Multi-region power system distributed control method considering market dynamics

Abstract

The invention relates to the technical field of multi-area power systems, in particular to a multi-area power system distributed control method considering market dynamics, which comprises the following steps: establishing a multi-area power system model considering market dynamics, constructing a distributed attack detection estimator based on output feedback, generating a residual signal through the distributed attack detection estimator, and outputting the residual signal. Selecting an evaluation function and a threshold function, constructing a closed-loop multi-region power system model based on the false data injection FDI attack, and constructing a distributed controller based on the false data injection FDI attack; according to the method, the defense capability for the FDI attack is improved, the robustness and the real-time response performance of the system are enhanced, and meanwhile, the distributed controller is designed for the system suffering from the FDI attack, so that the stability and the safety of the system are improved.

Description

Technical Field

[0001] This invention relates to the field of multi-regional power system technology, and in particular to a distributed control method for multi-regional power systems that takes into account market dynamics. Background Technology

[0002] The power system is undergoing a deep integration of energy structure transformation and market-oriented reforms. While multi-regional power systems are improving their capacity to absorb new energy sources, the dynamic characteristics and the interaction between market mechanisms are becoming increasingly prominent. Real-time electricity markets guide the optimal allocation of power generation resources through price signals, but the electromechanical oscillation risks and cyberattack threats brought about by long-distance power transmission pose a dual challenge, exposing the inherent shortcomings of traditional centralized control in dealing with cyberattacks. Traditional centralized control is also gradually shifting towards distributed control, thereby reducing the computational and communication burden on the central system.

[0003] Because distributed control relies on communication networks for information sharing, multi-regional power systems employing distributed control are highly vulnerable to cyberattacks. Among various malicious attacks, FDI attacks are considered the most common and destructive form, potentially disrupting the operation of multi-regional power systems by tampering with sensor data or control signals. Over long-term operation, this asynchronous effect can propagate through inter-regional tie lines, leading to dynamic instability throughout the interconnected system and, in severe cases, causing cascading failures across multiple regions. Summary of the Invention

[0004] This invention provides a distributed control method for multi-regional power systems that takes into account market dynamics, improves the defense against FDI attacks, enhances the robustness and real-time response performance of the system, and also designs a distributed controller for systems subjected to FDI attacks, thereby improving the stability and security of the system.

[0005] To achieve the above objectives, the present invention employs the following technical solution: A distributed control method for multi-regional power systems that considers market dynamics includes the following steps: S10. Establish a multi-regional power system model that takes into account market dynamics; S20. Construct a distributed attack detection estimator based on output feedback; S30. Generate residual signals using a distributed attack detection estimator and select an evaluation function and a threshold function; S40. Constructing a closed-loop multi-regional power system model based on FDI (Fake Data Injection) attacks; S50. Construct a distributed controller based on FDI (Fake Data Injection) attacks.

[0006] Furthermore, the specific steps for establishing a multi-regional power system model that considers market dynamics are as follows: By ignoring network losses, the producer and consumer behavior model in a market-driven environment is as follows: ; in, For the electricity supply of producers, To meet consumers' electricity needs, For the producer's marginal cost, For the marginal benefit of consumers, For electricity price, For the producer's power generation time constant, For the time constant of consumer electricity demand, Let the slope of the marginal cost of the generator set be denoted as . The slope of the marginal utility of the load. The rate of change of electricity supply over time. The rate of change of electricity demand over time; The ideal market dynamics for electricity producers and consumers are: ; in, Let be the electricity price response rate constant. For the benefit of market stabilizers of energy imbalances, The system is in an energy imbalance. The rate of change of electricity price over time; The multi-regional power system model considering market dynamics is as follows: ; in, ; ; ; ; in, For the region The rate of change of state over time For the region state, For the region state, To control the input, For system output, For load disturbance, N is a positive integer. The state matrix, For the control matrix, For interconnection matrix, Here is the perturbation matrix. For the output matrix, This is the frequency deviation coefficient. For integral control gain, For the region and Interconnection gain between For power system gain, The generator time constant, The prime mover time constant, The time constant of the speed controller, For frequency variation, For power output, To regulate the position change of the valve, For integral control, The rotor angular derivative, For load disturbance, The change in electricity price The time constant of the load disturbance. is the speed adjustment coefficient, and T is the time constant.

[0007] Furthermore, the construction of the distributed attack detection estimator based on output feedback is as follows: ; in, For the state of the estimator, The output of the estimator, The estimator gain to be solved is... For estimator rate of change of state For estimator The state.

[0008] Furthermore, step S30 specifically includes the following: (1) Generate residual signals using a distributed attack detection estimator: ; in, This represents the residual signal of the estimator; (2) The selected evaluation function and its threshold function are as follows: ; in, For the evaluation function, For threshold function, Let t be the start time of integration, and t be the current time. For the transpose of the estimator residual signal, It is a time constant; when This indicates that no FDI attack occurred in the multi-regional power system. This indicates that an FDI attack has occurred in the power system of multiple regions.

[0009] Furthermore, the multi-regional power system was subjected to an FDI attack, and the compromised system model is as follows: ; in, For the FDI (Fake Data Injection) attack suffered by the system, when Bounded, satisfied , For a bounded positive constant, For the attack matrix, ; Combining symbolic functions, distributed control is as follows: ; in, It is the controller gain. It is the gain of the neighbor controller. It is a symbolic function that satisfies: ; Obtain a closed-loop multi-region power system model under FDI attack: ; Furthermore, the construction of the distributed controller based on the FDI (Fake Data Injection) attack specifically includes: Selecting the dimension matrix , , This makes the following inequalities true: ; ; in, ; ; ; ; ; ; Obtain a distributed controller based on an FDI attack: in, For the matrix terms in Lyapunov's inequality, For matrix The inverse matrix, For an uncertain matrix transpose, For matrix The transpose of the inverse matrix, Weight matrix The inverse matrix of , where I is the identity matrix. For the matrix terms in the inequality, For an uncertain matrix transpose, For matrix The inverse matrix, For the system matrix transpose, It is a positive scalar parameter. To the system To the system The number of interconnect channels, To represent the system With system Between A matrix of interconnection uncertainties, for The transpose of , where k is the summation index. For the system The uncertainty matrix, For the system For the system The An interconnected attack or uncertainty vector For uncertain vectors transpose, To control the transpose of the matrix, For the region The positive parameter, For the region To the area The A vector of interconnection uncertainties, For the region To the area The Interconnection uncertainty vector transpose, To the region To the area The number of interconnect uncertain channels, For the region The positive parameter, To the region To the area The A vector of interconnection uncertainties, To the region To the area The Interconnection uncertainty vector transpose, For matrix The inverse matrix, For controller gain, For the interconnect gain of the controller.

[0010] Compared with the prior art, the beneficial effects of the present invention are: This invention proposes a distributed attack detection framework for multi-regional power systems that considers market dynamics, improving the defense capability against FDI attacks, enhancing the robustness and real-time response performance of the system, and designing a distributed controller for systems subjected to FDI attacks to achieve asymptotic stability of the system. Attached Figure Description

[0011] Figure 1 This invention relates to a multi-regional power system that considers market dynamics. Zone control block diagram.

[0012] Figure 2 This is a schematic diagram of the physical layer interconnection of the multi-region power system according to the present invention.

[0013] Figure 3 This is a schematic diagram of a three-region power system that takes into account market dynamics, as described in this invention.

[0014] Figure 4 shows the variation of the evaluation function of the present invention.

[0015] Figure 5 shows the load disturbance variation diagram of the present invention.

[0016] Figure 6 is a diagram showing the changes in the control input of the present invention.

[0017] Figure 7 shows the frequency response variation of the present invention.

[0018] Figure 8 is a comparison diagram of the control inputs of the present invention.

[0019] Figure 9 is a comparison diagram of the frequency response of the present invention. Detailed Implementation

[0020] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings: This invention provides a distributed control method for multi-regional power systems that considers market dynamics, such as... Figures 1-9 As shown, it includes the following steps: S10. Establish a multi-regional power system model that takes into account market dynamics; By neglecting network losses, the behavior of producers and consumers in a market-driven environment can be represented by the following equation: (1) in, For the electricity supply of producers, To meet consumers' electricity needs, For the producer's marginal cost, For the marginal benefit of consumers, For electricity price, For the producer's power generation time constant, For the time constant of consumer electricity demand, Let the slope of the marginal cost of the generator set be denoted as . The slope of the marginal utility of the load. The rate of change of electricity supply over time. The rate of change of electricity demand over time; Under this model, neglecting the impact of network losses, we propose the following equation to represent the ideal market dynamics for electricity producers and consumers: (2) in, Let be the electricity price response rate constant. For the benefit of market stabilizers of energy imbalances, The system is in an energy imbalance. The rate of change of electricity price over time; The multi-regional power system model considering market dynamics is as follows: (3) in, in, For the region The rate of change of state over time For the region state, For the region state, To control the input, For system output, For load disturbance, N is a positive integer. The state matrix, For the control matrix, For interconnection matrix, Here is the perturbation matrix. For the output matrix, This is the frequency deviation coefficient. For integral control gain, For the region and Interconnection gain between For power system gain, The generator time constant, The prime mover time constant, The time constant of the speed controller, For frequency variation, For power output, To regulate the position change of the valve, For integral control, The rotor angular derivative, For load disturbance, The change in electricity price The time constant of the load disturbance. For the attack matrix, is the speed adjustment coefficient, and T is the time constant.

[0021] S20. Construct a distributed attack detection estimator based on output feedback; The designed distributed attack detection estimator is shown below: (4) in, For the state of the estimator, The output of the estimator, The estimator gain to be solved is... For estimator rate of change of state For estimator The state.

[0022] S30. Generate residual signals using a distributed attack detection estimator and select an evaluation function and a threshold function; Define the residual signal of the estimator as The residual signal generated by the distributed attack detection estimator is: (5) Choose the evaluation function and threshold function: (6) in, For the evaluation function, For threshold function, Let t be the start time of integration, and t be the current time. For the transpose of the estimator residual signal, It is a time constant; when This indicates that no FDI attack occurred in the multi-regional power system. This indicates that an FDI attack has occurred in the power system of multiple regions.

[0023] S40. Constructing a closed-loop multi-regional power system model based on FDI (Fake Data Injection) attacks; When a multi-regional power system is subjected to an FDI attack, the compromised system model is as follows: (7) in, To inject FDI attacks with fake data into the system, when Bounded, satisfied , For a bounded positive constant, For the attack matrix, ; To achieve the desired control objective, a distributed control method combining symbolic functions is proposed. The specific form of this control method is shown below: (8) in, It is the controller gain. It is the gain of the neighbor controller. It is a symbolic function that satisfies: (9) Substituting the control input (8) into the system (7), we obtain the closed-loop multi-region power system model under FDI attack: (10).

[0024] S50. Construct a distributed controller based on a fake data injection FDI attack; Selecting the dimension matrix , , This makes the following inequalities true: (11) (12) in, The closed-loop multi-regional power system model considering market dynamics is asymptotically stable under FDI attacks, leading to a distributed controller based on FDI attacks: in, For the matrix terms in Lyapunov's inequality, For matrix The inverse matrix, For an uncertain matrix transpose, For matrix The transpose of the inverse matrix, Weight matrix The inverse matrix of , where I is the identity matrix. For the matrix terms in the inequality, For an uncertain matrix transpose, For matrix The inverse matrix, For the system matrix transpose, It is a positive scalar parameter. To the system To the system The number of interconnect channels, To represent the system With system Between A matrix of interconnection uncertainties, for The transpose of , where k is the summation index. For the system The uncertainty matrix, For the system For the system The An interconnected attack or uncertainty vector For uncertain vectors transpose, To control the transpose of the matrix, For the region The positive parameter, For the region To the area The A vector of interconnection uncertainties, For the region To the area The Interconnection uncertainty vector transpose, To the region To the area The number of interconnect uncertain channels, For the region The positive parameter, To the region To the area The A vector of interconnection uncertainties, To the region To the area The Interconnection uncertainty vector transpose, For matrix The inverse matrix, For controller gain, For the interconnect gain of the controller.

[0025] The following embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments. Unless otherwise specified, the methods used in the following embodiments are conventional methods.

[0026] Example A distributed control method for multi-regional power systems considering market dynamics follows the same steps as described above, using a three-regional power system as the simulation object, such as... Figure 3 As shown in Table 1, the parameters for the three-region power system are selected. Table 1. Parameter Setting Values ​​for the Power System in Three Regions area <imgwi="4.49"he="6.35"file="kwwQGwXrh3orTcIuotoBh2g5uacrbPn1xSt7Wq3G.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="5.84"he="6.60"file="8yeLoUJW93WUZitzxJA2M3C1imiDIfH8vFBDiVtT.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="5.25"he="6.35"file="D8huKJXy9Rn06cVuMPicRxJSSttehUiHoa936GEG.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="5.84"he="6.35"file="SDfUOo0YKOAARzrckwi4aGAS88Ndwl1RZTvQJqrL.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="6.60"he="6.60"file="g5wucaTodbhKj6LV7T9uE7LqovxYNGv1HGp4QGYS.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="6.86"he="6.60"file="TVzDEJULW52VyiNAFbNYc252q8R3harZq54hl4R7.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="6.86"he="6.35"file="wn8HCn6MCF795U29TGtgqPLvYKoBEv26AKERChz1.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> <imgwi="6.35"he="6.35"file="XY0Q6Huimk6Y57VuELAEt4pQhsozKgXZpPWMcufK.jpg"img-format="jpg"img-content="drawing"orientation="portrait"inline="no"> 1 2.4 20 0.31 0.08 120 0.55 10 0.41 2 2.7 25 0.33 0.07 112 0.65 9 0.37 3 2.5 20 0.35 0.07 115 0.54 7 0.43 Select Considering load disturbances, satisfy , , , and when , , The attacks occurred within 1.5–2.5, 2.5–3.5, and 3.5–4.5 seconds, respectively.

[0027] Figure 4 shows the values ​​of the evaluation functions for the three regions under both attacked and unattacked conditions.

[0028] threshold , and The following can be obtained from the simulation results: When the attack occurs, you can see , , All , and Above. Therefore, we can conclude that an attack has occurred in this area at this time.

[0029] The load disturbance considered in this invention is shown in Figure 5. The control input curve and frequency response curve under load disturbance are shown in Figures 6 and 7. It can be seen that under the load fluctuation shown in Figure 5, the proposed distributed control strategy can enable the system to quickly recover stability, proving the effectiveness of the proposed control scheme.

[0030] To demonstrate objectivity, we use the same example to compare control inputs and system performance, such as... Figure 8 and Figure 9 As shown, under the same parameters, the distributed control strategy proposed in this invention reduces the fluctuation of the control input compared with the traditional control strategy, thereby saving energy. Regarding system performance, especially frequency response, compared with the traditional control strategy, the distributed control strategy proposed in this invention produces a smoother frequency response curve, converges faster, and has less fluctuation, indicating higher stability.

Claims

1. A distributed control method for multi-regional power systems considering market dynamics, characterized in that, Includes the following steps: S10. Establish a multi-regional power system model that takes into account market dynamics; S20. Construct a distributed attack detection estimator based on output feedback; S30. Generate residual signals using a distributed attack detection estimator and select an evaluation function and a threshold function; S40. Constructing a closed-loop multi-regional power system model based on FDI (Fake Data Injection) attacks; S50. Construct a distributed controller based on FDI (Fake Data Injection) attacks.

2. The distributed control method for multi-regional power systems considering market dynamics as described in claim 1, characterized in that, The specific steps for establishing a multi-regional power system model that considers market dynamics are as follows: By ignoring network losses, the producer and consumer behavior model in a market-driven environment is as follows: ； in, For the electricity supply of producers, To meet consumers' electricity needs, For the producer's marginal cost, For the marginal benefit of consumers, For electricity price, For the producer's power generation time constant, For the time constant of consumer electricity demand, Let the slope of the marginal cost of the generator set be... The slope of the marginal utility of the load. The rate of change of electricity supply over time. The rate of change of electricity demand over time; The ideal market dynamics for electricity producers and consumers are: ； in, Let be the electricity price response rate constant. For the benefit of market stabilizers of energy imbalances, The system is in an energy imbalance. The rate of change of electricity price over time; The multi-regional power system model considering market dynamics is as follows: ； in, ； ； ； ； in, For the region The rate of change of state over time For the region state, For the region state, To control the input, For system output, For load disturbance, N is a positive integer. The state matrix, For the control matrix, For interconnection matrix, Here is the perturbation matrix. For the output matrix, This is the frequency deviation coefficient. For integral control gain, For the region and Interconnection gain between For power system gain, The generator time constant, The prime mover time constant, The time constant of the speed controller, For frequency variation, For power output, To regulate the position change of the valve, For integral control, The rotor angular derivative, For load disturbance, The change in electricity price The time constant of the load disturbance. is the speed adjustment coefficient, and T is the time constant.

3. The distributed control method for multi-regional power systems considering market dynamics according to claim 2, characterized in that, The distributed attack detection estimator built based on output feedback is described in detail below: ； in, For the state of the estimator, The output of the estimator, The estimator gain to be solved is... For estimator rate of change of state For estimator The state.

4. The distributed control method for multi-regional power systems considering market dynamics according to claim 3, characterized in that, Step S30 specifically includes the following: (1) Generate residual signals using a distributed attack detection estimator: ； in, This represents the residual signal of the estimator; (2) The selected evaluation function and its threshold function are as follows: ； in, For the evaluation function, For threshold function, Let t be the start time of integration, and t be the current time. For the transpose of the estimator residual signal, It is a time constant; when This indicates that no FDI attack occurred in the multi-regional power system. This indicates that an FDI attack has occurred in the power system of multiple regions.

5. A distributed control method for multi-regional power systems considering market dynamics according to claim 4, characterized in that, The multi-regional power system was subjected to an FDI attack, and the compromised system model is as follows: ； in, For the FDI (Fake Data Injection) attack suffered by the system, when Bounded, satisfied , For a bounded positive constant, For attack matrix, ； Combining symbolic functions, distributed control is as follows: ； in, It is the controller gain. It is the gain of the neighbor controller. It is a symbolic function that satisfies: ； Obtain a closed-loop multi-region power system model under FDI attack: 。 6. A distributed control method for multi-regional power systems considering market dynamics as described in claim 5, characterized in that, The construction of the distributed controller based on the FDI (Fake Data Injection) attack specifically includes: Selecting the dimension matrix , , This makes the following inequalities true: ； ； in, ； ； ； ； ； ； Obtain a distributed controller based on an FDI attack: in, For the matrix terms in Lyapunov's inequality, For matrix The inverse matrix, For an uncertain matrix transpose, For matrix The transpose of the inverse matrix, Weight matrix The inverse matrix of , where I is the identity matrix. For the matrix terms in the inequality, For an uncertain matrix transpose, For matrix The inverse matrix, For the system matrix transpose, It is a positive scalar parameter. To the system To the system The number of interconnect channels, To represent the system With system Between A matrix of interconnection uncertainties, for The transpose of , where k is the summation index. For the system The uncertainty matrix, For the system For the system The An interconnected attack or uncertainty vector For uncertain vectors transpose, To control the transpose of the matrix, For the region The positive parameter, For the region To the area The A vector of interconnection uncertainties, For the region To the area The Interconnection uncertainty vector transpose, To the region To the area The number of interconnect uncertain channels, For the region The positive parameter, To the region To the area The A vector of interconnection uncertainties, To the region To the area The Interconnection uncertainty vector transpose, For matrix The inverse matrix, For controller gain, For the interconnect gain of the controller.

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