Power distribution network optimization scheduling method based on improved convex internal approximation and feasible solution recovery cooperation
By improving the convex inner approximation method and feasible solution recovery mechanism, a dynamic safety boundary and multi-objective optimization model are constructed to solve the safety and economic problems of the distribution network under the high proportion of renewable energy access, and realize the efficient absorption of distributed power sources and the improvement of voltage stability.
Patent Information
- Application Number
- CN202511808237.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-03
- Publication Date
- 2026-02-13
AI Technical Summary
Existing power distribution network optimization technologies struggle to improve the absorption capacity and operational economy of new energy sources while ensuring the safe operation of the system in scenarios with a high proportion of renewable energy access. Traditional methods suffer from problems such as solution space compression, excessively conservative constraints, and insufficient multi-resource collaborative optimization.
A dynamic safety boundary is constructed using the improved In-Convex Approximation Method (ICIA). Combined with the Feasible Solution Recovery (FSR) mechanism, the scheduling scheme is optimized by guiding the coordinated adjustment of multiple resources through sensitivity and constructing a normalized multi-objective function with embedded voltage penalty terms for vulnerable nodes.
It significantly improves the distributed power absorption capacity, voltage safety and economy, has high computing efficiency, adapts to scenarios with a high proportion of renewable energy access, and meets real-time scheduling requirements.
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Figure CN121529664A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to power grid dispatching optimization technology, in particular to a power distribution network optimization dispatching method based on improved convex inner approximation and feasible solution recovery cooperation. BACKGROUND
[0002] Under the driving of the strategic targets of "carbon peak" and "carbon neutrality", high proportion of renewable energy represented by wind power and photovoltaic is connected to the distribution network, which promotes the transformation of the power system to low carbonization, but also makes the active distribution network optimization dispatching model present significant non-convex non-linear characteristics, and the solution difficulty is greatly improved. How to improve the new energy consumption capacity and operation economy within the framework of strictly guaranteeing the safe operation of the system (meeting the alternating current flow constraint, voltage boundary, etc.) has become the core problem to be solved in the current power distribution network optimization field.
[0003] Specifically, the traditional power distribution network optimization method gradually exposes the following technical bottlenecks when dealing with high proportion of renewable energy access scenarios: 1) Heuristic algorithms can handle complex solution space problems, but the theoretical basis is weak, and the feasibility of the solution and the constraint satisfaction degree are highly dependent on random mechanisms and parameter settings, making it difficult to ensure the physical executability of the dispatching scheme in practical applications; 2) In the mathematical programming method, the convex relaxation method represented by the second-order cone programming (SOCP) may have approximation errors, and the optimal solution is difficult to strictly meet the alternating current flow constraint, while the traditional convex inner approximation method (CIA) can guarantee the feasibility of the solution, but it is too conservative due to the use of global static current boundary, which significantly compresses the solution space and limits the new energy consumption and economic improvement; 3) The existing feasible solution recovery method has obvious defects, or ignores the dynamic adaptation of the unit, resulting in an infeasible solution, or tightens the constraints to deteriorate the economy, or lacks a reactive power-voltage coordination mechanism, and cannot achieve the coordinated optimization of safety and economy; In summary, the existing power distribution network optimization technology has significant shortcomings in model accuracy, conservatism control, and multi-resource coordination, and it is urgent to build a new optimization method that can strictly meet the alternating current flow constraint and break through the shackles of conservatism. SUMMARY
[0004] The present application aims to solve the problem that traditional methods are difficult to balance the strictness of alternating current flow constraint and operation economy in the optimization dispatching of power distribution network under high proportion of renewable energy access, and the problem that conservatism is too strong to limit new energy consumption, by improving the convex inner approximation to construct a dynamic safety boundary, and combining with the feasible solution recovery mechanism to realize the multi-resource coordinated adjustment under the guidance of sensitivity, and significantly improve the safety and economy of the dispatching scheme.
[0005] The present application is implemented by the following technical means: a power distribution network optimization dispatching method based on improved convex inner approximation and feasible solution recovery cooperation, comprising the following steps:
[0006] Step 1: Based on the power distribution network topology and equipment configuration, node load data, distributed power output data and time series prediction values, and equipment operation parameters are collected;
[0007] Step 2: An improved convex inner approximation method (ICIA) is used to construct an optimization model of the power distribution network. Compared with the traditional convex inner approximation method (CIA) which relies on fixed global static boundaries and is prone to compress the solution space, the ICIA reconstructs the constraints to form a dynamic boundary mechanism, releasing optimization potential and improving adaptability in the aspect of voltage safety guarantee. The ICIA can ensure the continuity and accuracy of the voltage safety domain without massive critical point calculation, avoiding misjudgment risk. In terms of objective function construction, traditional multi-objective optimization often focuses on a single dimension or simple weighting, and there is no key node control. The ICIA constructs a normalized multi-objective function and embeds a voltage overrun penalty term for vulnerable nodes, achieving safe and economic collaborative optimization and making up for the defects of traditional models in dynamic operation risk consideration.
[0008] Step 3: The initial solution is optimized based on the FSR mechanism. Based on the ICIA initial feasible solution generated in step 2, branch power flow sensitivity matrix and unit output sensitivity matrix are constructed. The construction of Jacobian matrix and Hessian matrix is based on the radial network characteristics, and the linear increment mapping of control variables and state variables is established. The step constraint and unit ramp rate constraint are introduced, and the distributed power output, energy storage charging and discharging power, and reactive power compensation are adjusted under the gradient guidance. The collaborative adjustment is performed according to the preset priority rules, and the feasibility of the adjusted solution is verified through AC power flow, including voltage amplitude, branch power flow, and power balance. If it does not meet the requirements, iterative correction is performed.
[0009] Step 4: The YALMIP modeling tool and CPLEX mathematical programming solver are used to solve the collaborative optimization model. The dynamic configuration parameters of the power distribution network (IEEE 33 nodes) are solved, and the safe and economically optimal dispatching scheme is output.
[0010] The technical scheme adopted by the present application has the following beneficial effects:
[0011] 1. The improved convex inner approximation method (ICIA) is used to construct a dynamic current boundary based on a local operating point second-order Taylor approximation, replacing the global static boundary of the traditional convex inner approximation method (CIA), and introducing a stability criterion D1 to effectively break through the shackles of conservatism. Under the premise of ensuring the continuity of the voltage safety domain, the solution space is significantly expanded, and the distributed power consumption capacity is greatly improved. The total output of distributed power of the IEEE 33 node system is 7.53% higher than that of the traditional SOCP method, solving the problem of wind and light curtailment caused by the excessive compression of the optimization space of the traditional static boundary.
[0012] 2, Combined with the feasible solution recovery (FSR) mechanism and the sensitivity matrix, the gradient guided fine adjustment of the initial feasible solution is realized, and the physical feasibility of the solution is ensured through the comprehensive check of alternating current flow. Compared with the traditional method, the voltage control accuracy is significantly improved: the voltage fluctuation amplitude of weak node 17 of IEEE 33 node system is reduced by 37% compared with SOCP method, and the network loss in late heavy load period is reduced by 44.8% compared with SOCP method, which balances safety and economy.
[0013] 3, It has good calculation efficiency and practicability, and the model is constructed based on the general physical law of radial distribution network, and only the network correction correlation matrix and branch impedance parameters need to be updated when the topology changes, and the Jacobian matrix and the Hessian matrix are calculated in a distributed manner according to the branch level, and the calculation cost increases linearly with the number of branches. At the same time, the solving efficiency is significantly improved: using YALMIP-CPLEX solver, compared with SOCP method, the solving speed is increased by 42%, even compared with the faster ICIA method, only 13.4% of the calculation time is increased, which meets the demand of real-time scheduling of distribution network for response speed.
[0014] 4, A normalized multi-objective function (weight α=0.637, β=0.258, γ=0.105) of minimizing voltage deviation, minimizing network loss and maximizing distributed power consumption is constructed, and a voltage out-of-limit punishment mechanism for weak nodes is embedded to realize multi-objective collaborative optimization. It is universal in different scale systems, and can offset the voltage lifting effect of high active power injection through reactive power-active power collaborative regulation, which ensures voltage safety and maximizes economic benefit in the scene of high penetration of new energy, and significantly enhances the accommodation capacity of distribution network to high proportion of renewable energy. BRIEF DESCRIPTION OF DRAWINGS
[0015] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description, taken in conjunction with the accompanying drawings, in which:
[0016] Figure 1 It is an improved convex inner approximation and feasible solution recovery collaborative distribution network optimization scheduling method workflow schematic diagram;
[0017] Figure 2 It is an IEEE 33 node system resource configuration schematic diagram;
[0018] Figure 3 It is a comparison chart of full-network voltage distribution at 12:00;
[0019] Figure 4 It is a voltage fluctuation comparison chart of weak node 17;
[0020] Figure 5 It is a comparison chart of full-day photovoltaic output curve. DETAILED DESCRIPTION
[0021] The technical solutions in the embodiments of the present application will be clearly and completely described in the following. Figures 1-5 The technical solutions in the embodiments of the present application will be clearly and completely described in the following.
[0022] The power distribution network optimization scheduling method based on improved convex inner approximation and feasible solution recovery cooperation described above includes the following processes:
[0023] Figure 1 The power distribution network optimization scheduling workflow based on improved convex inner approximation and feasible solution recovery cooperation is shown in the figure.
[0024] The data acquisition and model reconstruction method in step 1 includes:
[0025] 1) Data preprocessing: the distributed power output data is smoothed by using the moving average filter to smooth the fluctuation, the missing values of the load data are completed by using the time series interpolation, and the DG output prediction value (photovoltaic / LSTM prediction, wind power / time series prediction), load measured value and equipment operation data are aligned by time stamp;
[0026] 2) Equipment parameter configuration: the total installed capacity of the distributed power is configured according to 1.2-1.5 times of the power distribution network load, wherein the photovoltaic array, wind turbine generator set and micro gas turbine are respectively arranged at the load concentration or voltage weak node; the energy storage unit is symmetrically arranged in double nodes, the charge and discharge power is ≥400kW, the capacity is ≥1500kWh, and the efficiency is ≥95%; the reactive power compensation system contains SVC (adjustment range 0~1.0Mvar) and capacitor bank (single group capacity 0~0.5Mvar, group number ≥10 groups);
[0027] Figure 2 The resource configuration diagram of IEEE 33-node system is shown in the figure, which reflects the equipment layout (distributed power, energy storage, reactive power compensation device) and topology basis of data acquisition in step 1, and clearly shows the association between data acquisition object and network structure.
[0028] The dynamic boundary and stability criterion of the improved convex inner approximation method in step 2 are specifically:
[0029] 1) Dynamic boundary construction: based on the second-order Taylor approximation of the standard operating point of branch ij, the upper and lower bounds of branch current square are:
[0030] (1) ;
[0031] In the formula, is the current square value of branch ij at the standard operating point; is the first-order Jacobian matrix of the current square with respect to the operating variable at branch ij, which represents the linear sensitivity of the current to the operating parameter, is the transpose of ; and This is the deviation vector of the running variables relative to the standard running point; Let be the second-order Hessian matrix of the square of the current at branch ij with respect to the operating variables, used to characterize the influence of nonlinear terms; , These are Jacobian matrices. Non-negative and non-positive elements in the text; , These are the deviation vectors. The non-negative and non-positive parts of the text; , These are the upper and lower square bounds of the branch current ij, calculated by combining positive and negative components, respectively.
[0032] 2) Current boundary constraint system: (2);
[0033] In the formula, , These represent the upper and lower boundaries of the branch current, respectively. A globally unified upper limit.
[0034] 3) Stability criterion D1: The upper and lower bounds of the voltage sensitivity of any distributed power node i must have the same sign, i.e.:
[0035] (3);
[0036] In the formula, The active power output of the distributed power source at node i; upper bound function of voltage Active power output of distributed power sources at node i The partial derivatives; Lower bound function of voltage right The partial derivatives of .
[0037] When D1 is satisfied, the node voltage is always within the safe envelope: (4);
[0038] In the formula, and These are the lower and upper bound functions of the voltage constructed using sensitivity, respectively.
[0039] The multi-objective function mentioned in step 2 is specifically:
[0040] 1) Minimize voltage deviation: (5);
[0041] In the formula, N is the number of regular nodes; , These are the voltage amplitude and reference value of the node, respectively.
[0042] 2) Network loss minimization: (6);
[0043] where, is the conductance of branch ij; and are the voltage amplitude of node i and j, respectively; is the phase angle difference of voltage between node i and j at time t (unit: rad). 3) Distributed generation accommodation maximization:
[0044] (7); where, N g is the number of renewable DGs in the system; T represents the total time period;
[0045] is the output of DG at node i at time t. 4) Normalized multi-objective function:
[0046] (8); where,
[0047] and are the network loss and voltage deviation before optimization, respectively; is the predicted output of DG; α, β, γ are the proportions of each objective, determined by the analytic hierarchy process, α + β + γ = 1; Let the scale of f1, f2, f3 in the analytic hierarchy process be 1, 3, and 5, respectively, and the calculated weight coefficients α, β, γ be 0.637, 0.258, and 0.105, respectively. 5) Vulnerable node penalty term:
[0048] (9); where, k is the risk penalty coefficient of node voltage out-of-limit;
[0049] is the actual voltage amplitude of node i at time t; is the voltage reference value of node i.
[0050] Figure 3 The voltage distribution comparison chart of IEEE 33-node full network at 12:00, the voltage distribution difference of the traditional SOCP method is obvious, and the voltage over-limit situation appears at nodes 17, 18 and 19, the average voltage is 1.008 p.u., and the deviation of part of nodes from the standard value reaches 2.7%. The average voltage of the ICIA method proposed in the paper is reduced to 1.005 p.u., and the maximum deviation is reduced to 1.9%; and the average voltage of the ICIA-FSR method is reduced to 1.003 p.u., and the maximum deviation is controlled within 1.5%, which is closer to the standard value. The voltage control advantage of the improved convex inner approximation method (ICIA) in step 2 compared with the traditional SOCP method directly shows the effectiveness of the safety boundary of the optimization model constructed by ICIA; therefore, the method proposed in the application has significant advantages in improving the global voltage stability.
[0051] The sensitivity matrix construction and adjustment constraint in step 3 is specifically:
[0052] 1) Branch power flow sensitivity matrix: active power flow partial derivative of node voltage amplitude:
[0053] (10);
[0054] In the formula, is the active power flow of the branch; is the node voltage amplitude; is the voltage amplitude of the branch head node i; is the voltage amplitude of the branch end node j; is the conductance of the branch ij; is the susceptance of the branch ij; is the voltage phase angle difference of the nodes at both ends of the branch ij.
[0055] Active power flow partial derivative of node voltage phase angle:
[0056] (11);
[0057] In the formula, is the node voltage phase angle.
[0058] The partial derivative of the reactive power flow to the node voltage amplitude / phase angle is the same;
[0059] 2) Unit output sensitivity matrix: based on the linearization of the node power balance equation, the diagonal element is as follows:
[0060] (12);
[0061] In the formula, is the active power injection vector of the generator; is the transpose of the node voltage amplitude vector; the branch active power from node i to node j the partial derivative of the voltage amplitude of node i ; the self-conductance of node i the transpose of the voltage phase angle vector of node i the branch active power from node i to node j the partial derivative of the voltage phase angle of node i .
[0062] the off-diagonal elements are as follows: (13)
[0063] wherein, is the partial derivative of the active power of branch ij with respect to the voltage amplitude of its terminal node j is the partial derivative of the active power of branch ij with respect to the voltage phase angle of its terminal node j
[0064] the reactive power output sensitivity is the same;
[0065] 3) adjustment constraint: step constraint: (14)
[0066] wherein, is the absolute value of the active power of generator g at the current operating point is the active power adjustment amount of generator g is the active power adjustment step length coefficient is the absolute value of the reactive power of generator g at the current operating point is the reactive power adjustment amount of generator g is the reactive power adjustment step length coefficient
[0067] ramp constraint: (15)
[0068] wherein, is the planned active power output of generator g at time period t is the planned active power output of generator g at the previous time period t−1 are the maximum up / down ramp rates of the unit, respectively
[0069] The AC power flow check in step 3 specifically includes:
[0070] 1) check index: node voltage amplitude (0.98 p.u.~1.02 p.u.), branch active / reactive power flow (not exceeding the rated value of the equipment), node power balance (injected power = outgoing power + network loss);
[0071] 2) Iterative correction: If the verification is not satisfied, adjust the sensitivity matrix penalty factor ρ (initial value 1~10), reduce the step size coefficient (reduce by 20%~30%), and repeat the adjustment process in step 3(2) until all verification indicators are satisfied;
[0072] 3) Verification cycle: Executed once after each round of adjustment, and the full-time scheduling scheme is re-verified once every hour.
[0073] The Jacobian and Hessian matrices described in step 3 are constructed based on the characteristics of radial networks:
[0074] 1) Jacobian matrix: The elements are based on the partial derivative relationship between branch power and node voltage. It is a sparse matrix in radial networks, with non-zero elements concentrated in adjacent nodes.
[0075] 2) Hessian matrix: Based on the second-order partial derivative of the second-order Taylor approximation, the diagonal elements are positive (to ensure convexity), and the absolute value of the off-diagonal elements is ≤ 10% of the diagonal elements;
[0076] 3) Matrix invertibility: Under radial network, the combined impedance influence matrix is an upper triangular matrix, and the diagonal elements satisfy the condition, so it is invertible.
[0077] The priority rule for the coordinated adjustment mentioned in step 3 is as follows:
[0078] 1) Voltage over-limit node: Prioritize adjusting the reactive power compensation device (SVC > capacitor bank) of the node, and then adjust the reactive power output of the surrounding DG.
[0079] 2) During periods of excessive network loss: Prioritize adjusting the charging and discharging power of energy storage (peak shaving and valley filling), and then optimize the distribution of active power output of distributed generation (DG);
[0080] 3) When the curtailment rate of new energy is high: prioritize increasing the output of photovoltaic / wind power, and simultaneously adjust the reactive power absorption of SVC to suppress voltage rise and ensure that the voltage does not exceed the limit;
[0081] 4) Adjustment and evaluation: After each round of adjustment, calculate the economic indicators (reduction in network loss, increase in DG absorption) and retain adjustment plans with an economic improvement of ≥5%.
[0082] Figure 4For the voltage fluctuation contrast chart of the weak node 17 of the IEEE 33-node system, the analysis can obtain that the voltage fluctuation control effects of the three methods show significant progression: the voltage fluctuation range of the SOCP method is 0.972~1.0 p.u., and the fluctuation amplitude reaches 0.028 p.u.; the voltage fluctuation range of the ICIA method proposed in the paper is narrowed to 0.976~0.9987 p.u., and the amplitude is reduced to 0.0227 p.u.; and the ICIA-FSR method further compresses the fluctuation range to 0.98~0.9987 p.u. through the dynamic adjustment mechanism, and the fluctuation amplitude is only 0.0187 p.u., which is reduced by 37% compared with the SOCP, and the risk of node voltage out-of-limit is eliminated; the fine adjustment effect of the feasible solution recovery (FSR) mechanism on the initial solution in step 3 is embodied, and the role of FSR in suppressing voltage fluctuation and eliminating out-of-limit risk is verified; therefore, the method has outstanding advantages in suppressing voltage fluctuation and improving system stability.
[0083] The solving parameter configuration in step 4 is specifically:
[0084] 1) Solver parameters: the convergence accuracy of the YALMIP-CPLEX solver is set to 1e-6, the maximum iteration number is set to 1000, and the dual gap tolerance is set to 1e-4;
[0085] 2) Node system adaptation:
[0086] IEEE 33-node system: reference capacity 10 MVA, voltage level 12.66 kV, total load 3715 kW+2547 kvar;
[0087] 3) Data interaction: the OPC UA protocol is used to realize the data interaction between the device layer (DG / ESS / SVC) and the scheduling layer, and the time delay is ≤10 ms.
[0088] Figure 5 For the full-day photovoltaic output curve contrast chart of the IEEE 33-node system, the analysis can obtain that the ICIA-FSR method can significantly improve the distributed power output on the premise of ensuring the safety of the power grid. Compared with the traditional SOCP method, the power output of ICIA is still limited although the safety constraint is considered. The ICIA-FSR introduces the AC FSR mechanism on the basis of ICIA, effectively breaks through the safety constraint bottleneck: the photovoltaic output is improved by 19.32% on average compared with the SOCP method in the time period 12:00~16:00.
[0089] Therefore, the method can maintain the safe operation of the system while significantly enhancing the new energy consumption capacity, and realizes the dual optimization of safety and economy.
Claims
1. A power distribution network optimal scheduling method based on improved convex inner approximation and feasible solution recovery cooperation, characterized in that, Comprise the following steps: Step 1: based on power distribution network topology and equipment configuration, collect node load data, distributed power output data and time series prediction value, equipment operation parameter; Step 2: the improved convex inner approximation method ICIA is used to construct the optimization model of power distribution network, compared with the traditional convex inner approximation method which depends on fixed global static boundary and is easy to compress solution space, the approximate reconstruction constraint is formed dynamic boundary mechanism, the optimization potential is released, the adaptability is improved, and the voltage safety guarantee level is improved;The ICIA can ensure the continuity and accuracy of the voltage safety domain without mass critical point calculation, and can avoid misjudgment risk;On the construction of objective function, the traditional multi-objective optimization often focuses on single dimension or simple weighting, and there is no key node control;ICIA constructs a normalized multi-objective function and embeds a voltage overrun penalty term of vulnerable nodes, realizes the coordinated optimization of safety and economy, and makes up for the defects of the traditional model in dynamic operation risk consideration; Step 3: the initial solution is optimized based on the feasible solution recovery FSR mechanism, the ICIA initial feasible solution generated in step 2 is used as the basis to construct branch power flow sensitivity matrix and unit output sensitivity matrix, wherein the construction of Jacobian matrix and Hessian matrix is based on the characteristics of radial network, the linear increment mapping of control variable and state variable is established, the step constraint and unit climbing rate constraint are introduced, the distributed power output, energy storage charging and discharging power and reactive power compensation are adjusted under the gradient guidance, and the adjustment is carried out according to the preset priority rule, and the feasibility of the adjusted solution is verified through alternating current power flow, including voltage amplitude, branch power flow and power balance, if not satisfied, iterative correction is carried out; Step 4: YALMIP modeling tool and CPLEX mathematical programming solver are used to solve the coordinated optimization model, and the dynamic configuration parameters of power distribution network (IEEE 33 node) are solved, and the safety and economic optimal scheduling scheme is output.
2. The method of claim 1, wherein: The specific process of step 1 includes: 1) data preprocessing: the distributed power output data is smoothed by using moving average filter, the missing values of load data are completed by using time series interpolation, and the distributed generator (DG) output prediction value (photovoltaic / LSTM prediction, wind power / time series prediction), load measured value and equipment operation data are aligned through time stamp; 2) equipment parameter configuration: the total installed capacity of distributed power is configured according to 1.2-1.5 times of power distribution network load, wherein photovoltaic array, wind turbine generator and micro gas turbine are respectively arranged at load concentration or voltage weak node;The energy storage unit is symmetrically arranged with double nodes, the charging and discharging power is greater than or equal to 400kW, the capacity is greater than or equal to 1500kWh, and the efficiency is greater than or equal to 95%;The reactive power compensation system contains SVC: adjustment range 0~1.0Mvar, and capacitor bank: single group capacity 0~0.5Mvar, and the number of groups is greater than or equal to 10 groups.
3. The method of claim 1, wherein: The dynamic boundary and stability criterion of the improved convex inner approximation method in step 2 are as follows: 1) dynamic boundary construction: based on the second-order Taylor approximation of branch ij standard operating point, the upper and lower bounds of branch current square quantity are: (1); wherein is the current square value of branch ij at the standard operating point; is the first order Jacobian matrix of the current square at branch ij with respect to the operating variables, characterizing the linear sensitivity of the current to the operating parameters, is the transpose of ; is the deviation vector of the operating variables with respect to the standard operating point; is the second order Hessian matrix of the current square at branch ij with respect to the operating variables, used to characterize the influence of the nonlinear terms; , are the non-negative and non-positive elements in the Jacobian matrix , , are the non-negative and non-positive parts in the deviation vector , , are the upper and lower bounds of the branch ij current square calculated by the combination of positive and negative components; 2) Current boundary constraint system: (2); In the formula, , respectively represent the upper and lower boundaries of the branch current; is the global uniform upper limit; 3) Stability criterion D1: the upper bound sensitivity of the voltage of any distributed power supply node i is strictly the same as the lower bound sensitivity, that is: (3); wherein P is the active power output of the distributed generator at node i; V is the voltage upper bound function P is the active power output of the distributed generator at node i; the partial derivative of P with respect to V is the voltage lower bound function the partial derivative of P with respect to the partial derivative of P with respect to When D1 is satisfied, the node voltage is always within the safe envelope: (4); wherein, and are the lower and upper voltage functions constructed by sensitivity, respectively; and are the upper and lower limits of the node voltage safe operation, respectively.
4. The method of claim 1, wherein: The normalized multi-objective function constructed in step 2 is specifically: 1) Minimization of voltage deviation: (5); In the formula, N is the number of normal nodes; , are the voltage amplitude and reference value of the node, respectively. 2) Minimization of network losses: (6); wherein is the conductance of the branch ; and is the voltage amplitude of the node , ; is the phase angle difference of the voltages of the nodes at the ends of the branch ij at the time instant t. 3) Distributed power consumption maximization: (7); In the formula, N g is the number of renewable DGs in the system; T denotes the total number of time periods; Pi(t) denotes the output of DG at node i at time t; 4) Normalized multi-objective function: (8); In the formula, With Network loss and voltage deviation before optimization, respectively; The predicted output of DG; α, β, γ are the proportions of each target, determined by the analytic hierarchy process, α+β+γ=1; Let the scales of f1, f2, f3 in the analytic hierarchy process be 1, 3, 5 respectively, and the calculated weight coefficients α, β, γ be 0.637, 0.258, 0.105 respectively; 5) Fragile node penalty term: (9); In the formula, k is a node voltage out-of-limit risk penalty coefficient; is the actual voltage amplitude of node i at time t; is the voltage reference value of node i.
5. The method of claim 1, wherein: The sensitivity matrix construction and adjustment constraint in step 3 is specifically: 1) Branch power flow sensitivity matrix: active power flow partial derivative with respect to node voltage amplitude: (10); wherein is the active power flow of the branch; is the voltage magnitude of node; is the voltage magnitude of the first node i of the branch; is the voltage magnitude of the last node j of the branch; is the conductance of the branch ij; is the susceptance of the branch ij; is the phase angle difference of the voltages of the nodes at the ends of the branch ij; Active power flow partial derivative with respect to node voltage phase angle: (11); In the formula, is the node voltage phase angle; The partial derivative of reactive power flow with respect to node voltage amplitude / phase angle is the same; 2) Unit output sensitivity matrix: based on the linearization of the node power balance equation, the diagonal element is as follows: (12); In the formula, Inject an active power vector into the generator; This is the transpose of the node voltage magnitude vector; The active power of the branch flowing from node i to node j Voltage amplitude at node i The partial derivatives; Let be the self-conductance of node i; This is the transpose of the node voltage phase angle vector; The active power of the branch flowing from node i to node j Voltage phase angle at node i The partial derivatives; This represents the total number of branches connected to node i in the system; off-diagonal elements are as follows: (13); wherein Pij is the active power of branch ij; Pij is the active power of branch ij; The sensitivity of reactive power output is the same; 3) Adjustment constraints: step constraints: (14); wherein is the active power absolute value of the generator g at the current operating point; is the active power adjustment amount of the generator g; is the active power adjustment step coefficient; is the reactive power absolute value of the generator g at the current operating point; is the reactive power adjustment amount of the generator g; is the reactive power adjustment step coefficient; Climbing rate constraint: (15); wherein Pgi(t) is the planned active power output of generator g at time period t; Pgi(t−1) is the planned active power output of generator g at the preceding time period t−1 respectively the maximum up / down ramp rate of the unit.
6. The method of claim 1, wherein: The AC power flow check in step 3 specifically includes: 1) Check index: node voltage amplitude: 0.98 p.u.~1.02 p.u., branch active / reactive power flow: not more than equipment rating, node power balance: injected power = outflow power + network loss; 2) Iterative correction: if the check does not meet the requirements, adjust the sensitivity matrix penalty factor (initial value 1~10), reduce the step size coefficient (reduce by 20%~30%), and re-execute the adjustment process in step 3 until all check indexes are met; 3) Check period: perform 1 time after each round of adjustment, and recheck 1 time per hour for the full-period scheduling scheme.
7. The method of claim 1, wherein: The Jacobian matrix and Hessian matrix construction in step 3 is based on the radial network characteristics: 1) Jacobian matrix: the element is based on the partial derivative relationship between branch power and node voltage, which is a sparse matrix in radial network, and the non-zero elements are concentrated in adjacent nodes; 2) Hessian matrix: based on the second-order partial derivative of the second-order Taylor approximation, the diagonal elements are positive (to ensure convexity), and the absolute value of the off-diagonal elements is ≤10% of the diagonal elements; 3) Matrix invertibility: in radial network, the comprehensive impedance influence matrix is an upper triangular matrix, and the diagonal elements satisfy, so it is invertible.
8. The method of claim 1, wherein: The priority rules of the collaborative adjustment in step 3 are: 1) Voltage out-of-limit node: preferentially adjust the reactive power compensation device (SVC>capacitor bank) of the node, and then adjust the reactive power output of the surrounding DG; 2) When the network loss exceeds the standard period: preferentially adjust the charging and discharging power of the energy storage (peak shaving and valley filling), and then optimize the DG active power output distribution; 3) When the new energy curtailment rate is high: preferentially increase the output of photovoltaic / wind power, and simultaneously adjust the SVC to absorb reactive power to suppress voltage rise, to ensure that the voltage does not exceed the limit; 4) Adjustment evaluation: calculate the economic indicators (network loss reduction, DG consumption increase) after each round of adjustment, and retain the adjustment scheme with economic improvement ≥5%.
9. The method of claim 1, wherein: The parameter configuration for solving in step 4 is specifically: 1) Solver parameters: the convergence precision of YALMIP-CPLEX solver is set to 1e-6, the maximum number of iterations is set to 1000, and the dual gap tolerance is set to 1e-4; 2) Node system adaptation: IEEE 33-node system: reference capacity 10 MVA, voltage level 12.66 kV, total load 3715 kW+2547 kvar; 3) Data interaction: use OPC UA protocol to realize data interaction between device layer (DG / ESS / SVC) and scheduling layer, with time delay ≤10 ms.