Transmission network voltage on-line control method based on gradient dynamics and control barrier function

Abstract

The invention relates to the technical field of power systems, and particularly discloses a power transmission network voltage on-line control method based on gradient dynamics and a control barrier function, which comprises the following steps: constructing an optimal reactive power flow on-line control model based on gradient dynamics; carrying out gradient iteration on the target function by adopting a gradient dynamic method based on data measured by the PMU in real time; the optimal reactive power flow problem is converted into an online control problem; constructing a security domain for improving the control barrier function; a control barrier function and constraint conditions thereof are designed, an online optimal reactive power flow control law based on the improved control barrier function is formed, and optimal control input is obtained by adopting a quadratic programming solver for load nodes in a safety domain; and for load nodes outside the security domain, obtaining optimal control input by adopting sequential quadratic programming. The method has the advantages that the real-time performance, the safety and the robustness of voltage control of the power transmission network are improved through deep fusion of gradient dynamics and an improved control barrier function.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to an online voltage control method for power transmission networks based on gradient dynamics and control barrier functions. Background Technology

[0002] With the increasing penetration of renewable energy in power transmission networks, utilizing optimal reactive power flow (ORPF) to coordinate various types of reactive resources to maintain voltage stability has become crucial for ensuring the stable operation of power systems. Traditional offline ORPF solutions require constructing accurate physical models of the power grid and rely on high-precision forecasts of load and generation output. However, the complex structure of modern power grids increases the difficulty of accurate modeling, and the inherent volatility of renewable energy output leads to a significant increase in forecast uncertainty, severely challenging the applicability of traditional methods. rement The widespread deployment of physical models (PMUs) has made it possible to solve the ORPF problem online. Among them, the online voltage control strategy based on projected gradient descent (PGD) reduces the dependence on physical models and operating condition predictions, but its control robustness is still insufficient when encountering sudden disturbances, and it is difficult to completely avoid the risk of voltage exceeding the limit.

[0003] In recent years, based on control barrier functions (Control barrier function) The safety-constrained dynamic control method (CBF) has attracted much attention due to its excellent disturbance adaptability. This method significantly improves the robustness of the control strategy by tracking the system state in real time. However, the effective implementation of the CBF method is premised on the system state being within a safe range. When a serious fault occurs in the power grid, causing the voltage to exceed the limit, directly applying the CBF method may not yield a feasible optimal control solution. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an online voltage control method for power transmission networks based on gradient dynamics and control barrier functions.

[0005] The objective of this invention is achieved through the following technical solution: an online voltage control method for power transmission networks based on gradient dynamics and control barrier functions, the method comprising: Construct an optimal reactive power flow online control model based on gradient dynamics; The objective function of the optimal reactive power flow online control model is:

[0006]

[0007] In the formula, To control input The set of upper and lower limits for each vector in the set; , Represent and The reactive setpoint vector; , , All are symmetric positive definite matrices; For the reactive power setpoint vector of IBRs; The deviation between the reactive power output of IBRs and their steady-state equilibrium point. The deviation between the reactive power output of SGs and its steady-state equilibrium point. The deviation between the reactive power output of SVCs and their steady-state equilibrium point; Based on real-time measurement data from the PMU, a gradient dynamic method is used to iterate the objective function. The power flow equations are linearized using an approximate form of the Jacobian matrix, and the optimal reactive power flow problem is transformed into an online control problem by combining the dynamic expression of the control system. A safe region for an improved control barrier function is constructed. The control barrier function is designed based on voltage inequality constraints. Based on the improved control barrier function, an online optimal reactive power flow control law is used. For load nodes within the safe region, a quadratic programming solver is used to obtain the optimal control input. For load nodes outside the safe region, a sequential quadratic programming is used to obtain the optimal control input.

[0008] Specifically, the constraints of the optimal reactive power flow online control model are as follows:

[0009] In the formula, This is a vector of the voltage magnitudes of all load busbars. This is the superimposed vector of reactive power output from each reactive power control device. ; Represents the disturbance experienced by the power grid; nonlinear function This is a steady-state power flow model for the power grid; To control the input, ; Lower limit of load bus voltage amplitude Upper limit of load bus voltage amplitude Lower limit of reactive power output of reactive power equipment Upper limit of reactive power output of reactive equipment.

[0010] Specifically, the dynamics of the control system are expressed as follows:

[0011] In the formula, Representing system state variables, functions A function represents the natural dynamic behavior of a system when there is no external input. The function reflects the effect of control input on the system state; For control input; State variables Regarding time The derivative of .

[0012] Specifically, the online control problem is expressed as:

[0013] In the formula, This represents the gradient descent gain coefficient. Represents the initial state variable. Represents the steady-state value of a state variable. Represents an approximate Jacobian matrix; For control input; , These control the upper and lower limits of the input, respectively. , These are the upper and lower bounds of the state variable, respectively; ; State variables Regarding time The derivative; Indicates control input Regarding time The derivative;

[0014] It is the objective function.

[0015] Specifically, the safety domain of the control barrier function is defined as follows:

[0016] In the formula, To control the barrier function, satisfy the safety domain System status Within a safe range; express 3D real space.

[0017] Specifically, the control barrier function for:

[0018] In the formula, It is a control barrier function designed for the lower voltage limit. It is a control barrier function designed for the upper voltage limit; A vector representing the voltage magnitude of all load buses.

[0019] Specifically, the online optimal reactive power flow control law based on the improved control barrier function is as follows:

[0020] In the formula, This is a relaxation term; For a class function; For a non-class that adjusts security constraints function;

[0021] Indicates the control input for the next time step. This indicates the current time step control input. Indicates the steady-state value of the control input; A positive semi-definite matrix ; To suppress the oscillation coefficient; The relaxation coefficient; , The function reflects the effect of control input on the system state; This represents the load node within the security domain. , This indicates a load node outside the security domain. This represents the set of load nodes within the security domain. , This represents the set of load nodes outside the security domain. , , Represents the load node set; For the state of measurement; allocation The relevant CBF constraints are applied to the load nodes within the safety domain. ,distribute The relevant finite-time return safety domain constraints are applied to load nodes outside the safety domain. .

[0022] The present invention has the following advantages: This invention proposes an online voltage control method for power transmission networks based on gradient dynamics and control barrier functions. By combining real-time power grid measurement data, the gradient dynamics method is used to transform the optimal reactive power flow problem into an online control problem, enabling the control model to respond quickly to changes in the power grid state. Then, based on the system measurement state, a control model constraint set based on an improved control barrier function is constructed to ensure that the system voltage remains in the safe region or is driven to the safe region after being disturbed, thereby improving the system's disturbance rejection capability and robustness. Detailed Implementation

[0023] It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention. That is, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0024] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of the present invention.

[0025] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0026] The scope of protection of this invention is not limited to the following description.

[0027] A method for online voltage control of power transmission networks based on gradient dynamics and control barrier functions, comprising: Construct an optimal reactive power flow online control model based on gradient dynamics; define the control inputs of the reactive power control equipment as the reactive power setpoint vectors of IBRs, and the voltage setpoint vectors of SGs and SVCs. ; The objective function of the optimal reactive power flow online control model is: (1) The control effect provided by reactive power control equipment is quantified using a quadratic function: (2) In the formula, To control input The set of upper and lower limits for each vector in the set; , These represent the reactive setpoint vectors of SGs and SVCs, respectively; , , All are symmetric positive definite matrices; For the reactive power setpoint vector of IBRs; The deviation between the reactive power output of IBRs and their steady-state equilibrium point. The deviation between the reactive power output of SGs and its steady-state equilibrium point.

[0028] The deviation between the reactive power output of SVCs and their steady-state equilibrium point; Consider the steady-state power flow equality constraints, voltage inequality constraints, and equipment reactive power inequality constraints; The optimal reactive power flow online control model considers steady-state power flow equality constraints, voltage inequality constraints, and equipment reactive power inequality constraints: (3) In the formula, This is a vector of the voltage magnitudes of all load busbars. This is the superimposed vector of reactive power output from each reactive power control device. ; Represents the disturbance experienced by the power grid; nonlinear function This is a steady-state power flow model for the power grid; To control the input, ; Lower limit of load bus voltage amplitude Upper limit of load bus voltage amplitude Lower limit of reactive power output of reactive power equipment The upper limit of reactive power output of reactive equipment; this model describes the relationship between control input and measured value.

[0029] Based on real-time measurement data from the PMU, a gradient dynamic method is used to iterate the objective function. The power flow equations are linearized using an approximate form of the Jacobian matrix, and the optimal reactive power flow problem is transformed into an online control problem by combining the dynamic expression of the control system. The dynamics of the control system are expressed as: (4) In the formula, Representing system state variables, functions A function represents the natural dynamic behavior of a system when there is no external input. The function reflects the effect of control input on the system state; For control input; State variables Regarding time The derivative of .

[0030] The online control problem is represented as: (5) In the formula, This represents the gradient descent gain coefficient. Represents the initial state variable. Represents the steady-state value of a state variable. Represents an approximate Jacobian matrix; For control input; , These control the upper and lower limits of the input, respectively. , These are the upper and lower bounds of the state variable, respectively; ; State variables Regarding time The derivative; Indicates control input Regarding time The derivative; This is the objective function. The above formula provides a framework for controlling the dynamic updates of the input while satisfying static physical constraints.

[0031] A safe region for the improved control barrier function is constructed; and the control barrier function is designed based on the voltage inequality constraint to form an online optimal reactive power flow control law based on the improved control barrier function. For load nodes within the safe region, a quadratic programming solver is used to obtain the optimal control input; for load nodes outside the safe region, a sequential quadratic programming is used to obtain the optimal control input.

[0032] The safe domain of the control barrier function is defined as follows: (6) In the formula, To control the barrier function, satisfy the safety domain System status Within a safe range; express The control strategy of this invention based on the improved control barrier function must ensure: 1) Stability and safety, given the current state of the system. ,like Then it is necessary to ensure that the system state is always within a safe range; 2) Asymptotic safety, if Then the system state should be driven to a safe range within a finite time.

[0033] Design control obstacle function based on voltage inequality constraint for: (7) In the formula, It is a control barrier function designed for the lower voltage limit. It is a control barrier function designed for the upper voltage limit; A vector representing the voltage magnitude of all load buses.

[0034] When constructing control barrier function constraints, it is necessary to obtain the measured state. judge , The symbols are used to assign different constraints to load nodes inside and outside the safety region, respectively. Based on a quadratic programming control solution architecture, the following control law can be derived: (8) In the formula, This is a relaxation term; For a class function; For a non-class that adjusts security constraints function;

[0035] Indicates the control input for the next time step. This indicates the current time step control input. Indicates the steady-state value of the control input; A positive semi-definite matrix ; To suppress the oscillation coefficient; The relaxation coefficient; , The function reflects the effect of control input on the system state; This represents the load node within the security domain. , This indicates a load node outside the security domain. This represents the set of load nodes within the security domain. , This represents the set of load nodes outside the security domain. , , Represents the load node set; For the state of measurement; allocation The relevant CBF constraints are applied to the load nodes within the safety domain. ,distribute The relevant finite-time return safety domain constraints are applied to load nodes outside the safety domain. For load nodes within the safety region, a quadratic programming solver is used to obtain the optimal control input; for load nodes outside the safety region, a sequential quadratic programming approach is used to obtain the optimal control input.

[0036] Dynamic constraint integration: The static physical constraints of Formula 5 and the dynamic safety constraints of CBF (Formula 8) together constitute a complete set of control model constraints; Closed-loop control mechanism: Equation 5 dynamically generates the initial control input through gradient; CBF adjusts the input based on the real-time state. Adjust the constraints (Formula 8) to further optimize the control input. This forms a closed-loop feedback loop.

[0037] The introduction of CBF enables the gradient dynamic control in Equation 5 to adapt to sudden disturbances, such as voltage drops, and avoids control failure caused by model uncertainty in traditional methods.

[0038] In this invention, Equation 5 forms the basic framework for dynamically updating the control input, while the control barrier function is supplemented by real-time safety constraints (Equation 8), forming a two-layer control mechanism of "gradient-driven + safety constraints". The two work together to ensure control efficiency (rapid dynamic response of gradient) and improve the system's anti-disturbance capability and safety.

[0039] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention, or modify it into equivalent embodiments, without departing from the scope of the present invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technology of the present invention without departing from the scope of the present invention are within the protection scope of the present invention.

Claims

1. A method for on-line voltage control of power transmission network based on gradient dynamics and control barrier function, characterized in that: The method comprises the following steps of: constructing an optimal reactive power flow online control model based on gradient dynamics; An objective function of the optimal reactive power flow online control model is: F(Q ibr ,Q sg ,Q svc ) = (ΔQ ibr ) T R ibr (ΔQ ibr )+(ΔQ sg ) T R sg (ΔQ sg )+(ΔQ svc ) T R svc (ΔQ svc ) where U is the set of upper and lower limits on each vector in the control input u; Q sg , Q svc represent the reactive setpoint vectors for the SGs and SVCs, respectively; R ibr , R sg , R svc are symmetric positive definite matrices; Q ibr is the reactive setpoint vector for the IBRs; ΔQ ibr is the deviation of the reactive output of the IBRs from their steady state equilibrium point, ΔQ sg is the deviation of the reactive output of the SGs from their steady state equilibrium point, ΔQ svc is the deviation of the reactive output of the SVCs from their steady state equilibrium point; Based on real-time measurement data of the PMU, gradient iteration is performed on the objective function by using a gradient dynamic method; a flow equation is linearized by using an approximate form of a Jacobian matrix, and the optimal reactive power flow problem is converted into an online control problem in combination with a dynamic expression of a control system; A safety domain of an improved control barrier function is constructed; a control barrier function is designed according to voltage inequality constraints, an online optimal reactive power flow control law based on the improved control barrier function is formed, and an optimal control input is obtained by using a quadratic programming solver for load nodes in the safety domain; and an optimal control input is obtained by using a sequential quadratic programming for load nodes outside the safety domain.

2. The method for on-line voltage control of power grid based on gradient dynamics and control barrier function according to claim 1, characterized in that: Constraint conditions of the optimal reactive power flow online control model are: where V l is the vector of all load bus voltage magnitudes; Q c is the superposition vector of all reactive power outputs of the reactive power control devices, Q c = [Q ibr , Q sg , Q svc ]; w represents the disturbance to the power grid; the nonlinear function H p is the steady-state power flow model of the power grid; u is the control input, u = [Q ibr , V sg , V svc ]; represents the lower limit of the load bus voltage magnitude, represents the upper limit of the load bus voltage magnitude, represents the lower limit of the reactive power output of the reactive power device, represents the upper limit of the reactive power output of the reactive power device.

3. The method of claim 1, wherein the method is characterized by: The dynamic expression of the control system is: In the formula, x represents the system state variable, the function f(·) function represents the natural dynamic behavior of the system without external input, and the function g(·) reflects the influence of the control input on the system state; u is the control input; is the derivative of the state variable x with respect to time t.

4. The method of claim 3, wherein the method is characterized by: The online control problem is expressed as: where K represents a gradient descent gain coefficient, x0represents an initial state variable, x * represents a steady state value of the state variable, and Π represents an approximate Jacobian matrix; u is a control input; u max , u min are an upper limit and a lower limit of the control input, respectively; x max , x min are an upper limit and a lower limit of the state variable, respectively; is a derivative of the state variable x with respect to time t; is a derivative of the control input u with respect to time t; and F(Q) is an objective function.

5. The method of claim 1, wherein the method is characterized by: The safety domain of the control barrier function is defined as: where B(x) is a control barrier function satisfying the safety region x is in the safety region; R n denotes the n-dimensional real space.

6. The method of online voltage control for power grid based on gradient dynamics and control barrier function according to claim 5, characterized in that: The control barrier function B(x) is: where B (1) (x) is a control barrier function designed for the lower voltage limit, B (2) (x) is a control barrier function designed for the upper voltage limit; V l denotes the vector of all load bus voltage magnitudes.

7. The method of online voltage control for power grid based on gradient dynamics and control barrier function according to claim 6, characterized in that: The online optimal reactive power flow control law based on the improved control barrier function is: where u k+1 denotes the next time step control input, u k denotes the current time step control input, u * denotes the steady state value of the control input; R is a positive semi-definite matrix r is the damping coefficient; p is the relaxation coefficient g(·) function reflects the influence of the control input on the system state; δ is the relaxation term; α(·) is a function; is a non-class function that adjusts the security constraints; i denotes the load node within the security region, j, m denotes the load node outside the security region, I denotes the set of load nodes within the security region, J, M denotes the set of load nodes outside the security region, i≠j≠m, denotes the set of load nodes; x k is the measured state; the CBF constraint associated with α(·) is assigned to the load node i within the security region, and the finite time return to security region constraint associated with α(·) is assigned to the load node j / m outside the security region.

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