Low-carbon scheduling method for integrated energy system

Abstract

The invention discloses a low-carbon scheduling method for an integrated energy system, and belongs to the technical field of energy scheduling. The method comprises the steps that a low-carbon scheduling model of the comprehensive energy system is constructed, and cost items defined in a segmented mode in the low-carbon scheduling model are smoothed; according to the low-carbon scheduling model, constructing a double-time-scale augmented quotient gradient dynamic system; carrying out fast and slow subsystem decomposition on the double-time-scale augmented quotient gradient dynamic system to obtain a fast subsystem for describing fast variable evolution and a slow subsystem for describing slow variable evolution; and finally, numerical integration solution is carried out on the fast subsystem and the slow subsystem in sequence, and a stable equilibrium point of the slow subsystem is obtained. The method can effectively solve the problems that in low-carbon scheduling of an existing comprehensive energy system, stepped carbon price modeling cannot be achieved, the electricity-gas coupling solving efficiency is low, and energy storage cost modeling is incomplete.

Description

Technical Field

[0001] This invention relates to the field of energy dispatching technology, and more specifically to a low-carbon dispatching method for integrated energy systems. Background Technology

[0002] Integrated energy systems, as a new type of energy supply system that integrates multiple energy forms such as electricity, natural gas, and heat, can effectively improve energy utilization efficiency, promote the consumption of renewable energy, and reduce carbon emissions through multi-energy complementarity and synergistic optimization.

[0003] Currently, integrated energy systems have the following shortcomings in low-carbon dispatching: 1. Existing technologies typically use piecewise or step functions to represent tiered carbon prices. These functions have discontinuities at carbon emission quota thresholds, and are neither continuous nor differentiable. During optimization, gradient-based nonlinear programming algorithms (such as interior-point methods and sequential quadratic programming) cannot calculate effective gradients at these discontinuities, leading to difficulties in convergence, low computational efficiency, and even the inability to find a feasible solution. Some studies employ mixed-integer programming methods to handle piecewise functions, but this significantly increases the problem size and computational complexity, making it difficult to meet the real-time scheduling requirements of large-scale systems.

[0004] 2. In integrated energy systems, the power system and the natural gas system are coupled through equipment such as gas turbines. The dynamic response time of the power system is typically in the millisecond to second range, while the response time of the natural gas system, due to pipeline transmission delays, compressor operation, and other factors, is in the minute to hour range, indicating a significant time scale difference. Most existing technologies employ a unified time scale modeling approach, treating the power-gas system as a whole for optimization, failing to fully utilize the system's time scale separation characteristics. This method results in high-dimensional optimization models, complex constraints, and high computational costs, especially when considering detailed AC power flow constraints and nonlinear flow equations in natural gas pipeline networks, making it difficult to meet practical application requirements in terms of solution time.

[0005] 3. Energy storage systems play a crucial role in integrated energy systems, including peak shaving, valley filling, and mitigating fluctuations in renewable energy sources. Current energy storage optimization models typically only consider the charging and discharging power cost or simple linear depreciation cost, neglecting the lifespan degradation characteristics of energy storage batteries. In reality, the cycle life of energy storage batteries is closely related to operating conditions such as depth of discharge and charge / discharge rate, exhibiting a significant non-linear degradation pattern. If lifespan degradation costs are not considered in optimized scheduling, frequent deep charging and discharging may occur, accelerating battery aging, shortening actual lifespan, increasing total lifespan costs, and impacting the economic viability of energy storage investment.

[0006] 4. Renewable energy output exhibits randomness and volatility, necessitating multi-scenario optimization methods to address uncertainty. Existing technologies typically employ scenario enumeration or Monte Carlo methods when handling multi-scenario optimization; however, increasing the number of scenarios leads to a dramatic expansion of the optimization problem size and an exponential increase in computational complexity. Particularly when considering complex constraints such as tiered carbon pricing, electro-gas coupling, and energy storage lifetime, existing solution algorithms struggle to obtain high-quality solutions within a reasonable timeframe, limiting the practicality of these methods.

[0007] Therefore, there is an urgent need to propose a new technical solution to address the above problems. Summary of the Invention

[0008] In view of the above problems, the present invention is proposed to provide a low-carbon dispatching method for an integrated energy system that overcomes or at least partially solves the above problems.

[0009] To achieve the above objectives, the present invention adopts the following technical solution; This invention provides a low-carbon dispatching method for an integrated energy system, comprising the following steps: S1. Construct a low-carbon scheduling model for the integrated energy system, and smooth the segmented cost items in the low-carbon scheduling model. S2. Construct a dual-time-scale augmented quotient gradient dynamic system based on the low-carbon scheduling model, wherein the variables related to the power system are defined as fast variables and the variables related to the natural gas system are defined as slow variables. S3. Perform fast and slow subsystem decomposition on the dual-timescale augmented quotient gradient dynamic system to obtain a fast subsystem describing the evolution of fast variables and a slow subsystem describing the evolution of slow variables; S4. Numerical integration is performed sequentially on the fast subsystem and the slow subsystem to obtain the stable equilibrium point of the slow subsystem. The stable equilibrium point of the slow subsystem is the optimal solution of the low-carbon scheduling optimization model of the integrated energy system. The obtained optimal solution is used as a control command and sent to the power generation equipment and gas supply equipment in the integrated energy system for execution.

[0010] Preferably, in S1, the segmented cost items defined in the low-carbon scheduling model are smoothed, including: Within the neighborhood of each cost jump point, a smooth approximate model is obtained by using a low-order polynomial function for smooth concatenation. The smooth approximation model remains consistent with the original cost term function outside the neighborhood. When the neighborhood width approaches zero, the obtained solution converges to the solution of the original cost term function.

[0011] Preferably, in S2, the relevant variables include control variables and state variables. The state variables depend on the control variables. The control variables of the power system are the voltage amplitude and active power of the PV nodes, and the control variables of the natural gas system are the gas source injection and pressure.

[0012] Preferably, in S2, a dual-timescale augmented quotient gradient dynamic system is constructed, including: S21. Simplify the low-carbon dispatch model based on the relevant variables of the power system and the natural gas system; S22. The inequality constraints in the simplified low-carbon scheduling model are transformed into equality constraints by introducing slack variables, forming an optimization problem under equality constraints. S23. Based on the optimization problem under the aforementioned equality constraints, construct the following dynamic system:

[0013]

[0014] in, For slow dynamical systems, For fast dynamic systems, For fast power variables, For the control variables of the electric system, For the state variables of the electric system, For the slack variables of the electrical system, For slow natural gas variables, For the control variables of the natural gas system, For the state variables of the natural gas system, For the slack variables of the natural gas system, It is a punishment factor. It is a positive scalar. It is a Jacobian matrix. Let be the vector of the slow natural gas constraint set. For fast power system constraint vectors, This is the objective function of the low-carbon scheduling model.

[0015] Preferably, in S3, the fast and slow subsystem decomposition of the dual-time-scale augmented quotient gradient dynamic system includes: By Setting it to zero, we get the slow subsystem:

[0016]

[0017] By fixing the slow variable The fast subsystem is obtained as follows:

[0018] .

[0019] Preferably, in step S4, numerical integration is performed on the fast subsystem and the slow subsystem, including: With the slow variable fixed, the fast subsystem is numerically integrated using the fourth-order Runge-Kutta method until the fast subsystem reaches a quasi-equilibrium state. Using the quasi-equilibrium solution of the fast subsystem as the initial point, the slow subsystem is numerically integrated using the fourth-order Runge-Kutta method until the stable equilibrium point of the slow subsystem is reached.

[0020] Preferably, the low-carbon dispatch model takes minimizing total operating cost as its objective function, and the objective function includes at least one or more of the following: thermal power unit power generation cost, carbon emission cost, grid loss cost, green certificate trading cost, and wind and solar curtailment penalty cost.

[0021] Preferably, the trading volume of green certificates is coupled into the calculation of carbon emission costs in the form of equivalent carbon emission reductions, and the relationship is defined by the following formula:

[0022]

[0023] In the formula: This refers to the actual carbon trading volume. This represents the actual total carbon emissions. For carbon quotas, This is the green certificate conversion factor. For the amount of green certificate conversion, For the total number of green certificates, This represents the actual number of green certificates traded.

[0024] Preferably, the low-carbon dispatch model includes power system constraints and natural gas system constraints; The power system constraints include node power balance constraints, node voltage amplitude constraints, phase angle difference constraints, branch thermal stability capacity constraints, and / or generator output and ramping constraints. The natural gas system constraints include new energy output constraints, energy storage device operation constraints, green certificate conversion constraints, and / or a set of natural gas system safety constraints.

[0025] The low-carbon scheduling method for integrated energy systems provided by this invention first transforms the stepped carbon price model into a smooth approximation model, then constructs a dual-timescale augmented quotient gradient system and performs fast-slow decomposition. When solving the fast subsystem, the slow variables of the gas system are fixed, and the fourth-order Runge-Kutta method is used to numerically integrate the fast variables of the electrical system until a quasi-equilibrium state is reached. When solving the slow subsystem, the quasi-equilibrium solution of the fast system is used as the initial point, and the slow variables of the gas system are integrated until a stable equilibrium point is reached. This algorithm fully utilizes the time-scale separation characteristics of the system, avoids the curse of dimensionality caused by the strong coupling between the electrical and gas systems in traditional methods, and significantly improves the solution efficiency and numerical stability.

[0026] Compared with the prior art, the beneficial effects of the above-mentioned technical solutions provided by the embodiments of the present invention include at least the following: 1. Propose using a family Smoothing functions replace the original "step" relationship to obtain a unified equation that is differentiable everywhere without changing the physical meaning, which is convenient for numerical solutions. 2. By using the dual-timescale augmented quotient gradient system solution method, the original optimization problem is transformed into a problem of searching for the stable equilibrium point of the dynamic system, so as to make full use of the physical characteristic that the response time scale of the electric system in the integrated energy system is much faster than that of the gas system. 3. A low-carbon dispatch model for integrated energy systems that considers the cost of energy storage lifespan degradation and energy storage constraints is proposed; 4. A scenario generation architecture of "single typical day - multiple sub-scenarios" is proposed, which effectively portrays the random fluctuation characteristics of wind and solar power output while maintaining intraday structural consistency, avoiding the deep cycle problem caused by over-reliance on a single prediction curve, and effectively extending the service life of energy storage. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0028] Figure 1 This is a flowchart of the low-carbon dispatching method for the integrated energy system of the present invention; Figure 2 This is the smoothed carbon price curve of this invention; Figure 3 This is a flowchart illustrating the low-carbon dispatching method for the integrated energy system of the present invention. Figure 4 This invention provides a scenario for photovoltaic and wind power prediction and system load diagrams. Figure 5This is a 3D perspective view of photovoltaic power output in multiple scenarios according to the present invention; Figure 6 This is an hourly carbon emission diagram for scenario one in this embodiment of the invention; Figure 7 This is a cost breakdown diagram for scenario one in an embodiment of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] This invention discloses a low-carbon scheduling method for integrated energy systems. It mainly addresses the non-differentiability problem caused by the step function in the tiered carbon trading mechanism by proposing a smooth approximate tiered carbon price model. The method uses a low-order polynomial compact support splicing method to smooth the breakpoint jumps in the local interval, ensuring that the function is differentiable everywhere and converges to the original tiered model in the limiting sense.

[0031] Then, considering the dual-timescale characteristics of the electro-gas system, a dual-timescale augmented quotient gradient system is constructed. The electro-gas system is solved separately as a fast subsystem and the gas system as a slow subsystem through fast-slow dynamic decomposition. The fourth-order Runge-Kutta method is used for numerical integration, and the stable equilibrium point of the system is the optimal solution of the model.

[0032] This invention can effectively solve the problem of optimal scheduling of integrated energy systems with tiered carbon pricing, and improve the solution efficiency and convergence.

[0033] In one embodiment, such as Figure 1 The method includes the following steps: S1. Construct a low-carbon scheduling model for the integrated energy system, and smooth the segmented cost items in the low-carbon scheduling model. S2. Construct a dual-time-scale augmented quotient gradient dynamic system based on the low-carbon scheduling model, wherein the variables related to the power system are defined as fast variables and the variables related to the natural gas system are defined as slow variables. S3. Perform fast and slow subsystem decomposition on the dual-timescale augmented quotient gradient dynamic system to obtain a fast subsystem describing the evolution of fast variables and a slow subsystem describing the evolution of slow variables; S4. Perform numerical integration on the fast subsystem and the slow subsystem in sequence to obtain the stable equilibrium point of the slow subsystem, and take it as the optimal solution of the low-carbon scheduling optimization model of the integrated energy system. Use the obtained optimal solution as a control command and send it to the power generation equipment and gas supply equipment in the integrated energy system for execution.

[0034] In one optional embodiment, step S1 first constructs a low-carbon dispatch model for the integrated energy system. This model uses the minimization of total operating cost as its objective function and incorporates physical constraints for both the power system and the natural gas system.

[0035] In some implementation plans, the objective function comprehensively considers power generation costs, carbon emission costs, wind and solar curtailment penalty costs, and green certificate trading revenue; its form is as follows: (1) In the formula: The overall objective function of the low-carbon dispatch model consists of power generation cost, carbon emission cost, grid loss, and penalties for renewable energy absorption rate. For the cost of electricity generation; Cost of carbon emissions; for In the scene Wind curtailment power during certain periods; This is the wind curtailment penalty coefficient; for In the scene Wasted power during specific time periods; This is the penalty coefficient for discarded light; This represents the total number of scenes; Equivalent benefits from green certificates for new energy conversion; It is the cost of power grid losses.

[0036] further, 1) Electricity generation cost for: (2) In the formula: This represents the total number of scenes; Total running time; The number of thermal power units involved in operation; For the scene Lower thermal power unit exist Output power during the time period; 、 、 for thermal power units The cost coefficient.

[0037] Considering factors such as comprehensive operation and maintenance, depreciation, and environmental protection costs, the cost per kilowatt-hour for conventional coal-fired power units in China is typically in the range of 0.30–0.40 yuan / kWh. Within the load fluctuation range considered in this application, the incremental heat consumption curve of the unit is approximately linear, and the contribution of the quadratic term to the marginal cost is negligible; at the same time, the constant term only produces a constant shift and does not affect the relative comparison in the optimization decision. Therefore, the cost function of thermal power is represented linearly, retaining only the coefficients of the first-order term.

[0038] 2) Carbon emission costs Introducing a "tiered carbon emission cost" model, in the form of: (3) In the formula: For the basic carbon price, this application uses the national carbon market composite price of 66.07 yuan / ton in 2025; The negative half-axis is used as a dynamic constraint on return growth factors. The length of the carbon trading range; This refers to the actual carbon trading volume; The positive half-axis is used to dynamically constrain the price growth factor.

[0039] In one embodiment, because the carbon emission cost includes piecewise linear constraints with jump discontinuities, the KKT conditions are non-differentiable at the discontinuities, which can easily lead to difficulties in nonlinear programming convergence or increased computation time. Therefore, this embodiment proposes to use a family of... The smoothing function replaces the original "on / off / step / saturation" relationship: it changes the transition at each breakpoint within a certain width. Within a local interval, low-order polynomials are used for tight support and splicing; when At this point, the solution of the smooth model is externally consistent with any solution of the original model, and converges to the hard-step model in the limiting sense, thus achieving a uniformly differentiable solution without changing the economic meaning. equation This facilitates numerical solutions.

[0040] When applied to the carbon emission costs of this application, the breakpoint is... At each breakpoint neighborhood Internal introduction nuclear Construct 5 smooth segments as follows: (4) The smoothed carbon price curve is as follows Figure 2 As shown, this structure possesses the following properties: a. Locality: Only Since the integer part is non-zero, smoothing only works near the breakpoint. b. Differentiability and Alignment: The function value and first derivative are completely consistent with the adjacent plateau segment at all breakpoints, and the global domain is [not specified].C ¹ ; c. Monotonic slope: Marginal carbon price The monotony remains unchanged, maintaining the original economic meaning of "increasing penalties" in the ladder; d. Equivalent limit: when hour, As the point states become consistent, the marginal price also converges point by point to the original platform slope.

[0041] In this embodiment, to balance numerical stability and approximation accuracy, Taking 2%–10% of the step width as the empirically feasible range, the preferred value is... ; The smaller the value, the closer it is to a hard step, but the peak value of the derivative is sharper and the condition number increases; Slightly enlarging the curve can significantly improve the quality of the line search and the Newtonian direction. The final smoothed carbon price curve is shown in Figure 2.

[0042] Furthermore, 3) Grid loss cost for: (5) (6) in, This is the network loss penalty coefficient; This is due to network loss in the system. For the scene Lower thermal power unit exist Output power during the time period; Wind power and solar power respectively S Scene t Output value at any given moment; , Scenes Next Taiwan Energy Storage The discharge and charging power at any given time are represented as non-negative scalars (power amplitude) and do not contain directional information; For the scene Down Busbar of Time Active load.

[0043] 4) Equivalent benefits of green certificates for new energy conversion for: (7) In the formula: The price per unit of green certificate; This refers to the actual number of green certificates traded. The additional revenue generated by green certificates mainly comes from the independent pricing of the "environmental value" of green electricity and the requirements of key customers for the proportion of renewable electricity. For example, Apple requires its supply chain to shift to 100% renewable electricity, and companies use qualified green electricity attribute certificates.

[0044] To further optimize the aforementioned technical solutions, enhance the self-regulation motivation of market players, improve the generation and consumption of new energy sources, and achieve energy conservation and emission reduction, this application proposes a carbon-green certificate coordination mechanism: allowing green certificates to be converted into equivalent emission reductions within a limited proportion and incorporated into the optimization; simultaneously setting constraints such as a proportion ceiling, temporal and spatial consistency, and one-time write-off to avoid double counting. Thus, carbon prices and green certificate prices are mapped to the same comparable marginal scale—when the carbon price is higher than the unit cost of the green certificate after conversion, entities tend to purchase and write off certificates, reducing fossil fuel output; conversely, they do not write off certificates or resell them. This mechanism, referencing existing policy practices and with clear boundaries, can improve the output and utilization rate of new energy sources and reduce system carbon costs under the drive of price signals.

[0045] Specifically, Actual carbon trading volume for: (8) Actual number of green certificates traded for: (9) In the formula: This represents the actual total carbon emissions. For carbon quotas, This is the green certificate conversion factor. For the amount of green certificate conversion, This represents the total number of green certificates.

[0046] and

[0047] (10) In the formula: As a carbon emission factor, This is the carbon quota coefficient. For thermal power units Optimization in multiple scenarios The optimal output power for a given time period.

[0048] In some implementations, the constraints of the low-carbon scheduling model of the present invention include: (1) Node power balance constraints:

[0049]

[0050]

[0051] (11) In the formula, Scenes Down Time bus Net injected active power and reactive power; To connect to the busbar A combination of thermal power, wind power, solar power, and energy storage; Scenes Down Busbar of Time Active and reactive loads; Scenes Down Time bus and busbar The voltage amplitude; busbars and busbar The electrical conductance and susceptance between them; Scenes Down Time bus and busbar The voltage phase angle.

[0052] (2) Node voltage amplitude constraints: (12) In the formula and busbar Permissible upper and lower voltage limits.

[0053] (3) Phase angle difference constraint: (13) In the formula busbar and busbar The maximum allowable phase angle difference between them.

[0054] (4) Branch thermal stability capacity constraint: , ,

[0055] , , (14) In the formula, and busbar Flow to bus The apparent power amplitude and current amplitude; and busbar Flow to bus The apparent power amplitude and current amplitude; branch road Rated thermal stability capacity; branch road The rated current limit.

[0056] (5) Generator output and climbing constraints: During operation, thermal power units must maintain their power output above the minimum generating capacity to ensure stable operation. If the power output falls below this threshold, the unit may enter an unstable state. Similarly, the unit's power output cannot exceed its maximum generating capacity to ensure safety. Thermal power units also face ramp-up constraints; the amount of power a thermal power unit can increase or decrease per unit time is limited. These constraints are: (15) In the formula: 、 Generators The lower and upper limits of active power output; 、 Generators The maximum downward slope value and the maximum upward slope value.

[0057] (6) Constraints on new energy output: The output of wind turbines and solar power is constrained by the upper limit of the wind and solar generator output. Furthermore, due to the uncertainty of wind and solar output, the predicted wind and solar output values ​​are used as the maximum available output during actual dispatch. The constraint formula is: (16) In the formula: 、 These are wind turbine and photovoltaic unit scenarios, respectively. Down Always making actual contributions; 、 These are the upper limits of active power output for wind turbines and photovoltaic units, respectively. 、 Wind power and photovoltaic scenarios respectively Down Predict output power at all times.

[0058] (7) Operational constraints of energy storage devices: (17) In the formula: 、 The first The lower and upper limits of the output power of the energy storage device; 、 Representing the scene respectively Next Taiwan energy storage device The discharge and charge status at any given time; For the scene Next Taiwan energy storage device The state of charge at any given moment; 、 The first The initial and maximum capacity of the energy storage device; 、 The first The charging and discharging efficiency of the energy storage device; 、 The first The lower and upper limits of the charge level of Taiwan's energy storage devices; 、 The first The initial state of charge and the cut-off state of charge of the energy storage device indicate whether the energy storage device can return to its initial storage level after one scheduling cycle.

[0059] (8) Green certificate conversion constraints: (18) In the formula, The maximum allowed green certificate conversion rate.

[0060] (9) Safety constraint set for natural gas systems: (19) (20) (twenty one) (twenty two) (twenty three) (twenty four) (25) （ 26) (27) in, ， ， This represents the electro-gas conversion coefficient of the gas turbine unit. C mn Indicates natural gas pipeline mn The Weymouth constant, It is the compression ratio of the compressor. F G This refers to the natural gas consumption of the gas generator. It is gas source node injection, It is natural gas load. This refers to the gas consumption of the compressor. It is through the gas flow rate of the compressor. F mn Through pipes mn gas flow rate, π It is node pressure.

[0061] In some optional embodiments, step S2, constructing a dual-timescale augmented quotient gradient dynamic system based on the low-carbon scheduling model, includes the following steps: S21. Simplify the model based on the control variables and state variables in the low-carbon scheduling model; In this embodiment, the control variable The control variables for the electrical system are the voltage amplitude and active power at the PV nodes, while the control variables for the gas system are the gas injection and pressure. State variables. It depends on the control variable and can be represented by the control variable.

[0062] Based on the low-carbon dispatch model of the integrated energy system, its state variables and control variables can be related through equations 11-27, which can be concisely expressed as the following equations:

[0063] (28) in and These represent equation constraints 11 for the power system and equation constraints 19-22 for the natural gas system, respectively. and These represent inequality constraints 12-18 for the power system and inequality constraints 23-27 for the natural gas system, respectively. Control variables for the electrical system and the pneumatic system, respectively. These are the state variables for the electrical system and the gas system, respectively.

[0064] S22. The inequality constraints in the simplified model are transformed into equality constraints by introducing slack variables, forming an optimization problem under equality constraints:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] （ 29) in These are the slack variables for the electrical system and the pneumatic system, respectively.

[0071] Based on the above transformation, the low-carbon dispatch model for integrated energy bases can be concisely represented as follows:

[0072] (30) S23. Because the electrical system in an integrated energy system has an extremely short action and response time scale, much faster than that of the gas system, it naturally possesses a dual time scale characteristic. Therefore, combining the dual time scale characteristics of the low-carbon dispatch model of the integrated energy system, this application proposes a class of dual-time scale nonlinear dynamic systems—dual-time scale augmented quotient gradient systems—to solve the low-carbon dispatch model of the integrated energy base. In this dynamic system, the variables of the electrical system are treated as fast variables, and the variables of the gas system are treated as slow variables.

[0073] Specifically, the dynamic system constructed based on the optimization problem under the aforementioned equality constraints is as follows:

[0074] (31) in, For fast power variables, For slow natural gas variables, It is a penalty factor, a sufficiently large positive scalar, and For a sufficiently small positive scalar. Because Small enough, if the function and Having the same magnitude means that the variables The rate of change is greater than that of the variable The changes are happening much faster.

[0075] It is a system The equilibrium point satisfies:

[0076]

[0077] If for the equilibrium point An equilibrium point is a stable equilibrium point when all eigenvalues ​​of its Jacobian matrix have negative real parts.

[0078] The stable equilibrium point of the dual-time-scale augmented quotient gradient system constructed by the integrated energy system low-carbon scheduling model corresponds to the optimal solution of the integrated energy system low-carbon scheduling model. Therefore, solving for the optimal solution of the integrated energy system low-carbon scheduling model is equivalently transformed into searching for the stable equilibrium point of the dual-time-scale augmented quotient gradient system.

[0079] In some embodiments, step S3 involves decomposing the dual-timescale augmented quotient gradient dynamic system into fast and slow subsystems to obtain a fast subsystem describing the evolution of fast variables and a slow subsystem describing the evolution of slow variables.

[0080] In this embodiment, the gradient system of the augmented quotient at two time scales can be solved efficiently by performing fast and slow dynamic decomposition. The decomposition of the fast and slow dynamic system involves constructing two price reduction subsystems, fast and slow.

[0081] Slow systems: Focus on solving slow variables in the gas system. The dynamic process of the electric system is then ignored. The dynamic process, the slow system can be achieved by using 31... get:

[0082] (32) Fast systems: Focuses on the study of fast variables in electrical systems The dynamic process is assumed to be negligible in terms of slow variable changes. The fast system can be obtained through transformation (31):

[0083] (33) By setting A fast system can be obtained:

[0084] (34) in, If it is a fixed quantity, it can be regarded as a fixed control variable.

[0085] In some embodiments, numerical integration is performed sequentially on the fast subsystem and the slow subsystem in step S4 to obtain the stable equilibrium point of the slow subsystem, which is then used as the optimal solution of the low-carbon scheduling optimization model of the integrated energy system. The obtained optimal solution is then used as a control command and sent to the power generation equipment and gas supply equipment in the integrated energy system for execution.

[0086] In this application, such as Figure 3 The complete low-carbon scheduling steps include: Step 1: Construct a low-carbon scheduling model for integrated energy bases; Input data from the integrated energy base system and construct the objective function and constraints of the low-carbon scheduling model for the integrated energy base. Step 2: Convert the tiered carbon emission model of the integrated energy base low-carbon dispatch model into a smooth approximate tiered carbon price model; Step 3: Construct a dual-timescale augmented quotient gradient system; Step 4: Initialize system parameters; Set initial control variables for the electrical system, including PV node voltage amplitude and active power. Set initial control variables for the gas system, including gas source injection and node pressure. Initialize Lagrange multipliers and relaxation variables. Set the penalty factor to a sufficiently large positive scalar, the time scale parameter to be between 0.0001 and 0.001, and the convergence accuracy threshold to 10 to the power of -6.

[0087] Step 5: Construct the corresponding fast dynamics system; Step 6: Fix the slow variable, randomly select an initial point, and use the fourth-order Runge-Kutta method to numerically integrate the fast dynamics system until it reaches a stable equilibrium point of the fast dynamics system. Step 7: Construct the corresponding slow dynamics system; Step 8: Using the stable equilibrium point of the fast dynamic system as the initial point, numerically integrate the slow dynamic system using the fourth-order Runge-Kutta method until the integration reaches a stable equilibrium point of the slow dynamic system. Step 9: The stable equilibrium point of the slow dynamics system obtained is also the stable equilibrium point of the dual-time-scale augmented quotient gradient system, and it is also the optimal solution of the low-carbon scheduling model of the integrated energy base. The calculation is terminated.

[0088] Furthermore, in an exemplary embodiment, taking a certain integrated energy system (IES) in Ningxia as the research object, since the constructed model contains nonlinear constraints, in order to ensure the accuracy and stability of the solution, the IPOPT solver under the MATLAB platform is used for numerical solution.

[0089] To verify the applicability and universality of the model, simulation analysis was conducted on a 9-node system and a 118-node system, respectively.

[0090] Step 1: Basic Data and Scenario Construction; This paper uses 24-hour and 1-hour resolutions as scheduling cycles. Wind power, photovoltaic power, and system load are all derived from measured data, which are then incorporated into the model after outlier removal and unified resampling to ensure consistency in different dimensions and time alignment.

[0091] To characterize forecast uncertainty without introducing too many scenarios, K-means clustering was first used to extract typical days from the daily curves over 30 consecutive days. Then, using a typical day as the center, its neighborhood samples were subdivided into five sub-scenarios based on Euclidean distance, forming a scenario set of "single typical day – multiple sub-scenarios". This design achieves a balance between representativeness and comparability: preserving the consistency of intraday structure while controlling amplitude and phase differences across scenarios, ensuring comparability of the marginal effects of subsequent carbon trading, green certificates, multi-scenario optimization, and energy storage strategies. Figure 4 The study demonstrates typical intraday characteristics of Scenario 1: photovoltaic power forms a stable single peak at midday, while the load peak occurs in the evening, showing a significant temporal misalignment; wind power fluctuates considerably at night. This temporal difference between output and load leads to significant time-of-use (TOU) price fluctuations, echoing the use of TOU pricing in this paper. Subsequent cost decomposition, TOU analysis of carbon emissions, and analysis of wind and solar curtailment distribution are all based on this load-renewable energy output mismatch. Step 2: Analysis of single-scenario optimization results; Figure 5 The system supply and demand balance under Scenario 1 is demonstrated. Overall, the load is relatively stable, with fluctuations in wind and solar power output causing conventional units to dynamically adjust at different times. During the day, increased solar power output leads to decreased unit output, which then rebounds in the evening as solar power output declines. The results show that the system operation under this single scenario already demonstrates the direct impact of renewable energy fluctuations on the dispatch structure. Energy storage effectively buffers renewable energy fluctuations under this single scenario, playing a positive role in smoothing system dispatch and improving economic efficiency. Figure 6 and Figure 7 The time-of-use carbon emissions and cost breakdown results for Scenario 1 are presented separately. Figure 6It is evident that carbon emissions are mainly concentrated in the evening and nighttime hours, corresponding to the ramp-up and load increase phases of conventional units. Emissions decrease significantly during the day when photovoltaic output is sufficient, demonstrating the role of renewable energy in reducing the carbon intensity of the system. Figure 7 The data shows that the cost of thermal power fuel accounts for the highest proportion of the total cost, approximately 79%, which is the dominant factor in the system's economics. The operating and depreciation costs of energy storage account for a smaller proportion, but they play a positive role in time-of-use arbitrage and peak-valley regulation. Although carbon emission costs and green certificate revenues account for a limited proportion, they have a structural impact on the adjustment of marginal costs and revenues.

[0092] Overall, the results of the single-scenario operation reflect that the system cost is highly dependent on the fossil energy output structure, and also verify the necessity of time-sharing and carbon-constrained optimization.

[0093] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0094] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A low-carbon dispatching method for an integrated energy system, characterized in that, include: S1. Construct a low-carbon scheduling model for the integrated energy system, and smooth the segmented cost items in the low-carbon scheduling model. S2. Construct a dual-time-scale augmented quotient gradient dynamic system based on the low-carbon scheduling model, wherein the variables related to the power system are defined as fast variables and the variables related to the natural gas system are defined as slow variables. S3. Perform fast and slow subsystem decomposition on the dual-timescale augmented quotient gradient dynamic system to obtain a fast subsystem describing the evolution of fast variables and a slow subsystem describing the evolution of slow variables; S4. Numerical integration is performed sequentially on the fast subsystem and the slow subsystem to obtain the stable equilibrium point of the slow subsystem. The stable equilibrium point of the slow subsystem is the optimal solution of the low-carbon scheduling model.

2. The low-carbon dispatching method for integrated energy systems according to claim 1, characterized in that, In S1, the cost items defined in the segmented form in the low-carbon scheduling model are smoothed, including: Within the neighborhood of each cost jump point, a low-order polynomial function is used for smooth splicing; The concatenated cost term remains consistent with the original cost term function outside the neighborhood. When the neighborhood width approaches zero, the solution converges to the solution of the original cost term function.

3. The low-carbon dispatching method for integrated energy systems according to claim 1, characterized in that, In S2, the relevant variables include control variables and state variables. The state variables depend on the control variables. The control variables of the power system are the voltage amplitude and active power of the PV nodes, and the control variables of the natural gas system are the gas source injection and pressure.

4. The low-carbon dispatching method for integrated energy systems according to claim 1 or 3, characterized in that, In S2, a dynamic system of augmented quotient gradients with two time scales is constructed, including: S21. Simplify the low-carbon dispatch model based on the relevant variables of the power system and the natural gas system; S22. The inequality constraints in the simplified low-carbon scheduling model are transformed into equality constraints by introducing slack variables, forming an optimization problem under equality constraints. S23. Based on the optimization problem under the aforementioned equality constraints, construct the following dynamic system: in, For slow dynamical systems, For fast dynamic systems, For fast power variables, For the control variables of the electric system, For the state variables of the electric system, For the slack variables of the electrical system, For slow natural gas variables, For the control variables of the natural gas system, For the state variables of the natural gas system, For the slack variables of the natural gas system, It is a punishment factor. It is a positive scalar. It is a Jacobian matrix. Let be the vector of the slow natural gas constraint set. For fast power system constraint vectors, This is the objective function of the low-carbon scheduling model.

5. The low-carbon dispatching method for integrated energy systems according to claim 4, characterized in that, In S3, the dual-time-scale augmented quotient gradient dynamic system is decomposed into fast and slow subsystems, including: By Setting it to zero, we get the slow subsystem: By fixing the slow variable We obtain the fast subsystem: 。 6. The low-carbon dispatching method for integrated energy systems according to claim 1, characterized in that, In step S4, numerical integration is performed on the fast subsystem and the slow subsystem, including: With the slow variable fixed, the fast subsystem is numerically integrated using the fourth-order Runge-Kutta method until the fast subsystem reaches a quasi-equilibrium state. Using the quasi-equilibrium solution of the fast subsystem as the initial point, the slow subsystem is numerically integrated using the fourth-order Runge-Kutta method until the stable equilibrium point of the slow subsystem is reached.

7. The low-carbon dispatching method for integrated energy systems according to claim 1, characterized in that, The low-carbon dispatch model takes minimizing total operating costs as its objective function. The objective function includes at least one or more of the following: thermal power unit generation costs, carbon emission costs, grid loss costs, green certificate trading costs, and wind and solar curtailment penalty costs.

8. The low-carbon dispatching method for integrated energy systems according to claim 7, characterized in that, The trading volume of green certificates is coupled into the calculation of carbon emission costs in the form of equivalent carbon emission reductions, and the relationship is defined by the following formula: In the formula: This refers to the actual carbon trading volume. This represents the actual total carbon emissions. For carbon quotas, This is the green certificate conversion factor. For the amount of green certificate conversion, For the total number of green certificates, This represents the actual number of green certificates traded.

9. The low-carbon dispatching method for integrated energy systems according to claim 7, characterized in that, The low-carbon dispatch model includes power system constraints and natural gas system constraints; The power system constraints include node power balance constraints, node voltage amplitude constraints, phase angle difference constraints, branch thermal stability capacity constraints, and / or generator output and ramping constraints. The natural gas system constraints include new energy output constraints, energy storage device operation constraints, green certificate conversion constraints, and / or a set of natural gas system safety constraints.

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