A method and system for distributed economic dispatch of heterogeneous microgrids under communication constraints

Abstract

The application provides a kind of distributed economic dispatching method and system of heterogeneous micro-grid under communication constraint, it is related to micro-grid distributed economic dispatching field, method includes: constructing strong communication topology, establishing the third-order transfer function model of each power generation unit;Build double-layer information interaction framework containing distributed observer and incremental cost consistency protocol;Establish the state space model of whole system, complete time domain stability proof by constructing Lyapunov function, determine the stable setting condition of observer gain and control gain;Critical delay boundary under communication delay is derived using frequency domain analysis method, the quantitative relationship between observer gain, communication topology spectral radius and critical delay is established;Based on the parameters designed, execute distributed dispatching.The application quantitatively derives the stability criterion and delay boundary by introducing heterogeneous third-order kinetic model, and realizes the global optimal economic distribution of generator output under communication constraint and high-order dynamics.

Description

Technical Field

[0001] This application relates to the field of distributed economic dispatch of microgrids, and in particular to a distributed economic dispatch method and system for heterogeneous microgrids under communication constraints. Background Technology

[0002] Existing distributed economic dispatching methods for microgrids mostly employ consensus algorithms to achieve global power optimization allocation, using communication networks to facilitate information exchange between generation units. This paper analyzes the impact of communication delay on algorithm convergence based on a first-order simplified model, and derives the maximum allowable delay boundary using the generalized Nyquist criterion and matrix perturbation theory, providing theoretical support for dispatch stability under delay conditions. However, these schemes do not fully consider the higher-order dynamic characteristics of generator governors, turbines, and rotor motion, and fail to account for multiple constraints such as communication delay and communication interruption, making them difficult to adapt to the complex operating scenarios of actual heterogeneous microgrids. Summary of the Invention

[0003] The purpose of this invention is to address the problem that existing distributed economic dispatch methods for microgrids do not fully consider the coupling effects of high-order dynamic characteristics of generation units and multiple constraints such as communication delays and communication interruptions, resulting in deviations between dispatch commands and actual physical responses, and lack quantitative criteria for stability boundaries. This invention provides a distributed economic dispatch method and system for heterogeneous microgrids under communication constraints.

[0004] The above-mentioned objective of this application is achieved through the following technical solution: S1: Construct a strongly connected communication topology, determine the algebraic connectivity and spectral radius of the Laplace matrix, establish a third-order transfer function model for each power generation unit, and characterize the dynamic response of the governor, turbine and rotor motion. S2: A two-layer information interaction protocol is established. The first layer is a distributed observer, which realizes the distributed estimation of global power imbalance through neighbor information interaction. The second layer is an incremental cost consensus protocol, which calculates local incremental cost based on the equal incremental rate criterion to achieve global consensus on incremental cost across the entire network. S3: Based on the third-order transfer function model, distributed observer, and incremental cost consensus protocol, establish a full system state-space model including physical layer state, incremental cost state, and power deficit estimation state, construct Lyapunov function to complete the time-domain stability proof, and determine the stable tuning conditions of observer gain and control gain. S4: The critical delay boundary under communication delay is derived using frequency domain analysis, and the quantitative relationship between observer gain, communication topology spectral radius and critical delay is established to complete the robust design of parameters. S5: Based on the designed parameters, distributed scheduling is performed to achieve the globally optimal economic allocation of heterogeneous generator output under communication constraints and high-order dynamics.

[0005] Optionally, step S1 includes: The third-order transfer function is:

[0006] in The reference instructions are calculated by the nodes based on information exchange. This is the simulated response value output after the lag element; This refers to the time constants corresponding to the motion processes of the generator governor, turbine, and rotor. For the Laplace operator.

[0007] Optionally, step S2 includes: The dynamic equation of the distributed observer is:

[0008] in For observer gain, For nodes The neighborhood group, For elements of the adjacency matrix, This is a compensation term that includes information on local power variations and disturbances; nodes Maintain a local variable , This represents an estimate of the global power deficit; The dynamic equation for the incremental cost consensus protocol is:

[0009] in To control the gain; This indicates that incremental cost consistency among neighbors is achieved using communication topology; the right side... Then, as a driver, the power gap of the observer is fed back to the control layer, so that the system can eliminate the imbalance; and The first Taiwan and the The incremental cost of one generator.

[0010] Optionally, step S4 includes: For the third-order generator model of the system, its closed-loop dynamics are subject to the inertial constant. Due to strict constraints, its actual output power Lagging behind control commands, the state space is represented as follows:

[0011] in This represents the state vector within the unit. From the generator's internal time constant , and The decision describes how the governor, turbine, and rotor interact with each other without external commands; The power control input is calculated based on the constant incremental rate criterion. and For the first Cost function coefficients of generators, Indicates the first The incremental cost of one generator; It is an input matrix that describes how the power commands issued from the distributed controller affect the internal state of the generator; It is the output matrix, reflecting the mapping from state to output force. It is a direct feed matrix; Indicates the first The rate of change of the internal state of the generator; In the third-order generator model, due to mechanical inertia, the power command cannot instantaneously change the output power, and therefore remains zero. When all units are connected, the state vector of the entire system is defined as... , This represents the internal state vector of the third-order physical model of generator No. 1; This represents the transpose of the internal state vector of the third-order physical model of generator No. 6; This represents the transpose of the incremental cost vector of all nodes in the entire network; This represents the transpose of the vector of estimated power deficit values ​​for all nodes in the entire network.

[0012] Optionally, step S5 includes: To verify the algorithmic stability of the third-order transfer function model, distributed observer, and incremental cost consensus protocol, the stable state corresponding to the system equilibrium point is defined as follows: ; Constructing the global error vector ; Construct the following Lyapunov function:

[0013] in and = The energy states of the distributed observer and the incremental cost consensus protocol were characterized respectively. Represents the first State energy within the physical layer of the tactical unit; For observer bias, For incremental cost consistency deviation, For the first Internal state deviation of the generator; These are the physical layer weighting coefficients. A positive definite symmetric matrix to satisfy physical layer stability; right Regarding the time derivative, we get

[0014] Substitute into the system error dynamics equation and apply the properties of the Laplace matrix L Substituting, we get:

[0015] in For observer gain; To control the gain; The asymptotic stability of the generator set indicates the existence of a positive definite matrix. satisfy , This represents the state matrix of the state-space model of the i-th power generation unit; Simplifying the formula, we get:

[0016] in, Indicates the first The input matrix of the state-space model of each power generation unit; Indicates the first Control input variables for each power generation unit; By Young's inequality, for any scalar Therefore, we can conclude that:

[0017] in, Substituting Young's inequality into And combined with Rayleigh entropy properties We can obtain:

[0018] The coefficients and their definitions are as follows:

[0019] in The convergence rate benchmark of the observer, This represents the stability margin of the controller, while This describes the intensity of the decay of the internal state of the generator set; and Represents any positive scalar; This represents the second smallest eigenvalue of the communication topology matrix L; Represents a positive definite matrix The smallest eigenvalue; To ensure The system must meet the following requirements:

[0020] Select a sufficiently suitable gain as well as If the system meets the above conditions, then It is a negative definite function of the total system error vector E.

[0021] Optionally, step S6 includes: Assume the distributed observer is a pure integrator, and the observation gain is . The largest eigenvalue of the topology is Considering the most sensitive observer error mode, its open-loop transfer function is:

[0022] in Indicates communication delay time; at cutoff frequency At this point, the open-loop amplitude of the system is equal to 1, that is:

[0023] At this point, the system's phase is composed of the constant -90 degrees generated by the integration element and the lag phase angle caused by the time delay:

[0024] According to the Nyquist stability criterion, the condition for a system to remain stable is the phase margin. ,Right now When the instability critical point is reached, the phase margin is exactly zero.

[0025] Substituting the solutions, we get:

[0026] The results show the latency tolerance. With gain They are in a strictly inverse relationship.

[0027] A distributed economic dispatch system for heterogeneous microgrids under communication constraints, the system comprising: The communication topology module is used to construct strongly connected communication topologies and determine the algebraic connectivity and spectral radius of the Laplace matrix. The advanced modeling module is used to establish the third-order transfer function model of each power generation unit, characterizing the dynamic response of the governor, turbine and rotor motion; The two-layer protocol module is used to build a two-layer information interaction protocol. The first layer is a distributed observer, which realizes the distributed estimation of global power imbalance through neighbor information interaction. The second layer is an incremental cost consensus protocol, which calculates local incremental cost based on the equal incremental rate criterion and realizes global consensus on incremental cost across the entire network. The stability analysis module is used to establish a full system state-space model including physical layer state, incremental cost state and power deficit estimation state based on the third-order transfer function model, distributed observer and incremental cost consensus protocol, construct Lyapunov function to complete the time domain stability proof, and determine the stable tuning conditions of observer gain and control gain. The stability analysis module is also used to derive the critical delay boundary under communication delay using frequency domain analysis, establish the quantitative relationship between observer gain, communication topology spectral radius and critical delay, and complete the robust design of parameters. The scheduling and execution module is used to perform distributed scheduling based on the designed parameters, and to achieve the globally optimal economic allocation of heterogeneous generator output under communication constraints and high-order dynamics.

[0028] The beneficial effects of the technical solution provided in this application are: Introducing a third-order transfer function into the network information layer allows for a more accurate exposure of stability risks arising from higher-order dynamics and communication constraints in pure information interaction simulations. This invention constructs a two-layer information interaction framework comprising a distributed observer and an incremental cost consensus controller, working together to achieve global optimization computation. The topological spectral radius of the communication network is established. Observer gain The explicit quantitative relationship between the critical delay and the objective delay provides clear guidance for engineers to design robust gain parameters in a given communication environment. Using Lyapunov stability theory and the frequency-domain Nyquist criterion, the stability and delay tolerance boundary of the proposed information exchange method are rigorously proven from both time and frequency domain perspectives, demonstrating a comprehensive theoretical analysis.

[0029] Compared with existing technologies, the advantages of this invention are: More accurate physical layer modeling: By establishing a heterogeneous third-order dynamic model, the adaptation accuracy of scheduling instructions under complex conditions is significantly improved.

[0030] It provides quantitative tuning criteria: the mathematical relationship between the critical stability delay boundary and the control gain is quantitatively derived, providing clear theoretical guidance for the parameter design of microgrid controllers in communication-constrained environments.

[0031] The system is more self-healing and resilient: By integrating distributed observers and utilizing topological redundancy, the system balance and stability are ensured. Attached Figure Description

[0032] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a step diagram of an embodiment of this application; Figure 2 This is a graph showing the changes in generator output (left) and incremental rate λ (right) in the embodiments of this application; Figure 3 This is a graph showing the changes in generator output (left) and incremental rate λ (right) under continuous dynamic switching in the embodiments of this application; Figure 4 This is a graph showing the variation of the incremental rate λ under photovoltaic disturbance (left) and wind disturbance (right) conditions in the embodiments of this application; Figure 5 This is a graph showing the changes in generator output (left) and incremental rate λ (right) in the embodiments of this application; Figure 6 This is a graph showing the variation of the incremental rate λ in the embodiments of this application; Figure 7 This is a graph showing the variation of incremental rate (left) and observer error (right) under multi-point concurrent faults in an embodiment of this application; Figure 8 This is an example of the embodiments in this application. , The effect of parameters on the system; Figure 9 This is a scaled-down version of the embodiments in this application. and Graph showing the change in the incremental rate λ over time. Detailed Implementation

[0033] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0034] The embodiments of this application provide a distributed economic dispatch method for heterogeneous microgrids under communication constraints.

[0035] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a distributed economic dispatch method for heterogeneous microgrids under communication constraints, as described in an embodiment of this application, including: S1: Construct a strongly connected communication topology, determine the algebraic connectivity and spectral radius of the Laplace matrix, establish a third-order transfer function model for each power generation unit, and characterize the dynamic response of the governor, turbine and rotor motion. S2: A two-layer information interaction protocol is established. The first layer is a distributed observer, which realizes the distributed estimation of global power imbalance through neighbor information interaction. The second layer is an incremental cost consensus protocol, which calculates local incremental cost based on the equal incremental rate criterion to achieve global consensus on incremental cost across the entire network. S3: Based on the third-order transfer function model, distributed observer, and incremental cost consensus protocol, establish a full system state-space model including physical layer state, incremental cost state, and power deficit estimation state, construct Lyapunov function to complete the time-domain stability proof, and determine the stable tuning conditions of observer gain and control gain. S4: The critical delay boundary under communication delay is derived using frequency domain analysis, and the quantitative relationship between observer gain, communication topology spectral radius and critical delay is established to complete the robust design of parameters. S5: Based on the designed parameters, distributed scheduling is performed to achieve the globally optimal economic allocation of heterogeneous generator output under communication constraints and high-order dynamics.

[0036] As one embodiment, this invention discloses a distributed economic scheduling method considering a high-order motor model under communication constraints. This method operates on a communication network composed of multiple information nodes, without relying on the underlying physical power grid model. The network topology is as follows: Figure 1 As shown.

[0037] Step S1 includes: The third-order transfer function is:

[0038] in The reference instructions are calculated by the nodes based on information exchange. This is the simulated response value output after the lag element; This refers to the time constants corresponding to the motion processes of the generator governor, turbine, and rotor. For the Laplace operator.

[0039] In one embodiment, each information node represents a power generation unit. Since the communication topology in this paper has strong connectivity, according to graph theory properties, the zero eigenvalue has algebraic multiplicity 1, and its eigenvector is 1 / n. The eigenvalues ​​of the 6-node communication topology matrix L in this paper can be sorted as follows: This paper defines algebraic connectivity. The second smallest eigenvalue of L quantifies the baseline rate of information diffusion across the entire network, and the largest eigenvalue of the spectral radius. This defines the robustness boundary of the system under time-delay impacts.

[0040] Its response hysteresis characteristics are represented by the following third-order transfer function, which is used to distinguish it from the first-order simplified model, thereby more realistically reflecting the dynamic evolution process.

[0041] The physical characteristics of the six generators in this paper are given in Table 1.

[0042] Table 1

[0043] Step S2 includes: The dynamic equation of the distributed observer is:

[0044] in For observer gain, For nodes The neighborhood group, For elements of the adjacency matrix, This is a compensation term that includes information on local power variations and disturbances; nodes Maintain a local variable , This represents an estimate of the global power deficit; The dynamic equation for the incremental cost consensus protocol is:

[0045] in To control the gain; This indicates that incremental cost consistency among neighbors is achieved using communication topology; the right side... Then, as a driver, the power gap of the observer is fed back to the control layer, so that the system can eliminate the imbalance; and The first Taiwan and the The incremental cost of one generator.

[0046] As one embodiment, this invention proposes a two-layer information exchange protocol. The first layer is a distributed observer, used to address the problem that nodes cannot directly obtain global power imbalance. Maintain a local variable This represents an estimate of the global power deficit, which is exchanged with neighboring nodes to achieve network-wide awareness. The distributed observer is essentially a distributed average consensus protocol that drives all nodes to reach a consensus on their estimates of the global deficit.

[0047] In one embodiment, the second layer is an incremental cost consensus protocol. Each node calculates its local incremental cost based on the derivative of its cost function. And through information exchange, the incremental costs of all nodes reach a global consensus. and For the first The cost function coefficient of the generator, the actual output power is The synergistic effect of these two factors enables the information network to achieve global optimization even without a central node.

[0048] Step S4 includes: For the third-order generator model of the system, its closed-loop dynamics are subject to the inertial constant. Due to strict constraints, its actual output power Lagging behind control commands, the state space is represented as follows:

[0049] in This represents the state vector within the unit. From the generator's internal time constant , and The decision describes how the governor, turbine, and rotor interact with each other without external commands; The power control input is calculated based on the constant incremental rate criterion. and For the first Cost function coefficients of generators, Indicates the first The incremental cost of one generator; It is an input matrix that describes how the power commands issued from the distributed controller affect the internal state of the generator; It is the output matrix, reflecting the mapping from state to output force. It is a direct feed matrix; Indicates the first The rate of change of the internal state of the generator; In the third-order generator model, due to mechanical inertia, the power command cannot instantaneously change the output power, and therefore remains zero. When all units are connected, the state vector of the entire system is defined as... , This represents the internal state vector of the third-order physical model of generator No. 1; This represents the transpose of the internal state vector of the third-order physical model of generator No. 6; This represents the transpose of the incremental cost vector of all nodes in the entire network; This represents the transpose of the vector of estimated power deficit values ​​for all nodes in the entire network.

[0050] Step S5 includes: To verify the algorithmic stability of the third-order transfer function model, distributed observer, and incremental cost consensus protocol, the stable state corresponding to the system equilibrium point is defined as follows: ; Constructing the global error vector ; Construct the following Lyapunov function:

[0051] in and = The energy states of the distributed observer and the incremental cost consensus protocol were characterized respectively. Represents the first State energy within the physical layer of the tactical unit; For observer bias, For incremental cost consistency deviation, For the first Internal state deviation of the generator; These are the physical layer weighting coefficients. A positive definite symmetric matrix to satisfy physical layer stability; right Regarding the time derivative, we get

[0052] Substitute into the system error dynamics equation and apply the properties of the Laplace matrix L Substituting, we get:

[0053] in For observer gain; To control the gain; The asymptotic stability of the generator set indicates the existence of a positive definite matrix. satisfy , This represents the state matrix of the state-space model of the i-th power generation unit; Simplifying the formula, we get:

[0054] in, Indicates the first The input matrix of the state-space model of each power generation unit; Indicates the first Control input variables for each power generation unit; By Young's inequality, for any scalar Therefore, we can conclude that:

[0055] in, Substituting Young's inequality into And combined with Rayleigh entropy properties We can obtain:

[0056] The coefficients and their definitions are as follows:

[0057] in The convergence rate benchmark of the observer, This represents the stability margin of the controller, while This describes the intensity of the decay of the internal state of the generator set; and Represents any positive scalar; This represents the second smallest eigenvalue of the communication topology matrix L; Represents a positive definite matrix The smallest eigenvalue; To ensure The system must meet the following requirements:

[0058] Therefore, select a sufficiently suitable gain. as well as If the system meets the above conditions, then It is a negative definite function of the total system error vector E.

[0059] As one example, according to Lyapunov's stability theorem and LaSalle's Invariance Principle, the system error will asymptotically converge to zero. This means that even if the generators have completely different inertial response complexities, the distributed algorithm can still drive the system to achieve globally optimal incremental cost consistency.

[0060] Step S6 includes: As one example, this invention derives the critical delay boundary for information interaction stability using frequency domain analysis to address the key constraint of communication delay.

[0061] Assume the distributed observer is a pure integrator, and the observation gain is . The largest eigenvalue of the topology is Considering the most sensitive observer error mode, its open-loop transfer function is:

[0062] in Indicates communication delay time; at cutoff frequency At this point, the open-loop amplitude of the system is equal to 1, that is:

[0063] At this point, the system's phase is composed of the constant -90 degrees generated by the integration element and the lag phase angle caused by the time delay:

[0064] According to the Nyquist stability criterion, the condition for a system to remain stable is the phase margin. ,Right now When the instability critical point is reached, the phase margin is exactly zero.

[0065] Substituting the solutions, we get:

[0066] The results show the latency tolerance. With gain They are in a strictly inverse relationship.

[0067] A distributed economic dispatch system for heterogeneous microgrids under communication constraints, the system comprising: The communication topology module is used to construct strongly connected communication topologies and determine the algebraic connectivity and spectral radius of the Laplace matrix. The advanced modeling module is used to establish the third-order transfer function model of each power generation unit, characterizing the dynamic response of the governor, turbine and rotor motion; The two-layer protocol module is used to build a two-layer information interaction protocol. The first layer is a distributed observer, which realizes the distributed estimation of global power imbalance through neighbor information interaction. The second layer is an incremental cost consensus protocol, which calculates local incremental cost based on the equal incremental rate criterion and realizes global consensus on incremental cost across the entire network. The stability analysis module is used to establish a full system state-space model including physical layer state, incremental cost state and power deficit estimation state based on the third-order transfer function model, distributed observer and incremental cost consensus protocol, construct Lyapunov function to complete the time domain stability proof, and determine the stable tuning conditions of observer gain and control gain. The stability analysis module is also used to derive the critical delay boundary under communication delay using frequency domain analysis, establish the quantitative relationship between observer gain, communication topology spectral radius and critical delay, and complete the robust design of parameters. The scheduling and execution module is used to perform distributed scheduling based on the designed parameters, and to achieve the globally optimal economic allocation of heterogeneous generator output under communication constraints and high-order dynamics.

[0068] In one embodiment, by Figure 2 It can be seen that even if the physical characteristics of the six generators are completely different, and even if the initial electricity price and load are significantly different, under the action of the distributed algorithm, global consensus is achieved simply through communication between neighbors, and the convergence time is rapid, completing global consensus in about 10 seconds.

[0069] Continuing the analysis of system resilience under continuous dynamic load switching, at 20s, the power of generator 2 is suddenly increased; at 30s, the power of generator 4 is suddenly decreased to reduce the load; and at 40s, the load of generator 5 is increased. The results are as follows: Figure 3Results. After introducing photovoltaic and wind disturbances into the system respectively, we obtained... Figure 4 As a result, even after the introduction of photovoltaic disturbances, the system still exhibits excellent transient suppression capabilities.

[0070] like Figure 5 As shown, under varying degrees of output limiting, generators 2 and 5 quickly reached saturation and their power ceiling after the introduction of new disturbances. The power deficit was rapidly transmitted to the remaining nodes via the communication link, and the system remained stable.

[0071] This invention further investigates the performance limits of distributed scheduling schemes and simulates extreme communication disruption scenarios.

[0072] Disconnect the communication links between generator 2 and generator 1, and between generator 2 and generators 1 and 3, approximately every 20 seconds, and obtain the following results: Figure 6 The results are shown. Although the communication links between node 2 and other nodes are broken, as long as the spanning tree exists, the distributed observer can still work, and the system can still reach stability. Moreover, the more links are broken and the longer the information transmission time, the longer it takes for the system to reach stability.

[0073] To further verify the performance limits, communication links 1-2, 3-4, and 5-6 were sequentially disconnected during a multi-point continuous perturbation process. Simulation results are provided by... Figure 7 The results show that although the absence of critical links leads to a significant decrease in network algebraic connectivity and causes a large transient fluctuation in the incremental rate, the distributed protocol maintains the integrity of the critical control flow thanks to the inherent structural redundancy of the topology.

[0074] Finally, this invention determines the main system stability boundary introduced by both local communication delay and neighbor communication delay. For example... Figure 8 As shown in the figure, the process of color changing from yellow to green and then to blue represents the trend of the critical time delay decreasing as the gain increases. The higher the gain, the higher the closed-loop cutoff frequency of the system. According to frequency domain theory, the higher the bandwidth, the more sensitive the system is to phase lag. The contour lines in the figure are almost horizontal, indicating that the critical time delay decreases as the gain increases. The changes were extremely drastic, and with The changes were relatively gradual, but in reality, By changing the bandwidth of the closed-loop system, it still has a certain modulation effect on the time delay robustness.

[0075] In settings , Under the conditions, the calculation is as follows The delay was set to 0.17s at that time. When =1, we get Figure 9The results shown on the left exhibit significant oscillations. However, when the scale is reduced... and At that time, the system obtains the result under the same delay by Figure 9 As shown on the right, the incremental rate curve remains stable.

[0076] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.

[0077] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A distributed economic dispatch method for heterogeneous microgrids under communication constraints, characterized in that, The method includes the following steps: S1: Construct a strongly connected communication topology, determine the algebraic connectivity and spectral radius of the Laplace matrix, establish a third-order transfer function model for each power generation unit, and characterize the dynamic response of the governor, turbine and rotor motion. S2: A two-layer information interaction protocol is established. The first layer is a distributed observer, which realizes the distributed estimation of global power imbalance through neighbor information interaction. The second layer is an incremental cost consensus protocol, which calculates local incremental cost based on the equal incremental rate criterion to achieve global consensus on incremental cost across the entire network. S3: Based on the third-order transfer function model, distributed observer, and incremental cost consensus protocol, establish a full system state-space model including physical layer state, incremental cost state, and power deficit estimation state, construct Lyapunov function to complete the time-domain stability proof, and determine the stable tuning conditions of observer gain and control gain. S4: The critical delay boundary under communication delay is derived using frequency domain analysis, and the quantitative relationship between observer gain, communication topology spectral radius and critical delay is established to complete the robust design of parameters. S5: Based on the designed parameters, distributed scheduling is performed to achieve the globally optimal economic allocation of heterogeneous generator output under communication constraints and high-order dynamics.

2. The distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in claim 1, characterized in that, Step S1 includes: The third-order transfer function is: in The reference instructions are calculated by the nodes based on information exchange. This is the simulated response value output after the lag element; This refers to the time constants corresponding to the motion processes of the generator governor, turbine, and rotor. For the Laplace operator.

3. The distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in claim 1, characterized in that, Step S2 includes: The dynamic equation of the distributed observer is: in For observer gain, For nodes The neighborhood group, For adjacency matrix elements, This is a compensation term that includes information on local power variations and disturbances; nodes Maintain a local variable , This represents an estimate of the global power deficit; The dynamic equation for the incremental cost consensus protocol is: in To control the gain; This indicates that incremental cost consistency among neighbors is achieved using communication topology; the right side... Then, as a driver, the power gap of the observer is fed back to the control layer, so that the system can eliminate the imbalance; and The first Taiwan and the The incremental cost of one generator.

4. The distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in claim 1, characterized in that, Step S4 includes: For the third-order generator model of the system, its closed-loop dynamics are subject to the inertial constant. Due to strict constraints, its actual output power Lagging behind control commands, the state space is represented as follows: in This represents the state vector within the unit. From the generator's internal time constant , and The decision describes how the governor, turbine, and rotor interact with each other without external commands; The power control input is calculated based on the constant incremental rate criterion. and For the first Cost function coefficients of generators, Indicates the first The incremental cost of one generator; It is an input matrix that describes how the power commands issued from the distributed controller affect the internal state of the generator; It is the output matrix, reflecting the mapping from state to output force. It is a direct feed matrix; Indicates the first The rate of change of the internal state of the generator.

5. The distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in claim 4, characterized in that, Step S4 also includes: In the third-order generator model, due to mechanical inertia, the power command cannot instantaneously change the output power, and therefore remains zero. When all units are connected, the state vector of the entire system is defined as... , This represents the internal state vector of the third-order physical model of generator No. 1; This represents the transpose of the internal state vector of the third-order physical model of generator No. 6; This represents the transpose of the incremental cost vector of all nodes in the entire network; This represents the transpose of the vector of estimated power deficit values ​​for all nodes in the entire network.

6. The distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in claim 5, characterized in that, Step S5 includes: To verify the algorithmic stability of the third-order transfer function model, distributed observer, and incremental cost consensus protocol, the stable state corresponding to the system equilibrium point is defined as follows: ; Constructing the global error vector ; Construct the following Lyapunov function: in and = The energy states of the distributed observer and the incremental cost consensus protocol were characterized respectively. Represents the first State energy within the physical layer of the tactical unit; For observer bias, For incremental cost consistency deviation, For the first Internal state deviation of the generator; These are the physical layer weighting coefficients. A positive definite symmetric matrix to satisfy physical layer stability; right Regarding the time derivative, we get Substitute into the system error dynamics equation and apply the properties of the Laplace matrix L Substituting, we get: in For observer gain; To control the gain; The asymptotic stability of the generator set indicates the existence of a positive definite matrix. satisfy , This represents the state matrix of the state-space model of the i-th power generation unit; Simplifying the formula, we get: in, Indicates the first The input matrix of the state-space model of each power generation unit; Indicates the first Control input variables for each power generation unit; By Young's inequality, for any scalar Therefore, we can conclude that: in, Substituting Young's inequality into And combined with Rayleigh entropy properties We can obtain: The coefficients and their definitions are as follows: in The convergence rate benchmark of the observer, This represents the stability margin of the controller, while This describes the intensity of the decay of the internal state of the generator set; and Represents any positive scalar; This represents the second smallest eigenvalue of the communication topology matrix L; Represents a positive definite matrix The smallest eigenvalue; To ensure The system must meet the following requirements: Select a sufficiently suitable gain as well as If the system meets the above conditions, then It is a negative definite function of the total system error vector E.

7. The distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in claim 6, characterized in that, Step S6 includes: Assume the distributed observer is a pure integrator, and the observation gain is . The largest eigenvalue of the topology is Considering the most sensitive observer error mode, its open-loop transfer function is: in Indicates communication delay time; at cutoff frequency At this point, the open-loop amplitude of the system is equal to 1, that is: At this point, the system's phase is composed of the constant -90 degrees generated by the integration element and the lag phase angle caused by the time delay: According to the Nyquist stability criterion, the condition for a system to remain stable is the phase margin. ,Right now When the instability critical point is reached, the phase margin is exactly zero. Substituting the solutions, we get: The results show the latency tolerance. With gain They are in a strictly inverse relationship.

8. A distributed economic dispatch system for heterogeneous microgrids under communication constraints, used to implement the distributed economic dispatch method for heterogeneous microgrids under communication constraints as described in any one of claims 1-7, characterized in that, The system includes: The communication topology module is used to construct strongly connected communication topologies and determine the algebraic connectivity and spectral radius of the Laplace matrix. The advanced modeling module is used to establish the third-order transfer function model of each power generation unit, characterizing the dynamic response of the governor, turbine and rotor motion; The two-layer protocol module is used to build a two-layer information interaction protocol. The first layer is a distributed observer, which realizes the distributed estimation of global power imbalance through neighbor information interaction. The second layer is an incremental cost consensus protocol, which calculates local incremental cost based on the equal incremental rate criterion and realizes global consensus on incremental cost across the entire network. The stability analysis module is used to establish a full system state-space model based on a third-order transfer function model, a distributed observer, and an incremental cost consensus protocol. It includes the physical layer state, the incremental cost state, and the power deficit estimation state. It constructs a Lyapunov function to complete the time-domain stability proof and determines the stable tuning conditions for the observer gain and the control gain. The stability analysis module is also used to derive the critical delay boundary under communication delay using frequency domain analysis, establish the quantitative relationship between observer gain, communication topology spectral radius and critical delay, and complete the robust design of parameters. The scheduling and execution module is used to perform distributed scheduling based on the designed parameters, and to achieve the globally optimal economic allocation of heterogeneous generator output under communication constraints and high-order dynamics.

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