A method for economical distribution of active power and frequency recovery in microgrids

Abstract

A method for economic distribution of active power and frequency recovery in a microgrid comprises the following steps: adopting microgrid hierarchical control. Under primary control, the traditional microgrid active-frequency (P-w) droop control is replaced by micro-increase-frequency (IC-w) droop control. As the frequencies of all parallel distributed power sources in the microgrid are synchronized in steady state, their micro-increase rates can automatically tend to be equal. Under secondary control, a sparse communication network is constructed between distributed power sources, and a distributed control method is adopted to achieve frequency recovery; event-triggered control is introduced for secondary control, which avoids continuous communication between distributed power sources and is more in line with actual microgrid communication conditions. The technical effects of the present invention are: under primary control, economic dispatch can be completed without any communication; under secondary control, when the microgrid load changes, the frequency can be guaranteed to be stable at the rated value; event-triggered control can effectively alleviate communication pressure.

Description

Technical Field

[0001] The present invention belongs to the field of microgrid primary control and secondary control, and particularly relates to a microgrid economic droop control, an optimal consistency algorithm, and an event-triggered microgrid active power economic distribution and frequency recovery control method. Background Art

[0002] Power generation based primarily on non-renewable energy sources such as coal, oil, and natural gas is unsustainable and the resulting environmental pollution is becoming increasingly severe. This reality has given rise to distributed generation technologies based on renewable energy sources such as photovoltaics, wind power, and solar power. Distributed generators (DG), which can be used locally or connected to the power system, have gradually replaced traditional power generation and will play a key role in future smart grids. However, DG also faces challenges such as difficulty in control, high costs, and high intermittency. To reconcile DG with the larger power grid and fully explore the value of distributed generation, scholars have proposed the concept of microgrids (MGs).

[0003] The economic dispatch of microgrids is an optimization problem aimed at minimizing total operating costs, typically solved by a centralized controller using an optimization algorithm. These centralized control schemes offer advantages such as high accuracy and good controllability. However, they incur high communication and computational burdens, and may also present single points of failure. Furthermore, given the decentralized nature of DGs and the implementation of plug-and-play technology, centralized control schemes are economically unfeasible. Some studies have proposed control strategies based on multi-agent consensus to solve the economic dispatch problem in a distributed manner. These strategies select the incremental rate of each DG as a consensus variable and generate the optimal power command for each DG through communication with neighboring DGs. These control strategies eliminate the need for a central controller, improving reliability. However, communication overhead is still required between different DGs to achieve incremental rate consistency. To further improve system reliability, scalability, and economic efficiency, fully decentralized economic dispatch schemes are needed. Summary of the Invention

[0004] This paper proposes a method for economically distributing active power and restoring frequency in a microgrid, achieving economic dispatch without requiring any communication. Furthermore, a quadratic frequency controller, designed based on an optimal consensus algorithm, achieves frequency recovery and maintains stable microgrid operation through minimal communication between DGs. Event-triggered control is employed to reduce inter-DG communication, making it more suitable for practical microgrid communication environments.

[0005] This invention employs a droop control strategy based on incremental cost (IC) to optimize the economic operation of AC microgrids. All DGs use the same incremental cost-to-frequency (IC-w) droop control. With frequency synchronization across all DGs in a steady state, their ICs automatically converge to the same value. This optimizes the overall operating cost of the microgrid without any communication.

[0006] To address the frequency deviation issues in microgrids caused by IC-w droop control, this paper transforms frequency recovery into an optimization problem and designs a distributed secondary frequency controller using an optimal consistency algorithm. This controller's functionality requires only the exchange of frequency compensation information between the DGs. Distributed control relies heavily on continuous state measurement and information exchange. Given the limited communication bandwidth and channel capacity of microgrids, this design incorporates an event-triggered communication mechanism. This achieves control objectives while conserving communication resources, making it more suitable for practical microgrid network environments.

[0007] The present invention is achieved through the following technical solutions.

[0008] The method for economically distributing active power and restoring frequency in a microgrid according to the present invention is characterized by comprising the following steps:

[0009] (1) Based on the traditional Pw droop control equation and the expression of the incremental rate, a linear relationship between frequency and incremental rate is established, namely IC-w droop control. IC-w droop control can synchronize with the frequency of the parallel microgrid and spontaneously achieve the same incremental rate, which is equivalent to achieving the economic distribution of the active power of the microgrid without any communication. However, the frequency will still deviate from the rated value.

[0010] (2) To address the frequency deviation problem in IC-w droop control, a secondary frequency controller is designed based on the optimal consistency algorithm to achieve frequency recovery. However, the implementation of the frequency controller function at this time depends on continuous status monitoring and information exchange.

[0011] (3) Considering the limited communication resources of actual microgrids, event-triggered control is adopted. By constructing a function related to the sampling time as the trigger function and setting a threshold that meets the specific function, the trigger function is compared with the threshold in real time to determine when the DG should trigger communication in order to update its own and its neighbors' controllers and avoid continuous communication.

[0012] Furthermore, according to the traditional Pw droop control equation and the expression of the incremental rate in step (1), a linear relationship between frequency and incremental rate is established, namely IC-w droop control, to achieve the economic distribution method of the active power of the microgrid without any communication:

[0013] (1-1) The cost of DG power generation is related to many factors, but in general, it can be expressed by the quadratic function given below:

[0014] C i (P i )=a i P i 2 +b i P i +c i (1)

[0015] Among them, a i , b i , c i It's DG i Cost coefficient; P i For DG i Output active power; C i (P i ) is DG i total electricity generation cost.

[0016] (1-2) According to the traditional Lagrangian method, when the incremental rate of all DGs reaches the same level, the operation cost of the microgrid is the lowest. i The partial derivative of the operating cost with respect to power is defined as its rate of increase:

[0017]

[0018] Among them, IC i It's DG i Slight increase rate.

[0019] (1-3) In an AC microgrid, frequency can be considered a global state variable that remains constant for all DGs in steady state. If a connection can be established between frequency and incremental rate, then incremental rate can also converge to a consistent value spontaneously with the synchronization of the AC microgrid frequency. The traditional Pw droop control is:

[0020] w i =w n -m i P i (3)

[0021] From equations (2) and (3), we can see that there is a linear relationship between frequency and incremental rate. i The IC-w droop control can be expressed as:

[0022] w i =w n -m IC IC i (Pi ) (4)

[0023] Among them, the droop coefficient m of each DG IC In steady state, the output frequency w of all DGs is i Consistent, so IC i (P i ) is also consistent, in this case the microgrid can operate under the economic optimal condition.

[0024] Furthermore, in step (2), for the frequency deviation problem in the primary IC-w control, a secondary frequency controller is designed based on the optimal consistency algorithm to achieve frequency recovery:

[0025] (2-1) From equation (4), it can be seen that the frequency of the microgrid will still deviate from the rated value, which is not conducive to the stable operation of the microgrid. Therefore, it is necessary to design a secondary control scheme to compensate for the frequency deviation. The secondary frequency controller is established as follows:

[0026] w i =w n -m IC IC i (P i )+u wi (5)

[0027] Among them, u wi is the frequency compensation of the secondary frequency controller. Under IC-w droop control, the output frequency and frequency deviation of DG are equal. To restore all DG frequencies to the rated value, it is only necessary to minimize the deviation between the output frequency and the rated frequency, that is, to control (w i -w n ) is the smallest, which is equivalent to (u wi -m IC IC i (P i )) is minimal, so frequency recovery can be transformed into a convex optimization problem as follows:

[0028]

[0029] (2-2) The following multi-agent optimal consensus algorithm can be used to solve convex optimization problems:

[0030]

[0031] Among them, α>0; β>0; γ=αβ; L ij The corresponding communication relationship between intelligent agents; x is the state of the intelligent agent; q i It is an additional variable used to ensure the stability of the algorithm; is the gradient of the optimization objective.

[0032] (2-3) Considering each DG in the microgrid as an intelligent agent, the following frequency controller is designed according to the optimal consensus algorithm of formula (7):

[0033]

[0034] Among them, α>0; β>0; γ=αβ; L ij Corresponding to the communication relationship between DGs; is the gradient of the optimization objective function (6).

[0035] Furthermore, in step (3), considering the limited communication resources of the actual microgrid, event-triggered control is adopted, a function related to the sampling time is constructed as the trigger function, and a threshold that satisfies the specific function is set. Then, the trigger function is compared with the threshold in real time to determine when the DG should trigger communication so as to update its own and its neighbor's controllers. The method is as follows:

[0036] (3-1) Traditional microgrids communicate periodically. Therefore, when the microgrid is operating stably, it will still trigger control tasks periodically, which will inevitably lead to resource waste. Here we introduce a distributed event-triggered control method with non-periodic communication. Only when the current state of the DG meets the designed event trigger condition will communication occur and the control output be updated. Otherwise, the controller maintains the state at the last trigger moment. i , introducing event-triggered communication into the frequency controller can be expressed by the following formula:

[0037]

[0038] in For DG i The time of the most recent communication with the neighbor. Moment, DG i The measured frequency compensation is And it remains unchanged until the next trigger moment comes. is the pending trigger time sequence, and

[0039] (3-2) The key to event-triggered control lies in the design of trigger conditions, which must meet the following requirements: 1) Stability. This means that the controller performance must not be significantly affected, meaning that the control objective must be achieved. 2) Feasibility. When event-triggered control generates an infinite number of trigger moments (events) within a finite timeframe, the Zeno phenomenon occurs, making it unsuitable for practical microgrids. This issue should be considered in control design.

[0040] To meet the above conditions, all DGs use an event detector to determine when to communicate with neighbors and update the controller. The trigger conditions are designed as follows:

[0041]

[0042] in, for u wi The local measurement error represents the current time and the most recent triggering time u wi State deviation, after each communication e wi will be set to 0. ε wi is a constant greater than 0, ε wi The value of will affect the performance of the controller. Generally speaking, ε wi The value is inversely proportional to the number of communications and also inversely proportional to the convergence error.

[0043] Features and beneficial effects of the present invention:

[0044] (1) By adopting hierarchical control, the frequency can be kept stable at the rated value when the load of the microgrid changes.

[0045] (2) Economic dispatch can be completed under one-time control without any communication.

[0046] (3) Secondary control adopts a distributed control method to avoid dependence on a central controller.

[0047] (4) Introducing event-triggered control for microgrid secondary control can effectively alleviate the communication pressure of the microgrid, save communication resources, and better meet the actual microgrid communication conditions.

[0048] (5) Under the control mode of the present invention, DG can be plug-and-play, which is highly flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Attachment Figure 1 This is the overall block diagram of DG.

[0050] Attachment Figure 2 This is the event trigger control block diagram.

[0051] Attachment Figure 3 This is the structural diagram of the island AC microgrid test system.

[0052] Attachment Figure 4 It is the change of active power under Pw droop control.

[0053] Attachment Figure 5 It shows the frequency variation under Pw droop control.

[0054] Attachment Figure 6 Figure 2 shows the active power variation under IC-w droop control.

[0055] Attachment Figure 7The change of the slight increase rate of each DG under IC-w droop control.

[0056] Attachment Figure 8 The frequency changes of each DG under the secondary frequency controller.

[0057] Attachment Figure 9 It is the communication time of each DG under event trigger control. DETAILED DESCRIPTION

[0058] The present invention will be further illustrated by the following examples.

[0059] Built in MATLAB / SIMULINK environment Figure 3 The islanded AC microgrid test system shown here consists of four parallel DGs and a common load. The operating environment is as follows: a PC with an AMD Ryzen 7 5800H processor with Radeon Graphics, 3.20 GHz CPU, and 16 GB of RAM. The microgrid system and controller parameters are given in Table 1.

[0060] Table 1 Microgrid system and controller parameters

[0061]

[0062] 1. In order to verify the effectiveness of IC-w droop control, each DG is simulated only under traditional Pw droop control. The active power and frequency changes under the simulation results are as follows: Figure 4 and Figure 5 As shown. Figure 4 In the example, the active power shared by DG1, DG2, DG3, and DG4 are 2kW, 3kW, 4kW, and 5kW respectively. Obviously, each DG distributes active power in proportion to the droop coefficient. Figure 5 In the example, the output frequencies of all DGs are equal, namely 49.9 Hz, and the output frequencies all deviate from the rated value of 50 Hz.

[0063] 2. If Figure 1 As shown, the traditional Pw droop control is replaced by IC-w droop control, and all DG droop coefficients m IC In this case, the frequency consistency of the microgrid in parallel with DG is used to achieve the spontaneous convergence of the micro-increase rate IC to a consistent state, and the economic dispatch is completed without any communication. At this time, the changes in the active power and micro-increase rate of DG are as follows: Figure 6 and Figure 7As shown in the figure, unlike traditional Pw droop control, the active power of each DG is no longer distributed in proportion to the droop coefficient in the system steady state. The slight increase rate of each DG reaches a consistent level around 0.6s. Based on the theoretical analysis above, we can see that the active power is distributed according to the economic optimum.

[0064] 3. Build a sparse communication network between DGs so that DGs can transmit information to each other.

[0065] 4. DGs transmit frequency compensation u to each other through the communication network wi The local frequency compensation is updated under the action of the frequency controller (8), and the frequency compensation acts on the local droop control, and finally gradually realizes the frequency recovery. The simulation results at this time are as follows Figure 8 As shown, Figure 5 The simulation results are different because the frequency controller is added. The DG frequencies first deviate from the rated value and then gradually return to the rated value of 50 Hz. This shows the effectiveness of the frequency controller of the present invention.

[0066] 5. If Figure 2 As shown, under event trigger control, the frequency compensation information u is continuously wi Sampling is performed, and according to the trigger condition of formula (10), the current information is compared with the most recent communication information of DG. Based on the comparison, it is determined whether the trigger condition is met.

[0067] 6. If the trigger condition is met, the DG transmits its own information to its neighbors and the local controller is updated once. If the trigger condition is not met, no communication occurs, the controller is not updated, and sampling continues. Figure 9 The communication moments between each DG and its neighbors were recorded during the simulation. As can be seen from the figure, at system startup, the output frequency of each DG deviates significantly from the rated frequency, triggering frequent communication to quickly recover the frequency. As the frequency recovers to near the rated value, the number of DG triggers decreases. Communication between DGs is clearly discontinuous, demonstrating that the present invention can effectively alleviate communication pressure and conserve communication resources.

Claims

1. A method for economical distribution of active power and frequency recovery in a microgrid, characterized in that: The steps include: (1) Based on the traditional Pw droop control equation and the incremental rate expression, a linear relationship between frequency and incremental rate is established: IC-w droop control; (2) To address the frequency deviation problem in IC-w droop control, a secondary frequency controller is designed based on the optimal consistency algorithm to achieve frequency recovery. The following steps are taken: (2-1) A secondary control scheme is designed to compensate for the frequency deviation. The secondary frequency controller is established as follows: w i =w n -m IC ·IC i (P i )+u wi (1) Among them, u wi is the frequency compensation of the secondary frequency controller; under IC-w droop control, the output frequency and frequency deviation of the DG are equal. To restore all DG frequencies to the rated value, it is only necessary to minimize the deviation between the output frequency and the rated frequency, that is, to control (w i -w n ) is the smallest, which is equivalent to (u wi -m IC IC i (P i )) is minimal, so frequency recovery can be transformed into a convex optimization problem as follows: (2-2) The following multi-agent optimal consensus algorithm can be used to solve convex optimization problems: Among them, α>0; β>0; γ=αβ; L ij The corresponding communication relationship between intelligent agents; x is the state of the intelligent agent; q i It is an additional variable used to ensure the stability of the algorithm; is the gradient of the optimization objective; (2-3) Considering each DG in the microgrid as an intelligent agent, the following frequency controller is designed according to the optimal consensus algorithm of formula (7): Among them, α>0; β>0; γ=αβ; L ij Corresponding to the communication relationship between DGs; is the gradient of the optimization objective function (6); (3) Event-triggered control is adopted. By constructing a function related to the sampling time as the trigger function and setting a threshold that meets the specific function, the trigger function is compared with the threshold in real time to determine when the distributed power source DG should trigger communication in order to update its own and its neighbors' controllers and avoid continuous communication.

2. A microgrid active power economic distribution and frequency recovery method according to claim 1, characterized in that: The linear relationship between frequency and incremental rate as described in step (1) is established as follows: (1-1) The power generation cost of DG is expressed by the quadratic function given below: C i (P i )=a i P i 2 +b i P i +c i (5) Among them, a i , b i , c i It's DG i Cost coefficient; P i For DG i Output active power; C i (P i ) is DG i Total electricity generation cost; (1-2) According to the traditional Lagrangian method, when the incremental rate of all DGs reaches the same level, the operation cost of the microgrid is the lowest; i The partial derivative of the operating cost with respect to power is defined as its rate of increase: Among them, IC i It's DG i The slight increase rate; (1-3) Traditional Pw droop control is: w i =w n -m i P i (7) From equations (2) and (3), we can see that there is a linear relationship between frequency and incremental rate. i The IC-w droop control can be expressed as: w i =w n -m IC ·IC i (P i ) (8) Among them, the droop coefficient m of each DG IC Keep consistent; in steady state, the output frequency w of all DGs i Consistent, so IC i (P i ) are also consistent, which can enable the microgrid to operate under the most economical conditions.

3. A method for economically distributing active power and restoring frequency in a microgrid according to claim 1, characterized in that: The steps of step (3) are as follows: (3-1) vs. DG i , introducing event-triggered communication into the frequency controller, which is expressed by the following formula: in For DG i The time of the most recent communication with the neighbor; Moment, DG i The measured frequency compensation is And it remains unchanged until the next triggering moment comes; is the pending trigger time sequence, and (3-2) Conditions for event-triggered control: 1) Stability: The controller performance must not be significantly affected, i.e., the control objective must be achieved as expected; 2) Feasibility: When event-triggered control generates an infinite number of trigger moments or events within a limited time, the Zeno phenomenon will occur, making it unsuitable for practical microgrids; To meet the above conditions, all DGs use an event detector to determine when to communicate with neighbors and update the controller. The trigger conditions are designed as follows: in, for u wi The local measurement error represents the current time and the most recent triggering time u wi State deviation, after each communication e wi will be set to 0; ε wi is a constant greater than 0, ε wi The value of will affect the performance of the controller, ε wi The value is inversely proportional to the number of communications and also inversely proportional to the convergence error.

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