A distribution network closed-loop low-carbon dispatching method considering static voltage security

Abstract

The application provides a distribution network closed-loop low-carbon scheduling method considering static voltage safety, and belongs to the technical field of distribution network closed-loop low-carbon scheduling; in view of the problems of node voltage out-of-limit, reverse power flow, line loss change and difficulty in fine allocation of carbon emission responsibility caused by high proportion of new energy access to a distribution network, an alternating current power flow model considering static voltage safety is constructed based on input power grid topology, line parameters, load, new energy and unit parameters; the constructed alternating current power flow model is processed based on nonlinear constraints, whether the node voltage of the distribution network satisfies the static voltage safety constraint is judged, if not, the regulation model of OLTC, CB, new energy inverter and ESS is called to regulate voltage, the alternating current power flow model is further adjusted, the active power distribution of the system is obtained based on the adjusted alternating current power flow model, and a carbon emission flow model is constructed; the application is applied to distribution network closed-loop low-carbon scheduling control.

Description

Technical Field

[0001] This invention provides a closed-loop low-carbon dispatching method for distribution networks that considers static voltage safety, belonging to the field of closed-loop low-carbon dispatching technology for distribution networks. Background Technology

[0002] Driven by dual carbon targets, the power system is transforming from a traditional centralized structure to a new type of power system dominated by new energy sources. With the large-scale integration of distributed photovoltaic, wind power, energy storage and adjustable loads on the distribution network side, the operation mode of the distribution network has changed significantly. The power flow is gradually changing from unidirectional to bidirectional, and the power system is gradually transforming from a passive power receiving network to an active distribution network in which the source, grid, load and storage operate in coordination.

[0003] After a high proportion of new energy sources are connected, the voltage at distribution network nodes is affected by the combined effects of active power flow, reactive power distribution, and the operation of voltage regulating equipment. Since the resistance and reactance of distribution network lines are on the same order of magnitude, fluctuations in the output of distributed photovoltaic, wind power, and other new energy sources can easily cause significant voltage fluctuations and reverse power flow phenomena. Traditional DC power flow models will be difficult to accurately reflect the system's operating status. Therefore, before calculating the carbon factor of the distribution network, it is necessary to use an AC power flow model to explicitly characterize key factors such as node voltage, reactive power, line losses, and reverse power flow, thereby ensuring that subsequent carbon emission flow calculations are based on voltage-safe and feasible power flow results.

[0004] To address the voltage over-limit issue caused by a high proportion of renewable energy integration, it is necessary to consider the participation of regulation resources such as OLTC, CB, renewable energy inverters, and ESS in voltage control. Specifically, OLTC adjusts the overall voltage level of the feeder by changing the transformer tap changer; CB provides local reactive power support by switching capacitor banks; renewable energy inverters participate in node voltage control through dynamic reactive power regulation; and ESS changes the active power flow distribution by charging and discharging, thereby suppressing voltage rises caused by renewable energy backflow. These voltage regulation actions will change the power flow distribution, line losses, and reverse power flow status, thus affecting the carbon emission flow path and the node carbon factor calculation results. Therefore, voltage safety control and carbon factor calculation should not be isolated but coordinated within a unified distribution network low-carbon dispatch framework.

[0005] In existing technologies, some scheduling methods focus on calculating node carbon potential, branch carbon flow density, and user carbon emissions under a given power flow or operating state, mainly addressing the carbon emission accounting problem. Some scheduling methods directly incorporate carbon emission indicators into a unified optimization model, but when considering AC power flow, static voltage security, voltage regulation resource actions, and carbon constraints simultaneously, it can easily lead to strong model coupling, enhanced nonlinearity, and increased solution complexity. Especially when the AC power flow equation has voltage variable product terms and trigonometric function terms, directly solving the full electric-carbon coupling model will face significant computational pressure, which is not conducive to engineering applications. Summary of the Invention

[0006] To address the technical problems existing in the background art, the present invention adopts the following technical solution: providing a closed-loop low-carbon dispatching method for distribution networks considering static voltage security, comprising the following dispatching steps:

[0007] Step S1: Input the power grid topology, line parameters, load, new energy sources, and generator parameters;

[0008] Step S2: Construct an AC power flow model that considers static voltage safety based on the input parameters;

[0009] Step S3: Process the constructed AC power flow model based on nonlinear constraints, including:

[0010] By substituting variables, the nonlinear power flow equations containing trigonometric functions and product terms are transformed into a linear form;

[0011] By introducing the square of voltage as a variable, the physical relationship between variables is uniformly represented as a quadratic constraint;

[0012] By using second-order cone relaxation, non-convex equality constraints are transformed into convex inequality constraints, enabling the problem to be solved using convex optimization methods.

[0013] Step S4: Determine whether the node voltage of the distribution network meets the static voltage safety constraints. If not, call the regulation models of OLTC, CB, new energy inverter, and ESS to regulate the voltage and further adjust the AC power flow model, where:

[0014] OLTC adjusts the overall voltage level of the feeder by changing the transformer taps;

[0015] CB provides local reactive power compensation by switching capacitor banks;

[0016] New energy inverters participate in node voltage control through dynamic reactive power regulation;

[0017] ESS reconstructs the active power flow distribution through charging and discharging, thus suppressing voltage rise caused by back-feeding power from renewable energy sources.

[0018] Step S5: Obtain the system active power distribution based on the adjusted AC power flow model, construct the carbon emission flow model, and calculate the node electric carbon factor, node carbon emissions, and total system carbon emissions based on the carbon emission flow model;

[0019] Step S6: Determine whether the calculation results meet the carbon constraints:

[0020] If satisfied, output the scheduling scheme and the calculation results of the node carbon factor;

[0021] If the conditions are not met, output the outer layer correction cost of high-carbon units and the penalty coefficient for curtailment of renewable energy, and return to step S2 to continue adjusting the AC power flow model until the carbon constraint is met.

[0022] The specific method for step S2 is as follows:

[0023] The AC power flow model is modeled using the node injection method, including:

[0024] In the node injection model, the system network topology and line parameters are expressed through the node admittance matrix Y. bus For a unified description, the series impedance of line (i,j) is defined as:

[0025] ;

[0026] The corresponding line admittance is:

[0027] ;

[0028] Constructing the nodal admittance matrix Y from line parameters bus The element expression is:

[0029] ;

[0030] Further results were obtained:

[0031] ;

[0032] Where G and B represent the real and imaginary parts of the nodal admittance matrix, respectively, and G in the subsequent AC power flow equations ij With B ij All are obtained from the nodal admittance matrix;

[0033] Let N be the set of nodes in the power system, T be the set of time periods, and let the node voltage be represented in complex form as follows:

[0034] ;

[0035] To facilitate subsequent convex optimization, a voltage squared variable is introduced, expressed as follows:

[0036] ;

[0037] To eliminate the voltage product term and trigonometric function term in the AC power flow equations, an auxiliary variable is introduced, and the expression is:

[0038] ;

[0039] Define c ij,t and s ij,t These represent the real and imaginary coupling amounts between node voltage vectors, respectively.

[0040] Based on the parity of trigonometric functions, we can obtain:

[0041] ;

[0042] For node pairs in the network that do not have a direct connection, their auxiliary variables satisfy c. ij,t =0、s ij,t =0, thus allowing the use of variable c ij,t and s ij,t Reconstruct the AC power flow equations;

[0043] To ensure that the optimization model always has a feasible solution, an active power load shedding variable P is introduced. LS i,t and reactive load shedding variable Q LS i,t At this point, the active power balance equation at the node is expressed as:

[0044] ;

[0045] The power flow model at both ends of the line is further recovered based on node voltage variables and auxiliary variables;

[0046] The expression for the active power flow at the sending end of line (i,j) is:

[0047] ;

[0048] The expression for the reactive power flow at the sending end is:

[0049] ;

[0050] The expression for the active power flow at the receiving end is:

[0051] ;

[0052] The expression for reactive power flow at the receiving end is:

[0053] ;

[0054] Among them, G ij and B ij These are the real and imaginary parts of the nodal admittance matrix, respectively; g ij b ij b ch ij These represent the line conductance, susceptance, and line-to-ground charging susceptance, respectively.

[0055] Upper and lower bound constraints are imposed on the load shedding variable to avoid infeasible states in the system, while ensuring that the load shedding behavior is within a reasonable range. The expression is as follows:

[0056] ;

[0057] Regarding voltage constraints, the node voltages meet the safe operating range:

[0058] ;

[0059] To limit line overload, apparent power constraints are introduced for branch lines:

[0060] ;

[0061] The range of values ​​for the load shedding variable is limited by the load demand to ensure that the load shedding variable meets the actual operating requirements. The expression is:

[0062] ;

[0063] The above constraints ensure that the load shedding amount does not exceed the actual load demand of the node;

[0064] The inverter capacity limit for distributed generation is expressed as follows:

[0065] ;

[0066] Conventional generating units meet the following constraints: upper and lower output limits, start-stop logic, ramp-up constraints, and minimum start-up and shutdown time constraints.

[0067] The output constraint is:

[0068] ;

[0069] Start-stop constraints are:

[0070] ;

[0071] The climbing constraint is:

[0072] ;

[0073] Constraining output changes during start-up and shutdown processes to prevent unreasonable and large jumps in unit output, specifically regarding the unit's output P during time period t. g,t The changes in adjacent time periods should satisfy:

[0074] ;

[0075] The minimum start-up and shutdown time constraints are:

[0076] ;

[0077] Among them, T up g T is the minimum start-up time of the unit.down g This is the minimum downtime for the unit;

[0078] Based on the above constraints, a complete description of the feasible operating domain of the power system under AC conditions is provided.

[0079] Then, under the condition of minimizing operating costs, the optimal solution of the objective function of the AC power flow model is obtained, and the outer carbon constraint coordination is iteratively updated to construct the basic operating cost model, including:

[0080] Under the premise of satisfying the constraints of safe operation of the power grid, the system scheduling objective is to minimize the overall operating cost, and the objective function is constructed as follows:

[0081] ;

[0082] The cost of electricity generation reflects the operating expenses of conventional generating units, and is expressed as:

[0083] ;

[0084] Unit start-up and shutdown costs describe the additional expenses incurred during unit start-up and shutdown, and are expressed as:

[0085] ;

[0086] In the context of renewable energy integration, to encourage renewable energy consumption, a penalty cost for wind and solar curtailment is introduced, expressed as:

[0087] ;

[0088] To prevent node voltages from deviating from their rated values, a voltage deviation penalty term is constructed, with the following expression:

[0089] ;

[0090] Since load shedding directly affects the reliability of power supply to users, it is usually only allowed when the system cannot meet the safety operation constraints.

[0091] To avoid the optimization model from over-relying on the load shedding variable, this invention sets a high penalty coefficient for the load shedding, expressed as follows:

[0092] ;

[0093] This objective function comprehensively considers economic efficiency, voltage safety, renewable energy absorption capacity, and carbon emission levels, achieving unified optimization of multiple objectives.

[0094] The specific method for step S3 is as follows:

[0095] Based on the node injection method, the active power expression of node i is:

[0096] ;

[0097] Where θ ij =θ i -θ j ;

[0098] To reduce model complexity, the nonlinear structure is reconstructed through variable substitution, and new intermediate variables are defined:

[0099] ;

[0100] And introduce the squared voltage amplitude variable:

[0101] ;

[0102] By substituting the variables mentioned above, the original work injection equation is transformed into a linear form, expressed as:

[0103] ;

[0104] Reactive power can be written similarly as:

[0105] ;

[0106] By substituting variables, the original trigonometric and product terms are eliminated, transforming the power balance equation into a linear form. The variables must still satisfy the physical relationships determined by the voltage definition. According to the variable definitions:

[0107] ;

[0108] Combined with v i,t =V 2 i,t Furthermore, we obtain:

[0109] ;

[0110] This constraint reflects the essential coupling relationship between voltage variables and is a nonlinear constraint in the AC power flow model.

[0111] To achieve a convex optimization solution, the non-convex constraint needs to be relaxed. A second-order cone relaxation method is used to relax the original equality constraint into an inequality form, expressed as:

[0112] ;

[0113] The above constraint is transformed into the standard second-order cone constraint form, expressed as:

[0114] ;

[0115] This transformation converts the original non-convex constraints into convex second-order cone constraints, and transforms the AC power flow optimization problem into a second-order cone programming problem.

[0116] The OLTC model used in step S4 adjusts the low-voltage side voltage of the transformer by changing the tap position. The expression for the operating constraints of the OLTC model is as follows:

[0117] ;

[0118] In the formula, v i,t v j,t These represent the squares of the voltage amplitudes at the low-voltage and high-voltage nodes of the transformer, respectively; α i,t r is the squared voltage transformation ratio of the OLTC during time period t; min is the minimum transformation ratio of OLTC; is the voltage squared transformation ratio increment corresponding to the s-th stage; T max OLTC This is the maximum gear position for OLTC; σ OLTC i,s,t δ is a 0-1 variable, representing whether the s-th tier is invested in time period t; OLTC,IN i,t δ OLTC,DE i,t These represent whether OLTC performs an upshift and downshift during time period t, respectively; N max OLTC This represents the maximum number of actions allowed by the OLTC within the scheduling period.

[0119] The CB model used in step S4 provides capacitive reactive power compensation to the distribution network through discrete switching. The expression for the operating constraints of the CB model is as follows:

[0120] ;

[0121] In the formula, Q CB i,t q represents the reactive power output of node i in time period t; tap i For single-stage CB reactive power compensation capacity; T max CB CB is the maximum gear; σ CB i,s,t δ is a 0-1 variable, representing whether the s-th CB is invested; CB,IN i,t δ CB,DE i,t These represent whether CB engages or withdraws during time period t; N max CB This represents the maximum number of actions allowed by the CB within the scheduling period.

[0122] The active power output and capacity constraints of the new energy inverter used in step S4 are expressed as follows:

[0123] ;

[0124] In the formula, P PV i,t P WT i,t These represent the active power outputs of photovoltaic and wind power at node i during time period t; P PV,pre i,t P WT,pre i,t Forecasted power outputs for solar and wind power, respectively; Q PV i,t Q WT i,t These are the reactive power outputs of the photovoltaic and wind power inverters, respectively; S PV i S WT i These refer to the capacity of photovoltaic and wind power inverters, respectively.

[0125] The ESS model used in step S4 changes the active power flow distribution of the distribution network through charging and discharging. The expression for the operating constraints of the ESS model is as follows:

[0126] ;

[0127] In the formula, P cha i,t P dis i,t P represents the ESS charging and discharging power of node i during time period t, respectively. cha,max i P dis,min i These are the maximum charging and discharging power of ESS, respectively; D cha i,t D dis i,t These are 0-1 state variables, representing the charging and discharging states of the ESS, respectively; E ESS i,t Energy stored for ESS; η cha i η dis i These represent charge and discharge efficiencies, respectively; E ESS,max i E ESS,min i Do not set the upper and lower limits for ESS battery level.

[0128] The specific method for step S5 is as follows:

[0129] To uniformly describe the power flow direction, branch active power decomposition variables are introduced:

[0130] Let P be the active power flow of branch i→j. ij Then the definition is:

[0131] ;

[0132] Among them, P + ij P represents the positive power flow component from node i to node j. + ji This represents the positive power flow component from node j to node i;

[0133] Define the set of inflow branches of node n as Ω in n The set of outflowing branches is Ω. out n ;

[0134] According to the principle of proportional sharing, the power flow in any outflow branch within a node proportionally includes the contributions of all inflow branches, as expressed in the following expression:

[0135] ;

[0136] Among them, P nj,i This represents the power component from the inflow branch i in the outflow branch j;

[0137] Define the carbon flux density flowing into branch i as ρ i Then the carbon flow rate of the outflow branch j is:

[0138] ;

[0139] Substituting the proportional relationships and simplifying, we get:

[0140] ;

[0141] Therefore, the expression for the carbon flux density of branch j is:

[0142] ;

[0143] Considering node power generation injection, the node carbon conservation equation is obtained as follows:

[0144] ;

[0145] The resulting nodal electrocarbon factor is:

[0146] ;

[0147] The expression for nodal load carbon emissions is:

[0148] ;

[0149] In carbon emission flow analysis, it is also necessary to reasonably allocate network losses. The active power loss of branch i→j in time period t is defined as:

[0150] ;

[0151] Among them, P ij As a positive trend, P ji The components represent the reverse power flow; their difference reflects the power flow direction, and their sum reflects the line loss.

[0152] For the allocation of carbon emissions from network losses, the principle of attribution at the sending end is adopted, expressed as follows:

[0153] ;

[0154] After completing the calculation of the electrical carbon factor of the internal nodes of the distribution network, the node electrical carbon factor of the distribution micro boundary node is extracted and the boundary electrical carbon factor facing the microgrid side is formed. The distribution micro boundary electrical carbon factor is used as the input for the electrical carbon attribute of the microgrid or the low-carbon scheduling of the microgrid.

[0155] The specific method for step S6 is as follows:

[0156] Constructing an implicit low-carbon coordination mechanism based on economic signal regulation, including:

[0157] Define the total carbon emissions R of the system total for:

[0158] ;

[0159] With set carbon emission targets Comparison and judgment:

[0160] When R total ≤R target If the current scheduling scheme is deemed to meet the low-carbon requirements, the final result will be output.

[0161] When R total >R target If this occurs, it indicates that the system's total carbon emissions have not met the target carbon emission constraints, and the main problem needs to be corrected, including:

[0162] To suppress the output of high-carbon units, their output in optimization is reduced by increasing their power generation costs. The original power generation cost coefficient of unit g is defined as c. g , Δc (k) As for the additional cost, the corrected power generation cost coefficient in the k-th iteration is expressed as:

[0163] ;

[0164] And gradually increase it iteratively:

[0165] ;

[0166] To reduce carbon emissions, improve the utilization rate of wind and solar power, and reduce wind and solar curtailment, the curtailed power is defined as Curt. w,t The power of the abandoned light is Curt p,t The original cost of the power curtailment penalty is:

[0167] ;

[0168] In the k-th iteration, by introducing an adjustment coefficient β (k) Correct it to:

[0169] ;

[0170] ;

[0171] The implicit low-carbon coordination mechanism constructed above aims to reduce the tendency of wind and solar curtailment by increasing the cost of curtailing electricity, promote the priority consumption of new energy sources, and reduce system carbon emissions from the source.

[0172] Based on the above mechanism, the outer coordination process first initializes the scheduling parameters and then solves the AC power flow master problem.

[0173] Next, the carbon emission flow is calculated to obtain R. total If the carbon constraint is satisfied, stop the iteration; otherwise, update c. g C curt Then return to the main problem and solve it again until convergence.

[0174] The present invention has the following advantages over the prior art:

[0175] I. Before calculating the carbon factor, this invention first solves the AC power flow master problem considering static voltage safety, so that the node carbon factor, branch carbon flow density and distribution micro boundary carbon factor are all calculated based on power flow results that are feasible with voltage safety, thus overcoming the problem of carbon emission allocation based on infeasible power flow conditions.

[0176] II. This invention addresses the voltage over-limit problem caused by a high proportion of new energy access to the distribution network by considering the participation of regulation resources such as OLTC, CB, new energy inverters and ESS in voltage control, so that the impact of voltage regulation on power flow distribution, line loss, reverse power flow and carbon flow path can be included in the calculation process of electric carbon factor.

[0177] Third, this invention constructs a closed-loop mechanism of AC power flow main problem - carbon emission flow sub-problem - outer coordination. It adopts a technical route of first calculating electricity, then carbon, and then adjusting electricity, avoiding strong coupling of all complex carbon variables into the main problem and reducing the solution complexity. When carbon constraints are not met, the system scheduling results are indirectly changed by dynamically adjusting the operating cost of high-carbon units and the penalty coefficient for curtailment of new energy, so that the system gradually evolves towards a low-carbon operating state, realizing the synergistic optimization of voltage security and low-carbon operation. Attached Figure Description

[0178] The present invention will be further described below with reference to the accompanying drawings:

[0179] Figure 1 The flowchart illustrates the steps of the low-carbon distribution network closed-loop scheduling method that considers static voltage safety in this invention. Detailed Implementation

[0180] like Figure 1 As shown, this invention provides a closed-loop low-carbon dispatch control method for distribution networks. Specifically, it involves a closed-loop low-carbon dispatch control method for distribution networks that considers static voltage security constraints, voltage regulation resource coordination, electric carbon factor calculation, and outer carbon constraint correction iteration. This method first solves the AC power flow master problem considering static voltage security and voltage regulation resource actions to obtain feasible node voltages, branch power flows, and line losses. Secondly, based on the AC power flow results, it calculates the node electric carbon factor, branch carbon flow density, load carbon emissions, network loss carbon responsibility, and the electric carbon factor of the distribution micro-boundary node. Finally, when system carbon emissions or node carbon emissions do not meet the targets, it corrects the operating costs of high-carbon units and the renewable energy curtailment penalty coefficient through outer coordination, and returns to the AC power flow master problem for re-solving, forming a closed-loop low-carbon dispatch mechanism that first calculates electricity, then carbon, and then adjusts electricity. This invention addresses the node voltage exceeding limits caused by a high proportion of renewable energy access to the distribution network. To address the challenges of reverse power flow, line loss variations, and the difficulty in finely allocating carbon emission responsibilities, this invention proposes a closed-loop low-carbon dispatching method for distribution networks that considers static voltage safety. When the total carbon emissions of the system or the carbon emissions of individual nodes meet the preset carbon constraints, the method outputs the dispatching scheme and the calculated carbon factor. When the carbon constraints are not met, the method coordinates and corrects the operating costs of high-carbon units and the penalty coefficient for renewable energy curtailment through outer carbon constraints, returning to the AC power flow master problem for re-solution, thus gradually evolving the system towards a low-carbon operating state. This invention enables the distribution network operation scheme to meet both physical operating constraints and static voltage safety constraints, while simultaneously realizing the calculation of node carbon factors, the output of distribution micro-boundary carbon factors, and the closed-loop correction of low-carbon dispatching. This solves the problems of high model complexity caused by the direct and strong coupling of AC power flow constraints, unit constraints, voltage regulating equipment constraints, and carbon emission constraints in existing low-carbon dispatching methods, as well as the lack of a closed-loop correction mechanism when carbon constraints are not met.

[0181] Furthermore, to achieve closed-loop low-carbon dispatch control of the distribution network, this invention constructs a hierarchical closed-loop framework consisting of the AC power flow master problem, the carbon emission sub-problem, and outer coordination, wherein:

[0182] The first layer is the main problem of AC power flow, which is used to determine the feasible operating state of the distribution network under given load and power supply conditions, and to consider static voltage safety and voltage regulation resource operation.

[0183] The second layer is the carbon emission flow problem, which calculates the spatial distribution of carbon emissions based on the known tidal flow distribution.

[0184] The third layer is the outer carbon constraint coordination, which adjusts the power generation structure or dispatch strategy to ensure that the system meets both physical constraints and carbon constraint requirements.

[0185] Furthermore, the present invention provides a closed-loop low-carbon dispatching method for distribution networks that considers static voltage safety, comprising the following dispatching steps:

[0186] Step S1: Input the power grid topology, line parameters, load, new energy sources, and generator parameters;

[0187] Step S2: Construct an AC power flow model considering static voltage safety based on the input parameters:

[0188] AC power flow modeling is the foundation of electrical-carbon coupling analysis. Its core lies in describing the nonlinear relationship between voltage, current and power in the power grid. This invention uses the node injection method to model AC power flow.

[0189] In the node injection model, the system network topology and line parameters are expressed through the node admittance matrix Y. bus A unified description. Let the series impedance of line (i,j) be:

[0190] ;

[0191] The corresponding line admittance is:

[0192] ;

[0193] The nodal admittance matrix Y can be constructed from the line parameters. bus Its elements are represented as:

[0194] ;

[0195] This can be further written as:

[0196] ;

[0197] Where G and B represent the real and imaginary parts of the nodal admittance matrix, respectively. G in the subsequent AC power flow equations... ij With Bij All are obtained from the nodal admittance matrix.

[0198] Let N be the set of nodes in the power system, T be the set of time periods, and let the node voltages be expressed in complex form:

[0199] ;

[0200] To facilitate subsequent convex optimization, a voltage squared variable is introduced:

[0201] ;

[0202] To eliminate voltage product terms and trigonometric function terms in the AC power flow equations, auxiliary variables are introduced:

[0203] ;

[0204] The processing of AC power flow models can be summarized in the following three steps: First, by variable substitution, the nonlinear power flow equations containing trigonometric functions and product terms are transformed into linear form; second, voltage square variables are introduced to unify the physical relationships between variables into quadratic constraints; finally, by second-order cone relaxation, the non-convex equality constraints are transformed into convex inequality constraints, enabling the problem to be solved efficiently using convex optimization methods.

[0205] Among them, c ij,t and s ij,t Let these represent the real and imaginary coupling amounts between the node voltage vectors, respectively. Based on the parity of trigonometric functions, we can obtain:

[0206] ;

[0207] For node pairs in the network that do not have a direct connection, their auxiliary variables satisfy c. ij,t =0、s ij,t =0, thus allowing the use of variable c ij,t and s ij,t The AC power flow equations are reconstructed.

[0208] To address the potential power supply insufficiency issue under extreme operating conditions and ensure the optimization model always has a feasible solution, an active power load shedding variable P is introduced. LS i,t and reactive load shedding variable Q LS i,t At this point, the active power balance equation at the node can be expressed as:

[0209] ;

[0210] While the node injection model can directly describe the node power balance relationship, it cannot directly obtain the power flow information at both ends of the line. Since line capacity constraints, line loss calculations, and subsequent carbon flow transfer processes all depend on the line power flow, it is necessary to further recover the power flow at both ends of the line based on node voltage variables and auxiliary variables.

[0211] The active power flow at the transmitting end of line (i,j) can be represented as:

[0212] ;

[0213] The reactive power flow at the transmitting end can be represented as:

[0214] ;

[0215] The active power flow at the receiving end can be represented as:

[0216] ;

[0217] The reactive power flow at the receiving end can be represented as:

[0218] ;

[0219] Among them, G ij and B ij g represents the real and imaginary parts of the nodal admittance matrix, respectively. ij b ij and b ch ij These represent the line conductance, susceptance, and line-to-ground charging susceptance, respectively. Because AC lines experience power losses, the power flow at both ends of a line typically does not satisfy a strict inverse relationship; the difference corresponds to the line loss.

[0220] To avoid infeasible states in the system and to ensure that load shedding behavior is within a reasonable range, upper and lower limit constraints need to be imposed on the load shedding variables:

[0221] ;

[0222] Regarding voltage constraints, node voltages must meet the safe operating range:

[0223] ;

[0224] Meanwhile, to limit line overload, apparent power constraints are introduced for branch lines:

[0225] ;

[0226] The power flow at both ends of the line does not strictly satisfy the opposite number relationship, which is due to the existence of active and reactive power losses in AC lines.

[0227] To ensure that the load shedding variable meets actual operating requirements, its value range should be limited by the load demand, that is:

[0228] ;

[0229] The above constraints ensure that the load shedding amount will not exceed the actual load demand of the node.

[0230] For distributed power sources, the inverter capacity limit can be expressed as:

[0231] ;

[0232] In addition, conventional units must meet upper and lower output limits, start-stop logic, ramp-up constraints, and minimum start-up and shutdown time constraints. Their output constraints are as follows:

[0233] ;

[0234] Start-stop constraints are:

[0235] ;

[0236] Climbing constraints:

[0237] ;

[0238] In addition to conventional ramp-up constraints, the output changes during unit start-up and shutdown are often subject to stricter limitations. Without constraints, the optimization model may produce unreasonable abrupt changes in output, such as the unit reaching a high output level immediately after startup, which is difficult to achieve in practice. Therefore, it is necessary to constrain the output changes during start-up and shutdown to effectively prevent unreasonable and large jumps in unit output.

[0239] For the unit's output P during time period t g,t The changes in adjacent time periods should satisfy:

[0240] ;

[0241] In actual power system operation, once a generating unit starts or stops, it typically needs to maintain a certain operating time or shutdown time to avoid damage to the equipment caused by frequent start-ups and shutdowns. Therefore, minimum start-up time and minimum shutdown time constraints need to be introduced into the unit combination model.

[0242] The minimum start-up and shutdown time constraint can be expressed as:

[0243] ;

[0244] Among them, T up g T is the minimum start-up time of the unit. down gThis represents the minimum downtime of the generating unit. These constraints provide a complete description of the feasible operating domain of the power system under AC conditions.

[0245] Then, under the condition of minimizing operating costs, the optimal solution of the objective function of the AC power flow model is obtained, and the outer carbon constraint coordination is iteratively updated to construct the basic operating cost model, including:

[0246] Under the premise of satisfying the constraints of power grid safe operation, the system scheduling objective is to minimize the overall operating cost. Based on the code implementation, this invention constructs the following objective function:

[0247] ;

[0248] First, the cost of power generation reflects the operating expenses of conventional units:

[0249] ;

[0250] Secondly, the unit start-up and shutdown cost describes the additional expenses incurred during unit start-up and shutdown:

[0251] ;

[0252] In the context of renewable energy integration, to encourage the consumption of renewable energy, penalties for wind and solar curtailment are introduced:

[0253] ;

[0254] To prevent node voltage from deviating from the rated value, a voltage deviation penalty term is constructed:

[0255] ;

[0256] Since load shedding directly affects the reliability of user power supply, it is typically only allowed when the system cannot meet safe operation constraints. To avoid the optimization model relying too heavily on load shedding variables, this invention sets a high penalty coefficient for load shedding:

[0257] ;

[0258] This objective function comprehensively considers economic efficiency, voltage safety, renewable energy absorption capacity, and carbon emission levels, achieving unified optimization of multiple objectives.

[0259] Step S3: Process the constructed AC power flow model based on nonlinear constraints, including transforming the nonlinear power flow equations containing trigonometric functions and product terms into a linear form through variable substitution; introducing voltage square variables to unify the physical relationships between variables into quadratic constraints; and transforming non-convex equality constraints into convex inequality constraints through second-order cone relaxation, enabling the problem to be solved using convex optimization methods, wherein:

[0260] In choosing a power flow modeling method, common approaches include the branch flow method and the node injection method. The branch flow method has good computational performance in radial networks, but it is highly dependent on the network topology. This invention focuses on ring topologies; therefore, it employs the node injection method for modeling, enabling the model to adapt to more general ring network topologies.

[0261] Based on the node injection method, the active power expression of node i is:

[0262] ;

[0263] Where θ ij =θ i -θ j From a mathematical perspective, the nonlinearity of AC power flow equations mainly stems from the following two aspects: (1) the product terms between voltage variables. The power expression in the nodal injection form contains V i V j This term reflects the coupling relationship between voltage amplitudes at different nodes and is a typical bilinear term; (2) trigonometric function term. The power expression includes cos(θ) i -θ j ) and sin(θ i -θ j This results in a model exhibiting strong nonlinearity and nonconvexity. The combined effect of these two types of nonlinearity makes the AC power flow optimization problem a nonconvex optimization problem. Introducing integer variables such as unit start-up and shutdown further transforms the problem into a mixed-integer nonlinear programming problem, significantly increasing its solution complexity and making it difficult to meet practical application requirements. To reduce model complexity, the nonlinear structure is first reconstructed through variable substitution.

[0264] Define a new intermediate variable:

[0265] ;

[0266] And introduce the squared voltage amplitude variable:

[0267] ;

[0268] By substituting the variables as described above, the original work injection equation can be transformed into a linear form:

[0269] ;

[0270] Reactive power can be written similarly as:

[0271] ;

[0272] It can be seen that by substituting variables, the original trigonometric terms and product terms have been eliminated, and the power balance equation has been transformed into a linear form. However, this linearization comes at the cost of introducing new variables, and the physical relationships between these variables still need to be satisfied by the definition of voltage.

[0273] According to the variable definition:

[0274] ;

[0275] Combined with v i,t =V 2 i,t Furthermore, we can obtain:

[0276] ;

[0277] This constraint reflects the essential coupling relationship between voltage variables and is the core nonlinear constraint in the AC power flow model. Because it is a quadratic equality constraint with a product term on the right side, it is non-convex, which is the key reason why the original problem is difficult to solve. To achieve a convex optimization solution, this non-convex constraint needs to be relaxed. This invention uses a second-order cone relaxation method to relax the original equality constraint into an inequality form:

[0278] ;

[0279] The physical meaning of this relaxation lies in allowing the variable to deviate from the strict voltage relationship within a certain range, thereby expanding the feasible region and transforming the problem into a convex optimization problem. Furthermore, the above constraint can be transformed into a standard second-order cone constraint form:

[0280] ;

[0281] Through this transformation, the original non-convex constraint is transformed into a convex second-order cone constraint, thereby transforming the AC power flow optimization problem into a second-order cone programming problem.

[0282] Step S4: Determine whether the node voltage of the distribution network meets the static voltage safety constraint. If not, call the regulation models of OLTC, CB, new energy inverter, and ESS to regulate the voltage and further adjust the AC power flow model.

[0283] With the integration of a high proportion of renewable energy sources, the voltage at distribution network nodes is affected by the combined effects of active power flow, reactive power distribution, and the operation of voltage regulating equipment. To achieve synergistic optimization of voltage security and low-carbon operation, this invention considers multiple regulation resources, including OLTC, CB, renewable energy inverters, and ESS. Specifically, the OLTC regulates the overall voltage level of the feeders by changing the transformer taps; the CB provides local reactive power support by switching capacitor banks; the renewable energy inverter participates in node voltage control through dynamic reactive power regulation; and the ESS alters the active power flow distribution through charging and discharging, thereby suppressing voltage rises caused by renewable energy backflow.

[0284] OLTC mainly regulates the low-voltage side voltage of the transformer by changing the tap position. Its mathematical model is as follows:

[0285] ;

[0286] The above formula represents the OLTC operating constraints. In the formula, v i,t v j,t These represent the squares of the voltage amplitudes at the low-voltage and high-voltage nodes of the transformer, respectively; α i,t r is the squared voltage transformation ratio of the OLTC during time period t; min is the minimum transformation ratio of OLTC; is the voltage squared transformation ratio increment corresponding to the s-th stage; T max OLTC This is the maximum gear position for OLTC; σ OLTC i,s,t δ is a 0-1 variable, representing whether the s-th tier is invested in time period t; OLTC,IN i,t δ OLTC,DE i,t These represent whether OLTC performs an upshift and downshift during time period t, respectively; N max OLTC This represents the maximum number of operations allowed by the OLTC within the scheduling cycle. The meanings of each line of the formula from top to bottom are as follows: the first line represents the voltage relationship across the transformer; the second line represents the relationship between the OLTC tap position and the turns ratio; the third and fourth lines represent the tap position sequence and range constraints; the fifth and sixth lines describe the relationship between tap position changes and tap-up / down action variables in adjacent time periods; the seventh line limits the maximum number of operations of the OLTC within the scheduling cycle; and the eighth line constrains that tap-up and tap-down cannot occur simultaneously within the same time period.

[0287] The CB provides capacitive reactive power compensation to the distribution network through discrete switching. Its mathematical model is as follows:

[0288] ;

[0289] The above formula represents the CB operating constraint. In the formula, Q... CB i,t q represents the reactive power output of node i in time period t; tapi For single-stage CB reactive power compensation capacity; T max CB CB is the maximum gear; σ CB i,s,t δ is a 0-1 variable, representing whether the s-th CB is invested; CB,IN i,t δ CB,DE i,t These represent whether CB engages or withdraws during time period t; N max CB This represents the maximum number of operations allowed for the CB within the scheduling cycle. The meanings of each line of the formula from top to bottom are as follows: the first line represents the relationship between the CB gear position and the reactive power compensation amount; the second and third lines are the constraints on the CB gear sequence and range; the fourth and fifth lines describe the relationship between CB gear changes in adjacent time periods and switching operation variables; the sixth line limits the maximum number of operations for the CB within the scheduling cycle; and the seventh line constrains that the CB cannot be simultaneously engaged and disengaged during the same time period.

[0290] New energy inverters not only handle active power output but also provide reactive power support within their capacity limits. Their active power output and capacity constraints are expressed as follows:

[0291] ;

[0292] The above formula represents the operational constraints of new energy sources. In the formula, P... PV i,t P WT i,t These represent the active power outputs of photovoltaic and wind power at node i during time period t; P PV,pre i,t P WT,pre i,t Forecasted power outputs for solar and wind power, respectively; Q PV i,t Q WT i,t These are the reactive power outputs of the photovoltaic and wind power inverters, respectively; S PV i S WT i These represent the capacities of the photovoltaic and wind power inverters, respectively. The meanings of each line of formulas from top to bottom are: the first and second lines represent the active power output constraints for photovoltaic and wind power, respectively; and the third and fourth lines represent the capacity constraints for photovoltaic and wind power inverters, respectively.

[0293] ESS can change the active power flow distribution of the distribution network through charging and discharging. Its mathematical model is as follows:

[0294] ;

[0295] The above formula represents the ESS operational constraints. In the formula, P... chai,t P dis i,t P represents the ESS charging and discharging power of node i during time period t, respectively. cha,max i P dis,min i These are the maximum charging and discharging power of ESS, respectively; D cha i,t D dis i,t These are 0-1 state variables, representing the charging and discharging states of the ESS, respectively; E ESS i,t Energy stored for ESS; η cha i η dis i These represent charge and discharge efficiencies, respectively; E ESS,max i E ESS ,min i These represent the upper and lower limits of the ESS power. The meaning of each line of formula from top to bottom is as follows: the first and second lines represent the ESS charging and discharging power constraints, the third line represents the charging and discharging mutual exclusion constraints, the fourth line represents the ESS power state transition equation, the fifth line represents the ESS power upper and lower limit constraints, and the sixth line constrains the ESS to restore to its initial energy storage state at the end of the scheduling cycle, where T is the total number of time periods in the scheduling cycle.

[0296] Through the above model, OLTC, CB, new energy inverter and ESS participate in system optimization from aspects such as overall feeder voltage regulation, local reactive power compensation, fast reactive power response and active power flow reconstruction, providing a regulation basis for voltage safety control and low-carbon optimized operation in scenarios with high proportion of new energy access.

[0297] Step S5: Obtain the system active power distribution based on the adjusted AC power flow model, construct the carbon emission flow model, and calculate the node electric carbon factor, node carbon emissions, and total system carbon emissions based on the carbon emission flow model.

[0298] After obtaining the active power distribution of the system through AC power flow calculation, carbon emission flow can be further calculated. As a virtual flow attached to the active power flow, the carbon emission flow is distributed in the network according to a proportional sharing principle. Compared to the DC power flow model, the key difference in carbon flow modeling under AC power flow is that the power flow distribution is not only determined by the phase angle but also affected by voltage amplitude, reactive power, and line parameters, thus making the carbon flow path more complex. To uniformly describe the power flow direction, branch active power decomposition variables are introduced.

[0299] Let P be the active power flow of branch i→j. ij Then the definition is:

[0300] ;

[0301] Among them, P + ij P represents the positive power flow component from node i to node j. + ji This represents the positive power flow component flowing from node j to node i. This decomposition method serves two purposes in the code: firstly, it clarifies the power flow direction, and secondly, it calculates carbon flow allocation and line loss attribution.

[0302] Based on this, consider node n, and let its inflow branch set be Ω. in n The set of outflowing branches is Ω. out n According to the principle of proportional sharing, the power flow in any outflow branch within a node includes the contributions of all inflow branches proportionally, that is:

[0303] ;

[0304] Among them, P nj,i This represents the power component in the outflow branch j that originates from the inflow branch i.

[0305] Further considering the carbon emission flow, let the carbon flow density flowing into branch i be ρ. i Then the carbon flow rate of the outflow branch j is:

[0306] ;

[0307] Substituting the proportional relationships and simplifying, we get:

[0308] ;

[0309] Therefore, the carbon flux density of branch j is:

[0310] ;

[0311] Considering node power generation injection further, the node carbon conservation equation can be written as:

[0312] ;

[0313] The nodal electrocarbon factor can be obtained by simplification:

[0314] ;

[0315] Furthermore, the carbon emissions from node loads are:

[0316] ;

[0317] The above derivation shows that, under AC power flow conditions, although power flow calculation is more complex, carbon flow allocation can still be based on active power flow, and the principle of proportional sharing remains valid.

[0318] In AC power flow models, the presence of line resistance leads to non-negligible active power losses. These losses mean the system needs to generate additional electricity to maintain power balance, resulting in additional carbon emissions. Therefore, network losses must be properly allocated in carbon emission flow analysis.

[0319] Let the active power loss of branch i→j in time period t be:

[0320] ;

[0321] Among them, P ij As a positive trend, P ji The difference between the components represents the direction of the current flow, while their sum reflects the line loss.

[0322] Regarding the allocation of carbon emissions from network losses, this invention adopts the principle of attribution at the sending end, namely:

[0323] ;

[0324] The physical meaning of this method is: carbon emissions originate from the power generation side, so the carbon responsibility corresponding to the losses should be borne by the power transmitter; when long-distance power transmission or reverse power flow increases, losses increase, thereby increasing the carbon responsibility of the transmitting node; it can reflect the coupling relationship between voltage over-limit, reactive power regulation, loss changes and carbon emission changes in the distribution network.

[0325] After calculating the carbon factor of nodes within the distribution network, the nodal carbon factor of the distribution micro-boundary nodes is extracted, forming the boundary carbon factor facing the microgrid side. This distribution micro-boundary carbon factor can be used as input for the microgrid's carbon purchase attribute or low-carbon scheduling. This realizes the transmission process of main distribution boundary carbon factor input, distribution network internal carbon factor calculation, and distribution micro-boundary carbon factor output.

[0326] Step S6: Determine whether the calculation results meet the carbon constraints:

[0327] If satisfied, output the scheduling scheme and the calculation results of the node carbon factor;

[0328] If the conditions are not met, output the outer layer correction cost of high-carbon units and the penalty coefficient for curtailment of renewable energy, and return to step S2 to continue adjusting the AC power flow model until the carbon constraint is met.

[0329] Furthermore, in the aforementioned objective function, system operation optimization is primarily guided by economic efficiency and safety. However, with a high proportion of renewable energy integration, relying solely on traditional economic dispatch often prioritizes the use of thermal power units with lower marginal costs but higher carbon emissions, leading to an overall high level of carbon emissions in the system. Therefore, it is necessary to further consider the impact of carbon constraints on dispatch strategies. Unlike traditional methods that directly introduce explicit carbon trading costs into the objective function, this invention does not construct a separate carbon cost term but instead employs an implicit low-carbon coordination mechanism based on economic signal adjustment. This method indirectly alters the system dispatch results by dynamically adjusting the operating costs of high-carbon units and the renewable energy curtailment penalty coefficient, gradually causing the system to evolve towards a low-carbon operating state.

[0330] First, we will construct an implicit low-carbon coordination mechanism based on economic signal regulation, including:

[0331] Assume the total carbon emissions of the system are:

[0332] ;

[0333] Given carbon emission targets :

[0334] When R is satisfied total ≤R target At that time, it was considered that the current scheduling scheme met the low-carbon requirements;

[0335] Otherwise, the main problem needs to be modified, and the modification method is as follows:

[0336] First, to suppress the output of high-carbon units, their output in optimization is reduced by increasing their power generation costs. Let the original power generation cost coefficient of unit g be c. g , Δc (k) As for the additional cost, the corrected power generation cost coefficient in the k-th iteration can be expressed as:

[0337] ;

[0338] And gradually increase it iteratively:

[0339] ;

[0340] This method can gradually increase the marginal cost of high-carbon units, making the optimization results tend to reduce their output.

[0341] On the other hand, under the condition of renewable energy integration, system carbon emissions depend not only on the output of high-carbon units, but also on the level of renewable energy consumption. To further reduce carbon emissions, it is necessary to improve the utilization rate of wind and solar power and reduce wind and solar curtailment.

[0342] Let the curtailed wind power be Curt w,tThe power of the abandoned light is Curt p,t The original cost of the power curtailment penalty is:

[0343] ;

[0344] In the k-th iteration, an adjustment coefficient β is introduced. (k) Correct it to:

[0345] ;

[0346] ;

[0347] The mechanism aims to reduce the tendency to curtail wind and solar power by increasing the cost of curtailing electricity, thereby promoting the priority consumption of new energy sources and reducing system carbon emissions at the source.

[0348] The two adjustment methods described above act on the system from the supply side and the consumption side, respectively. They suppress the output of high-carbon power sources by increasing the cost of high-carbon units and improve the utilization rate of renewable energy by increasing the penalty for curtailment. These two methods work synergistically to gradually evolve the system towards a low-carbon operating state. Based on this mechanism, the outer coordination process first initializes the scheduling parameters and solves the AC power flow master problem; then, it calculates the carbon emission flow to obtain R. total If the carbon constraint is satisfied, stop the iteration; otherwise, update c. g C curt The solution process returns to the main problem and is repeated until convergence. This outer coordination method avoids introducing complex carbon variables, achieves low-carbon scheduling through economic signals, is naturally compatible with hierarchical solution frameworks, has high computational efficiency, is suitable for multi-level power grid scenarios, and is highly scalable.

[0349] This invention constructs a master AC power flow problem that considers static voltage safety. Under constraints of node voltage, line capacity, power balance, renewable energy output, energy storage operation, and voltage regulation resource operation, it solves for distribution network node voltage, branch power flow, line losses, and equipment output. Furthermore, by involving regulation resources such as OLTC, CB, renewable energy inverters, and ESS in voltage control, the subsequent calculation of the carbon factor is based on AC power flow results that satisfy static voltage safety. This effectively solves the problem that after a high proportion of renewable energy is connected to the distribution network, node voltage may exceed limits due to the influence of active power flow, reactive power distribution, and reverse power flow, which prevents traditional carbon factor calculations from being based on voltage-safe feasible power flow results.

[0350] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A closed-loop low-carbon dispatching method for distribution networks considering static voltage security, characterized in that: The scheduling steps include the following: Step S1: Input the power grid topology, line parameters, load, new energy sources, and generator parameters; Step S2: Construct an AC power flow model that considers static voltage safety based on the input parameters; Step S3: Process the constructed AC power flow model based on nonlinear constraints, including: By substituting variables, the nonlinear power flow equations containing trigonometric functions and product terms are transformed into a linear form; By introducing the square of voltage as a variable, the physical relationship between variables is uniformly represented as a quadratic constraint; By using second-order cone relaxation, non-convex equality constraints are transformed into convex inequality constraints, enabling the problem to be solved using convex optimization methods. Step S4: Determine whether the node voltage of the distribution network meets the static voltage safety constraints. If not, call the regulation models of OLTC, CB, new energy inverter, and ESS to regulate the voltage and further adjust the AC power flow model, where: OLTC adjusts the overall voltage level of the feeder by changing the transformer taps; CB provides local reactive power compensation by switching capacitor banks; New energy inverters participate in node voltage control through dynamic reactive power regulation; ESS reconstructs the active power flow distribution through charging and discharging, thus suppressing voltage rise caused by back-feeding power from renewable energy sources. Step S5: Obtain the system active power distribution based on the adjusted AC power flow model, construct the carbon emission flow model, and calculate the node electric carbon factor, node carbon emissions, and total system carbon emissions based on the carbon emission flow model; Step S6: Determine whether the calculation results meet the carbon constraints: If satisfied, output the scheduling scheme and the calculation results of the node carbon factor; If the conditions are not met, output the outer layer correction cost of high-carbon units and the penalty coefficient for curtailment of renewable energy, and return to step S2 to continue adjusting the AC power flow model until the carbon constraint is met.

2. The low-carbon closed-loop dispatching method for distribution networks considering static voltage safety according to claim 1, characterized in that: The specific method for step S2 is as follows: The AC power flow model is modeled using the node injection method, including: In the node injection model, the system network topology and line parameters are expressed through the node admittance matrix Y. bus For a unified description, the series impedance of line (i,j) is defined as: ； The corresponding line admittance is: ； Constructing the nodal admittance matrix Y from line parameters bus The element expression is: ； Further results were obtained: ； Where G and B represent the real and imaginary parts of the nodal admittance matrix, respectively, and G in the subsequent AC power flow equations ij With B ij All are obtained from the nodal admittance matrix; Let N be the set of nodes in the power system, T be the set of time periods, and let the node voltage be represented in complex form as follows: ； To facilitate subsequent convex optimization, a voltage squared variable is introduced, expressed as follows: ； To eliminate the voltage product term and trigonometric function term in the AC power flow equations, an auxiliary variable is introduced, and the expression is: ； Define c ij,t and s ij,t These represent the real and imaginary coupling amounts between node voltage vectors, respectively. Based on the parity of trigonometric functions, we can obtain: ； For node pairs in the network that do not have a direct connection, their auxiliary variables satisfy c. ij,t =0、s ij,t =0, thus allowing the use of variable c ij,t and s ij,t Reconstruct the AC power flow equations; To ensure that the optimization model always has a feasible solution, an active power load shedding variable P is introduced. LS i,t and reactive load shedding variable Q LS i,t At this point, the active power balance equation at the node is expressed as: ； The power flow model at both ends of the line is further recovered based on node voltage variables and auxiliary variables; The expression for the active power flow at the sending end of line (i,j) is: ； The expression for the reactive power flow at the sending end is: ； The expression for the active power flow at the receiving end is: ； The expression for reactive power flow at the receiving end is: ； Among them, G ij and B ij These are the real and imaginary parts of the nodal admittance matrix, respectively; g ij b ij b ch ij These represent the line conductance, susceptance, and line-to-ground charging susceptance, respectively. Upper and lower bound constraints are imposed on the load shedding variable to avoid infeasible states in the system, while ensuring that the load shedding behavior is within a reasonable range. The expression is as follows: ； Regarding voltage constraints, the node voltages meet the safe operating range: ； To limit line overload, apparent power constraints are introduced for branch lines: ； The range of values ​​for the load shedding variable is limited by the load demand to ensure that the load shedding variable meets the actual operating requirements. The expression is: ； The above constraints ensure that the load shedding amount does not exceed the actual load demand of the node; The inverter capacity limit for distributed generation is expressed as follows: ； Conventional generating units meet the following constraints: upper and lower output limits, start-stop logic, ramp-up constraints, and minimum start-up and shutdown time constraints. The output constraint is: ； Start-stop constraints are: ； The climbing constraint is: ； Constraining output changes during start-up and shutdown processes to prevent unreasonable and large jumps in unit output, specifically regarding the unit's output P during time period t. g,t The changes in adjacent time periods should satisfy: ； The minimum start-up and shutdown time constraints are: ； Among them, T up g T is the minimum start-up time of the unit. down g This is the minimum downtime for the unit; Based on the above constraints, a complete description of the feasible operating domain of the power system under AC conditions is provided. Then, under the condition of minimizing operating costs, the optimal solution of the objective function of the AC power flow model is obtained, and the outer carbon constraint coordination is iteratively updated to construct the basic operating cost model, including: Under the premise of satisfying the constraints of safe operation of the power grid, the system scheduling objective is to minimize the overall operating cost, and the objective function is constructed as follows: ； The cost of electricity generation reflects the operating expenses of conventional generating units, and is expressed as: ； Unit start-up and shutdown costs describe the additional expenses incurred during unit start-up and shutdown, and are expressed as: ； In the context of renewable energy integration, to encourage renewable energy consumption, a penalty cost for wind and solar curtailment is introduced, expressed as: ； To prevent node voltages from deviating from their rated values, a voltage deviation penalty term is constructed, with the following expression: ； Since load shedding directly affects the reliability of power supply to users, it is usually only allowed when the system cannot meet the safety operation constraints. To avoid the optimization model from over-relying on the load shedding variable, this invention sets a high penalty coefficient for the load shedding, expressed as follows: ； This objective function comprehensively considers economic efficiency, voltage safety, renewable energy absorption capacity, and carbon emission levels, achieving unified optimization of multiple objectives.

3. The low-carbon distribution network closed-loop dispatching method considering static voltage safety according to claim 2, characterized in that: The specific method for step S3 is as follows: Based on the node injection method, the active power expression of node i is: ； among them ij =θ i -θ j ; To reduce model complexity, the nonlinear structure is reconstructed through variable substitution, and new intermediate variables are defined: ； And introduce the squared voltage amplitude variable: ； By substituting the variables mentioned above, the original work injection equation is transformed into a linear form, expressed as: ； Reactive power can be written similarly as: ； By substituting variables, the original trigonometric and product terms are eliminated, transforming the power balance equation into a linear form. The variables must still satisfy the physical relationships determined by the voltage definition. According to the variable definitions: ； Combined with v i,t =V 2 i,t Furthermore, we obtain: ； This constraint reflects the essential coupling relationship between voltage variables and is a nonlinear constraint in the AC power flow model. To achieve a convex optimization solution, the non-convex constraint needs to be relaxed. A second-order cone relaxation method is used to relax the original equality constraint into an inequality form, expressed as: ； The above constraint is transformed into the standard second-order cone constraint form, expressed as: ； This transformation converts the original non-convex constraints into convex second-order cone constraints, and transforms the AC power flow optimization problem into a second-order cone programming problem.

4. The low-carbon closed-loop dispatching method for distribution networks considering static voltage safety according to claim 3, characterized in that: The OLTC model used in step S4 adjusts the low-voltage side voltage of the transformer by changing the tap position. The expression for the operating constraints of the OLTC model is as follows: ； In the formula, v i,t v j,t These represent the squares of the voltage amplitudes at the low-voltage and high-voltage nodes of the transformer, respectively; α i,t r is the squared voltage transformation ratio of the OLTC during time period t; min is the minimum transformation ratio of OLTC; is the voltage squared transformation ratio increment corresponding to the s-th stage; T max OLTC This is the maximum gear position for OLTC; σ OLTC i,s,t δ is a 0-1 variable, representing whether the s-th tier is invested in time period t; OLTC,IN i,t δ OLTC,DE i,t These represent whether OLTC performs an upshift and downshift during time period t, respectively; N max OLTC This represents the maximum number of actions allowed by the OLTC within the scheduling period.

5. A low-carbon distribution network closed-loop dispatching method considering static voltage safety according to claim 4, characterized in that: The CB model used in step S4 provides capacitive reactive power compensation to the distribution network through discrete switching. The expression for the operating constraints of the CB model is as follows: ； In the formula, Q CB i,t q represents the reactive power output of node i in time period t; tap i For single-stage CB reactive power compensation capacity; T max CB CB is the maximum gear; σ CB i,s,t δ is a 0-1 variable, representing whether the s-th CB is invested; CB,IN i,t δ CB,DE i,t These represent whether CB engages or withdraws during time period t; N max CB This represents the maximum number of actions allowed by the CB within the scheduling period.

6. A low-carbon distribution network closed-loop dispatching method considering static voltage safety according to claim 5, characterized in that: The active power output and capacity constraints of the new energy inverter used in step S4 are expressed as follows: ； In the formula, P PV i,t P WT i,t These represent the active power outputs of photovoltaic and wind power at node i during time period t; P PV,pre i,t P WT,pre i,t Forecasted power outputs for solar and wind power, respectively; Q PV i,t Q WT i,t These are the reactive power outputs of the photovoltaic and wind power inverters, respectively; S PV i S WT i These refer to the capacity of photovoltaic and wind power inverters, respectively.

7. A low-carbon distribution network closed-loop dispatching method considering static voltage safety according to claim 6, characterized in that: The ESS model used in step S4 changes the active power flow distribution of the distribution network through charging and discharging. The expression for the operating constraints of the ESS model is as follows: ； In the formula, P cha i,t P dis i,t P represents the ESS charging and discharging power of node i during time period t, respectively. cha,max i P dis,min i These are the maximum charging and discharging power of ESS, respectively; D cha i,t D dis i,t These are 0-1 state variables, representing the charging and discharging states of the ESS, respectively; E ESS i,t Energy stored for ESS; η cha i η dis i These represent charge and discharge efficiencies, respectively; E ESS,max i E ESS,min i These are the upper and lower limits of the ESS battery level, respectively.

8. A low-carbon distribution network closed-loop dispatching method considering static voltage safety according to claim 7, characterized in that: The specific method for step S5 is as follows: To uniformly describe the power flow direction, branch active power decomposition variables are introduced: Let P be the active power flow of branch i→j. ij Then the definition is: ； Among them, P + ij P represents the positive power flow component from node i to node j. + ji This represents the positive power flow component from node j to node i; Define the set of inflow branches of node n as Ω in n The set of outflowing branches is Ω. out n ; According to the principle of proportional sharing, the power flow in any outflow branch within a node includes the contribution of all inflow branches proportionally, as expressed in the following expression: ； Among them, P nj,i This represents the power component from the inflow branch i in the outflow branch j; Define the carbon flux density flowing into branch i as ρ i Then the carbon flow rate of the outflow branch j is: ； Substituting the proportional relationships and simplifying, we get: ； Therefore, the expression for the carbon flux density of branch j is: ； Considering node power generation injection, the node carbon conservation equation is obtained as follows: ； The resulting nodal electrocarbon factor is: ； The expression for nodal load carbon emissions is: ； In carbon emission flow analysis, it is also necessary to reasonably allocate network losses. The active power loss of branch i→j in time period t is defined as: ； Among them, P ij As a positive trend, P ji The components represent the reverse power flow; their difference reflects the power flow direction, and their sum reflects the line loss. For the allocation of carbon emissions from network losses, the principle of attribution at the sending end is adopted, expressed as follows: ； After completing the calculation of the electrical carbon factor of the internal nodes of the distribution network, the node electrical carbon factor of the distribution micro boundary node is extracted and the boundary electrical carbon factor facing the microgrid side is formed. The distribution micro boundary electrical carbon factor is used as the input for the electrical carbon attribute of the microgrid or the low-carbon scheduling of the microgrid.

9. A low-carbon distribution network closed-loop dispatching method considering static voltage safety according to claim 8, characterized in that: The specific method for step S6 is as follows: Constructing an implicit low-carbon coordination mechanism based on economic signal regulation, including: Define the total carbon emissions R of the system total for: ； With set carbon emission targets Comparison and judgment: When R total ≤R target If the current scheduling scheme is deemed to meet the low-carbon requirements, the final result will be output. When R total >R target If this occurs, it indicates that the system's total carbon emissions have not met the target carbon emission constraints, and the main problem needs to be corrected, including: To suppress the output of high-carbon units, their output in optimization is reduced by increasing their power generation costs. The original power generation cost coefficient of unit g is defined as c. g , Δc (k) As for the additional cost, the corrected power generation cost coefficient in the k-th iteration is expressed as: ； And gradually increase it iteratively: ； To reduce carbon emissions, improve the utilization rate of wind and solar power, and reduce wind and solar curtailment, the curtailed power is defined as Curt. w,t The power of the abandoned light is Curt p,t The original cost of the power curtailment penalty is: ； In the k-th iteration, by introducing an adjustment coefficient β (k) Correct it to: ； ； The implicit low-carbon coordination mechanism constructed above aims to reduce the tendency of wind and solar curtailment by increasing the cost of curtailing electricity, promote the priority consumption of new energy sources, and reduce system carbon emissions from the source. Based on the above mechanism, the outer coordination process first initializes the scheduling parameters and then solves the AC power flow master problem. Next, the carbon emission flow is calculated to obtain R. total If the carbon constraint is satisfied, stop the iteration; otherwise, update c. g C curt Then return to the main problem and solve it again until convergence.

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