CN108767844A - The adaptive state estimation method of Data Injection Attacks lower network multi-region power system - Google Patents

Abstract

The invention discloses an adaptive state estimation method of a multi-area networked power system under data injection attack. Firstly, a new measurement equation is given for each region while considering the system state and attack signal at the same time, and the state estimation is transformed into an optimization solution problem with constraints; then some virtual nodes are constructed to connect the boundary system to realize the adjacent Communication constraints between regions, and the Lagrangian function with constraint information is given by using the principle of variational inequality; finally, a state estimation method with variable penalty parameters is proposed to realize state estimation under data injection attacks, where the penalty parameter It can adjust its size adaptively according to the estimation error and boundary error, thereby improving the estimation accuracy and speed. The present invention is applied to state estimation of large-scale multi-area power systems under data injection attacks, and can well ensure accuracy and speed, so as to meet the development requirements of future smart grids.

Description

Adaptive state estimation of networked multi-regional power systems under data injection attacks method

technical field

The invention relates to a state estimation method of a power system, in particular to an adaptive state estimation method of a networked multi-area power system under data injection attacks.

Background technique

Power system state estimation (PSSE) is the core component of energy management system (EMS). In the current power system, the user's power demand is getting higher and higher, which makes the scale of the power system gradually larger and the structure more complex, and gradually develops in the direction of a multi-regional power system. For a multi-area interconnected power system, there are usually two communication connection methods within the subsystem and between regions: one is a point-to-point dedicated line communication method, and the other is an open power communication network. Compared with the traditional point-to-point dedicated line communication connection, the open power communication network has the advantages of easy wiring, easy installation and maintenance, simple operation, low cost, and great flexibility. However, due to the open communication of the networked multi-regional power system, it is extremely vulnerable to malicious network attacks, causing extremely destructive damage to the multi-regional power system. Common forms of attack include: false data injection attack (FDI), denial of service attack, replay attack, etc. Since the data acquisition and monitoring system of Iran's Bushehr nuclear power plant was attacked by StuxNet ("Stuxnet" virus) in 2010, it caused serious consequences and shocked the world, exposing serious problems in the real-time monitoring and processing of the system by traditional EMS. State estimation is the core of EMS and undertakes an important task, so it is urgent to study the state estimation strategy under attack. Control system security has gradually become the focus of attention of countries all over the world. The international academic community has attached great importance to the research on security issues. For example, IEEE Systems Journal (2012), IEEE Control System Magazine (2015), IEEE Transaction on Control and Network Systems (2015), etc. have published special issues on network security research.

At present, the state estimation of multi-regional power systems can be roughly divided into two categories: 1) hierarchical distributed state estimation methods based on decomposition and coordination, but the partition side and the coordination side are iteratively solved separately, and generally only obtain suboptimal solutions; 2) Distributed method without coordination side, without central coordination side, but weak convergence performance. Therefore, the above two methods have certain deficiencies, and only consider the noise that obeys a specific distribution, which cannot be adapted to the power system with random attack signals, and it is difficult to meet the development needs of modern large-scale power systems.

In a multi-area power system, there must be mutual communication between subsystems, and some nodes share the same state information. Therefore, the communication constraints between adjacent subsystems must be considered in state estimation. Since malicious attack signals exist in networked power systems and are extremely destructive, research on state estimation algorithms for networked multi-regional power systems under malicious attacks is urgent. How to design a reasonable state estimation algorithm to estimate the state of the power system without changing the control structure of the power system is also a major problem that researchers must solve.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, and use the idea of variational inequality to design an adaptive state estimation method for networked multi-regional power systems under data injection attacks.

For achieving the above object, design of the present invention is as follows:

Firstly, a new measurement equation is given for each subsystem under the condition of considering the system state and the attack signal at the same time, and the state estimation problem is transformed into a constrained optimal solution problem by using the measurement equation. Then some effective virtual nodes are constructed to connect the boundary systems to realize the power system communication between different subsystems. Then a distributed state estimation method based on penalty parameters is proposed to realize the state recovery of the power system under FDI attack, in which the penalty parameters can be adaptively adjusted according to the dynamic internal error and boundary error, which is different from the existing power system Compared with state estimation methods, this algorithm has been improved in accuracy and real-time performance, and at the same time, it can also estimate malicious attack signals. Finally, a simulation example illustrates the effectiveness of the adaptive state estimation method.

In order to achieve the above object, the technical solution of the present invention is:

An adaptive state estimation method for networked multi-regional power systems under data injection attacks, including the following specific steps:

Step 1: Divide the large-scale networked power system into multiple control areas, and each control area is one or several buses and generators connected to it, that is, a subsystem; suppose a given power system is divided into p subsystems, where p is a positive integer.

Step 2: Read the measurement data in different areas. The measurement of the system includes the measurement of voltage amplitude and phase angle, the measurement of the active and reactive power injection of the busbar, and the measurement of the active and reactive power flow of the branch. The measurement equation is as follows :

P _ik ＝V _i ² (g _ik +g _sik )-V _i V _k (g _ik cos(θ _i -θ _k )+b _ik sin(θ _i -θ _k ))

Q _ik ＝-V _i ² (b _ik +b _sik )-V _i V _k (g _ik sin(θ _i -θ _m )-b _ik cos(θ _i -θ _k ))

θ _i =arctan(f _i /e _i )

Among them, i is a connection belonging to the subsystem S _a ; V _i , P _ik , Qi _ik , P _i , Q _i are voltage amplitudes, active and reactive power flows, and active and reactive power injection flows at connections l and m, respectively V _i , V _k are the voltage amplitudes of connection l and m respectively; θ _i , θ _k are the phase angle values of connection l and m respectively; g _i +jb _ik is the series admittance value of branch ik ; g _sik +jb _sik is the parallel admittance value of branch ik; g _i +jb _i is the parallel admittance value connected to line i; a(i) is the set of all lines connected to i and belonging to area S _a ; b(i) is the set of all lines connected to i and belonging to area S _a (i≠k); e _i represents the active component of branch i; f _i represents the reactive component of branch i;

Step 3: Assume that the measurement of each subsystem has a linear relationship with the state quantity, and give the measurement equation under FDI attack, which contains both attack information and state information:

In the formula: z _i is the quantity measurement of subsystem i, H _i is the Jacobian matrix of subsystem i, I is the identity matrix, x _i is the state variable of subsystem i, and a _i is the FDI attack signal of subsystem i.

Due to the large number of measuring instruments in the power system and the limited energy of the attacker, only a small number of measured values are subject to malicious attacks, that is, the attack signal is sparse. Compared with measurement noise, measurement noise generally satisfies a specific distribution, while FDI has strong randomness.

There are two ways to estimate the state in the power system: one is to use the power flow calculation method, and the other is to use the state estimation method. In the power flow calculation, the dimension of the measurement vector is the same as that of the unknown state vector, but in the state estimation method, the dimension of the measurement vector is larger than that of the unknown state vector, that is to say, in the state estimation, H _i is a measurement matrix of order m×n, so if an appropriate measurement equation is selected, it can be guaranteed that Φ _i is a full-rank matrix. Power flow calculation can be regarded as a special state estimation when m=n.

Step 4: In order to ensure that the boundary state quantities of the subsystems of the multi-area networked power system are consistent, the following equation constraints are introduced:

In the formula: x _s [t], x _t [s] are the boundary state variables of subsystems s and t respectively. N _s is the set of subsystems adjacent to subsystem s.

In a networked multi-area power system, a more accurate state estimation optimization model should include boundary constraint information. The state estimation objective function with boundary information constraints is given below:

Step 5: In order to better represent the constraint information, construct virtual node b, and the communication connection between adjacent subsystems can be regarded as the connection between some nodes in the subsystem and virtual node b. Therefore, the constraints are transformed into the following form:

In the formula: y _b represents the state of the virtual node, and the set Contains all bridge nodes, and A represents the set of all nodes. The set N _b represents the neighbor nodes connected to the bridge node b. ∑ _|B| |N _b | represents the communication constraints between all nodes and bridge node b.

According to the principle of variational inequality, solving the above state estimation problem can be transformed into solving the following variational inequality problem:

(xx ^* ) ^T F'(x ^* )≥0, Belongs to a non-empty closed set

Where x ^* is the minimum value of the function F, and it belongs to a non-empty closed set.

Step 6: According to the idea of variational inequality and the constructed virtual node b, in order to solve the state estimation problem, in consideration of boundary information constraints, establish a Lagrangian function with variable penalty parameters β _i,b :

Among them, λ _{i, b} are adjustment parameters, and β _{i, b} are variable penalty parameters.

Furthermore, the state estimation problem is transformed into solving the following variational inequality, and its purpose is to find the optimal solution r _i ^k+1 of the following variational inequality, The variational inequality is as follows:

Where k is the number of iterations, F'(r _i ^k+1 ), represent F(r _i ,y _b ,λ _i,b ) function pair r _i ^k+1 and The derivative function of , γ∈(0,2), generally, the performance is optimal when γ=1.618.

In the existing research, the penalty parameter β is a fixed value, or a monotonic sequence, and its calculation efficiency is not high in the state estimation process, so the present invention proposes a variable penalty parameter Its size can be dynamically adjusted according to the estimation error, which in turn can improve the speed of state estimation.

Step 7: The change rules are as follows:

in Represents the iterative error of the system state and attack signal at step k, μ∈(0,1), λ _i,b ∈N _b , non-negative sequence Satisfy and

if Then in the next iteration, should increase, conversely, if , during the next iteration should be reduced, which is the basic idea of the strategy. During iteration, the parameters Its size can be dynamically adjusted according to the estimation error, thereby improving the estimation speed of the algorithm and realizing the self-adaptive characteristic of state estimation.

According to the above formula, iteratively solve the optimal value until the error accuracy meets the requirements of the system for the estimated value.

The self-adaptive state estimation method of networked multi-area power system under data injection attack proposed by the present invention has the following advantages:

1) Scalability: After partitioning, the sub-problems in each region of this method are very small, so it can deal with large-scale networked power systems;

2) Maintainability: On the whole, this method only requires the collaborative iteration of each subsystem and adjacent subsystems, and does not need a control center to coordinate and process, and does not need to maintain several huge models;

3) Speed: By establishing virtual nodes, an adaptive state estimation method with variable penalty parameters is proposed, which can improve the speed of state estimation and meet the real-time requirements of the power system for the state.

Description of drawings

Figure 1 is a flow chart of the method of the present invention.

Figure 2 is a distribution map of the 4-region power system under FDI attack.

Figure 3 is a schematic diagram of virtual node construction.

Figure 4 is a three-area networked power system under FDI attack.

Figure 5 is the frequency state estimation curve and real frequency curve of area 1 under FDI attack.

Figure 6 is the frequency state estimation curve and real frequency curve of area 2 under FDI attack.

Figure 7 is the frequency state estimation curve and real frequency curve of area 3 under FDI attack.

Fig. 8 is the estimated curve and the real attack signal curve of the FDI attack signal suffered by area 1.

Figure 9 is the estimation error for the three-region power system.

Figure 10 shows the change process of penalty parameter β _1,b in area 1.

Detailed ways

The present invention proposes an adaptive state estimation method for networked multi-regional power systems under data injection attacks. The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention Effects are not intended to limit the scope of the present invention. After reading the present invention, modifications to various equivalent forms of the present invention by those skilled in the art all fall within the scope defined by the appended claims of the present application.

As shown in Figure 1, an adaptive state estimation method for networked multi-regional power systems under data injection attacks includes the following steps:

1) Divide the large-scale networked power system into multiple control areas. A control area is one or several buses and generators connected to it, that is, a subsystem. Assuming that a given power system is divided into p subsystems, p is a positive integer, as shown in Figure 2, a 4-area networked power system is given, and p=4. There are communication transmissions between some nodes in area 1 and areas 2 and 3, which are adjacent areas, for example: nodes 1 and 2 in area 1 communicate with nodes 5 and 7 in area 2; nodes in area 1 2 nodes communicate with 11 nodes in area 3 (the following specific description steps take area 1 as an example, which means any area, and each area is processed in the same way).

2) Establish a new measurement model for each area of the divided power system, which includes FDI attack signals, as follows:

Among them, z _i is the quantity measurement of area i, x _i indicates the state of area i, a _i indicates the attack signal suffered by area i, H _i is the measurement matrix of area i, and its elements are determined by the following measurement equation:

P _ik ＝V _i ² (g _ik +g _sik )-V _i V _k (g _ik cos(θ _i -θ _k )+b _ik sin(θ _i -θ _k ))

Q _ik ＝-V _i ² (b _ik +b _sik )-V _i V _k (g _ik sin(θ _i -θ _m )-b _ik cos(θ _i -θ _k ))

θ _i =arctan(f _i /e _i )

Among them, the above are the quantity measurements in area i, and V _i , P _ik , Qi _ik , P _i , Q _i are voltage amplitudes, active and reactive power flows, and active and reactive power injection flows at connections l and m, respectively V _i , V _k are the voltage amplitudes of connection l and m respectively; θ _i , θ _k are the phase angle values of connection l and m respectively; g _i +jb _ik is the series admittance value of branch ik ; g _sik +jb _sik is the parallel admittance value of branch ik; g _i +jb _i is the parallel admittance value connected to line i; a(i) is the set of all lines connected to i and belonging to area S _a ; b(i) is the set of all lines connected to i and belonging to the area S _a (i≠k); e _i represents the active component of branch i; f _i represents the reactive component of branch i.

3) Establish the objective function and constraints of state estimation in region i:

4) In order to better represent the communication constraints between area i and neighboring areas, virtual node b is constructed to represent the communication constraints, as shown in Figure 3, the interconnection between border nodes is regarded as the connection between virtual nodes The dotted line represents the communication connection between the boundary subsystems, and the virtual node is used to transform the connection into a horizontal dotted line connection with the virtual node b, that is, the constraint condition can be transformed into the following form:

Among them, y _b represents the state of the virtual node, and the set Contains all bridge nodes, and A represents the set of all nodes. The set N _b represents the neighbor nodes connected to the bridge node b. The research object of this example is the three-area networked power system under FDI attack, as shown in Figure 4.

5) Using the principle of variational inequality, for state estimation, first solve the problem according to the above state estimation, and propose a Lagrangian function with variable penalty parameters β _i,b :

6) Then according to the above Lagrangian function, the problem of state estimation is transformed into solving a variational inequality problem, that is, the optimal solution r _i ^k+1 of the following variational inequality is solved, The inequality is as follows:

Where k is the number of iterations, F'(r _i ^k+1 ), represent F(r _i ,y _b ,λ _i,b ) function pair r _i ^k+1 and The derivative function of , γ∈(0,2), generally, the performance is optimal when γ=1.618.

7) First, the first iteration solves the optimal solution r _i ¹ that satisfies the inequality in the current situation of area i; secondly, substitutes the optimal solution into the solution In the inequality, solve the optimal solution at this time; then solve the r _i ¹ and substitute The value of λ in the next iteration is calculated from the solved equation. At this point, the optimal solution for region i has been solved, and the optimal solutions for other regions are similar to those for region i.

Note: The penalty parameters β _{i, b} are dynamically adjusted in each iteration. In this example, the adjustment rules are as follows:

If the relationship between the kth iteration error and the boundary error is And when the number of iterations k≤50, then the penalty parameter of the k+1 iteration is twice the penalty parameter of the k iteration, that is If the relationship between the kth iteration error and the boundary error is And when the number of iterations k≤50, then the penalty parameter of the k+1 iteration is half of the penalty parameter of the k iteration, that is Conversely, for other cases, the penalty parameter of the k+1 iteration is equal to the penalty parameter of the k iteration, namely

8) Judgment of convergence conditions, iterative calculation step by step according to the above steps, until the obtained solution satisfies ‖e(r ^k+1 )‖<ε (ε is the required estimation error accuracy), stop the iterative process, the optimal The solution can be approximated as the real solution that needs to be solved.

Finally, the frequency state bands in each region are subjected to FDI attack under the estimated value and the change curve of the real value as shown in Figures 5, 6, and 7. From the figure, it can be seen that the method proposed by the present invention can avoid the influence of FDI attack, and then accurately The state of the system can be accurately estimated, and at the same time, the change curve of the attack signal suffered by the system can also be estimated, as shown in Figure 8. Compared with the traditional distributed estimation method, it can be seen that the method proposed by the present invention has faster estimation speed and higher estimation accuracy, as shown in FIG. 9 . In this example, the change process curve of variable penalty parameter β _1,b in area 1 is shown in Figure 10 . It should be pointed out that the present invention only uses a three-area networked interconnected power system to elaborate on the implementation process. In the case of a larger-scale multi-area power system, the advantages of the present invention in terms of calculation speed and estimation accuracy will be more prominent and significant.

To sum up, the present invention can estimate the state of the multi-regional power system after being attacked by FDI online in real time, and can avoid the destructiveness caused by malicious attacks to the power system, and the state estimation has high precision, fast estimation speed, and timely The influence of the FDI attack signal can be eliminated to obtain accurate system state information; at the same time, the present invention realizes multi-area communication by constructing virtual nodes, coordinates the operating states of each area well, and proposes variable penalty parameters to improve state estimation. Speed, to meet the real-time requirements of the system for status. For a complex, large-scale, multi-regional networked power system, its state estimation under FDI attack is one of the traditional Chinese medicine modules in the energy management center of the future smart grid, and it is of great significance to promote the further development of the smart grid.

Claims (1)

1. a kind of adaptive state estimation method of Data Injection Attacks lower network multi-region power system, utilizes the amount of system Measured data carries out state estimation, which is characterized in that the method includes the steps of：

Step 1：The networked power system of big scale is divided into multiple control zones, each control zone is exactly one or several Busbar and generator connected to it, i.e. a subsystem；If given electric system is divided into p subsystem, wherein p For positive integer；

Step 2：Read the metric data of different zones, the measurement of system, which includes voltage magnitude and phase angle measurements, busbar, to be had Work(and idle injecting power measurement, branch active reactive trend measurement, measurement equation are as follows：

P_ik=V_i ²(g_ik+g_sik)-V_iV_k(g_ikcos(θ_i-θ_k)+b_iksin(θ_i-θ_k))

Q_ik=-V_i ²(b_ik+b_sik)-V_iV_k(g_iksin(θ_i-θ_m)-b_ikcos(θ_i-θ_k))

θ_i=arctan (f_i/e_i)

Wherein, i is to belong to subsystem S_aA wiring；V_i、P_ik、Q_ik、P_i、Q_iIt is voltage magnitude at wiring l and m respectively, active With reactive power flow, the measuring value of active and idle injection trend；V_i、V_kIt is the voltage magnitude of wiring l and m respectively；θ_i、θ_kRespectively It is the angle values of wiring l and m；g_i+jb_ikIt is branch i-k series admittance values；g_sik+jb_sikIt is branch i-k shunt admittance values；g_i+ jb_iIt is attached to the shunt admittance value of line i；A (i) is to be connected on i and belong to region S_aWired set；B (i) is It is connected on i and belongs to region S_aWired set (i ≠ k)；e_iIndicate the active component of branch i；f_iIndicate branch i Reactive component；

Step 3：Assuming that the measurement of subsystems and quantity of state are linear, and provide the lower measurement equation of FDI attacks, it is same When include attack information and status information：

In formula：z_iFor the measurement of subsystem i, H_iFor the Jacobian matrix of subsystem i, I is unit battle array, x_iFor the shape of subsystem i State variable, a_iFor the FDI signal to attack of subsystem i；

Step 4：Provide the object function and boundary communication constraints of state estimation：

In formula：x_s[t]、x_t[s] is respectively the boundary condition variable of subsystem s, t, N_sFor the subsystem collection adjacent with subsystem s It closes；

Step 5：In order to preferably carry out the state estimation of multizone, the communication between different zones is realized, by building virtually The form of node indicates the communication constraint between adjacent area：

In formula：y_bIndicate the state of dummy node, setIncluding all bridge nodes, A indicates the collection of all node compositions It closes, set N_bIndicate the neighbor node being connected with bridge node b；

Step 6：Using variational inequality principle, above-mentioned state estimation problem is converted to solution Variational Inequalities Problem, is found out The optimal solution for meeting inequality condition, provides Lagrangian first,

Wherein λ_i,bFor adjustment parameter, β_i,bTo become punishment parameter；

Based on Lagrangian F (r_i,y_b,λ_i,b), provide and need the variational inequality that solves, below three formulas solve respectively Go out optimal solution r_i ^k+1,

Wherein k is iterations, F (r are indicated respectively_i,y_b,λ_i,b) function pairWithLead letter Number, adjustment parameter γ ∈ (0,2)；

Step 7：It is required to judge the requirement whether current state estimation error precision reaches system before iteration each time, Stop iteration if reaching, needs the relationship according to current evaluated error and boundary error dynamically to be adjusted if not reaching Integral function F (r_i,y_b,λ_i,b) change punishment parameterIt adjusts rule：

WhereinIndicate the iteration error that system mode and signal to attack are walked in kth, μ ∈ (0,1), λ_i,b∈N_b, nonnegative sequenceMeetAndAccording to above equation iteration Optimal value is solved, until error precision meets requirement of the system to estimated value.