A robust attraction domain geometric configuration control method for direct current power systems

Abstract

The present application belongs to the technical field of direct current power system, and discloses a kind of robust attraction domain geometric form control method of direct current power system, comprising the following steps: the dynamic model and static flow model of direct current power system are established;Under the given operation range and load uncertainty set, the robust stability condition of guaranteeing attraction domain is derived: the robust stability condition is embedded in OPF control synthesis model in the form of linear constraint, and the power supply voltage reference is obtained by solving, to realize the efficient control parameter design of calculation;Numerical examples are carried out on single-bus direct current system and IEEE14 node direct current system, to verify the effectiveness of the proposed method.The present application proposes and realizes the robust control idea of "guaranteeing attraction domain" to load interval uncertain working condition, so that the attraction domain corresponding to any operating point in the load uncertainty set can move adaptively with the operating point, and continuously and completely envelope the preset operating range, so as to still provide clear transient stability guarantee under load fluctuation.

Description

Technical Field

[0001] This invention relates to the field of DC power system technology, and in particular to a robust attraction domain geometry control method for DC power systems. Background Technology

[0002] In recent years, DC power systems have been increasingly widely used in new energy power generation, data centers, rail transit, and industrial power distribution, but their safe and stable operation faces severe challenges. The nonlinear characteristics of constant power loads within the system, the fluctuations of intermittent new energy sources, and various random disturbances make the transient stability problem of DC systems under large disturbances particularly prominent. The attraction domain, as a key concept for evaluating the system's ability to recover to a stable equilibrium point from large disturbances, has become a core research topic for improving the robustness of DC systems.

[0003] Research on the attraction domain has mainly followed two paths: one is the estimation and analysis of the attraction domain, which is usually based on Lyapunov stability theory. By constructing energy functions and combining numerical tools such as linear matrix inequalities, the attraction domain near a specific operating point is approximated internally to quantify the transient stability margin of the system; the other is the control design oriented towards the attraction domain, which aims to expand or shape the attraction domain near the equilibrium point by tuning control parameters (such as droop coefficient, voltage reference value, etc.), thereby enhancing the system's ability to resist disturbances.

[0004] However, in practical engineering, the load of DC systems often exhibits significant uncertainty, with its power continuously varying within a certain range, causing the system's steady-state operating point to constantly shift. Under this dynamically changing operating environment, existing technologies reveal the following systemic defects, making it difficult to meet the comprehensive requirements of engineering applications for robustness, real-time performance, and stringent assurance: 1. Poor adaptability to operating conditions and lack of robust coverage: Most existing methods estimate the attraction domain or design controllers for a single or a few pre-set nominal operating conditions, and the shape and location of the obtained attraction domain are fixed. When the actual load deviates from the nominal value and causes the operating point to migrate, the originally designed attraction domain may not be able to effectively enclose the new operating neighborhood, making the original stability conclusions invalid and failing to guarantee global stability within the uncertain load range.

[0005] 2. Heavy computational burden and difficulty in online implementation: To cope with changes in operating point, existing technologies typically require periodically repeating complex numerical estimations of the attraction domain or optimization of controller parameters. These processes involve nonlinear programming or multiple solutions to linear matrix inequalities, resulting in high computational costs and long processing times, severely limiting their application in control scenarios requiring rapid response or online adaptive adjustment.

[0006] 3. Insufficient theoretical guarantees and ambiguous performance boundaries: Existing attraction domain estimation methods mostly rely on iterative algorithms or numerical searches. Although they can provide an approximate shape of the attraction domain, they usually lack rigorous mathematical proofs and cannot ensure that the obtained attraction domain has deterministic and verifiable "guarantee" properties throughout the entire target operating range. This makes it difficult to clearly answer the key engineering question of "whether the system is absolutely safe within a given operating set".

[0007] 4. Lack of a comprehensive control framework and passive design objectives: Existing research mainly focuses on stability "analysis and verification" under given control parameters, and has not yet formed a systematic "comprehensive" framework. This framework should be able to reverse and actively solve for the optimal control parameters that make the attraction domain accurately contain the target set based on the preset safe operating range (target set) and performance indicators, thereby achieving active "shaping" of the geometry of the attraction domain.

[0008] 5. Limited model complexity and weak engineering scalability: The theoretical derivation and verification of most existing methods are limited to single-converter or simple single-bus system models. For complex DC networks with multiple nodes, branches, and ports, existing methods face significant challenges in terms of model processing, problem-scale expansion, and computational complexity, resulting in insufficient universality and scalability.

[0009] In summary, under the reality of uncertain loads, existing technologies cannot provide a systematic design method for control parameters that, under rigorous theoretical guarantees and with acceptable computational cost, ensures that a DC system possesses a robust attraction domain throughout its preset operating range. This technological gap hinders the in-depth optimization of DC power systems to achieve the dual objectives of safe and stable operation and economical operation under wide operating conditions and high uncertainty. Therefore, there is an urgent need to develop a new method for controlling the geometric shape of the attraction domain of DC power systems that balances robustness, rigor, and practicality. Summary of the Invention

[0010] To overcome the technical deficiencies of existing technologies, this invention provides a robust attraction domain geometry control method for DC power systems, comprising the following steps: Step 1: Based on the topology and component parameters of the DC power system, establish a nonlinear dynamic model and a steady-state power flow model for the DC power system including constant power loads; Step 2: Based on the nonlinear dynamic model, under the condition that the load power is an interval uncertain parameter and the system is given a preset operating range, a linear robust stability condition is derived. Step 3: Using the active power cost of the power supply as the objective function, construct and solve an optimization model. The constraints of the optimization model include the steady-state power flow model, the robust stability condition, and the system operation constraints. The optimization model solves for the power supply voltage reference value that ensures the system has a robust attraction domain under load uncertainty conditions, so as to achieve computationally efficient control parameter design. Step 4: Conduct numerical examples on the simulation system using a single-bus DC system and an IEEE 14-bus DC system to verify the effectiveness of the proposed method.

[0011] Preferably, the method for establishing the nonlinear dynamic model is to construct a node admittance matrix including the power supply side nodes and the load side nodes based on the above-mentioned topology and component parameters of the DC power system, and to select physical quantities such as capacitor voltage and inductor current to form a state vector. A state-space model of an RLC circuit, including line inductance, resistance, node capacitance, and constant power load, is established, yielding nonlinear dynamic equations with line current and bus voltage as state variables: ; in For state vectors, For power supply voltage reference, For load power vector, It is a diagonal array composed of inductors and capacitors. , , , The system matrix is ​​determined by the circuit parameters; Given load power vector and power supply voltage reference Under these conditions, the corresponding equilibrium point can be obtained by solving the power flow equations. And define the state deviation relative to the equilibrium point. Based on this, By performing a coordinate transformation, the nonlinear dynamic behavior of the DC power system can be equivalently represented as: ; Among them, the system matrix nonlinear terms ,symbol This indicates element-wise division. This indicates element-wise multiplication. This is the load-side bus voltage vector. It is a diagonal matrix composed of vector elements.

[0012] Preferably, the method for establishing the steady-state power flow model is as follows: based on the block form of the nodal admittance matrix, the power flow equations at the equilibrium point are established: ; ; In the above formula This is the load-side balancing voltage. Inject power into the power source. For the corresponding sub-block of the admittance matrix, It is a diagonal matrix composed of vector elements.

[0013] Preferably, step 2 specifically includes the following steps: defining the guaranteed attraction domain and providing sufficient stability conditions under a single nominal load; introducing a load uncertainty set and analyzing the dependence of the criterion on the load; and finally obtaining a linear robust stability criterion.

[0014] Preferably, the definition guarantees the attraction domain and provides sufficient stability conditions under a single nominal load. Specifically, the operation is as follows: within a preset operating range... Based on this, the concept of the attraction field is introduced, which is derived from step 1. The described DC power system ROA can completely encompass the set If so, the system is said to have a guaranteed attraction domain; Subsequently, at a given nominal load and equilibrium point Under the condition of selecting an ellipsoidal candidate set As a set of ROA guarantees, a set of stability parameters is introduced. Using the Lyapunov function and linear matrix inequality method, the following sufficient condition for transient stability under given operating conditions is obtained: If the equilibrium point voltage vector satisfy: ; Then the system is said to be related to the set It possesses transient stability with a guaranteed attraction domain; where , , and It can be obtained by solving a set of LMIs.

[0015] Preferably, the operation of introducing a load uncertainty set and analyzing the dependence of the criterion on the load is as follows: modeling the load power vector as... ,in , These are the lower and upper limits of the load, respectively. The value is usually negative, representing a high-load scenario; In this case: Nonlinear terms in system dynamics Follow It changes and becomes an uncertain quantity; criterion The right end explicitly contains It has uncertainty; equilibrium point and left-hand vector Also The function is uncertain; Based on this, maintain , and Assuming the calculation results remain unchanged; The formula The right end is denoted as ; Based on observations, Regarding load Monotonically decreasing; simultaneously, based on the conclusions of existing DC power flow equations, it can be concluded that the equilibrium voltage monotonically decreases as the load increases, i.e. It is with the load If it is monotonically increasing, then for any have ; This shows that in high-load scenarios The following satisfies ; Then for the interval For all lighter load conditions, the above inequality holds automatically.

[0016] The preferred method for obtaining the linear robust stability criterion is as follows: Based on the above analysis, it is formally proposed that, given an equilibrium point... Stability set , ensure ROA set and load uncertainty set If the inequality is under high load conditions If it is established, then it applies to all , All in the set It has a guaranteed attraction field, thus ensuring operation within the operating range. Robust transient stability is achieved.

[0017] Preferably, step 3 specifically involves: based on the robust stability criterion given in step 2, adjusting the robust stability inequality conditions... DC power flow constraints They are all embedded into a control synthesis and optimization framework similar to optimal power flow; Specifically, with the active power cost of the power supply as the target, the power supply voltage reference... Equilibrium state Load-side balance voltage and power injection power As decision variables, the following optimization model is constructed: ; ; ; Among them, constraints Describe the physical and engineering limits and constraints of the power supply voltage, operating point range, and power output. Ensuring steady-state power flow is solvable, constraints This directly reflects the linear robust stability condition derived in step 2; By solving the above optimization model, a power supply voltage reference that balances operational economy is obtained while satisfying the robust guarantee of the attraction domain condition. and corresponding running points Based on the conclusion of step 2, the control optimization model has a feasible solution. Therefore, the power supply voltage corresponding to any feasible solution is... To ensure that in the uncertain set of loads Under all feasible load conditions, the system has a preset operating range. The guaranteed attraction domain is adaptively shifted as the operating point changes; thus, step 3 realizes the geometric shape control function of maintaining a robust envelope of the attraction domain geometry across the entire load range by comprehensively optimizing the power supply voltage through a primary OPF-like design.

[0018] Preferably, step 4 specifically involves: conducting numerical simulation verification using MATLAB / Simulink on a single-bus DC system and an IEEE 14-bus DC system. In the single-bus example, the operating range is set and the load varies between 150-800W. After obtaining the power supply voltage reference, it is observed that the ROA can adaptively move with the operating point and continuously enclose the preset operating range, and the boundary initial value trajectories converge. Simultaneously, a comparison is made with the baseline control designed only for the nominal load. In the IEEE 14-bus example, voltage and output limits, a load range of 5-25kW, and the operating range are set. The power supply voltage reference obtained by control synthesis enables the trajectories under different loads and different initial boundary values ​​to converge to the corresponding equilibrium point, thereby verifying the robust transient stability under load uncertainty, ensuring the geometric following characteristics of the attraction domain, and the scalability to multi-node DC systems.

[0019] The beneficial effects of this invention are: 1. This invention addresses uncertain load conditions by proposing and implementing a robust control concept called "Guaranteed ROA," which enables the attraction domain corresponding to any operating point within the uncertain load set to adaptively move with the operating point and continuously and completely enclose the preset operating range, thereby providing a clear guarantee of transient stability under load fluctuations.

[0020] 2. This invention transforms "single-condition stability" into "load range robustness conditions," reducing the complexity of robustness verification scenarios: The core innovation of this invention lies in systematically transforming existing stability certification conditions for a single nominal load into robust stability conditions applicable to a set of uncertain loads. Utilizing structural characteristics such as the monotonicity of the DC system's balance voltage changing with load, the robustness problem, which originally required verifying "infinitely many scenarios" within the set of uncertain loads, is equivalently reduced to determining a finite number of representative conditions (e.g., high-load representative conditions). This significantly reduces the computational load of robustness analysis and design, forming robust stability conditions that can be directly used for engineering design and verification, solving the problem of easy failure of stability guarantees under load changes in existing technologies.

[0021] 3. The present invention takes "the attraction domain completely encompassing the given operating range" as its direct objective. By comprehensively designing the power supply voltage reference, the geometric shape (position and size) of the attraction domain meets the preset envelope requirements and maintains this envelope relationship when the load changes. This realizes and quantifies key operational issues such as "whether the system is stable throughout the entire operating range", forming an interpretable and implementable transient safety boundary.

[0022] 4. This invention embeds the robust stability linear condition into the control synthesis optimization framework in the form of a programmable constraint. While satisfying power flow feasibility and equipment operation constraints, it obtains the power supply voltage reference. It can also be proven that any feasible solution can guarantee the robust transient stability within the load uncertainty set and guarantee the attraction domain property, thus achieving the unity of "computability" and "provability".

[0023] 5. This invention is not only applicable to single-bus DC systems, but also to typical DC system structures with multiple nodes, multiple branches, and multiple power sources. Through numerical examples, it is shown that this invention can maintain trajectory convergence and clear stability margin under uncertain load conditions, and can be extended to larger-scale DC network scenarios, showing good engineering application prospects. Attached Figure Description

[0024] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0025] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is the equivalent topology diagram of the DC system of the present invention; Figure 3 This is a schematic diagram of the attraction field of the adaptive geometric shape designed in this invention; Figure 4 This is a schematic diagram comparing the bus voltage trajectory under the proposed method of the present invention with that under reference control. Figure 5 This is a schematic diagram of a representative two-dimensional state trajectory of the IEEE 14-node system under different initial conditions within the load range of 5–25kW according to the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the various embodiments of this invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this invention to facilitate a better understanding of this application. However, the technical solutions claimed in the claims of this application can be implemented even without these technical details and with various variations and modifications based on the following embodiments.

[0027] like Figure 1-4 As shown, this embodiment provides a robust attraction domain geometry control method for a DC power system, including the following steps: Step 1: Based on the topology and component parameters of the DC power system, establish a nonlinear dynamic model and a steady-state power flow model for the DC power system including constant power loads; Step 2: Based on the nonlinear dynamic model, under the condition that the load power is an interval uncertain parameter and the system is given a preset operating range, a linear robust stability condition is derived. Step 3: Using the active power cost of the power supply as the objective function, construct and solve an optimization model. The constraints of the optimization model include the steady-state power flow model, the robust stability condition, and the system operation constraints. The optimization model solves for the power supply voltage reference value that ensures the system has a robust attraction domain under load uncertainty conditions, so as to achieve computationally efficient control parameter design. Step 4: Conduct numerical examples on the simulation system using a single-bus DC system and an IEEE 14-bus DC system to verify the effectiveness of the proposed method.

[0028] To address the shortcomings of existing ROA design and control methods under uncertain load conditions, this invention proposes a comprehensive control scheme that adaptively adjusts the geometry of the attraction domain. This ensures that, within a given range of load uncertainty, the pre-specified operating range is always completely encompassed by the attraction domain, thereby achieving robust transient stability. Specifically, this invention provides solutions to the following technical problems: (1) In view of the problem that existing ROA design technology can only provide stability conditions under a single nominal working condition and it is difficult to calculate ROA in real time under varying load conditions, this invention constructs a class of computable robust stability criteria, establishes an explicit relationship between the geometric shape change of the attraction domain and state variable parameters such as the equilibrium point voltage, and simplifies the nonlinear numerical problem of real-time ROA calculation into a set of algebraic inequality stability criteria, providing a mathematical basis that can be directly called for subsequent ROA-based geometric shape control technology.

[0029] (2) When the load has interval uncertainty, traditional methods need to verify the stability of an infinite number of load scenarios one by one and it is difficult to obtain robust conclusions in a timely manner. This invention utilizes the structural characteristics such as the monotonicity of the balance voltage of the DC power system with load changes to establish a monotonic relationship between the threshold on the right end of the attraction domain criterion and the load. This realizes the strict equivalent transformation of "transient stability check of the entire load uncertainty set" into "judgment of high load conditions". Thus, without reducing the safety margin, the original single-scenario stability condition is systematically improved into a robust stability condition on the load interval, and the computational complexity of analysis and design is significantly reduced.

[0030] (3) To address the problems of existing ROA control technologies lacking a comprehensive system control framework, being unable to obtain appropriate control quantities based on the target operating range, and being difficult to actively "shape" the geometry of the attraction domain, this invention, based on equipment constraints and operating constraints, writes the robust attraction domain criterion as a programmable constraint and embeds it into the comprehensive control model to solve for the control voltage reference quantity of the DC power system. Under this control voltage, transient performance ensures that the ROA can adaptively move within the load uncertainty range as the operating point moves and continuously envelop the preset operating range, thus realizing adaptive control of the attraction domain geometry.

[0031] (4) In view of the problem that existing methods are mostly limited to single converter or single bus structure and are difficult to extend to multi-node DC systems, this invention proposes a robust attraction domain geometry control method applicable to multi-node, multi-branch, and multi-port DC power systems under a unified DC system state space and power flow model framework. This makes the proposed technology not only applicable to simple single-bus microgrid structures, but also extendable to general DC network scenarios with multiple converters and multiple load nodes. Under the premise of keeping the computational complexity acceptable, it provides an attraction domain geometry control technology that is scalable, implementable and has robust stability guarantee for engineering applications.

[0032] Step 1 specifically includes the following steps: Assume the DC system consists of several power supply nodes and load nodes, and the nodes are interconnected through equivalent RLC transmission lines. The DC system topology is shown below. Figure 2 As shown.

[0033] The method for establishing the nonlinear dynamic model is as follows: First, based on the aforementioned topology and component parameters of the DC power system, this invention constructs a node admittance matrix including power supply-side nodes and load-side nodes, and selects physical quantities such as capacitor voltage and inductor current to form a state vector. Based on the network topology and component parameters of the DC power system, an RLC state-space model including line inductance, resistance, node capacitance, and constant power load (CPL) is established, yielding nonlinear dynamic equations with line current and bus voltage as state variables: (1) in For state vectors, For power supply voltage reference, For load power vector, It is a diagonal array composed of inductors and capacitors. , , , The system matrix is ​​determined by the circuit parameters.

[0034] Given a load power vector and power supply voltage reference Under these conditions, the corresponding equilibrium point can be obtained by solving the power flow equations. And define the state deviation relative to the equilibrium point. Based on this, the present invention performs coordinate transformation on the system dynamic equation (1), and expresses the nonlinear dynamic behavior of the DC power system equivalently as follows: (2) Among them, the system matrix nonlinear terms .symbol This indicates element-wise division. This indicates element-wise multiplication. This is the load-side bus voltage vector. It is a diagonal matrix composed of vector elements.

[0035] Meanwhile, this invention establishes a steady-state power flow model at the equilibrium point based on the block form of the nodal admittance matrix: ; (3) in, This is the load-side balancing voltage. Inject power into the power source. For the corresponding sub-block of the admittance matrix, This is a diagonal matrix composed of vector elements. Through the above modeling steps, a mathematical model characterizing the dynamic behavior and steady-state operating point of the DC power system is obtained, providing a foundation for subsequent derivation of robust stability criteria and geometric control of the attraction domain.

[0036] Step 2 specifically includes the following steps: Under the condition that the load has an interval uncertainty, construct a robust stability criterion for "guaranteed attraction domain" with strict mathematical basis, so as to provide a constraint basis for subsequent geometric shape control synthesis, specifically including the following three aspects: (1) Define the guaranteed attraction domain and provide sufficient stability conditions under a single nominal load. This invention first defines the operating range... Based on this, the concept of "guaranteed attraction domain" is introduced: if the DC power system ROA described by equation (2) in step 1 can completely contain the set If so, the system is said to have a guaranteed attraction domain.

[0037] Subsequently, at a given nominal load and equilibrium point Under the condition of selecting an ellipsoidal candidate set As a set of ROA guarantees, a set of stability parameters is introduced. Using the Lyapunov function and the linear matrix inequality (LMI) method, the following sufficient condition for transient stability under given operating conditions can be obtained: If the equilibrium point voltage vector satisfy (4) Then the system is said to be related to the set It possesses transient stability with a guaranteed attraction domain; where , , and It can be obtained by solving a set of LMIs.

[0038] (2) Introducing a load uncertainty set and analyzing the dependence of the criterion on the load. Considering that most DC system loads have interval uncertainty, this invention models the load power vector as follows: ,in , These are the lower and upper limits of the load, respectively. Typically negative, representing high-load scenarios. In this case: 1) Nonlinear terms in system dynamics Follow 1) Changes into an uncertain quantity; 2) Criterion (3) Explicit inclusion on the right side It has uncertainty; 3) Equilibrium point and left-hand vector Also The function is uncertain.

[0039] Based on this, the present invention maintains , and Under the premise that the calculation result remains unchanged, the right side of equation (3) is denoted as (5) Based on observation, it can be concluded that Regarding load Monotonically decreasing; simultaneously, based on the conclusions of existing DC power flow equations, it can be concluded that the equilibrium voltage monotonically decreases as the load increases, i.e. It is with the load If it is monotonically increasing, then for any have (6) This shows that in high-load scenarios The following satisfies (7) Then for the interval For all lighter load conditions, the above inequality automatically holds. Therefore, what was originally required for the entire uncertain set... The stability conditions that were checked point by point were strictly and equivalently "contracted" to only needing to be verified on a single high-load representative scenario.

[0040] (3) Finally, a linear robust stability criterion is obtained. Based on the above analysis, this invention further formalizes the following: given an equilibrium point Stability set , ensure ROA set and load uncertainty set If inequality (7) holds under high load conditions, then for all System (2) is in the set It has a guaranteed attraction field, thus ensuring operation within the operating range. Robust transient stability is achieved. This conclusion systematically elevates the original "guaranteed ROA condition for a single load scenario" to "robust guaranteed ROA condition over the entire uncertain load range," and the final criterion is retained in the form of a linear inequality, which facilitates its embedding into the control integrated optimization model along with the operating constraints in step 3.

[0041] Step 3 is used to comprehensively design the power supply voltage reference under operational and equipment constraints, and to achieve control over the robust attraction domain geometry of the DC system. Specifically, it includes: based on the robust stability criterion given in step 2, embedding the robust stability inequality condition (7) and the DC power flow constraint (3) together into a near-optimal power flow (OPF) control comprehensive optimization framework. Specifically, with the active power cost of the power supply as the objective, the power supply voltage reference is... Equilibrium state Load-side balance voltage and power injection power As decision variables, the following optimization model (8) is constructed: (8a) (8b) (8c) Among them, constraints Describe the physical and engineering limits and constraints of the power supply voltage, operating point range, and power output. Ensuring steady-state power flow is solvable, constraints This directly reflects the linear robust stability condition derived in step 2.

[0042] By solving the above optimization model, this invention can obtain a power supply voltage reference that balances operational economy, while satisfying the robust guarantee of the attraction domain condition. and corresponding running points Based on the conclusion of step 2, as long as the optimization model is controlled... If a feasible solution exists, then the power supply voltage corresponding to any feasible solution is... Both can guarantee that in a load uncertainty set Under all feasible load conditions, the system has a preset operating range. The guaranteed attraction domain is adaptively shifted as the operating point changes. Thus, step 3 achieves the geometric shape control function of maintaining a robust envelope of the attraction domain geometry across the entire load range through comprehensive optimization design of the power supply voltage using a primary OPF-like approach, while preserving the convex structure of the OPF problem and high computational efficiency.

[0043] Step 4 is verified through numerical simulations using MATLAB / Simulink on a single-bus DC system and an IEEE 14-bus DC system. In the single-bus example, the operating range (upper bound of voltage / current disturbance) is set, and the load varies between 150-800W. After obtaining the power supply voltage reference using the method of this invention, it can be observed that the ROA can adaptively move with the operating point and continuously enclose the preset operating range, and the boundary initial value trajectories converge. At the same time, compared with the reference control designed only for nominal load, the reference control shows obvious oscillations or even instability under high load conditions, while the present invention still maintains transient stability. In the IEEE 14-bus example, voltage and output limits, load range of 5-25kW and operating range are set. The power supply voltage reference obtained by the control synthesis of this invention enables the trajectories under different loads and different initial boundary values ​​to converge to the corresponding equilibrium point, thereby verifying the robust transient stability of this invention under load uncertainty, the geometric following characteristics of the attraction domain, and the scalability to multi-node DC systems.

[0044] This invention uses MATLAB / Simulink to build a DC system simulation platform, and performs comparative verification on a single-bus DC system and an IEEE 14-bus DC system to verify the ability of the power supply voltage reference designed in this invention to maintain the "guaranteed attraction domain" and transient stability within the load uncertainty set.

[0045] (1) Verification and comparison of single busbar calculation examples A single-bus DC system is selected as a case study. The load is a constant power load model with a nominal power of 150W, and primary droop control is used on the power supply side. The preset operating range is characterized by the upper bounds of voltage and current disturbances relative to the equilibrium point, i.e., voltage fluctuations do not exceed 20V and current fluctuations do not exceed 20A. The load uncertainty set is assumed to be... W. Since this example involves only a single power source, the cost function does not affect the discriminative power of the optimal solution. Therefore, the objective function of the integrated control is rewritten as minimizing the power source voltage reference. The power supply voltage reference is obtained by solving the control synthesis problem. V, and in Disturbance simulations were conducted across the entire range. Simulation results show that, under different load levels, the guaranteed ROA obtained by the method of this invention can adaptively follow the movement of the operating point and continuously cover the preset operating range; the state trajectories starting from the boundary of the operating range can all converge to the corresponding equilibrium point, thus verifying the guarantee of transient stability under load uncertainty.

[0046] (2) Stability comparison with fixed nominal operating condition reference control Selecting the existing ROA design method under given operating conditions, at nominal load The baseline control designed under W was used as a comparison object. When the steady-state load deviates from the nominal value, the ROA corresponding to this baseline control cannot provide a stability guarantee for the new operating point. By increasing the steady-state load to 800 W, and... When boundary disturbances are applied to the system, simulations show that the method of the present invention can still maintain the convergence of the bus voltage trajectory and maintain transient stability, while the reference control exhibits significant oscillations and eventually becomes unstable. This verifies the advantage of the method of the present invention in terms of robustness compared to the fixed operating condition design.

[0047] (3) Scalability verification of the IEEE 14-node example The applicability of this invention was further verified on the IEEE 14-node DC system reference system. The nominal system load was set at 5 kW, and the per-unit basis value was... V. kW, power generation cost coefficient The source voltage and the steady-state voltage of each node are constrained by... PU, the output power of each power supply is limited to pu, the load uncertainty set is set as kW, transient feasible operating range set to pu. The power supply voltage reference vector is obtained by solving the integrated control design proposed in this invention. In the simulation, the initial state of the system is set to... The boundary conditions were determined, and tests were conducted under different load levels. Representative two-dimensional trajectory results show that all trajectories converge to the corresponding equilibrium point, verifying the robust transient stability and scalability of the proposed method in multi-node DC systems.

[0048] (4) Experimental results in, Figure 3 For the designed, controllable geometry of the attraction domain, the "guarantee ROA ellipsoid" can adaptively adjust its geometry to fully cover the pre-defined operating range and throughout the entire... Within the range, it adaptively "tracks" as the operating point moves; the voltage trajectories starting from the boundary of the operating range all converge to their respective operating points; Figure 4 For the case where the steady-state load jumps to 800W in 0.1s and a boundary disturbance is applied, the method of the present invention is compared with the bus voltage trajectory under reference control; Figure 5 The diagram illustrates representative two-dimensional state trajectories of an IEEE 14-bus system under different initial conditions within a load range of 5–25 kW. The verification results demonstrate that the control synthesis method proposed in this invention can achieve robust transient stability with a guaranteed attraction domain within a load uncertainty range, and possesses good computational feasibility and engineering applicability.

[0049] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A robust attraction domain geometry control method for a DC power system, characterized in that: Includes the following steps: Step 1: Based on the topology and component parameters of the DC power system, establish a nonlinear dynamic model and a steady-state power flow model for the DC power system including constant power loads; Step 2: Based on the nonlinear dynamic model, under the condition that the load power is an interval uncertain parameter and the system is given a preset operating range, a linear robust stability condition is derived. Step 3: Using the active power cost of the power supply as the objective function, construct and solve an optimization model. The constraints of the optimization model include the steady-state power flow model, the robust stability condition, and the system operation constraints. The optimization model solves for the power supply voltage reference value that ensures the system has a robust attraction domain under the load uncertainty condition. To achieve computationally efficient control parameter design; Step 4: Conduct numerical examples on a single-bus DC system and an IEEE 14-bus DC system in the simulation system to verify the effectiveness of the proposed method; The method for establishing the nonlinear dynamic model is as follows: based on the aforementioned topology and component parameters of the DC power system, a node admittance matrix including the power supply side nodes and the load side nodes is constructed, and the state vector is composed of the physical quantities of capacitor voltage and inductor current. A state-space model of an RLC circuit, including line inductance, resistance, node capacitance, and constant power load, is established to obtain the nonlinear dynamic equations with line current and bus voltage as state variables. ； in For state vectors, For power supply voltage reference, For load power vector, It is a diagonal array composed of inductors and capacitors. The system matrix is ​​determined by the circuit parameters; Given load power vector and power supply voltage reference Under these conditions, the corresponding equilibrium point can be obtained by solving the power flow equations. And define the state deviation relative to the equilibrium point. Based on this, By performing a coordinate transformation, the nonlinear dynamic behavior of the DC power system can be equivalently represented as: ； Among them, the system matrix nonlinear terms ,symbol This indicates element-wise division. This indicates element-wise multiplication. It is a diagonal matrix composed of vector elements; The method for establishing the steady-state power flow model is as follows: Based on the block form of the nodal admittance matrix, the power flow equations at the equilibrium point are established: ； ； In the above formula This is the load-side balancing voltage. Inject power into the power source. For the corresponding sub-block of the admittance matrix, It is a diagonal matrix composed of vector elements.

2. The robust attraction domain geometry control method for a DC power system according to claim 1, characterized in that: Step 2 specifically includes the following steps: defining the guaranteed attraction domain and providing sufficient stability conditions under a single nominal load; introducing a load uncertainty set and analyzing the dependence of the criterion on the load; and finally obtaining a linear robust stability criterion.

3. The robust attraction domain geometry control method for a DC power system according to claim 2, characterized in that: The definition guarantees the attraction domain and provides sufficient stability conditions under a single nominal load. Specifically, the operation is as follows: within the preset operating range... Based on this, the concept of a guaranteed attraction domain is introduced, which is derived from step S1. The described DC power system ROA can completely encompass the set If so, the system is said to have a guaranteed attraction domain; Subsequently, at a given nominal load and equilibrium point Under the condition of selecting an ellipsoidal candidate set As a guarantee for the ROA set, a set of stability parameters is introduced. Using Lyapunov functions and linear matrix inequalities, the following sufficient condition for transient stability under given operating conditions is obtained: If the equilibrium point voltage vector satisfy: ； Then the system is said to be related to the set It possesses transient stability with a guaranteed attraction domain; where , , and It can be obtained by solving a set of LMIs.

4. The robust attraction domain geometry control method for a DC power system according to claim 3, characterized in that: The specific operation of step S4 is as follows: numerical simulation verification is carried out on a single-bus DC system and an IEEE 14-bus DC system using MATLAB / Simulink. In the single-bus example, the operating range is set and the load is varied in the range of 150-800W. After obtaining the power supply voltage reference, it is observed that the ROA can adaptively move with the operating point and continuously enclose the preset operating range, and the boundary initial value trajectories converge. At the same time, it is compared with the benchmark control designed only for the nominal load. In the IEEE 14-bus simulation, voltage and output limits, load range of 5-25kW, and operating range are set. The power supply voltage reference obtained by the control synthesis makes the trajectories under different loads and different initial boundary values ​​converge to the corresponding equilibrium point, thereby verifying the robust transient stability of the present invention under load uncertainty, ensuring the geometric following characteristics of the attraction domain, and the scalability to multi-node DC systems.

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