CN116094769B - Port micro-grid control method for resisting false data injection attack - Google Patents
Port micro-grid control method for resisting false data injection attack Download PDFInfo
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Abstract
The invention provides a port micro-grid control method for resisting false data injection attack, which belongs to the technical field of micro-grid safety and comprises the steps of constructing a port micro-grid model based on distributed secondary control under FDI attack, constructing a secondary controller based on an extended state observer, expanding an attack signal into a system state to obtain an augmentation system, estimating the attack signal in real time by using the proposed extended state observer, and compensating the attack by using the proposed secondary controller when the FDI attack occurs, so as to realize the frequency, voltage recovery and power distribution of the port micro-grid. The method can estimate the FDI attack of the system in real time, can resist the negative influence of the attack, and ensures the stable operation of the port micro-grid system.
Description
Technical Field
The invention belongs to the technical field of micro-grid security, and particularly relates to a port micro-grid control method for resisting false data injection attack.
Background
As the share of maritime in global maritime trade increases, port hubs become more complex and port micro-grids (seaport microgrid, SMG) are a promising technology aimed at shaping future green maritime traffic. SMG is a self-controlling power system that uses micro-grid control technology to interconnect devices such as distributed power generation units, energy storage units, electric vehicles, service loads, all-electric ships, and communications, and the like, and the existence of SMG enables the integration of more and more distributed energy sources (distributed energy resources, debs) that can improve the energy utilization and economic benefits of the port power system, and improve the port operation efficiency.
SMGs have the same components and framework as land-based micro-grids, and they can all operate in grid-connected and island modes. In this regard, their basic control and operating frameworks may be similar. SMGs typically implement energy management in island mode of operation using a hierarchical control architecture consisting of discrete primary and distributed secondary control stages. The primary control is typically power distribution and primary settling control based on droop principles, and since the primary droop control is a differential control, the secondary control is typically required to adjust the primary set point to achieve frequency and voltage recovery.
Distributed secondary control often requires a combination of communication networks, making the SMG a informative physical system where network systems and physical processes are tightly coupled, and the operation of the SMG depends on efficient and reliable data flows in the network system. While the distributed control architecture provides a superior control concept for SMGs, the measurement and control units (communication links, sensors and actuators) are exposed to potential cyber attack threats due to the lack of a central controller capable of acquiring global information. False data injection (false data injection, FDI) attacks, which are a type of fraudulent network attacks, can lead to instability of the power system and even serious accidents by accessing and tampering with the real data of sensors and actuators. Therefore, designing a distributed control strategy capable of resisting the influence of FDI attack has important significance for SMG stable and safe operation.
Disclosure of Invention
The invention aims to provide a port micro-grid (seaport microgrid, SMG) control method for resisting false data injection (false data injection, FDI) attacks, which is based on an elastic control strategy of an extended state observer (extended state observers, ESO) and realizes frequency and voltage recovery and power distribution of island SMG under the two conditions of FDI attacks and no attacks.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a port micro-grid control method for resisting false data injection attack comprises a hierarchical control model of a port micro-grid, a false data injection attack model based on the hierarchical control model and a distributed elastic control strategy based on an extended state observer, so that the port micro-grid bus frequency, voltage recovery and output power proportional distribution under the false data injection attack are realized.
The invention further improves a layered control model of the port micro-grid, a false data injection attack model based on the layered control model and a distributed elastic control strategy based on an extended state observer, so as to realize the frequency, voltage recovery and output power proportional distribution of the port micro-grid bus under the false data injection attack, wherein the method comprises the following steps:
1) Calculating the output power of each distributed power supply according to the voltage and current components obtained through dq conversion;
2) Controlling output power through a droop controller of a secondary control stage to obtain a given input value of an inner loop voltage current controller;
3) The inner loop voltage current controller generates PWM modulation signals through the PI controller to control the inverter output frequency and the voltage amplitude to track a given input value;
4) The output power, the frequency and the voltage value of the distributed power inverter are obtained through sensor measurement, the secondary controller based on a communication network generates frequency and voltage auxiliary control input, the auxiliary control input issues an executor to generate frequency and voltage control compensation items, and the given input value output by the droop controller is changed to be a rated value;
5) Considering that false data injection attacks respectively occur on the sensor and the actuator, respectively destroying frequency, voltage and power measurement results and auxiliary control input, and finally destroying the output value of the inverter;
6) Designing an extended state observer to estimate the output frequency, voltage and power of the distributed power inverter and an attack signal;
7) Introducing a virtual variable to estimate reference information of each distributed power supply, and designing a distributed elastic control protocol based on estimated attack signals, state signals and virtual variables so as to realize port micro-grid bus frequency, voltage recovery and output power proportional distribution under false data injection attack.
The invention further improves the hierarchical control model of the port micro-grid, which comprises the following steps:
based on the droop control strategy, the frequency and voltage expression of DERs are obtained as shown in a formula (1):
wherein,and->As frequency and voltage references for inner loop control, respectively, real-time frequency and voltage may be tracked by dual loop control and Pulse Width Modulation (PWM) tracking references, ω ref And v ref Rated frequency and rated voltage, m, respectively, of micro-grid system operation i And n i Droop control coefficients p-f and q-v, respectively, for the ith DER, delta 1i And delta 2i Correction values for frequency and voltage control of the ith DER, respectively, are generated by the secondary controller in accordance with the control target. To achieve frequency, voltage recovery, and power allocation, the frequency and voltage control correction values for the ith DER may be morphed to:
wherein u is ωi The rate of change of the DER frequency is represented as a frequency recovery control rate; u (u) pi The control rate for the active power allocation represents the rate of change of the active power allocation. Delta ωi Represented by u ωi The generated correction value component; delta pi Is composed of u pi The generated correction value component. Similarly, the variables in the expression (3) mean control rate and correction value components corresponding to the voltage control.
The control rate is distributed secondary control rate based on a sparse communication network, and is respectively as follows:
wherein a is ij Indicating the connection between the ith DER and the jth DER, a when the former can acquire the information of the latter ij > 0, otherwise a ij ＝0；b i0 Representing the case where the ith DER obtains the reference value information, b if and only if the ith DER is selected as a fixed DER to access the reference information i0 > 0, otherwise, b i0 ＝0；ω ref ,v ref ,/>The reference values are allocated for the frequency, active power allocation, voltage and reactive power of the SMG system, respectively.
Since the inverter response is fast, it is assumed that the frequency and voltage of the SMG can track its reference value in real time. To simplify the analysis, the dynamics of the inner ring are ignored, i.eAnd->
The invention is further improved in that the false data is injected into an attack model, and two positions are considered to be attacked by FDI, and the process is as follows:
when the i-th DER sensor is attacked, the attacker's goal is to destroy the measurements of frequency, voltage and power information obtained by the sensor, propagate the measurements injected with false data through the communication network, and model the destroyed information as:
wherein,and->The frequency recovery control and active power distribution control attacker inject false data of the sensor, which is a derivative bounded signal; />And->The voltage recovery control and active power distribution control attackers inject false data of the sensor, which is a derivative bounded signal.
When the i-th DER's actuator is attacked, the attacker's goal is to destroy the feedback control signal, which is modeled as:
wherein,and->The frequency recovery control and active power distribution control attacker inject false data of the actuator, which is a derivative bounded signal; />And->The voltage recovery control and active power distribution control attacks inject false data into the actuator, which is a derivative bounded signal.
The invention further improves the distributed elastic control strategy based on the extended state observer, which comprises the following steps:
definition of intermediate variablesThe distributed extended state observer is:
wherein,and->Respectively the frequency omega i And active power standard value->Is>And->Correction value component +.>And->Is>And->Attack signals respectively injected into the sensor +.>And->Is>Andattack signals respectively injected into the actuator>And->The correction value equation form of the frequency recovery control and the active power distribution control is still the form in (2). F (F) ωi ,G ωi ,G pi ,H ωi ,H pi Is the gain of ESO. Zeta type toy ωi And xi pi Is an introduced virtual variable, is controlThe internal variables of the controller, which are estimates of the reference information from a per DER perspective, are modeled as:
by estimating the attack signal, the elasticity control rate designed by using the estimated value is as follows:
wherein K is ωi ,K pi Is the controller gain.
Similarly defined intermediate variables The voltage controlled distributed elastic control strategy is:
by adopting the technical scheme, the invention has the following technical progress:
compared with a control strategy based on detection, the elastic control method does not need a detection mechanism, false detection and missing detection caused by detection errors are avoided, and the method is suitable for SMG control under a non-attack scene and can offset adverse effects of attacks on a system under an FDI attack scene. The adopted ESO introduces a correction value component, the attack signal of the actuator is estimated in real time, the observer does not need any information of the attack signal, and the required parameters can be measured by the sensor. The control method introduces virtual variables to realize the estimation of each DER on the reference information, changes the information such as the attacked unreliable frequency and the like into local variables, and does not overflow the attack influence through a communication channel.
Drawings
FIG. 1 is a topological structure diagram of an SMG;
FIG. 2 is a hierarchical control structure of SMG and FDI attack location graph;
FIG. 3 is a block diagram of a proposed distributed elastic control strategy;
FIG. 4 is a graph of the frequency of each DER in the primary and secondary control strategy after addition of an attack signal in the experiment of the present invention;
FIG. 5 is a frequency chart of DERs in the distributed elastic control strategy proposed by the present invention after adding an attack signal in the experiment of the present invention;
FIG. 6 is a graph of the active power of each DER in the primary and secondary control strategy after addition of an attack signal in the experiment of the present invention;
FIG. 7 is a graph of the active power of each DER in the distributed elastic control strategy proposed by the present invention after addition of an attack signal in the experiment of the present invention;
FIG. 8 is a graph of voltage across DERs in the primary and secondary control strategy after addition of an attack signal in the experiment of the present invention;
FIG. 9 is a voltage plot of each DER under the distributed elastic control strategy proposed by the present invention after addition of an attack signal in the present invention experiment;
FIG. 10 is a graph of reactive power of each DER under the primary and secondary control strategy after addition of an attack signal in the experiment of the present invention;
fig. 11 is a reactive power diagram of each DER in the distributed elastic control strategy proposed by the present invention after adding an attack signal in the present invention experiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the technical solutions of the present invention are further described below with reference to the accompanying drawings and experiments.
Referring to fig. 1 to 11, the present invention proposes a port micro-grid control method for resisting a false data injection attack:
for an inverter-type island SMG consisting of a plurality of distributed power supplies (distributed energy resources, deres), a hierarchical control structure is adopted, and the ESO-based elastic control strategy for resisting FDI attacks comprises the following steps:
(1) The SMG model under FDI attack is established as follows:
(1.1) consider a typical SMG with n DER's as shown in fig. 1, each DER accessing the bus through an inverter and LC filter, with the control objective of maintaining the frequency, voltage stability, and power sharing of the SMG. To achieve this control goal, as the distributed hierarchical control architecture in fig. 2 is employed, one-time control of each DER includes droop control that generates a given input to the internal control loop and an internal voltage-current control loop that generates pulse width modulation (pulse width modulation, PWM) that controls the output frequency, voltage, and power of the inverter. In order to coordinate control of multiple DERs, droop control is applied with the following characteristics:
wherein,and->Omega as frequency and voltage reference for inner loop control ref And v ref Rated frequency and rated voltage, m, respectively, of SMG system operation i And n i Droop control coefficients p-f and q-v, respectively, for the ith DER, delta 1i And delta 2i Correction values for frequency and voltage control, respectively, for the ith DER are generated by the secondary controller according to the following control objectives:
1) Synchronizing the output frequency and voltage of DER at nominal values, namely:
2) DER power scaling to maintain power limits of individual DER in balance with microgrid power, namely:
wherein the sagging coefficient m i ,n i Is arranged asThe output power limit of the DER is shown.
To achieve frequency, voltage recovery, and power allocation, the frequency and voltage control correction values for the ith DER may be morphed to:
wherein u is ωi The rate of change of the DER frequency is represented as a frequency recovery control rate; u (u) pi The control rate for the active power allocation represents the rate of change of the active power allocation. Delta ωi Represented by u ωi The generated correction value component; delta pi Is composed of u pi The generated correction value component. Similarly, the variables in the expression (6) mean control rate and correction value components corresponding to the voltage control.
Since the inverter response is fast, to simplify the analysis, the dynamics of the internal control loop are ignored, assuming that the frequency and voltage of the SMG can track its reference value in real time, i.eAnd->
(1.2) secondary control objective of SMG is to restore the frequency and voltage of debs to rated values while achieving power distribution, and distributed secondary control rates based on sparse communication network are respectively:
wherein a is ij Indicating the connection between the ith DER and the jth DER, a when the former can acquire the information of the latter ij > 0, otherwise a ij ＝0；b i0 Representing the case where the ith DER obtains the reference value information, b if and only if the ith DER is selected as a fixed DER to access the reference information i0 > 0, otherwise, b i0 ＝0；Respectively standardized active power output and reactive power output; omega ref ,/>v ref ,/>Frequency, normalized active power, voltage and standard of SMG system respectivelyAnd (3) normalizing the reference value of the reactive power, wherein the two normalized power reference values are as follows:
wherein P is L ,Q L As a function of the total power demand of the load,is the maximum output power of the ith DER.
(1.3) as shown in fig. 2 where the SMG is attacked by the FDI, consider two possible locations of attack by the FDI, namely, a sensor and an actuator, assuming that the information measured by the sensor is attacked by the FDI as follows:
wherein,and->Frequency recovery control and respectivelyActive power distribution controls an attacker to inject false data of a sensor, and the false data is a derivative bounded signal; />And->The voltage recovery control and active power distribution control attackers inject false data of the sensor, which is a derivative bounded signal.
When the i-th DER's actuator is attacked, the attacker's goal is to destroy the feedback control signal, which is modeled as:
wherein,and->The frequency recovery control and active power distribution control attacker inject false data of the actuator, which is a derivative bounded signal; />And->The voltage recovery control and active power distribution control attacks inject false data into the actuator, which is a derivative bounded signal.
The secondary control process of the i-th DER after being attacked becomes:
(2) Establishing an ESO-based distributed elastic control strategy, wherein the control structure is shown in fig. 3, and the process is as follows:
(2.1) taking frequency control as an example, define intermediate variables The dispersed ESO is:
wherein,and->Respectively the frequency omega i And active power standard value->Is>And->Respectively the correction value component delta ωi And->Is>And->Attack signals respectively injected into the sensor +.>And->Is>Andattack signals respectively injected into the actuator>And->The correction value equation form of the frequency recovery control and the active power distribution control is still equation (4). F (F) ωi ，G ωi ，G pi ，H ωi ，H pi Is the gain of ESO. Zeta type toy ωi And xi pi Is an introduced virtual variable, is an internal variable of the controller, is an estimate of the reference information at the perspective of each DER, isModeling is as follows:
s3.2, by estimating attack signals, the elasticity control rate designed by using the estimated value is as follows:
wherein K is ωi ,K pi Is the controller gain.
(2.2) definition of intermediate variables by the same theory The voltage controlled distributed elastic control strategy is:
wherein,and->Respectively the voltage v i And reactive power standard value->Is>And->Respectively the correction value component delta vi And->Is>And->Attack signals respectively injected into the sensor +.>And->Is>And->Attack signals respectively injected into the actuator>And->The correction value equation form of the voltage recovery control and the reactive power distribution control is still equation (5). F (F) vi ，G vi ，G qi ，H vi ，H qi Is the gain of ESO. Zeta type toy vi And xi qi Is an introduced virtual variable, is an internal variable of the controller, and is an estimate of the reference information from the perspective of each DER. K (K) vi ,K qi Is the controller gain.
(3) In order to intuitively verify the effect of the control strategy provided by the present invention, the following description is given by way of specific examples:
1) Parameter setting: the experiment uses matlab/simulink software to build an SMG simulation model consisting of 4 DERs. The main parameters and controller parameters are shown in table 1:
table 1 system parameters and observer and controller parameters
2) The experimental scenario and results are as follows:
1. before t=1 s, all DER uses one droop control;
2. at t=1s, the secondary control strategy is activated;
3. at t=2s, the sensor of der3 isAttack signal attack by (a); at t=2.5s, the sensor of der4 is +.>Attack signal attack by (a);
4. at t=3 s, the sensor attacks on DER3 and DER4 are reduced, at t=3.5 s, at In the case of DER1 and DER4, attacks on the actuators;
5. at t=4s, actuator attacks on DER1 and DER4 are mitigated, but DER2Is signaled by a new attackAttack;
6. at t=5 s, FDI attacks by all DER are mitigated.
Fig. 4 and fig. 5 are frequency diagrams of the above scenario using the primary secondary control strategy and the proposed elastic control strategy, respectively, and comparing the two diagrams can show that the frequency under the primary secondary control strategy oscillates and is unstable when the FDI attack exists, and the frequency of the DER that is not attacked also oscillates, which is the result of the propagation of the FDI attack signal through the communication network. Figure 5 shows that only the frequency of the attacked DER fluctuates before and after the onset of the FDI attack and then quickly stabilizes at 50Hz, with no fluctuations in the frequency of the non-attacked DER.
Fig. 6 and fig. 7 are respectively normalized active power diagrams using the primary and secondary control strategies and the proposed elastic control strategy in the above scenario, and comparing the two diagrams can show that the active power under the primary and secondary control strategies oscillates and is unstable even exceeds the DER output power limit value in the presence of an FDI attack. Fig. 7 shows that only the active power of the attacked DER fluctuates before and after the FDI attack is initiated and then stabilizes rapidly, and the active power of the non-attacked DER does not fluctuate. In the period of no attack, the power standard value under the original secondary control strategy and the proposed elastic control strategy both meet the control target shown in the formula (3). The proposed elastic control strategy is shown to be capable of achieving similar control effects as conventional control strategies when no attack is present.
Fig. 8 and fig. 9 are voltage diagrams of the above scenario using the primary secondary control strategy and the proposed elastic control strategy, respectively, and comparing the two diagrams can show that the voltage under the primary secondary control strategy oscillates and is unstable when the FDI attack exists. Fig. 9 shows that only the voltage of the attacked DER fluctuates before and after the FDI attack is initiated and then stabilizes rapidly, and the voltage of the non-attacked DER does not fluctuate.
Fig. 10 and 11 are respectively standardized reactive power diagrams using the primary and secondary control strategies and the proposed elastic control strategy under the above-mentioned scenario, and it can be seen by comparing the two diagrams that the reactive power under the primary and secondary control strategies oscillates and is unstable even exceeds the DER output power limit value when the FDI attack exists. Fig. 11 shows that only the reactive power of the attacked DER fluctuates before and after the onset of the FDI attack and then stabilizes rapidly, and the reactive power of the non-attacked DER does not fluctuate. In the period of no attack, the power standard value under the original secondary control strategy and the proposed elastic control strategy both meet the control target shown in the formula (3).
The working principle of the invention is as follows: firstly modeling FDI attack in an SMG system, then regarding an attack signal as disturbance expansion to be in an augmentation system state, constructing ESO real-time estimation attack signals according to the output of the SMG system, and finally designing a distributed secondary elasticity controller by utilizing the attack signal estimation value to realize frequency and voltage recovery and power distribution.
In summary, the present invention proposes a distributed elastic control strategy based on ESO, where the control strategy can achieve the same control effect as the primary and secondary control strategies when no attack occurs, that is, the objectives shown in formulas (2) and (3) are satisfied. In the FDI attack period, the proposed control strategy can resist the adverse effect brought by the attack and still meet the control target.
The above examples are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the present invention.
Claims (1)
1. A port micro-grid control method for resisting false data injection attack is characterized by comprising a hierarchical control model of a port micro-grid, a false data injection attack model based on the hierarchical control model and a distributed elastic control strategy based on an extended state observer, so that the port micro-grid bus frequency, voltage recovery and output power proportional distribution under the false data injection attack are realized;
the port micro-grid hierarchical control model is based on a false data injection attack model of the hierarchical control model and a distributed elastic control strategy based on an extended state observer, so that the port micro-grid bus frequency, voltage recovery and output power under the false data injection attack are proportionally distributed:
1) Calculating the output power of each distributed power supply according to the voltage and current components obtained through dq conversion;
2) Controlling output power through a droop controller of a secondary control stage to obtain a given input value of an inner loop voltage current controller;
3) The inner loop voltage current controller generates PWM modulation signals through the PI controller to control the inverter output frequency and the voltage amplitude to track a given input value;
4) The output power, the frequency and the voltage value of the distributed power inverter are obtained through sensor measurement, the secondary controller based on a communication network generates frequency and voltage auxiliary control input, the auxiliary control input issues an executor to generate frequency and voltage control compensation items, and the given input value output by the droop controller is changed to be a rated value;
5) Considering that false data injection attacks respectively occur on the sensor and the actuator, respectively destroying frequency, voltage and power measurement results and auxiliary control input, and finally destroying the output value of the inverter;
6) Designing an extended state observer to estimate the output frequency, voltage and power of the distributed power inverter and an attack signal;
7) Introducing a virtual variable to estimate reference information of each distributed power supply, and designing a distributed elastic control protocol based on estimated attack signals, state signals and virtual variables so as to realize port micro-grid bus frequency, voltage recovery and output power proportional distribution under false data injection attack;
the hierarchical control model of the port micro-grid comprises the following steps:
the frequency and voltage expression for obtaining the debs based on droop control and consistency algorithms is shown in formula (1):
wherein,and->As frequency and voltage references for inner loop control, respectively, real-time frequency and voltage tracking references, ω, by dual loop control and Pulse Width Modulation (PWM) ref And v ref Rated frequency and rated voltage, m, respectively, of port micro-grid system operation i And n i Droop control coefficients p-f and q-v, respectively, for the ith DER, delta 1i And delta 2i Correction values for frequency and voltage control for the ith DER, respectively, are the outputs of the secondary controller:
wherein u is ωi The rate of change of the DER frequency is represented as a frequency recovery control rate; u (u) pi The control rate for the active power allocation represents the rate of change of the active power allocation; delta ωi Represented by u ωi The generated correction value component; delta pi Is composed of u pi The generated correction value component; similarly, each variable in the formula (3) means a control rate and a correction value component corresponding to voltage control; the control rate is distributed secondary control rate based on a sparse communication network, and is respectively as follows:
wherein a is ij Indicating the connection between the ith DER and the jth DER, a when the former obtains the information of the latter ij > 0, otherwise a ij ＝0；b i0 Representing the case where the ith DER obtains the reference value information, b if and only if the ith DER is selected as a fixed DER to access the reference information i0 > 0, otherwise, b i0 ＝0；ω ref ,v ref ,/>Respectively distributing reference values for frequency, active power distribution, voltage and reactive power of the micro-grid system;
the dummy data injection attack model includes:
when the i-th DER's sensor is attacked, the attacker's goal is to destroy the measurements of frequency, voltage, and power information obtained by the sensor, propagate the measurements injected with false data through the communication network, and the sensor attack is modeled as:
wherein,and->The frequency recovery control and active power distribution control attacker inject false data of the sensor, which is a derivative bounded signal; />And->The false data of the sensor is injected by an attacker of voltage recovery control and active power distribution control respectively, and the false data is a derivative bounded signal;
when the i-th DER's actuator is attacked, the attacker's goal is to destroy the feedback control signal, the actuator attack is modeled as:
wherein,and->The frequency recovery control and active power distribution control attacker inject false data of the actuator, which is a derivative bounded signal; />And->The voltage recovery control and active power distribution control attacks inject false data of the actuator, which are derivative bounded signals;
the distributed elastic control strategy based on the extended state observer comprises the following steps:
first, virtual variable xi is introduced ωi And xi pi As an internal variable of the controller, the estimation of the reference information from the per DER point of view, a virtual variable ζ as part of the frequency distributed elastic control strategy ωi And xi pi The dynamics of (2) are:
definition of intermediate variables The distributed extended state observer is:
wherein,and->Respectively the frequency omega i And active power standard value->Is>And->Respectively the correction value component delta ωi And->Is>And->Attack signals respectively injected into the sensor +.>And->Is>And->Attack signals respectively injected into the actuator>And->The form of the correction value equation of the frequency recovery control and the active power allocation control is still the form in (2); f (F) ωi ,G ωi ,G pi ,H ωi ,H pi Is the gain of ESO;
by estimating the attack signal, the elasticity control rate designed by using the estimated value is as follows:
wherein K is ωi ,K pi Is the controller gain;
similarly defined intermediate variables The voltage controlled distributed elastic control strategy is:
wherein,and->Respectively the voltage v i And reactive power standard value->Is>And->Respectively the correction value component delta vi And->Is>And->Attack signals respectively injected into the sensor +.>And->Is>And->Attack signals respectively injected into the actuator>And->The form of the correction value equation of the voltage recovery control and the reactive power distribution control is still the form in (3); f (F) vi ,G vi ,G qi ,H vi ,H qi Is the gain of ESO; zeta type toy vi And xi qi Is an introduced virtual variable, is an internal variable of the controller, is an estimate of the reference information from the perspective of each DER, is a virtual variable ζ that is part of the voltage distributed elastic control strategy vi And xi qi The dynamics of (2) are:
by estimating the attack signal, the elasticity control rate designed by using the estimated value is as follows:
wherein K is vi ,K qi Is the controller gain.
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