A distributed economic dispatch method based on periodic event-triggered communication

Abstract

The application discloses a kind of distributed economic dispatching methods based on periodic event triggered communication, specifically: the mathematical model of economic dispatching of power system is established, and distributed periodic event triggered communication optimization algorithm is used to solve, whether generator is latest communication time, if yes, then generator sends the virtual incremental cost of latest communication time to the neighbor generator with the communication connection of generator, then the update of economic dispatching algorithm is carried out;If not, the generator does not send information, and directly updates the economic dispatching algorithm.The application solves the economic dispatching problem under the constraints of power generation load supply and demand balance and upper and lower limits of power generation capacity at exponential rate, and has the advantages of being conducive to implementation, reducing communication burden, protecting privacy information, etc.

Description

Technical Field

[0001] This invention pertains to energy management technology for power systems, and particularly relates to a distributed economic dispatch method based on periodic event-triggered communication. Background Technology

[0002] A large amount of electricity generated from renewable energy sources such as solar and wind power is being connected to the power system, resulting in a future power system characterized by numerous and geographically dispersed power generation units. To achieve economical, efficient, reliable, and safe operation of the power supply, economic dispatch of the power system is required. This involves minimizing the total power generation cost of the grid, which is the sum of the cost functions of all power generation units, while satisfying the constraints of power generation and load balance and the upper and lower limits of power generation.

[0003] In recent years, distributed cooperative optimization methods based on multi-agent systems have been widely used to solve economic dispatch problems. The biggest advantage of distributed optimization methods compared to traditional methods is that they do not require coordination from a control center. Each generator uses only its own local information and information from its communication neighbors to gradually estimate the optimal power generation. Therefore, distributed economic dispatch has advantages such as strong robustness, good scalability, low communication and computational burden, and easy privacy protection. To reduce the algorithm's demand for communication bandwidth, event-triggered mechanisms have been integrated into distributed economic dispatch. For example, invention patent application number 201510875398.8 describes a power system economic dispatch method based on an event-triggered consensus algorithm; invention patent application number 202211452338.1 describes a smart grid economic dispatch control method based on a fixed-time event-triggered consensus algorithm; and invention patent application number 201910857825.8 describes a microgrid economic dispatch consensus algorithm based on distributed event-triggered control.

[0004] Existing continuous-time event-triggered distributed economic scheduling algorithms have the following shortcomings: First, the optimization problem does not consider the upper and lower limits of power generation constraints, and the obtained optimal power generation cannot guarantee that the generator operates within a safe range; second, the communication triggers of the algorithm need to be detected in real time, which requires the configuration of dedicated analog circuits, thereby increasing equipment costs and reducing system flexibility; third, the lower bound of the time interval between two consecutive communication events may be very small, which generally requires a large communication bandwidth to ensure the stability of the algorithm; fourth, existing event-triggered optimization algorithms mainly consider economic scheduling problems under quadratic strongly convex objective functions, while the objective functions of some economic scheduling problems may be in a more general strongly convex form. Summary of the Invention

[0005] To reduce the communication bandwidth requirements of optimization algorithms and avoid real-time detection of triggers, this invention provides a distributed economic scheduling method based on periodic event-triggered communication.

[0006] The present invention provides a distributed economic scheduling method based on periodic event-triggered communication, specifically as follows:

[0007] Establish a mathematical model for economic dispatch, assuming the power system is powered by n generators, where n ≥ 2 and is a positive integer, and generator i is related to its active power generation p. i The power generation cost function is f i (p i The power system has integers 1 ≤ i ≤ n and are positive integers. The objective of economic dispatch is to minimize the total generation cost f(p) of the power system as follows:

[0008]

[0009] Where p = [p1, p2, ..., p n ] T It is a column vector consisting of the active power generated by all generators, f i (p i ) is twice continuously differentiable, and f i (p i The Hessian matrix satisfies m i and M i It is the convexity parameter of the cost function of generator i.

[0010] Optimizing the total generation cost of the power system requires meeting the supply and demand balance constraint of generation load:

[0011]

[0012] Among them, D i It is the local active power demand of the area where generator i is located.

[0013] Optimizing the total generation cost of the power system also requires meeting the upper and lower limits of generator output constraints:

[0014]

[0015] in, and These are the lower and upper limits of generator i's power generation, respectively.

[0016] The solution is obtained using a distributed periodic event-triggered communication optimization algorithm.

[0017] Generator i determines whether it is the latest communication time. If it is, generator i sends the virtual incremental cost of the latest communication time to neighboring generators that have a communication connection with generator i, and then updates the economic scheduling algorithm. If it is not, generator i does not send information and directly updates the economic scheduling algorithm.

[0018] The latest communication time of generator i includes the initial time of algorithm execution and the time when the trigger decision is periodically evaluated as follows:

[0019]

[0020] in, It is the trigger function for generator i. It is the generator i at time {t} in the l-th sampling period. l =lh|l=0,1,2,3,…} is the virtual incremental cost measurement error, where h is the system sampling period, and its value range is... This represents the communication degree of generator i, c > 0 is the control gain of the economic scheduling algorithm, and N i a represents the set of generators that have a communication connection with generator i. ij This represents the weighting coefficient for communication. If generators i and j have a communication connection to obtain information from each other, then j∈N i And a ij =a ji >0, otherwise And a ij =a ji =0, α i >d i M i / m i and β i >d i M i / m i λ is the trigger control parameter for generator i. n It is the largest eigenvalue of the Laplace matrix of the communication graph formed by the communication connections between all generators. These are the trigger parameters for generator i, 0 < δ i <1 is the trigger control parameter for generator i, β j >d j M j / m j These are the trigger control parameters for generator j, d j m represents the communication degree of generator j. j and M j It is the convexity parameter of the cost function of generator j. It is the latest local virtual incremental cost inconsistency error of generator i.

[0021] If at time {t} in the l-th sampling period l If equation (4) holds true, then this is the latest communication time of generator i; otherwise, this is not the latest communication time of generator i.

[0022] The virtual incremental cost measurement error of generator i at time l of the sampling period is:

[0023]

[0024] in, It is the virtual incremental cost of generator i at the latest communication moment. It is the virtual incremental cost of generator i at the l-th sampling period.

[0025] The latest local virtual incremental cost inconsistency error of generator i is:

[0026]

[0027] in, It is the virtual incremental cost of generator j at its latest communication moment.

[0028] The virtual incremental cost of generator i at the latest communication moment is:

[0029]

[0030] in, It is the gradient of the cost function of generator i at the latest communication time. This is the auxiliary variable constraining the lower limit of generator i's power generation at the latest communication time. It is an auxiliary variable constraining the upper limit of generator i's power generation at the latest communication time.

[0031] The virtual incremental cost of generator i at time l of the sampling period is:

[0032]

[0033] in, It is the gradient of the cost function of generator i at the l-th sampling period. It is the auxiliary variable for the lower limit constraint of the power generation of generator i at the l-th sampling period. It is the auxiliary variable constraining the upper limit of power generation of generator i at the l-th sampling period.

[0034] The auxiliary variable for the lower limit constraint of generator i's power generation at the latest communication time is:

[0035]

[0036] Where max{s,0} represents the maximum value between the real number s and 0. It is the lower limit constraint multiplier variable of generator i's power generation at the latest communication time. It is the active power generation of generator i at the latest communication time.

[0037] The auxiliary variable for the upper limit constraint on the power generation of generator i at the latest communication time is:

[0038]

[0039] in, It is the upper limit constraint multiplier variable of generator i at the latest communication time.

[0040] The auxiliary variable for the lower limit constraint of generator i's power generation at time l of the sampling period is:

[0041]

[0042] in, It is the lower limit constraint multiplier variable of the power generation of generator i at the l-th sampling period. It is the active power generation of generator i at the l-th sampling period.

[0043] The auxiliary variable for the upper limit constraint on the power generation of generator i at time l of the sampling period is:

[0044]

[0045] in, It is the upper limit constraint multiplier variable of the power generation of generator i at the l-th sampling period.

[0046] The active power generation of generator i in the economic dispatch algorithm is updated as follows:

[0047] p i =z i +D i (13)

[0048] Among them, z i z is the internal state variable of the generator i economic dispatch algorithm. i Update as follows:

[0049]

[0050] Among them, z i initial value z i (0) satisfies

[0051] The lower limit constraint of power generation in the economic dispatch algorithm for generator i, multiplier variable y i,1 and the multiplier variable y of the upper limit constraint on power generation i,2 Update them as follows:

[0052]

[0053]

[0054] Among them, c i,1 and c i,2 This is the control gain parameter of the generator i economic dispatch algorithm, and its value is a positive constant, y i,1 and y i,2 initial value y i,1 (0) and y i,2 (0) is any non-negative constant.

[0055] Under the condition that the communication diagram formed by the communication connections between all generators is connected, if the time set for calculations (4) to (16) has not expired, the calculation continues; otherwise, the variable p in equation (13) i It converges at an exponential rate to the unique optimal power generation.

[0056] The beneficial technical effects of this invention are as follows:

[0057] (1) The generator’s trigger is only detected at the periodic sampling time to determine whether communication is needed, instead of detecting the trigger in real time, which is beneficial for implementing the algorithm on a digital controller;

[0058] (2) The economic dispatch algorithm always satisfies the supply and demand balance constraints between power generation loads during the execution process, which is conducive to the online application of the algorithm;

[0059] (3) The trigger dynamically adjusts the communication frequency according to the changes in generator state. Therefore, the proposed event-triggered algorithm can effectively reduce the communication burden compared with the algorithm without event triggering.

[0060] (4) This scheme only requires the generator to exchange virtual incremental cost information with its communication neighbor generators, rather than real incremental cost information, which is beneficial to the protection of the generator's privacy information;

[0061] (5) Compared with the existing event triggering schemes that do not consider the upper and lower limits of power generation, this scheme uses the multiplier method to solve the upper and lower limits of power generation of the generator, which can ensure that the generator output power operates within a safe range. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating the distributed economic scheduling method based on periodic event-triggered communication according to the present invention.

[0063] Figure 2 This is a diagram illustrating the communication connection between generators in an example.

[0064] Figure 3 The example generator's cost coefficient, upper and lower limits of power generation, and power requirements are shown.

[0065] Figure 4 The convexity parameters and trigger parameters of the generator are shown in the example.

[0066] Figure 5 The weighting coefficients for communication in this example are used. Detailed Implementation

[0067] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0068] The flow of the distributed economic scheduling method based on periodic event-triggered communication of the present invention is as follows: Figure 1 As shown in the example, the embodiment considers a power system powered by four generators, with the communication connections between the generators as follows: Figure 2 As shown, generator i (1≤i≤4 and are positive integers) has a relationship with its active power generation p i The power generation cost function is b i,1 b i,2 b i,3 b i,4 These are the cost coefficients of generator i, and the values ​​of these cost coefficients are within... Figure 3 Given that the objective of economic dispatch is to minimize the total power generation cost f(p) of the power system as follows:

[0069]

[0070] Where p = [p1, p2, p3, p4] T It is a column vector consisting of the active power generated by the four generators, f i (p i ) is twice continuously differentiable, and f i (p i The Hessian matrix satisfies m i and M i These are the convexity parameters of the cost function of generator i, and the values ​​of these convexity parameters are within... Figure 4 Provided.

[0071] Optimizing the total generation cost of the power system (17) requires meeting the supply and demand balance constraint of the generation load:

[0072]

[0073] Among them, D i This represents the local active power demand in the region where generator i is located, and its value is within... Figure 3 Provided.

[0074] At the same time, optimizing the total power generation cost of the power system (17) also requires meeting the upper and lower limits of generator output constraints:

[0075]

[0076] in, and These are the lower and upper limits of generator i's power generation, respectively, and their values ​​range from... Figure 3 Provided.

[0077] The economic scheduling problem described by equations (17) to (19) is solved using the following distributed periodic event-triggered communication optimization algorithm. Generator i determines whether it is the latest communication time. If it is, generator i sends the virtual incremental cost of the latest communication time to neighboring generators that have a communication connection with generator i, and then updates the economic scheduling algorithm. If it is not, generator i does not send information and directly updates the economic scheduling algorithm.

[0078] The latest communication time of generator i includes the initial time of algorithm execution and the time when the trigger decision is periodically evaluated as follows:

[0079]

[0080] in, It is the trigger function for generator i. It is the generator i at time {t} in the l-th sampling period. l The virtual incremental cost measurement error is defined as lh | l = 0, 1, 2, 3, ...}, where h = 0.002 seconds is the system sampling period, and the set sampling period is within the range... Inside, This represents the communication degree of generator i, c=3 is the control gain of the economic scheduling algorithm, and N... i a represents the set of generators that have a communication connection with generator i. ij This represents the weighting coefficient for communication, and its value ranges from... Figure 5 Given, α i >d i M i / m i and β i >d i M i / m i These are the trigger control parameters for generator i, and their values ​​are within... Figure 4 Given that the largest eigenvalue of the Laplace matrix of the communication graph formed by the communication connections between all generators is λ. n =4, These are the trigger parameters for generator i, 0 < δ i <1 is the trigger control parameter for generator i, and its value is within... Figure 4 Given, β j vd j M j / m jThese are the trigger control parameters for generator j, d j m represents the communication degree of generator j. j and M j It is the convexity parameter of the cost function of generator j. It is the latest local virtual incremental cost inconsistency error of generator i.

[0081] If at time {t} in the l-th sampling period l If equation (20) holds true, then this is the latest communication time of generator i; otherwise, this is not the latest communication time of generator i.

[0082] The virtual incremental cost measurement error of generator i at time l of the sampling period is:

[0083]

[0084] in, It is the virtual incremental cost of generator i at the latest communication moment. It is the virtual incremental cost of generator i at the l-th sampling period.

[0085] The latest local virtual incremental cost inconsistency error of generator i is:

[0086]

[0087] in, It is the virtual incremental cost of generator j at its latest communication moment.

[0088] The virtual incremental cost of generator i at the latest communication moment is:

[0089]

[0090] in, It is the gradient of the cost function of generator i at the latest communication time. It is the active power generation of generator i at the latest communication time. This is the auxiliary variable constraining the lower limit of generator i's power generation at the latest communication time. It is an auxiliary variable constraining the upper limit of generator i's power generation at the latest communication time.

[0091] The virtual incremental cost of generator i at time l of the sampling period is:

[0092]

[0093] in, It is the gradient of the cost function of generator i at the l-th sampling period. It is the active power generated by generator i at time l in the sampling period. It is the auxiliary variable for the lower limit constraint of the power generation of generator i at the l-th sampling period. It is the auxiliary variable constraining the upper limit of power generation of generator i at the l-th sampling period.

[0094] The auxiliary variable for the lower limit constraint of generator i's power generation at the latest communication time is:

[0095]

[0096] Where max{s,0} represents the maximum value between the real number s and 0. It is the lower limit constraint multiplier variable of generator i's power generation at the latest communication time. It is the active power generation of generator i at the latest communication time.

[0097] The auxiliary variable for the upper limit constraint on the power generation of generator i at the latest communication time is:

[0098]

[0099] in, It is the upper limit constraint multiplier variable of generator i at the latest communication time.

[0100] The auxiliary variable for the lower limit constraint of generator i's power generation at time l of the sampling period is:

[0101]

[0102] in, It is the lower limit constraint multiplier variable of the power generation of generator i at the l-th sampling period. It is the active power generation of generator i at the l-th sampling period.

[0103] The auxiliary variable for the upper limit constraint on the power generation of generator i at time l of the sampling period is:

[0104]

[0105] in, It is the upper limit constraint multiplier variable of the power generation of generator i at the l-th sampling period.

[0106] The active power generation of generator i in the economic dispatch algorithm is updated as follows:

[0107] p i =z i +D i (29)

[0108] Among them, z iz is the internal state variable of the generator i economic dispatch algorithm. i Update as follows:

[0109]

[0110] Among them, z i initial value z i (0) is set to z i (0) = 0.

[0111] The lower limit constraint of power generation in the economic dispatch algorithm for generator i, multiplier variable y i,1 and the multiplier variable y of the upper limit constraint on power generation i,2 Update them as follows:

[0112]

[0113]

[0114] Among them, the control gain parameter c of the generator i economic dispatch algorithm i,1 and c i,2 Set all to 3, y i,1 and y i,2 initial value y i,1 (0) and y i,2 (0) is set to 0.

[0115] If the time for calculations (20) to (32) is less than 50 seconds, the calculation continues; otherwise, the variable p in equation (29) i It converges at an exponential rate to the unique optimal power generation.

Claims

1. A distributed economic scheduling method based on periodic event-triggered communication, characterized in that, Specifically: Establish a mathematical model for economic dispatch, assuming the power system is powered by n generators, where n ≥ 2 and is a positive integer, and generator i is related to its active power generation p. i The power generation cost function is f i (p i Given a power system with integers 1 ≤ i ≤ n and all values ​​being positive integers, the objective of economic dispatch is to minimize the total generation cost f(p) of the power system as follows: Where p = [p1, p2, ..., p n ] T It is a column vector consisting of the active power generated by all generators, f i (p i ) is twice continuously differentiable, and f i (p i The Hessian matrix satisfies m i and M i It is the convexity parameter of the cost function of generator i; Optimizing the total generation cost of the power system requires meeting the supply and demand balance constraint of generation load: Among them, D i It is the local active power demand in the area where generator i is located; Optimizing the total generation cost of the power system also requires meeting the upper and lower limits of generator output constraints: in, and These are the lower and upper limits of generator i's power generation, respectively; The solution is obtained using a distributed periodic event-triggered communication optimization algorithm. Generator i determines whether it is the latest communication time. If it is, generator i sends the virtual incremental cost of the latest communication time to neighboring generators that have a communication connection with generator i, and then updates the economic scheduling algorithm. If it is not, generator i does not send information and directly updates the economic scheduling algorithm. The latest communication time of generator i includes the initial time of algorithm execution and the time when the trigger decision is periodically evaluated as follows: in, It is the trigger function for generator i. It is the generator i at time {t} in the l-th sampling period. l =lh|l=0,1,2,3,…} is the virtual incremental cost measurement error, where h is the system sampling period, and its value range is... This represents the communication degree of generator i, c > 0 is the control gain of the economic scheduling algorithm, and N i a represents the set of generators that have a communication connection with generator i. ij This represents the weighting coefficient for communication. If generators i and j have a communication connection to obtain information from each other, then j∈N i And a ij =a ji >0, otherwise And a ij =a ji =0, α i >d i M i / m i and β i >d i M i / m i λ is the trigger control parameter for generator i. n It is the largest eigenvalue of the Laplace matrix of the communication graph formed by the communication connections between all generators. These are the trigger parameters for generator i, 0 < δ i <1 is the trigger control parameter for generator i, β j >d j M j / m j These are the trigger control parameters for generator j, d j m represents the communication degree of generator j. j and M j It is the convexity parameter of the cost function of generator j. It is the latest local virtual incremental cost inconsistency error of generator i; If at time {t} in the l-th sampling period l If equation (4) holds true, then this is the latest communication time of generator i; otherwise, this is not the latest communication time of generator i. The virtual incremental cost measurement error of generator i at time l of the sampling period is: in, It is the virtual incremental cost of generator i at the latest communication moment. It is the virtual incremental cost of generator i at the l-th sampling period; The latest local virtual incremental cost inconsistency error of generator i is: in, It is the virtual incremental cost of generator j at its latest communication moment; The virtual incremental cost of generator i at the latest communication moment is: in, It is the gradient of the cost function of generator i at the latest communication time. This is an auxiliary variable constraining the lower limit of generator i's power generation at the latest communication time. It is an auxiliary variable constraining the upper limit of generator i's power generation at the latest communication time; The virtual incremental cost of generator i at time l of the sampling period is: in, It is the gradient of the cost function of generator i at the l-th sampling period. It is the auxiliary variable for the lower limit constraint of the power generation of generator i at the l-th sampling period. It is the auxiliary variable constraining the upper limit of power generation of generator i at the l-th sampling period; The auxiliary variable for the lower limit constraint of generator i's power generation at the latest communication time is: Where max{s,0} represents the maximum value between the real number s and 0. It is the lower limit constraint multiplier variable of generator i's power generation at the latest communication time. It is the active power generation of generator i at the latest communication time; The auxiliary variable for the upper limit constraint on the power generation of generator i at the latest communication time is: in, It is the multiplier variable of the upper limit constraint on the power generation of generator i at the latest communication time; The auxiliary variable for the lower limit constraint of generator i's power generation at time l of the sampling period is: in, It is the lower limit constraint multiplier variable of the power generation of generator i at the l-th sampling period. It is the active power generation of generator i at the l-th sampling period; The auxiliary variable for the upper limit constraint on the power generation of generator i at time l of the sampling period is: in, It is the upper limit constraint multiplier variable of the power generation of generator i at the l-th sampling period; The active power generation of generator i in the economic dispatch algorithm is updated as follows: p i =z i +D i (13) Among them, z i z is the internal state variable of the generator i economic dispatch algorithm. i Update as follows: Among them, z i initial value z i (0) satisfies The lower limit constraint of power generation in the economic dispatch algorithm for generator i, multiplier variable y i,1 and the multiplier variable y of the upper limit constraint on power generation i,2 Update them as follows: Among them, c i,1 and c i,2 This is the control gain parameter of the generator i economic dispatch algorithm, and its value is a positive constant, y i,1 and y i,2 initial value y i,1 (0) and y i,2 (0) is any nonnegative constant; Under the condition that the communication diagram formed by the communication connections between all generators is connected, if the time set for calculations (4) to (16) has not expired, the calculation continues; otherwise, the variable p in equation (13) i It converges at an exponential rate to the unique optimal power generation.

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