of the function has reached the set maximum number of evaluations. If it has not reached the maximum number of evaluations, take the population that ended in the previous step as the parent population and execute the next iteration. If it has reached the maximum number of evaluations, obtain the optimal parameter vector according to the size of the objective function value and output it as the optimized fractional-order dynamic photovoltaic model parameter vector.