Static power flow analysis method and system of electric heating hybrid system

Abstract

The invention relates to the technical field of electric power systems, in particular to a static power flow analysis method and system for an electric heating hybrid system, and the method comprises the following steps: S1, electric heating power equivalent modeling: building a relation between electric power and heat flow through thermal power calculation and equivalent conversion, and forming a unified time domain model; s2, heat supply pipe network average temperature response modeling: based on thermodynamics and heat transfer theories, constructing a response model considering heat input and loss, and deriving differential and Laplace expression; s3, equivalent modeling of external characteristics of the electric boiler: modeling the electric boiler as a pi-type circuit, calculating impedance and admittance parameters, and establishing a relation between thermal power and electric power; and S4, static power flow unified solving: constructing an electrothermal coupling solving framework, combining power flow and hydraulic calculation, and expanding Jacobian matrix optimization convergence. According to the method, high-precision power flow analysis and efficient solution of the electric heating hybrid system in a unified time domain are realized, and the modeling precision, the calculation efficiency and the engineering applicability are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of power systems, in particular to a static power flow analysis method and system of an electric-thermal hybrid system. BACKGROUND

[0002] With the continuous expansion of the installed capacity of clean energy such as photovoltaic and wind power, the electric-thermal hybrid system with flexible load regulation capability plays an increasingly important role in the integrated energy system, especially in the multi-energy collaborative application scenario centered on electric heating, the efficient collaborative scheduling of electricity and heat systems has become an important means to realize the optimization of source, network, load and storage collaboration. Due to the significant differences in energy form, time and space characteristics and operation dynamics between the power system and the heat supply pipe network, it is urgent to develop a power flow analysis method that can uniformly represent the electric-thermal coupling behavior to support system operation state evaluation and optimization control.

[0003] The existing electric-thermal hybrid system power flow analysis method has obvious deficiencies in multiple key links: first, the calculation time domain of electricity and heat systems is not unified, making it difficult to perform synchronous analysis, second, the heat-to-power ratio and electric heating efficiency are generally considered as constant parameters, without considering their dynamic characteristics with changes in operating environment, third, it relies on alternating solution between the power grid and the heat network, with complex calculation process and low efficiency, fourth, there is a lack of effective electric-thermal energy conversion and physical parameter coupling mechanism, which cannot accurately reflect the real state of energy two-way flow. These problems seriously restrict the engineering applicability and scheduling accuracy of the electric-thermal hybrid system in multi-energy collaboration. SUMMARY

[0004] The application provides a static power flow analysis method and system of an electric-thermal hybrid system, which realizes unified analysis and optimization of power system and heat supply pipe network power flow by establishing an electric-thermal power equivalent model, a temperature response dynamic model and an electric boiler external characteristic equivalent model.

[0005] A static power flow analysis method of an electric-thermal hybrid system, comprising the following steps:

[0006] S1, electric-thermal power equivalent modeling: through heat power calculation, electric-thermal power equivalent conversion and time domain synchronization processing, a dynamic correlation between electric power and heat flow is established, and an equivalent temperature difference variable k is used to reflect the change of electric-thermal conversion efficiency with temperature and device type, forming an electric-thermal power equivalent model for power flow analysis in a unified time scale;

[0007] S2, average temperature response modeling of heat supply pipe network: on the premise that the water supply temperature of electric heating equipment and the return water temperature of user are known, based on the first law of thermodynamics (energy conservation) and heat transfer theory, a dynamic temperature response model considering electric heating power input, pipe network thermal inertia and heat loss is constructed, the differential equation of temperature response and its Laplace transform form are derived, combined with the node mixed temperature equation and pipe section temperature decay model, the dynamic process and steady-state characteristics of heat supply pipe network temperature rise are obtained;

[0008] S3, equivalent modeling of electric boiler external characteristics: the electric boiler is modeled as a π-type equivalent circuit including series impedance and parallel admittance, the resistance, inductance and capacitance parameters are calculated respectively, the mapping relationship between heat power demand and electric power, resistance change is established, considering the influence of inductance, capacitance and other factors on electromagnetic loss and leakage current, a dynamic external characteristic equivalent model suitable for electric boilers of different structures is constructed;

[0009] S4, unified solution of static flow: using the Newton-Raphson method-based unified solution framework of electric-thermal coupling, the coupling interface equation of power grid and heat network is established, the processes of power flow calculation, hydraulic calculation and coupling variable updating are combined, the extended Jacobian matrix is constructed, and the sparse matrix optimization, adaptive step control and three-level convergence criterion are used to realize the unified iterative solution of static flow of electric-thermal mixed system.

[0010] Optionally, the electric-thermal power equivalent modeling in S1 comprises:

[0011] S11, heat power calculation: according to the thermodynamic formula, the heat power Ph of heat supply pipe network and the fluid mass flow g n are defined as:

[0012] P h h p g n (t xy -t at );

[0013] Wherein, c p represents the specific heat capacity of fluid, t xy and t at represent the water supply temperature and return water temperature respectively;

[0014] S12, electric-thermal power equivalent conversion: the performance parameters η exp of electric heating equipment (such as electric boiler, heat pump) are referenced, the electric power P d on the power grid side is equivalent to the flow on the heat network side, and is expressed as:

[0015]

[0016] S13, time domain synchronization processing: the electric power P d and the heat flow g nSynchronize time discretization.

[0017] Optionally, the average temperature response modeling of the heat supply pipe network in S2 comprises:

[0018] S21, system heat balance modeling: in a time microelement dT, the heat balance equation of the electric-thermal hybrid system is expressed as:

[0019]

[0020] wherein, P h,i represents the thermal power of the i-th user load, L l represents the length of the l-th pipe segment, t env represents the ambient temperature, t hi represents the average temperature of the pipe network, M ω represents the total mass of the pipe network fluid, λ represents the pipe segment heat loss coefficient, η exp represents the performance coefficient of the electric heating device;

[0021] S22, differential equation establishment and simplification: ignoring the pipe segment heat loss (short-term analysis), simplifying the heat balance equation, expressed as:

[0022]

[0023] S23, temperature response Laplace transform: the simplified heat balance equation is subjected to Laplace transform, and a transfer function is obtained, expressed as:

[0024]

[0025] S24, temperature dynamic response solving: assuming that the electric power P d is a step input, the user load is constant, the average temperature dynamic response is calculated, expressed as:

[0026]

[0027] S25, definition of node temperature mixing equation: assuming that the node j receives fluid from m pipe segments, the temperature t is expressed as:

[0028]

[0029] wherein, q k is the flow rate of the k-th pipe segment, t k,in is the inlet temperature of the pipe segment k;

[0030] S26, pipe segment temperature decay model definition: the outlet temperature t l,out of the pipe segment l is expressed as:

[0031]

[0032] S27, system steady-state temperature and response time constant calculation: calculate the average temperature of the electro-thermal hybrid system to reach steady state, and define the time constant τ to represent the system response speed, expressed as:

[0033]

[0034] Optionally, the S3 external characteristic equivalent modeling of the electric boiler includes:

[0035] S31, thermal-electric power equivalent conversion: combine the performance coefficient η of the electric heating device exp , based on the thermal power to calculate the electric power demand of the power grid, expressed as:

[0036] P h =c p g n (t xy -t at );

[0037]

[0038] Where g n is the heat grid-power grid coupling variable;

[0039] S32, equivalent resistance dynamic calculation: based on Ohm's law, convert the electric power demand into an equivalent DC resistance, and according to the flow dependence, introduce the resistance temperature coefficient α T for temperature correction, expressed as:

[0040]

[0041] S33, series impedance parameter: construct the series impedance part in the π-type equivalent circuit of the electric boiler, including the winding inductance effect, additional loss caused by harmonics, and measure the phase angle θ through no-load experiment, expressed as:

[0042]

[0043] S34, parallel admittance parameter calculation: by considering the capacitance effect, based on the relationship between the insulation structure parameters or rated voltage and reactive power, determine the capacitive admittance B ch , expressed as:

[0044]

[0045] S35, comprehensive efficiency closed-loop verification: after substituting the electric power demand, equivalent resistance, series impedance parameter, and parallel admittance parameter into the power flow calculation, verify the comprehensive efficiency η of the electric boiler, when the comprehensive efficiency η of the electric boiler deviates from the design value by more than 5%, preferentially adjust L ch and C ch .

[0046] Optionally, the capacitive susceptance B in S34 ch Also included are:

[0047]

[0048] Optionally, the comprehensive efficiency η of the electric boiler is represented as:

[0049]

[0050] Optionally, the unified solution of the static power flow in S4 includes:

[0051] S41, constructing a unified solution framework for electric-thermal coupling: based on the Newton-Raphson method, a unified solution framework for the electric-thermal hybrid system is constructed, including an electric grid power flow calculation unit (node voltage and electrical power), a heat network hydraulic calculation unit (pipe segment flow and node pressure), and a coupling interface unit (electric boiler energy conversion constraint);

[0052] S42, variable initialization strategy: the variable initialization strategy includes grid side initialization and heat network side initialization, wherein;

[0053] The grid side initialization adopts a flat start method, all PQ node voltage amplitudes are initialized to 1.0 p.u., and the phase angle is set to 0°, and the PV node voltage amplitude takes the given value;

[0054] The heat network side initialization adopts an improved equal-mooring resistance distribution method to calculate the pipe segment flow, and calculates the initial value of the node pressure according to the outlet pressure of the heat source, represented as:

[0055]

[0056] Wherein, P j represents the path to node j, R l is the mooring coefficient of pipe segment l;

[0057] S43, constructing a correction equation system: the Newton method in polar form is used to establish the grid side correction equation, the heat network side correction equation is established based on the mass conservation and energy equation, and the electric boiler is constructed as a connecting element to build the coupling interface equation, represented as:

[0058]

[0059] Wherein, G ij +jB ij is the node admittance matrix element, θ ij = θ i - θ j , represents the Hadamard product, Φ = diag(φ1,...,φs) is the mooring coefficient matrix, L ka pipe section set connected to the electric boiler k;

[0060] S44, coupling term processing: on the basis of the original power grid and heat grid Jacobian matrix, an electric-heat coupling sub-block is added, denoted as:

[0061]

[0062] S45, sparse matrix optimization: the Jacobian matrix is stored in the CSR format, including reducing 40% storage by using the node admittance matrix symmetry and optimizing the filling sequence based on the tree structure of the pipe network topology;

[0063] S46, adaptive step size and convergence control: when the residual error reduction rate is less than 15% for two consecutive times, the step size reduction mechanism is triggered, and three-level criteria are set to ensure overall convergence.

[0064] Optionally, the step size adjustment is represented as:

[0065]

[0066] Optionally, the three-level criteria include:

[0067] Primary criterion: max(|ΔP|,|ΔQ|)≤ε1;

[0068] Secondary criterion: ||Δq||2≤ε2;

[0069] Auxiliary criterion: coupling variable change amount ≤10 -5 .

[0070] A static load flow analysis system of an electric-heat hybrid system, for implementing the static load flow analysis method of the electric-heat hybrid system, comprising the following modules:

[0071] Electric-heat power equivalent modeling module: through heat power calculation, electric-heat power equivalent conversion and time domain synchronization processing, a dynamic correlation between electric power and heat flow is established, and an electric-heat power equivalent model for load flow analysis under a unified time scale is generated;

[0072] Heating pipe network average temperature response modeling module: on the premise that the electric heating device supply water temperature and user return water temperature are known, a dynamic temperature response model considering electric-heat power input, thermal inertia and heat loss is constructed based on energy conservation and heat transfer theory, and the pipe network temperature rise dynamic process and steady state characteristics are obtained;

[0073] Electric boiler external characteristic equivalent modeling module: the electric boiler is modeled as a π-type equivalent circuit containing series impedance and parallel admittance, the resistance, inductance and capacitance parameters are calculated respectively, a mapping model between heat power demand and electric power, resistance change is constructed, and the influence of electromagnetic loss and leakage current is characterized;

[0074] Static power flow unified solution module: based on Newton-Raphson method, an electric-thermal coupling unified solution framework is constructed, the coupling interface equation of the power grid and the heat network is established, the power flow calculation of the power grid, the hydraulic calculation of the heat network and the iterative updating process of the coupling variable are combined, the extended Jacobian matrix is constructed, and through sparse matrix optimization, adaptive step control and three-level convergence criterion, the static power flow unified iterative solution of the electric-thermal hybrid system is realized.

[0075] The beneficial effects of the present application are:

[0076] The present application realizes high-precision conversion and dynamic response analysis of electric energy and heat energy on a unified time scale by constructing an electric-thermal power dynamic equivalent model based on temperature difference variable k, a heat supply pipe network average temperature response model and an electric boiler pi-type external characteristic equivalent model, makes up for the deficiencies of traditional methods such as fixed heat-to-power ratio and electric heating efficiency, time domain asynchronization, heat inertia and loss neglect, has theoretical innovation and structural modeling depth, can accurately reflect the power variation, temperature rise trend and equipment characteristics of the electric-thermal hybrid system in actual operation, and thus improves the overall modeling accuracy and simulation reliability.

[0077] The present application greatly improves the solution efficiency and engineering adaptability by adopting an electric-thermal coupling unified solution framework, cooperating with extended Jacobian matrix, electric-thermal interface coupling processing, sparse matrix optimization, adaptive step control and three-level convergence criterion, can control the solution time to be within 5 seconds in a typical 200-node system, reduce the iteration number by 50%, improve the calculation accuracy to within 1.5%, and support system modeling analysis of a maximum of 500 nodes, is significantly superior to the traditional alternating solution method, and has wide engineering application value in power flow analysis, planning and real-time simulation of comprehensive energy systems. BRIEF DESCRIPTION OF DRAWINGS

[0078] In order to more clearly illustrate the technical solutions in the present application or prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only illustrate the present application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0079] Figure 1 The present application is an analysis method flowchart of the embodiment.

[0080] Figure 2 The present application is a static power flow unified solution flowchart of the embodiment.

[0081] Figure 3 The present application is a system function module schematic diagram of the embodiment. DETAILED DESCRIPTION

[0082] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art may employ other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0083] like Figures 1-2 As shown, a static power flow analysis method for an electrothermal hybrid system includes the following steps:

[0084] Step 1, Equivalent Modeling of Electrothermal Power:

[0085] The purpose of this step is to unify the energy representation methods of the power system and the heating network, and to establish a dynamic relationship between the two. The specific implementation steps include the following three parts:

[0086] The first step is to calculate the thermal power. According to thermodynamic formulas, the thermal power P of the heating network... h With fluid mass flow rate g n The relationship is:

[0087] P h =c p g n (t xy -t at (1.1)

[0088] Among them, c p t represents the specific heat capacity of a fluid, expressed in kJ / (kg·℃); xy ,t at These represent the supply water temperature and the return water temperature, respectively.

[0089] It should be noted that the return water temperature of electric heating equipment is determined by the network temperature analysis and hydraulic calculations, and its losses also vary with the system operating environment.

[0090] The second is the equivalent conversion of electrical and thermal power. Here, the performance parameter η of electric heating equipment (such as electric boilers and heat pumps) is cited. exp The grid-side power P d The equivalent value is the flow rate on the heating network side.

[0091]

[0092] The key variable in this step is the equivalent temperature difference variable k, which dynamically reflects the change in electrothermal conversion efficiency with temperature and equipment type.

[0093] Third is time-domain synchronization processing. This applies to the electrical power P. d and heat flow g n Perform synchronous time discretization to ensure that both are analyzed at the same time step.

[0094] It should be noted that: for the heating pipe network system with multiple electric heating devices, in order to avoid negative values of the flow and heat provided by the first end device after equivalence, the supply and return water temperatures should be taken as the node that absorbs the maximum electric power, and other electric heating devices can be equivalent as negative heat load; When the heating pipe network system runs at constant flow, if the heat transfer coefficient of the heat exchanger is high and the heat exchange area is large, the return water temperature of the pipe network is higher, and the average temperature is higher; When the above parameters are constant, the greater the electric power provided, the faster the average temperature rise speed of the heating pipe network.

[0095] Step 2, average temperature response modeling of heating pipe network:

[0096] For any electric heating mixed system with n heat exchangers and user loads, the initial conditions of its operation are assumed as follows:

[0097] 1) The system runs at constant power and is in steady state before starting, and the supply and return water pipe sections of the heating pipe network are symmetrically arranged, and the pipe diameters, distances, flow rates and other parameters of the pipe sections at the same symmetric position are equal and known;

[0098] 2) The supply water temperature of the electric heating device and the return water temperature of each user load are known and constant, and the heat loss of the electric heating device is 0;

[0099] 3) At time T, the average temperature of each heat exchanger is the arithmetic mean of the supply water node and the return water node, the heat transfer coefficient and the heat exchange area are known, the heat exchange mode is convection, and the pipeline along the heat exchanger to the user load is 0.

[0100] The temperature dynamic characteristics of the heating pipe network directly affect the system energy efficiency and the user side heating quality. The traditional method regards temperature as a static parameter, which cannot reflect the dynamic influence of electric power input, pipe network structure and running environment on temperature. Based on the first law of thermodynamics (energy conservation) and heat transfer theory, a dynamic temperature response model considering the following factors is constructed:

[0101] a. Electric heating power input: the real-time process of converting electric power of electric boiler / heat pump into heat;

[0102] b. Pipe network thermal inertia: temperature change delay caused by fluid mass and specific heat capacity;

[0103] c. Heat loss: the influence of pipe section heat dissipation and heat exchanger efficiency.

[0104] The purpose of modeling the average temperature response of the heating pipe network is to quantify the influence of electric power input on the temperature of the pipe network and analyze the thermal dynamic characteristics. The key variables are defined as follows:

[0105] Symbol Physical meaning Unit [cat hi ]] Pipe network average temperature ℃ [cat xy ]]> Electric heating device supply water temperature ℃ t at ]]> User return water temperature ℃ M ω ]]> Pipe network fluid total mass kg exp ]]> ​ Electric heating device coefficient of performance - λ Pipe segment heat loss coefficient W / (m·℃)

[0106] In time microelement dT, the system satisfies:

[0107] Electric heating input = pipe network heat storage change + user load heat absorption + pipe segment heat loss;

[0108] The mathematical expression is:

[0109]

[0110] Where: P h,i represents the thermal power of the i-th user load (kW); L l represents the length of the l-th pipe segment (m); t env represents the ambient temperature (℃).

[0111] Neglecting the pipe segment heat loss (short-term analysis), the equation is simplified as:

[0112]

[0113] Taking the Laplace transform of the above differential equation, the transfer function is obtained:

[0114]

[0115] Assuming that the electric power P d is a step input, the user load is constant, and the average temperature dynamic response is obtained:

[0116]

[0117] For a heating pipe network with a branch structure, the following constraints need to be supplemented:

[0118] (1) Node temperature mixing equation:

[0119] If node j receives fluid from m pipe segments, its temperature t is:

[0120]

[0121] Where, q k is the flow rate of the k-th pipe segment (kg / s); t k,in is the inlet temperature of pipe segment k (℃).(2) Pipe segment temperature decay model:

[0122] The outlet temperature t l,out of pipe segment l is considered along the heat loss:

[0123]

[0124] So far we have analyzed the steady-state and dynamic characteristics. When T→∞, the system reaches steady state, and the average temperature is:

[0125]

[0126] The definition time constant τ characterizes the system response speed, called τ as the temperature rise time constant:

[0127]

[0128] The engineering significance is that the smaller τ is, the faster the system responds to the change of electric power.

[0129] Step 3, equivalent modeling of the external characteristics of the electric boiler:

[0130] As the core conversion equipment of the electric-thermal hybrid system, the external characteristic modeling of the electric boiler needs to meet:

[0131] (1) Electric-thermal two-way coupling: accurately reflect the dynamic relationship between electric energy input and thermal energy output;

[0132] (2) Loss quantification: represent the influence of resistance heating, reactive loss, etc. on efficiency;

[0133] (3) Operation adaptability: compatible with electric boilers of different capacities and structures (such as electrode type / resistance type).

[0134] The traditional method regards the electric boiler as a pure resistance load, ignoring its dynamic impedance characteristics, resulting in a power flow calculation error of up to 10%-15%. The present invention proposes a multi-parameter dynamic model based on equivalent circuit.

[0135] The external characteristics of the electric boiler use an improved π-type equivalent circuit, which includes:

[0136] Series branch: impedance Z ch = R ch +jX ch Z ch = R ch +jX ch Characterize active / reactive loss;

[0137] Parallel branch: admittance Y ch = G ch +jB ch Y ch = G ch +jB ch Reflect the leakage to the ground and electromagnetic effect.

[0138] To realize the accurate equivalent modeling of the external characteristics of the electric boiler, the equivalent circuit parameters need to be calculated systematically. This scheme establishes a closed-loop derivation process from the thermal power demand to the impedance parameters on the grid side through multi-physical field coupling analysis, and the specific steps are as follows:

[0139] 1. Thermal-electric power equivalent conversion (connecting the output of the heat network model):

[0140] P h = cp g n (t xy -t at ), combined with the heating device coefficient of performance η exp , the required electrical power of the grid side is back-calculated:

[0141]

[0142] At this time g n , as a coupling variable between the heat grid and the power grid, becomes the basis for subsequent impedance calculation.

[0143] 2. Equivalent resistance R d Dynamic calculation (reflecting the operating condition):

[0144] Based on Ohm's law, the electrical power requirement is converted to an equivalent DC resistance:

[0145]

[0146] Flow dependence: R d ∝1 / g n , the resistance decreases as the flow increases;

[0147] Temperature correction: the resistance temperature coefficient α T needs to be introduced in actual operation:

[0148]

[0149] 3. Series impedance Z ch Comprehensive modeling (compatible with electromagnetic loss):

[0150] Expand the pure resistance model and add inductive components to represent:

[0151] (1) winding inductance effect; (2) additional loss caused by harmonics.

[0152]

[0153] Parameter determination method:

[0154] Inductance L ch : by measuring the phase angle θ through no-load experiment, then:

[0155]

[0156] Engineering simplification: for electric boilers below 10 MW, the typical value X ch / R ch ≈0.3-0.5. Parallel admittance Y ch Calculation (suppress model error):

[0157] Mainly consider the inter-electrode capacitance effect, and its capacitive admittance is:

[0158]

[0159] Measured calibration suggestion:

[0160] Measure the reactive power Q at rated voltage:

[0161]

[0162] Typical range: 0.01-0.05 s (negatively related to the thickness of the insulating medium).

[0163] 4. Dynamic efficiency closed-loop verification (convergent power iteration):

[0164] After substituting the above parameters into the power flow calculation, the comprehensive efficiency of the electric boiler needs to be verified:

[0165]

[0166] If the deviation of η from the design value is >5%, adjust L ch and C ch ;

[0167] For electrode-type boilers, additional consideration should be given to the electrolytic loss term ΔP electrolysis .

[0168] This method combines physical mechanisms with experimental data to ensure consistency in dynamic operation and multi-scale analysis, providing a high-precision equivalent modeling tool for electric-thermal hybrid systems.

[0169] Step 4, static power flow unified solution:

[0170] 1. Solution framework and overall process:

[0171] This method uses a unified solution framework based on the Newton-Raphson method for electric-thermal coupling, which realizes the collaborative calculation of two types of heterogeneous energy systems by establishing a two-way data interaction mechanism between the power grid and the heat grid. As Figure 1 shown, this process includes three core modules:

[0172] (1) Power grid power flow calculation module: handles node voltage, power balance, and other electrical quantity calculations;

[0173] (2) Heat network hydraulic calculation module: solves pipe segment flow, node pressure, and other thermal parameters;

[0174] (3) Coupling interface module: realizes energy conversion and parameter mapping through the equivalent model of electric boilers.

[0175] 2. Variable initialization strategy:

[0176] 2.1 Initialization on the power grid side:

[0177] With flat start method, all PQ bus voltage magnitudes are initialized to 1.0 p.u. (per unit) and phase angles are set to 0°; PV bus voltage magnitudes are given values and phase angles are initialized to 0°; balanced bus voltage magnitudes and phase angles are fixed to dispatch values. This initialization method can ensure that more than 80% of cases converge within 10 iterations.

[0178] 2.2 Heat network side initialization:

[0179] (1) Pipe flow is calculated by improved equal-moisture resistance distribution method:

[0180]

[0181] (2) Node pressure initial value is calculated according to heat source outlet pressure:

[0182]

[0183] where P j represents the path to node j, and R l is the resistance coefficient of pipe section l.

[0184] 3. Correction equation system construction:

[0185] 3.1 Power grid side correction equation:

[0186] The active / reactive power imbalance equation is established by using polar form Newton method:

[0187]

[0188] where G ij and jB ij are node admittance matrix elements, and θ ij = θ i - θ j .

[0189] 3.2 Heat network side correction equation:

[0190] Based on mass conservation and energy equation:

[0191]

[0192] where, represents Hadamard product, and Φ = diag(φ1,...,φs) is the resistance coefficient matrix. 3.3 Coupling interface equation:

[0193] The electric boiler as a connecting element needs to satisfy:

[0194]

[0195] where L kTo connect the pipe section set of electric boiler k.

[0196] 4. Jacobian matrix special processing technology:

[0197] 4.1 Coupling term processing:

[0198] On the basis of traditional power grid Jacobian matrix, increase the electric-thermal coupling sub-block:

[0199]

[0200] Where the non-zero element calculation formula is:

[0201]

[0202] 4.2 Sparse matrix optimization:

[0203] The Jacobian matrix is stored in CSR (Compressed Sparse Row) format, and the following is realized:

[0204] Power grid part: reduce 40% storage by using node admittance matrix symmetry

[0205] Heat network part: tree structure optimization filling sequence based on pipe network topology

[0206] 5. Iterative optimization and convergence control:

[0207] 5.1 Adaptive step size algorithm:

[0208] The kth iteration step size is dynamically adjusted according to the historical convergence situation:

[0209]

[0210] When the residual error reduction rate is less than 15% for two consecutive times, trigger the step size reduction mechanism.

[0211] 5.2 Comprehensive convergence criterion:

[0212] Set three-level criteria to ensure overall convergence:

[0213] (1) Main criterion: max(|ΔP|,|ΔQ|)≤ε1(typical value 10 -6 p.u.).

[0214] (2) Secondary criterion: ||Δq||2≤ε2(typical value 10 -4 kg / s).

[0215] (3) Auxiliary criterion: coupling variable change ≤10 -5

[0216] 6. Analysis of typical convergence characteristics:

[0217] Take a certain regional integrated energy system as an example (including 38 power grid nodes and 24 heat grid nodes), the convergence process is shown in Table 1:

[0218] Table 1 measured data of iterative convergence process

[0219]

[0220]

[0221] 7. Engineering implementation specification:

[0222] Data interface standard:

[0223] Power grid data: conforms to IEC 61970 CIM / XML specification;

[0224] Heat grid data: adopts Modelica FMI 2.0 standard;

[0225] Coupling interface: define intermediate data packet in JSON format;

[0226] Hardware configuration requirements:

[0227] Small system (<50 nodes): Intel i7-12800H + 32GB RAM;

[0228] Medium system (50-200 nodes): Xeon Silver 4310x2 + 128GB RAM;

[0229] Large system (>200 nodes): NVIDIA DGX A100 compute node cluster;

[0230] In a certain 330kV / 130℃ regional electric-thermal system, the key indicators are compared as follows:

[0231] Table 2 comparison of measured verification data in a certain 330kV / 130℃ regional electric-thermal system

[0232] Parameter Method herein Conventional alternating method Error reduction Voltage deviation 0.32％ 1.05％ 69.5％ Flow deviation 1.8％ 6.7％ 73.1％ Calculation time 3.2s 11.7s 72.6％

[0233] This scheme realizes the synchronous improvement of the accuracy and efficiency of the electric-thermal hybrid system power flow analysis through rigorous mathematical modeling and engineering optimization, and provides reliable technical support for the planning and operation of integrated energy systems.

[0234] As shown in Figure 3 A static power flow analysis system of an electric-thermal hybrid system for realizing the above-mentioned static power flow analysis method of an electric-thermal hybrid system, comprising the following modules:

[0235] An electric heating power equivalent modeling module: through thermal power calculation, electric-thermal power equivalent conversion and time domain synchronization processing, a dynamic correlation between electric power and heat flow is established, and an electric-thermal power equivalent model for power flow analysis under a unified time scale is generated;

[0236] A heating pipe network average temperature response modeling module: on the premise that the electric heating equipment water supply temperature and the user return water temperature are known, a dynamic temperature response model considering electric heating power input, thermal inertia and heat loss is constructed based on energy conservation and heat transfer theory, and the pipe network temperature rise dynamic process and steady state characteristics are obtained;

[0237] An electric boiler external characteristic equivalent modeling module: the electric boiler is modeled as a π-type equivalent circuit containing series impedance and parallel admittance, the resistance, inductance and capacitance parameters are calculated respectively, a mapping model between heat power demand and electric power, resistance change is constructed, and the influence of electromagnetic loss and leakage current is characterized;

[0238] A static power flow unified solution module: based on the Newton-Raphson method, an electric-thermal coupling unified solution framework is constructed, the coupling interface equation of the power grid and the heat network is established, the power grid power flow calculation, the heat network hydraulic calculation and the coupling variable iteration update process are combined, the extended Jacobian matrix is constructed, and through sparse matrix optimization, adaptive step control and three-level convergence criterion, the static power flow unified iteration solution of the electric-thermal mixed system is realized.

[0239] The present application encompasses any substitution, modification, equivalent method and scheme made on the essence and scope of the present application. In order to make the public have a thorough understanding of the present application, specific details are described in the following preferred embodiments of the present application, and the present application can also be fully understood without the description of these details to those skilled in the art. In addition, in order to avoid unnecessary confusion to the essence of the present application, well-known methods, processes, procedures, elements and circuits are not described in detail.

[0240] The above is only the preferred embodiment of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principle of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be regarded as the protection scope of the present application.

Claims

1. A method for static power flow analysis of an electric-thermal hybrid system, characterized in that, The method comprises the following steps: S1, electric-thermal power equivalent modeling: by means of thermal power calculation, electric-thermal power equivalent conversion and time domain synchronization processing, a dynamic correlation between electric power and heat flow is established, and an equivalent temperature difference variable k is used to reflect the change of electric-thermal conversion efficiency with temperature and equipment type, thereby forming an electric-thermal power equivalent model for power flow analysis under a unified time scale; S2, average temperature response modeling of a heating pipe network: on the premise that the supply water temperature of an electric heating device and the return water temperature of a user are known, a dynamic temperature response model considering electric-thermal power input, pipe network thermal inertia and heat loss is constructed based on the first law of thermodynamics and heat transfer theory, a temperature response differential equation and its Laplace transform form are derived, a node mixed temperature equation and a pipe section temperature decay model are combined, and the temperature rise dynamic process and the steady state characteristics of the heating pipe network are obtained; S3, electric boiler external characteristic equivalent modeling: the electric boiler is modeled as a π-type equivalent circuit comprising series impedance and parallel admittance, parameters of resistance, inductance and capacitance are calculated respectively, a mapping relationship between heat power demand and electric power and resistance change is established, the influence of inductance and capacitance on electromagnetic loss and leakage current is considered, and a dynamic external characteristic equivalent model suitable for electric boilers of different structures is constructed; S4, unified solution of static power flow: a unified solution framework of electric-thermal coupling based on the Newton-Raphson method is used, a coupling interface equation of the electric grid and the heat grid is established, the processes of electric grid power flow calculation, heat grid hydraulic calculation and coupling variable updating are combined, an extended Jacobian matrix is constructed, and sparse matrix optimization, adaptive step control and three-level convergence criterion are used to realize unified iterative solution of the static power flow of the electric-thermal mixed system.

2. The method of static power flow analysis of an electric-thermal hybrid system according to claim 1, wherein, The electric-thermal power equivalent modeling in S1 comprises: S11, thermal power calculation: according to the thermodynamic formula, the heat power Ph of the heat supply pipe network and the fluid mass flow g are defined n , expressed as: P h = c p g n (t xy -t at ); where c p represents the specific heat capacity of the fluid, t xy , t at represent the supply water temperature and the return water temperature, respectively; S12, electric-thermal power equivalent conversion: reference performance parameter η of electric heating device exp The electric grid side electric power P d The equivalent is the heat grid side flow, expressed as: S13, time synchronization processing: the electric power P d and the thermal flow g n is discretized in synchronization with time.

3. The method of claim 2, wherein, The average temperature response modeling of a heating pipe network in S2 comprises: S21, system heat balance modeling: in a time microelement dT, the heat balance equation of the electric-thermal mixed system is represented as: where P h,i represents the thermal power of the i-th user load, L l represents the length of the i-th pipe section, t env represents the ambient temperature, t hi represents the average temperature of the pipe network, M ω represents the total mass of the fluid in the pipe network, λ represents the heat loss coefficient of the pipe section, η exp represents the coefficient of performance of the electric heating device; S22, differential equation establishment and simplification: the heat balance equation is simplified by ignoring the heat loss of the pipe section, and is represented as: S23, temperature response Laplace transform: the simplified heat balance equation is subjected to Laplace transform, and a transfer function is obtained, which is represented as: S24, temperature dynamic response solution: set the electric power P d Step input, user load constant, calculate the average temperature dynamic response, expressed as: S25, definition of node temperature mixed equation: the temperature t of node j receiving fluid from m pipe sections is represented as: where q k is the flow rate of the kth pipe segment, t k,in is the inlet temperature of pipe segment k; S26, define the temperature decay model of the pipe segment: the outlet temperature t of the pipe segment l l,out Considering the heat loss along the pipeline, it is expressed as: S27, calculation of system steady state temperature and response time constant: the average temperature of the electric-thermal mixed system reaching the steady state is calculated, and a time constant τ is defined to represent the response speed of the system, which is represented as:

4. The method of claim 3, wherein, The electric boiler external characteristic equivalent modeling in S3 comprises: S31, thermal-electric power equivalent conversion: combining the coefficient of performance η of the electric heating device exp , the electric power demand of the grid is calculated based on the thermal power, expressed as: P h = c p g n (t xy -t at ); where g n is the heat grid-power grid coupling variable; S32, equivalent resistance dynamic calculation: based on Ohm's law, convert the electrical power demand into an equivalent DC resistance, introduce the resistance temperature coefficient a according to the flow dependence T Temperature correction is made, expressed as: ΔT = t winding -t ambient ; S33, series impedance parameters: the series impedance part in the π-type equivalent circuit of the electric boiler is constructed, including the winding inductance effect and additional loss caused by harmonics, and the phase angle θ is measured through no-load experiment, which is represented as: S34, parallel admittance parameter calculation: by considering the capacitive effect, based on the insulation structure parameters or rated voltage and reactive power relationship, determine the capacitive susceptance B ch , is expressed as: S35, comprehensive efficiency closed loop verification: after substituting the electric power demand, equivalent resistance, series impedance parameter, and parallel admittance parameter into the power flow calculation, verify the comprehensive efficiency η of the electric boiler; when the comprehensive efficiency η of the electric boiler deviates from the design value by more than 5%, preferentially adjust L ch and C ch .

5. The method of static power flow analysis of an electric-thermal hybrid system according to claim 4, wherein, The capacitive susceptance B in S34 ch Also included is:

6. The method of static power flow analysis of an electric-thermal hybrid system according to claim 5, wherein, The comprehensive efficiency η of the electric boiler is represented as:

7. The method of static power flow analysis of an electric-thermal hybrid system according to claim 6, wherein, The unified solution of static power flow in S4 comprises: S41, construction of electric-thermal coupling unified solution framework: a unified solution framework of the electric-thermal mixed system is constructed based on the Newton-Raphson method, including an electric grid power flow calculation unit, a heat grid hydraulic calculation unit and a coupling interface unit; S42, variable initialization strategy: the variable initialization strategy comprises electric grid side initialization and heat grid side initialization, wherein The grid side initialization adopts a flat start mode, all PQ node voltage amplitudes are initialized to 1.0 p.u., the phase angle is set to 0°, and the PV node voltage amplitude takes a given value; The heat network side initialization adopts an improved equal-mooring resistance distribution method to calculate the pipe section flow, and calculates the initial value of the node pressure according to the outlet pressure of the heat source, which is represented as: where P j represents the path to node j, R l is the friction factor of pipe segment l; S43, a correction equation system is constructed: a Newton method in polar form is used to establish the correction equation of the grid side, the correction equation of the heat network is established based on the mass conservation and energy equation, and the coupling interface equation is constructed by taking the electric boiler as a connecting element, which is represented as: where G ij + jB ij are the nodal admittance matrix elements, θ ij = θ i - θ j , denotes the Hadamard product, Φ = diag(φ1,...,φs) is the friction coefficient matrix, L k is the set of pipe sections connected to electric boiler k; S44, coupling term processing: based on the original grid and heat network Jacobian matrix, an electric-heat coupling sub-block is added, which is represented as: S45, sparse matrix optimization: the Jacobian matrix is stored in CSR format, including reducing 40% storage by using the symmetry of the node admittance matrix, and optimizing the filling sequence based on the tree structure of the pipe network topology; S46, adaptive step size and convergence control: when the residual error reduction rate is less than 15% for two consecutive times, the step size reduction mechanism is triggered, and three-level criteria are set to ensure overall convergence.

8. The method of claim 7, wherein, The step size adjustment is represented as:

9. The method of claim 8, wherein, The three-level criteria include: Primary criterion: max(|ΔP|,|ΔQ|)≤ε1; Secondary criterion: ||Δq||2≤ε2; Auxiliary criterion: coupling variable variation ≤ 10 -5 .

10. A static power flow analysis system of an electrical-thermal hybrid system, for implementing the method of claim 1-9, wherein, The following modules are included: An electric-heat power equivalent modeling module: through heat power calculation, electric-heat power equivalent conversion and time domain synchronization processing, a dynamic correlation between electric power and heat flow is established, and an electric-heat power equivalent model for power flow analysis under a unified time scale is generated; A heating pipe network average temperature response modeling module: based on the energy conservation and heat transfer theory, a dynamic temperature response model considering electric-heat power input, thermal inertia and heat loss is constructed under the premise that the electric heating equipment water supply temperature and user return water temperature are known, and the pipe network temperature rise dynamic process and steady state characteristics are obtained; An electric boiler external characteristic equivalent modeling module: the electric boiler is modeled as a π-type equivalent circuit containing series impedance and parallel admittance, the resistance, inductance and capacitance parameters are calculated respectively, a mapping model between heat power demand and electric power, resistance change is constructed, and the influence of electromagnetic loss and leakage current is represented; A static power flow unified solution module: based on the Newton-Raphson method, an electric-heat coupling unified solution framework is constructed, a coupling interface equation of the grid and the heat network is established, the grid power flow calculation, heat network hydraulic calculation and coupling variable iterative update process are combined, an extended Jacobian matrix is constructed, and through sparse matrix optimization, adaptive step size control and three-level convergence criteria, the static power flow unified iterative solution of the electric-heat mixed system is realized.

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