Power system optimal power flow global optimization method based on dynamic system optimal bifurcation

Abstract

The invention discloses a power system optimal power flow global optimization method based on dynamic system optimal bifurcation, which comprises the following steps of: giving an optimal power flow problem, calculating a local optimal solution by adopting a local optimization algorithm, constructing a corresponding augmented quotient gradient system, and calculating the optimal power flow problem according to the augmented quotient gradient system. The local optimal solution corresponds to a conventional stable equilibrium point of the system when the penalty factor is large enough; starting from the calculated stable balance point, continuously reducing penalty factors, tracking the change of the stable balance point of the system, recording the out-of-limit information of the stable balance point until the out-of-limit is reduced and the saddle node bifurcation disappears in the tracked original stable balance point at the moment, and continuing to integrate the system to find a new stable balance point; starting from a new stable equilibrium point, penalty factors are continuously increased until the penalty factors are large enough to enable the stable equilibrium point to meet epsilon feasibility, at the moment, the stable equilibrium point corresponds to a new local optimal solution of the optimal power flow problem, the optimal solution is better than the optimal solution in the first stage until new bifurcation cannot occur, and a new local optimal solution is found; and at the moment, finding a global optimal solution of the original optimal power flow problem. According to the method, a local optimization method is helped to efficiently jump out of a current local optimal solution, a better local optimal solution is continuously searched, and a global optimal solution is finally found.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular, to an optimal power flow global optimization method for power systems based on optimal bifurcation of dynamic systems. Background Art

[0002] With the rapid development of the power system towards the direction of clean, low-carbon, and high-proportion renewable energy penetration, the complexity, dynamics, and uncertainty of system operation are continuously increasing, posing higher requirements for the safe, economic, and stable operation of the power grid. Optimal Power Flow (OPF), as one of the core issues in power system scheduling and planning, aims to optimize system operation costs, losses, or other target parameters on the premise of meeting various operation constraints, and has become a basic tool for power grid operation optimization and intelligent scheduling.

[0003] Currently, the widely used optimal power flow solution methods mainly include interior point method, Newton method, Lagrange multiplier method, heuristic algorithm, etc., which have good convergence and feasibility in small and medium-sized systems. Especially commercial nonlinear solvers such as IPOPT, KNITRO, etc., have been able to efficiently solve the nonlinear AC optimal power flow model on medium-scale systems. However, in the engineering practice of power systems, the optimal power flow model still faces many challenges, mainly manifested in the following aspects:

[0004] (1) Non-convexity and multi-solution of the AC model: The AC optimal power flow is essentially a nonlinear non-convex optimization problem, which is prone to generate multiple local optimal solutions. In the context of high renewable energy penetration and high load fluctuations, the distribution of system operation states is more complex, and traditional local optimization algorithms are easily trapped in local optima, resulting in non-global optimal scheduling results, thus affecting operation economy.

[0005] (2) Frequent occurrence of non-convergence problems in solving: In scenarios such as high load, fault disturbance, and new energy output fluctuations, the constraint space of the system will shrink significantly, and the feasible region of the optimization problem will be significantly reduced. Conventional solution algorithms (such as interior point method) are prone to convergence failure when the initial point is far from the feasible region, affecting the robustness and practicality of the power grid online scheduling system.

[0006] (3) Accuracy limitations of the linear model: To avoid calculation instability caused by the AC model, a DC optimal power flow (DC-OPF) approximate model is often used in engineering. However, DC-OPF ignores key factors such as reactive power, voltage constraints, and line losses, and is difficult to reflect the true operation state of the system. Especially in high-voltage transmission and strongly coupled systems, the error is obvious, and it cannot meet the actual safety checking and control requirements.

[0007] (4) Lack of effective global optimization methods: Although some global optimization methods based on meta-heuristic algorithms (such as genetic algorithms, particle swarms, simulated annealing, etc.) have made progress in recent years, these methods have problems such as large computational complexity, parameter sensitivity, and poor stability, and it is still difficult to be popularized and applied in large-scale power grids. Currently, there is generally a lack of a global optimization method with mathematical theory support, good stability, and high efficiency, resulting in the solution of the optimal power flow problem still mainly relying on local optimal results.

[0008] In summary, how to construct a global optimization method for optimal power flow that not only has local optimization efficiency but also can jump out of local traps, approach or even reach the global optimum is a key problem that urgently needs to be solved in the field of optimal power flow in the current power system. Especially in the context of a new power system with strong volatility of new energy and complex power grid load structure, developing a new method with strong feasibility, stable convergence, and stronger globality has important engineering value and practical application prospects. Summary of the Invention

[0009] Purpose of the Invention: The present invention provides a global optimization method for optimal power flow of a power system based on optimal bifurcation of a dynamic system, which helps the local optimization method to efficiently jump out of the current local optimal solution, continuously search for a better local optimal solution, and finally find the global optimal solution.

[0010] Technical Solution: A global optimization method for optimal power flow of a power system based on optimal bifurcation of a dynamic system according to the present invention includes the following steps:

[0011] Step 1: Given an optimal power flow problem, use a local optimization algorithm to calculate a local optimal solution; construct a corresponding augmented quotient gradient system, and this local optimal solution corresponds to the regular stable equilibrium point of the system when the penalty factor is large enough.

[0012] Step 2: Starting from the stable equilibrium point calculated in Step 1, continuously reduce the penalty factor, track the change of the stable equilibrium point of the system, where the stable equilibrium point is the steady state of the system under each penalty factor, record the over-limitation information of the stable equilibrium point until the reduction of the over-limitation occurs. At this time, the original stable equilibrium point being tracked has disappeared due to saddle-node bifurcation, and continue to integrate the system to find the new stable equilibrium point.

[0013] Step 3: Starting from the new stable equilibrium point in Step 2, continuously increase the penalty factor until the penalty factor is large enough to make the stable equilibrium point satisfy ε feasibility. At this time, the stable equilibrium point corresponds to a new local optimal solution of the optimal power flow problem, and this optimal solution is better than the optimal solution in the first stage.

[0014] Step 4: Repeat Step 2 and Step 3 until no new bifurcation occurs and a new local optimal solution is found. Then, the global optimal solution of the original optimal power flow problem is found at this time.

[0015] Furthermore, in step 1, the optimal power flow problem adopts non-linear AC power flow equations, defined as follows:

[0016] The objective function is: min.f = ax 2 + bx + c

[0017] where f is in the form of a fuel cost as the objective function, which is a continuously differentiable function, a, b, and c are constant vectors representing the structure of the objective function, and x is a variable vector including the active power, reactive power of generator nodes, and voltage magnitudes and phase angles of all nodes;

[0018] The constraint set is:

[0019]

[0020] V i min ≤ V i ≤ V i max i ∈ {1, 2,..., N B}

[0021]

[0022] where N B , N L , N G represent the numbers of bus nodes, transmission lines, and generators in the power system respectively. Constants G ij and B ij are the equivalent conductance and equivalent susceptance of the line from node i to node j respectively. P Li and Q Li are the active load value and reactive load value of node i respectively. The variable θ i is the voltage phase angle of node i, and θ ij = θ i - θ j , where the voltage phase angle of the slack node is set as a constant. The variable V i is the voltage magnitude of node i. P Gi and Q Gi are the active output power value and reactive output power value of the generator connected to node i respectively. Expressions S fl and S tl are the apparent powers at the sending end and receiving end of line l respectively.

[0023] Furthermore, the slack variable technique is adopted. By introducing slack variables (SL AC 2) can be added to the inequality constraint set, and the inequality constraint can be equivalently transformed into an equality constraint form; the AC optimal power flow constraint set with slack variables is expressed in the following compact form:

[0024]

[0025] Among them, is the equality constraint set, is the inequality constraint set, and the variable x = [u AC , y AC (u AC ), SL AC (u AC , y(u AC ))];

[0026] The AC optimal power flow model is simply expressed in the following form:

[0027] Minimize f(x)

[0028] s.t. H(x) = 0

[0029] Among them, is the objective function; is the constraint set. The inequality constraint has been transformed into an equality constraint by adding slack variables. Among them, n is the number of variables, including all variables (2N G + 2N B - 1) and slack variables (4N G + 3N B + 2N L ), so n = 6N G + 5N B + 2N L - 1; m is the number of constraints, m = 4N G + 5N B + 2N L .

[0030] Furthermore, in step 1, the Augmented Quotient Gradient System (AQGS) is related to the objective function and non-linear constraints:

[0031]

[0032] Among them, DH(x) is the Jacobian matrix of H(x), is the gradient vector of the objective function, is a positive constant penalty factor.

[0033] Furthermore, in Step 2, there will be multiple saddle-node bifurcations during the penalty factor reduction phase, and there are two flexible handling strategies: (1) Immediately end Step 2 and enter Step 3 after the bifurcation occurs; (2) Continuously reduce the penalty factor until it reaches a very small value, and then perform the calculations of Step 3 for each bifurcation or the last bifurcation.

[0034] Furthermore, in Step 2, continuously reduce the penalty factor and track the change of the stable equilibrium point with the penalty factor until a saddle-node bifurcation occurs, which specifically includes the following steps:

[0035] Step 21. Let δ k+1 = c1δ k , starting from , integrate the system until it converges to a stable equilibrium point, denoted as

[0036] Step 22. Calculate the constraint mismatch degree of

[0037] Step 23. If , then a saddle-node bifurcation occurs and disappears, and the penalty factor δ * , δ k > δ * > δ k+1 . Let be the new stable equilibrium point, i = i + 1;

[0038] Step 24. If δ k+1 < ε, go to Step 25; otherwise, let k = k + 1 and go to Step 21;

[0039] Step 25. If S b is an empty set, terminate the calculation; otherwise, go to Phase 3.

[0040] Furthermore, in Step 3, starting from the new stable equilibrium point, continuously increase the penalty factor until the penalty factor is large enough so that the stable equilibrium point satisfies ε feasibility. At this time, the stable equilibrium point corresponds to a new local optimal solution of the optimal power flow problem, which specifically includes the following steps:

[0041] Step 31. Let j = j + 1,

[0042] Step 32. Let , starting from , integrate the system until it converges to a stable equilibrium point, denoted as

[0043] Step 33. If , let Go to step 32; otherwise, find a new local optimal solution to the problem, and let

[0044] Step 34. If j > i - 1, terminate the calculation and output the new local optimal solution set S new ; otherwise, go to step 31.

[0045] Beneficial effects: Compared with the prior art, the present invention not only has theoretical advantages at the algorithm level, but also demonstrates remarkable engineering practicability and innovation in the actual operation of power systems, which are specifically reflected in the following aspects:

[0046] (1) Significantly enhance the robustness and adaptability of the algorithm: Based on the saddle-node bifurcation mechanism of stable equilibrium points in dynamic systems, the present invention can jump out of the current solution when "structural bifurcation" occurs in local optimal traps by constructing an augmented quotient gradient system (AQGS), thereby effectively addressing the problems that conventional algorithms are prone to falling into local optima or being unable to converge due to narrow constraint spaces, and significantly improving the stability and robustness of optimal power flow calculations;

[0047] (2) Efficiently achieve the global optimal scheduling of power systems: Through the path tracking strategy of dynamic systems, this method can search for multiple better local optimal solutions with low computational complexity and further approach or even directly find the global optimal solution. This ability is of great significance for improving the economy, security, and comprehensive operation benefits of power grid scheduling, and is particularly applicable to regional power grid scenarios with high renewable energy access and complex scheduling spaces;

[0048] (3) Have clear mathematical convergence guarantees and engineering implementation paths: Compared with existing meta-heuristic global optimization algorithms, the method of the present invention has clear mathematical theoretical support, does not rely on random perturbations, does not require multiple initial value attempts, and only needs one path tracking process to obtain better solutions or global solutions, avoiding redundant calculations and repeated experiments, and having better engineering deployability and real-time advantages;

[0049] (4) Applicable to various types and scales of power systems: Verification in typical multi-solution systems (such as Case9mod) shows that the present invention can stably and quickly start from any non-global solution and finally search for the global optimal solution, and the improvement of the objective function is significant (such as up to 27.6%). The algorithm has good adaptability and scalability in power grids ranging from small distribution networks to large-scale interconnected power grids;

[0050] (5) Support the friendly access and flexible scheduling of new energy: In power grids with a high proportion of new energy, the uncertainty of system operating states increases significantly, and conventional scheduling methods face problems such as poor convergence and low solution quality. The method of the present invention has good problem adaptation ability by tracking the change process of stable structures, and can be used as a key algorithm tool to support the friendly access of new energy and the coordinated optimization of sources, grids, loads, and energy storage in the future;

[0051] Therefore, the present invention not only provides a global optimization strategy with novel theory, clear path, and high computational efficiency, but also effectively solves the key problems such as multiple solutions, non-convergence, and low solution quality widely existing in the current optimal power flow calculation from the perspective of the actual operation of the power system, and has broad engineering application prospects and promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0053] Figure 2 It is a distribution diagram of 4 optimal solutions and 4 unstable equilibrium points of the augmented merchant gradient system for the Case9mod system.

[0054] Figure 3(a) is a schematic diagram of the decreasing stage of the LOS2 penalty factor.

[0055] Figure 3(b) is a schematic diagram of the increasing stage of the LOS2 penalty factor.

[0056] Figure 3(c) is a curve graph of the constraint violation amount and the objective function change during the decreasing stage of the LOS2 penalty factor.

[0057] Figure 4(a) is a schematic diagram of the decreasing stage of the LOS3 penalty factor.

[0058] Figure 4(b) is a schematic diagram of the increasing stage of the LOS3 penalty factor.

[0059] Figure 4(c) is a curve graph of the constraint violation amount and the objective function change during the decreasing stage of the LOS3 penalty factor.

[0060] Figure 5(a) is a schematic diagram of the decreasing stage of the LOS4 penalty factor.

[0061] Figure 5(b) is a schematic diagram of the increasing stage of the LOS4 penalty factor.

[0062] Figure 5(c) is a curve graph of the constraint violation amount and the objective function change during the decreasing stage of the LOS4 penalty factor. DETAILED DESCRIPTION OF THE INVENTION

[0063] As Figure 1 shown, a global optimization method for optimal power flow of a power system based on optimal bifurcation of a dynamic system includes the following steps:

[0064] Step 1: Given an optimal power flow problem, use a local optimization algorithm to calculate a local optimal solution; construct a corresponding augmented merchant gradient system, and this local optimal solution corresponds to the conventional stable equilibrium point of the system when the penalty factor is large enough;

[0065] Step 2: Starting from the stable equilibrium point calculated in Step 1, continuously reduce the penalty factor, track the change of the stable equilibrium point of the system, where the stable equilibrium point is the steady state of the system under each penalty factor, record the over-limitation information of the stable equilibrium point until the reduction of the over-limitation occurs. At this time, the original stable equilibrium point being tracked has disappeared due to saddle-node bifurcation, and continue to integrate the system to find the new stable equilibrium point;

[0066] Step 3: Starting from the new stable equilibrium point in Step 2, continuously increase the penalty factor until the penalty factor is large enough so that the stable equilibrium point satisfies ε feasibility. At this time, the stable equilibrium point corresponds to a new local optimal solution of the optimal power flow problem, and this optimal solution is better than the optimal solution in the first stage;

[0067] Step 4: Repeat Step 2 and Step 3 until no new bifurcation occurs and a new local optimal solution is found. Then, the global optimal solution of the original optimal power flow problem is found at this time.

[0068] In Step 1, the optimal power flow problem uses a non-linear AC power flow equation, which is defined as follows:

[0069] The objective function is: min.f = ax 2 + bx + c

[0070] where f is in the form of a fuel cost as the objective function, which is a continuously differentiable function, a, b, c are constant vectors representing the structure of the objective function, and x is a variable vector including the active power, reactive power of the generator nodes, and the voltage magnitudes and voltage phase angles of all nodes;

[0071] The constraint set is:

[0072]

[0073] V i min ≤ V i ≤ V i max i ∈ {1, 2,..., N B}

[0074]

[0075] where N B , N L , N G represent the numbers of bus nodes, transmission lines, and generators in the power system respectively. The constants G ij and B ij are the equivalent conductance and equivalent susceptance of the line from node i to node j respectively. P Li and Q Li are the active load value and reactive load value of node i respectively. The variable θ iis the voltage phase angle of node i, and θ ij = θ i - θ j , where the voltage phase angle of the slack node is set to a constant, and the variable V i is the voltage magnitude of node i, P Gi and Q Gi are the active power output value and reactive power output value of the generator connected to node i respectively. The expressions S fl and S tl are the apparent powers at the sending end and receiving end of line l respectively;

[0076] By using the slack variable technique, the inequality constraints can be equivalently transformed into equality constraint form by adding the slack variables (SL AC 2 ) to the inequality constraint set; The AC optimal power flow constraint set with slack variables is expressed in the following compact form:

[0077]

[0078] where, is the equality constraint set, is the inequality constraint set, and the variable x = [u AC , y AC (u AC ), SL AC (u AC , y(u AC ));

[0079] The AC optimal power flow model is simply expressed in the following form:

[0080] Minimize f(x)

[0081] s.t. H(x) = 0

[0082] where, is the objective function; is the constraint set. The inequality constraints have been transformed into equality constraints by adding slack variables. Among them, n is the number of variables, including all variables (2N G + 2N B - 1) and slack variables (4N G + 3N B + 2N L ), so n = 6N G + 5N B + 2N L - 1; m is the number of constraints, m = 4N G + 5N B + 2N L .

[0083] In Step 1, the Augmented Quotient Gradient System (AQGS) is related to the objective function and the non-linear constraints:

[0084]

[0085] where \(DH(x)\) is the Jacobian matrix of \(H(x)\), is the gradient vector of the objective function, is a positive constant penalty factor.

[0086] In Step 2, there are multiple saddle-node bifurcations during the penalty factor reduction phase, and there are two flexible handling strategies: (1) Immediately end Step 2 and enter Step 3 after a bifurcation occurs; (2) Continuously reduce the penalty factor until a very small value, and then perform the calculations in Step 3 for each bifurcation or the last bifurcation.

[0087] In Step 2, continuously reduce the penalty factor and track the change of the stable equilibrium point with the penalty factor until a saddle-node bifurcation occurs. Specifically, it includes the following steps:

[0088] Step 21: Let \(\delta\) k+1 \(= c1\delta\) k , starting from , integrate the system until it converges to a stable equilibrium point, denoted as

[0089] Step 22: Calculate the constraint mismatch degree of

[0090] Step 23: If , then a saddle-node bifurcation occurs and disappears, and the penalty factor \(\delta\) at the bifurcation point * , \(\delta\) k \(>\delta\) * \(>\delta\) k+1 , let be the new stable equilibrium point,

[0091] i = i + 1;

[0092] Step 24: If \(\delta\) k+1 \(<\varepsilon\), go to Step 25; otherwise, let k = k + 1 and go to Step 21;

[0093] Step 25: If \(S\) b is an empty set, terminate the calculation; otherwise, go to Phase 3.

[0094] In Step 3, starting from the new stable equilibrium point, continuously increase the penalty factor until the penalty factor is large enough such that the stable equilibrium point satisfies ε - feasibility. At this time, the stable equilibrium point corresponds to a new local optimal solution of the optimal power flow problem. The specific steps are as follows:

[0095] Step 31: Let j = j + 1.

[0096] Step 32: Let Starting from Integrate the system until it converges to a stable equilibrium point, denoted as

[0097] Step 33: If Let Go to Step 32; otherwise, find the new local optimal solution of the problem, and let

[0098] Step 34: If j > i - 1, terminate the calculation and output the new local optimal solution set S new ; otherwise, go to Step 31.

[0099] In the case9mod system, there are 3 generators and 9 branches, and there are 4 local optimal solutions. Table 1 lists the location and objective function value information of the four optimal solutions. Obviously, LOS1 is the global optimal solution. Figure 2 Shows the location distribution of the optimal solutions of the optimal power flow and the unstable equilibrium points of the augmented quotient gradient system, which contains 4 unstable equilibrium points. Starting from the three non - global optimal solutions, the global solution LOS1 can be solved, and the maximum improvement in the objective function can reach 27.6%.

[0100] Table 1 shows the calculation results using the four optimal solutions of the case9mod system as the known local solutions

[0101]

[0102] Stage 1 (local search stage): Given three local optimal solutions (x los.2 , x los.3 and x los.4 ), respectively, which are not the global optimal solutions. Construct the corresponding augmented quotient gradient system and set the initial penalty factor δ0 = 1×10 6 , and the penalty factor magnification coefficient in the second stage is set to 0.5, that is, δ k+1 = δ k / 2, and the penalty factor is reduced by half each time it is updated.

[0103] Stage 2 (escaping from the optimal solution / problem relaxation stage): Using the local optimal solutions x los.i, i = 2, 3, 4, as input, reduce the penalty factor from δ0, and obtain three different stable equilibrium point sequences, as shown in Figure 3 (a), Figure 4 (a) and Figure 5 (a). At the same time, record the maximum constraint mismatch and objective function value information of the stable equilibrium point, as shown in Figure 3 (c), Figure 4 (c) and Figure 5 (c). The parts marked with red boxes in the figures have a decrease in constraint mismatch, indicating that the tracked stable equilibrium point has a saddle-node bifurcation and disappears, which also verifies that the change in constraint mismatch can be used to determine whether a bifurcation has occurred. After a bifurcation occurs, jump out of the original stable equilibrium point and find a new stable equilibrium point.

[0104] Specifically, for LOS2, as shown in Figure 3(a), a saddle-node bifurcation occurs and LOS2 disappears when the penalty factor is iterated from the 11th to the 12th time (δ = 244.14 → 122.07). Therefore, at the 12th step (δ = 122.07), a saddle-node bifurcation has occurred, causing LOS2 to disappear and finding a new stable equilibrium point LOS1. As shown in Figure 3(c), the maximum constraint mismatch of the tracked stable equilibrium point decreases at the corresponding position. In addition, the objective function also decreases significantly, but since the objective function itself has been decreasing with the change of the penalty factor, it is not easy to identify in one example. This also shows that the occurrence of saddle-node bifurcation can be easily identified based on the change of constraint mismatch, but it is challenging to identify it from the objective function value.

[0105] For LOS3, as shown in Figures 4(a) and 4(c), the over-limit decrease occurs at the 12th-13th penalty factor iteration (δ=488.28→244.14), at which time a saddle-node bifurcation also occurs, causing LOS3 to disappear, and a new stable equilibrium point LOS1 is found. For LOS4, as shown in Figures 5(a) and 5(c), the over-limit decrease also occurs at the 12th-13th penalty factor iteration (δ=488.28→244.14), at which time a saddle-node bifurcation occurs, causing LOS4 to disappear, and a new stable equilibrium point LOS1 is found.

[0106] In the second stage of penalty factor reduction, a larger penalty factor reduction step size strategy is used to generate the penalty factor sequence, which does not affect the final result. Therefore, in practical applications, the step size can be appropriately increased to balance the algorithm's computational speed and robustness.

[0107] Stage 3 (Problem recovery stage): After the over-limit value drops, starting from the newly found stable equilibrium points respectively, continuously increase the penalty factor and calculate a set of stable equilibrium point sequences, as shown in Fig. 3(b), Fig. 4(b) and Fig. 5(b). Finally, when the penalty factor returns to the initial penalty factor size, all three sets of stable equilibrium point sequences finally find LOS1, that is, the global optimal solution. This algorithm realizes starting from three different non-global optimal solutions in the case9mod system, jumping out of the original local optimal solution, and finally achieving global optimization.

[0108] The method based on the augmented quotient gradient system proposed by the present invention is more effective and always finds higher-quality solutions. While the branch tracking method and the filled function method can only enumerate multiple different optimal solutions and then find the optimal one from them. In addition, the parameter penalty factor is one-dimensional and does not require specifying a search direction, which is more convenient.

[0109] In summary, the present invention has the following advantages: (1) It has theoretical support and can ensure finding a better solution after bifurcation; (2) It can jump out of the local optimal solution and find a better local optimal solution, and finally achieve global optimization; (3) It is an efficient deterministic method and there is no convergence problem, only need to solve once without repeated calculations; (4) When multiple bifurcations occur in Stage 2, different strategies can be adopted to find multiple local optimal solutions or directly solve the global optimal solution; in Stage 2, the situation of multiple saddle-node bifurcations is considered, and a new stable equilibrium point can be found after each bifurcation, and a new local optimal solution can be found in Stage 3. Therefore, multiple different local optimal solutions can be found or only one new local optimal solution can be solved. Generally, the later the bifurcation occurs, the better the optimal solution found, and even the global optimal solution can be found. The practicality of this method lies in that it can continuously find better solutions of the objective function instead of exhaustively searching all local optimal solutions, which may include solutions of poor quality.

Claims

1. A global optimization method for optimal power flow of power system based on optimal bifurcation of dynamic system, characterized in that: The steps include: Step 1: Given an optimal power flow problem, a local optimization algorithm is used to calculate a local optimal solution; a corresponding augmented quotient gradient system is constructed, and the local optimal solution corresponds to the conventional stable equilibrium point of the system when the penalty factor is large enough; Step 2: Starting from the stable equilibrium point calculated in step 1, the penalty factor is continuously reduced to track the changes in the stable equilibrium point of the system, where the stable equilibrium point is the steady state of the system under each penalty factor, and the information of the over-limit of the stable equilibrium point is recorded until the over-limit decreases, at which time the original stable equilibrium point being tracked has disappeared due to the saddle-node bifurcation, and the new stable equilibrium point found by the integration system is continued; Step 3: Starting from the new stable equilibrium point in step 2, the penalty factor is continuously increased until the penalty factor is large enough to make the stable equilibrium point satisfy ε feasibility. The stable equilibrium point at this time corresponds to a new local optimal solution of the optimal power flow problem, which is better than the optimal solution in the first stage. Step 4: Repeat steps 2 and 3 until no new bifurcation occurs and a new local optimal solution is found. At this time, the global optimal solution to the original optimal power flow problem is found.

2. The method for global optimization of optimal power flow of power system based on optimal bifurcation of dynamic system according to claim 1, characterized in that: In step 1, the optimal power flow problem uses a nonlinear AC power flow equation, which is defined as follows: The objective function is: min.f = ax 2 +bx+c Among them, f is the form of the objective function with fuel cost as the objective function, which is a continuously differentiable function, a, b, c are constant vectors, representing the structure of the objective function, and x is a variable vector, including the active power and reactive power of the generator node and the voltage amplitude and voltage phase angle of all nodes; The constraint set is: V i min ≤V i ≤V i max i∈{1,2,...,N B } Among them, N B ,N L ,N G Respectively represent the number of busbar nodes, transmission lines and generators in the power system, and the constant G ij and B ij are the equivalent conductance and equivalent susceptance of the line from node i to node j, respectively, Li and Q Li are the active load value and reactive load value of node i respectively, and the variable θ i is the voltage phase angle of node i, and θ ij =θ i -θ j , where the voltage phase angle of the balance node is set to a constant, and the variable V i is the voltage amplitude of node i, P Gi and Q Gi are respectively the active output power value and reactive output power value of the generator connected to node i, and the expression S fl and S tl are the apparent powers at the beginning and end of line l respectively.

3. The method for global optimization of optimal power flow of power system based on optimal bifurcation of dynamic system according to claim 2, characterized in that: Using the slack variable technique, the slack variable SL AC 2 Add the inequality constraint set and convert the inequality constraint into the equality constraint form; the AC optimal power flow constraint set with slack variables is expressed in the following compact form: in, is the set of equality constraints, is the set of inequality constraints, variable x=[u AC ,y AC (u AC ),SL AC (u AC ,y(u AC ))]; The AC optimal power flow model is simply expressed as follows: Minimize f(x) stH(x)=0 in, is the objective function; is a constraint set. The inequality constraints have been converted into equality constraints by adding slack variables, where n is the number of variables, including all variables (2N G +2N B -1) and slack variables (4N G +3N B +2N L ), so n = 6N G +5N B +2N L -1; m is the number of constraints, m = 4N G +5N B +2N L .

4. The method for global optimization of optimal power flow of power system based on optimal bifurcation of dynamic system according to claim 1, characterized in that: In step 1, the augmented quotient gradient system, referred to as AQGS, is related to the objective function and nonlinear constraints: Where DH(x) is the Jacobian matrix of H(x), ▽f(x) is the gradient vector of the objective function, is a positive constant penalty factor.

5. The method for global optimization of optimal power flow of power system based on optimal bifurcation of dynamic system according to claim 1, characterized in that: In step 2, multiple saddle-node bifurcations will occur during the penalty factor reduction stage. There are two flexible handling strategies: (1) end step 2 immediately after the bifurcation occurs and proceed to step 3; (2) continue to reduce the penalty factor until it reaches a very small value, and then perform step 3 calculation for each bifurcation or the last bifurcation.

6. The method for global optimization of optimal power flow of power system based on optimal bifurcation of dynamic system according to claim 1, characterized in that: In step 2, the penalty factor is continuously reduced, and the stable equilibrium point is tracked as the penalty factor changes until a saddle-node bifurcation occurs. The specific steps include the following: Step 21: Let δ k+1 =c1δ k ,from Starting from, the integral system converges to a stable equilibrium point, denoted as Step 22: Calculate Constraint mismatch Step 23: If but Saddle-node bifurcation occurs and disappears, and the penalty factor δ at the bifurcation point * ,δ k >δ * >δ k+1 ,make is the new stable equilibrium point, Step 24: If δ k+1 <ε, go ​​to step 25; otherwise, let k=k+1 and go to step 21; Step 25: If S b If it is an empty set, the calculation is terminated; otherwise, go to stage 3.

7. The method for global optimization of optimal power flow of power system based on optimal bifurcation of dynamic system according to claim 1, characterized in that: In step 3, starting from the new stable equilibrium point, the penalty factor is continuously increased until the penalty factor is large enough to make the stable equilibrium point meet the ε feasibility. The stable equilibrium point at this time corresponds to a new local optimal solution of the optimal power flow problem. Specifically, it includes the following steps: Step 31: Let j=j+1, Step 32: from Starting from, the integral system converges to a stable equilibrium point, denoted as Step 33: If make Go to step 32; otherwise, find a new local optimal solution to the problem, let Step 34: If j>i-1, terminate the calculation and output the new local optimal solution set S new ; Otherwise, go to step 31.

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