A probabilistic day-ahead market transaction method considering time value and virtual inertia

Abstract

The application belongs to the field of power market, and discloses a probabilistic day-ahead market transaction method considering time value and virtual inertia, which generates a probabilistic prediction corridor of next-day load and wind-solar output by using a TCN-LSTM hybrid model and quantile regression technology; if wind power, photovoltaic and energy storage systems are selected as virtual inertia suppliers, their rapid power regulation capacity is quantified as equivalent inertia products to participate in declaration; based on the inertia demand of the scene in the prediction corridor, a probabilistic inertia safety constraint and virtual inertia credibility constraint are established; an improved Aumann-Shapley method considering time value coefficient is used for inertia cost allocation. A joint clearing model is solved with the minimum total cost of the power generation side as the target, the application expands the inertia supply, improves the robustness of the system in dealing with uncertainty through probabilistic constraints, and uses clear economic signals to encourage resources to provide support in critical periods.

Description

Technical Field

[0001] This invention belongs to the field of electricity market technology, specifically relating to a probabilistic day-ahead market trading method that considers time value and virtual inertia. Background Technology

[0002] With the advancement of "dual-carbon" energy conservation, the penetration rate of fluctuating renewable energy sources such as wind power and photovoltaics in the power system has increased dramatically, posing unprecedented challenges to maintaining real-time power balance and frequency stability. The large-scale replacement of traditional synchronous generators has led to a continuous decline in system inertial response capability and a significant increase in the risk of frequency instability. To ensure grid security, it is necessary to quantitatively and cost-effectively acquire sufficient inertial support services.

[0003] Currently, although wind power, photovoltaics, and energy storage can provide rapid virtual inertia support through power electronic devices, existing inertia demand assessments and market constraints largely rely on deterministic new energy output and load forecasts at the prediction and modeling levels, failing to fully consider the power fluctuation uncertainties caused by high-proportion new energy grid connection. While existing technologies include new energy power forecasting methods based on BiLSTM-TPA-MTCN, QTCN-stochastic LSTM, and LSTM combination frameworks that can improve single-point forecast accuracy, they all focus on deterministic forecasting or simple accuracy optimization, without incorporating quantile regression techniques to generate probabilistic forecast corridors to characterize uncertainty boundaries. Furthermore, some studies employ methods such as bibliometric chance constraint optimization to address uncertainty, but these largely focus on reserve capacity pricing, failing to deeply integrate uncertainty modeling with the inertia service market. This results in overly conservative market clearing outcomes or insufficient safety margins, failing to balance system robustness and operational economics.

[0004] At the resource mobilization level, the existing market typically only recognizes the physical inertia provided by synchronous generators. Its trading model is essentially based on the procurement of physical characteristics of the unit in grid-connected state, and virtual inertia has not yet been incorporated into the standardized market product system. Although there are technologies that can achieve virtual inertia control through power electronic devices such as energy storage converters, and related patents (such as CN116885733A) have mentioned incorporating virtual inertia compensation costs into the power system optimization operation model and considering the power regulation constraints of new energy and energy storage, this solution only treats virtual inertia as an auxiliary constraint item. It cannot achieve independent declaration, measurement and settlement of virtual inertia, and the huge potential inertia supply resources have not been effectively activated, which is contrary to the market development trend of "source-grid-load-storage" collaborative participation in ancillary services.

[0005] At the level of economic signals, existing cost allocation methods (such as the Aumann-Shapley value method) often fail to accurately characterize the spatiotemporal value differences supported by inertia, and their model basis also does not take uncertainty into account. This makes it difficult to provide sufficiently accurate economic incentives for resources that provide critical services during the most vulnerable period of the system, thus failing to optimally guide investment and operational behavior. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a probabilistic day-ahead market trading method that considers time value and virtual inertia. This method can enhance the system's robustness in the face of uncertainty and effectively allocate inertia responsibility through probabilistic constraints. It can stimulate diversified supply at the lowest economic cost and provide precise incentives for resources that provide services during the critical periods when the system needs them most, thereby achieving efficient market-based allocation of safe resources and providing strong support for the safe operation of high-proportion renewable energy power systems.

[0007] The probabilistic day-ahead market trading method considering time value and virtual inertia, as described in this invention, includes the following steps:

[0008] Step 1: Collect historical load data and preprocess it. Use the TCN-LSTM hybrid model and quantile regression technology to generate a probabilistic prediction corridor that describes the uncertainty of the future.

[0009] Step 2: If wind power, photovoltaic and energy storage systems are selected as virtual inertia, then wind farms, photovoltaic power plants and energy storage systems are defined as virtual inertia suppliers, the virtual inertia declaration method is defined, and they participate in the day-ahead market declaration of electrical energy and inertia capacity together with traditional synchronous generator sets.

[0010] Step 3: Evaluate the inertia requirements under adverse scenarios based on the lower boundary extreme scenarios in the probabilistic prediction corridor, and establish probabilistic inertia safety constraints and virtual inertia reliability constraints;

[0011] Step 4: Taking the minimization of the total cost of the generation side considering electricity trading and inertia service trading as the objective function, and combining the constraints, construct and solve the day-ahead electricity-inertia joint clearing market model to determine the clearing result;

[0012] Step 5: Based on the clearing results, the improved Aumann-Shapley value method, which takes into account the time value of money, is used to allocate inertia costs, so that virtual inertia providers who provide inertia services during critical periods can receive higher compensation.

[0013] Furthermore, step 1 specifically includes:

[0014] Step 1.1: Collect historical data, including grid load power, total output of wind farm clusters, total output of photovoltaic power station clusters, and corresponding meteorological data and time labels. Using the predicted time point n as the benchmark, extract the historical sequence {X1, X2, ..., X} for the preceding T time periods. n} constitutes a set R n As input features, it predicts the feature sequence {Y1,Y2,...,Y} for T time periods in the future. n} as the prediction target F n The input features and the prediction target constitute the training samples (R). n ,F n ); perform max-min normalization on all input feature data and prediction target data, scaling them to the [0,1] interval;

[0015] Step 1.2: Construct a TCN-LSTM hybrid prediction model, train the model using the quantile regression loss function, and generate probabilistic prediction corridors, including:

[0016] Step 1.2.1: The TCN-LSTM hybrid prediction model includes a TCN module, a Long Short-Term Memory (LSTM) network, and a quantile regression output layer;

[0017] The TCN module uses multi-layer dilated causal convolution to extract input features R. n The long-term cycle and trend characteristics are used to output the prediction target F. n :

[0018] (1)

[0019] Where n is the current time step, Let f be the feature value output after n convolution operations, f be the weight function of the convolution kernel, K be the size of the convolution kernel, d be the dilation factor, and k be the weight index within the convolution kernel. The input sequence is the value at historical time step nd·k;

[0020] Predict the target The entire input is a Long Short-Term Memory (LSTM) network, which outputs feature vectors containing rich temporal context. ;

[0021] Will The input quantile regression output layer simultaneously outputs predicted values ​​for multiple target quantiles at each prediction time interval t, forming the initial probabilistic prediction sequence. ;

[0022] Step 1.2.2: For each target quantile Define the quantile loss function:

[0023] (2)

[0024] (3)

[0025] Where u is the deviation between the predicted value and the actual value. ; y is the actual value; This represents the true value of the i-th training sample. For model output Quantile predicted value; N is the sample size;

[0026] The total loss of the TCN-LSTM hybrid prediction model is the sum of the losses of multiple target quantiles:

[0027] (4)

[0028] Where Q represents the set of target quantile levels, and the total loss is minimized using the backpropagation algorithm and gradient descent optimizer. ;

[0029] Step 1.2.3: Input feature data R corresponding to the prediction date. n Input the trained model and output the three-line prediction results for the next 24 hours, i.e., the lower boundary curve. Median curve Upper boundary curve Select the lower boundary curve With the upper boundary curve The area between these points constitutes the probabilistic prediction corridor.

[0030] Furthermore, step 2 specifically involves:

[0031] Divide the next day of operation into T time periods, t=1,2,...,T;

[0032] The equivalent virtual inertia capacity that virtual inertia provider j can provide during time period t. Calculated by the following formula:

[0033] (5)

[0034] in, The system's rated frequency, For rapid power regulation capacity, The response time constant;

[0035] This is a collection of virtual inertia providers, including only those generators that voluntarily declare their virtual inertia service; virtual inertia providers To predict the median curve of the corridor using probabilistic methods Based on this, declare the amount of electrical energy it is willing to sell. and corresponding quotes If a virtual inertia supplier chooses to declare virtual inertia, it should declare its fast power regulation capacity. Response time constant Equivalent virtual inertia capacity And the price of providing equivalent virtual inertia capacity services and promised to meet its requirements. ,in Contribute to the planned foundation of virtual inertia supplier j. To predict the lower boundary curve of the corridor using probabilistic methods;

[0036] Synchronous generator set Declare its electricity price quotation curve and its inherent technical parameters, including inertia constant. The actual physical inertia it can provide In the clearing model, the unit start-up state variables will be used. Decide; The rated apparent capacity of unit i; A collection of synchronous generator sets;

[0037] After collecting and verifying all declared data, the market operation agency forms the market declaration dataset D:

[0038] (6)

[0039] Where J is the inertial constant vector of the synchronous generator set. This is a virtual inertia capacity declaration matrix. For the set of all quotes.

[0040] Furthermore, step 3 specifically involves:

[0041] Step 3.1: Based on the probabilistic prediction of the lower boundary extreme scenarios in the corridor, evaluate the minimum inertia required to maintain frequency stability, including:

[0042] Calculate the net system load under extreme scenarios. :

[0043] (7)

[0044] in, This is the median of the load forecast. , The lower boundary is predicted for wind power and solar power;

[0045] Calculate the minimum inertia required by the system in time period t to meet frequency safety standards. The calculation formula is:

[0046] (8)

[0047] in, As the system's baseline capacity, The equivalent comprehensive frequency modulation coefficient of the system during time period t. It is a vector that changes over time. For the maximum allowable rate of frequency change, For the maximum allowable frequency deviation, The maximum power deficit for a single fault is preset.

[0048] Step 3.2: Establish probabilistic inertia safety constraints:

[0049] (9)

[0050] in, It is a binary start-up state variable of synchronous generator set i in time period t, where 1 indicates start-up and 0 indicates shutdown; This is the virtual inertia bid-winning status variable of virtual inertia supplier j in time period t. It is a continuous variable between 0 and 1, representing the proportion of its bid capacity to the declared capacity. The proportion;

[0051] Establish virtual inertia credibility constraints:

[0052] (10)

[0053] (11)

[0054] in, It is the power of electrical energy won by virtual inertia supplier j in time period t. This is the power regulation capacity that needs to be reserved to provide the virtual inertia for winning the bid.

[0055] Furthermore, step 4 specifically involves:

[0056] In the recent joint clearing market model of electricity and inertia, the total cost on the generation side is considered in relation to electricity trading and inertia service trading. Minimize the impact, clear out every 15 minutes:

[0057] (12)

[0058] (13)

[0059] (14)

[0060] in, To clear costs in the electricity market, Clearing out costs in the inertia market; , , , These represent the collections of synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems, respectively; g, w, pv, and e represent the synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems, respectively. The prices listed are for synchronous generator sets, wind turbine sets, photovoltaic units, and energy storage systems, respectively. These represent the rated power of electrical energy for synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems during time period t. For synchronous unit g, the start / stop status variable during time period t, 1 indicates running and 0 indicates stopping; The no-load cost of providing physical inertia services for synchronous generator unit g; Quotation for virtual inertia services from virtual inertia provider j;

[0061] The constraints are as follows:

[0062] System power balance constraints:

[0063] (15)

[0064] Operating constraints of synchronous generator sets:

[0065] (16)

[0066] (17)

[0067] (18)

[0068] in, , The unit output limit; , This is the limit for the gradient rate;

[0069] Wind power / solar power unit operating constraints:

[0070] (19)

[0071] Energy storage system operating constraints:

[0072] (20)

[0073] (twenty one)

[0074] (twenty two)

[0075] (twenty three)

[0076] in, , This refers to the charging / discharging power. The stored energy for time period t; , For charge / discharge efficiency; The duration of the time period; , Energy storage limit;

[0077] Virtual inertia reliability constraints:

[0078] (twenty four)

[0079] Probabilistic inertia safety constraints:

[0080] (25).

[0081] Furthermore, step 5 specifically includes:

[0082] Step 5.1: To quantify the differentiated value of inertia support at different time periods, define a time value coefficient. :

[0083] (26)

[0084] in, Indicates the time period The system inertia requirements;

[0085] Calculate the time-weighted inertia contribution of each actual inertia provider, a, including synchronous generator i and virtual inertia supplier j. :

[0086] (27)

[0087] in, The inertia actually provided by market participant a in time period t;

[0088] Step 5.2: Calculate the cost allocation ratio for each participant using the weighted contribution ratio method that considers time-series value. :

[0089] (28)

[0090] Where Ω represents the set of all market participants that actually provide inertia, and the denominator is the weighted contribution W of all participants in the set Ω. j The sum of them satisfies This ensures that all costs are shared.

[0091] According to the sharing ratio and inertia market clearing costs Calculate the final settlement amount that each market participant a should pay or receive. :

[0092] (29)

[0093] For synchronous generator sets, the settlement amount is positive, representing the portion of the fixed cost that should be recovered for providing physical inertia reserves to the system. For virtual inertia suppliers, the settlement amount is negative, and its absolute value is the economic compensation they receive for providing virtual inertia services.

[0094] The beneficial effects of this invention are as follows:

[0095] 1) This invention innovatively adopts a TCN-LSTM hybrid model and quantile regression to generate a probabilistic prediction corridor describing uncertainty, and evaluates inertia requirements based on extreme scenarios at its lower boundary, establishing probabilistic inertia safety constraints; it upgrades market clearing decisions from relying on a single prediction value to meeting safety standards under adverse scenarios, providing an endogenous guarantee for system frequency stability, fundamentally enhancing the robustness of high-proportion renewable energy power grids in the face of random fluctuations, and achieving an optimal balance between safety and economy;

[0096] 2) This invention clearly defines the role of the "virtual inertia supplier" and the standardized trading product of "equivalent virtual inertia capacity," and stipulates a quantitative application method based on rapid power regulation capacity and response time constant. It successfully incorporates a large number of new entities such as wind power, photovoltaics, and energy storage into the inertia supply system, realizing the coordinated participation of diverse resources from "source-grid-load-storage." Through joint clearing with electricity, it can efficiently mobilize flexible resources across society at the lowest economic cost, providing much-needed inertia support for the system.

[0097] 3) This invention proposes an "improved Aumann-Shapley value method that considers the value of time." The core improvement of this method lies in the introduction of a time value coefficient. When calculating the marginal contribution of each participant, the inertia they provide at different times is weighted differently. This improvement enables the unit inertia service provided during critical periods when system inertia is scarce and the risk of frequency instability is high (such as during peak loads or sudden drops in renewable energy) to obtain economic compensation far higher than during normal periods. This generates clear and accurate time-series price signals, optimally guiding and incentivizing market investment and operational behavior, and ensuring safe and reliable power supply during critical periods. Attached Figure Description

[0098] Figure 1 This is a flowchart of the method described in this invention;

[0099] Figure 2 This is a flowchart illustrating the market application and selection process for wind-solar-storage energy storage units according to the present invention.

[0100] Figure 3 This invention provides a probabilistic prediction corridor plot based on a TCN-LSTM hybrid model and quantile regression techniques, as an embodiment of the present invention.

[0101] Figure 4 A market clearing result diagram provided for one embodiment of the present invention;

[0102] Figure 5 A time value coefficient diagram of the improved Aumann-Shapley value method provided in an embodiment of the present invention. Detailed Implementation

[0103] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0104] like Figure 1 As shown, the probabilistic day-ahead market clearing method considering time value and virtual inertia of the present invention includes the following steps:

[0105] Step 1: Collect historical load data of grid load, photovoltaic power output, and wind power output, perform preprocessing such as cleaning and normalization, and use TCN-LSTM hybrid model and quantile regression technology to generate probabilistic prediction corridors (including upper, middle and lower boundary curves) that describe their future uncertainties.

[0106] Step 2: If wind power, photovoltaic and energy storage systems are selected as virtual inertia, then wind farms, photovoltaic power plants and energy storage systems are defined as virtual inertia suppliers, the virtual inertia declaration method is defined, and they participate in the day-ahead market declaration of electrical energy and inertia capacity together with traditional synchronous generator sets.

[0107] Step 3: Based on the lower boundary extreme scenario assessment system in the predicted corridor, evaluate the inertia requirements under harsh scenarios and establish probabilistic inertia safety constraints and virtual inertia reliability constraints;

[0108] Step 4: Taking the minimization of the total cost of the generation side considering electricity trading and inertia service trading as the objective function, and combining the constraints, construct and solve the day-ahead electricity-inertia joint clearing market model to determine the clearing result;

[0109] Step 5: Based on the clearing results, the improved Aumann-Shapley value method, which takes into account the time value of money, is used to allocate inertia costs. Different time value coefficients are defined for different time periods, and the marginal contribution of each unit is calculated so that virtual inertia suppliers that provide inertia services during critical periods can receive higher compensation.

[0110] Furthermore, step 1 specifically includes:

[0111] Step 1.1: The system collects historical data, including grid load power, total output of wind farm clusters, total output of photovoltaic power station clusters, and corresponding meteorological data (wind speed, sunshine, temperature) and time labels. Based on the predicted time point n, the system extracts the historical sequence of the preceding T time periods (e.g., 168 hours) as the input feature R. n Its future prediction data for T time periods (e.g., 24 hours) is used as the prediction target F. n , constitute training samples (R n ,F n ).

[0112] In this embodiment, for the training samples, outlier detection and removal based on statistical distribution, and missing data filling by linear interpolation are performed. Among them, outlier processing uses the interquartile range (IQR) method to identify and remove obvious abnormal data points caused by measurement or communication failures. Missing value filling: for a small number of consecutive missing data points, linear interpolation is used to fill them; for time periods with large areas of missing data, the entire period is removed.

[0113] Max-min normalization is applied to all feature data and target data, scaling them to the [0,1] interval. The normalization formula is:

[0114] (1)

[0115] Where x is any observation value of a certain feature in the original data; This is the minimum value of the feature across the entire training set; This is the maximum value of the feature across the entire training set; This is the normalized corresponding value.

[0116] Step 1.2: Construct a TCN-LSTM hybrid prediction model with powerful feature extraction and temporal modeling capabilities. Train the model using a quantile regression loss function to directly output probabilistic prediction results; including:

[0117] Step 1.2.1: The TCN-LSTM hybrid prediction model includes a TCN module, a Long Short-Term Memory (LSTM) network, and a quantile regression output layer;

[0118] Process the input sequence R using a temporal convolutional network. n The TCN module uses dilated causal convolution, and its formula is:

[0119] (2)

[0120] Here, d is the inflation factor. By stacking multiple layers, the model obtains a broad receptive field, effectively extracting macroscopic features such as long-term cycles and trends in load and wind and solar power output. The temporal convolutional network performs multi-layer nonlinear convolutional transformations on the input multi-dimensional time-series data, outputting a high-level feature sequence F that carries the high-order temporal dependencies and abstract patterns of the input data. n This feature sequence serves as the input to the subsequent Long Short-Term Memory (LSTM) network, which will... n The input vector to the LSTM layer is equal to the feature vector F extracted by the TCN at that time step n. n To capture sequence dynamics, the core computation of the LSTM unit is as follows:

[0121] (3)

[0122] (4)

[0123] (5)

[0124] (6)

[0125] (7)

[0126] (8)

[0127] in, It represents the hidden state of the previous moment, serving as a memory carrier; It represents the cell state at the previous moment and signifies long-term memory; , , , and , , , The weight matrices and bias terms correspond to the forget gate, input gate, candidate cell state, and output gate, respectively. , , These represent the sigmoid function ( The activation vectors of the forget gate, input gate, and output gate are calculated, with values ​​between 0 and 1, and are used to control the proportion of information flow. It is the candidate cell state vector generated by the tanh function at the current time step, containing new information from the current input; cell state The hidden state is updated by adding the previous state (after being filtered by the forget gate) and the current candidate state (after being filtered by the input gate); The updated cell state is then transformed using the tanh transform and controlled by the output gate, and is passed as the output of the current time step to the next time step or the output layer; the final output of the LSTM is a feature vector representing the temporal context. ;

[0128] Will The input quantile regression output layer simultaneously outputs predicted values ​​for multiple target quantiles, for each prediction time step. Each neuron has a corresponding output neuron; therefore, a single forward propagation of the model can directly output multiple quantile predictions for each time point in the next 24 hours, forming the initial probabilistic prediction sequence. .

[0129] The quantile regression output layer is structurally a fully connected neural network, consisting of an input adaptation layer, a hidden layer, and a quantile output layer in sequence.

[0130] The input adaptation layer has an input dimension that is strictly consistent with the dimension of the feature vector output by the upstream LSTM module, ensuring lossless reception of features. The hidden layer may contain one or more fully connected layers. The role of this layer is to further fuse and refine the high-level features from the LSTM, enhancing the nonlinear expressive power of the model. This part can be configured according to the model complexity requirements. The quantile output layer is the functional implementation layer of the module. This layer is a specially designed fully connected layer. The total number of its neurons (nodes) is determined by the product of the number of target quantiles (denoted as M) and the total number of prediction time periods (denoted as T), i.e., M×T.

[0131] The connections between the components are as follows: The feature vector output by the LSTM module is first transmitted to the input adaptation layer. Subsequently, the data can be fed into the hidden layer for deep nonlinear transformation. The processed features are then fed into the quantile output layer. Each neuron in this layer is fully connected to all neurons in the previous layer, and its activation value is calculated through linear weighted summation. These activation values ​​are the model's original, unnormalized quantile predictions.

[0132] During model initialization, each neuron in the quantile regression output layer is pre-assigned a unique coordinate (τ, t), where τ represents a target quantile (e.g., τ = 0.1) and t represents a specific future time period. The training objective of the model is to minimize the quantile regression loss function, which imposes an asymmetric penalty on the prediction error. For the target quantile τ, if the true value is higher than the predicted value, the error weight B = τ; if it is lower than the predicted value, the weight B = (1-τ). Each neuron actively adjusts its internal weights to ensure that the output value satisfies the condition that τ × 100% of the samples in the entire training set have a true value lower than this output value.

[0133] Step 1.2.2: The training objective of the model is to minimize the quantile loss, rather than the traditional mean squared error for each target quantile. Define the quantile loss function:

[0134] (9)

[0135] (10)

[0136] Where y is the true value; For model output Quantile predicted value; N is the sample size;

[0137] The sum of the models:

[0138] (11)

[0139] Minimize the total loss using the backpropagation algorithm and gradient descent optimizer. This means using the backpropagation algorithm and gradient descent optimizer to iteratively update the model parameters to minimize the loss; when the total loss no longer decreases significantly on the training set, or when a preset number of training rounds is reached, the model is considered to have converged.

[0140] Step 1.2.3: The model trained through the above process has its parameters optimized to minimize quantile loss. Therefore, the predicted τ quantile value output by this model should statistically satisfy the condition that for future samples, the true value has a probability of τ*100% lower than the predicted value. After the model training is completed, it is used for prediction the next day, and the feature data R corresponding to the prediction day is used. n Input the model, and the model outputs the "three lines" prediction results for the next 24 hours (96 time points): lower boundary curve (τ=0.1, representing the pessimistic scenario), median curve (τ=0.5, representing the most likely scenario), upper boundary curve (τ=0.9, representing the optimistic scenario), select the lower boundary curve. With the upper boundary curve The area between these points constitutes an 80% confidence level probabilistic prediction corridor. This corridor visually demonstrates the possible fluctuation range of future renewable energy output and load. The generated probabilistic prediction corridor is then transmitted to the market clearing module as the core basis for assessing the worst-case operating scenario and constructing probabilistic inertia demand constraints.

[0141] Step 2 is as follows:

[0142] Step 2.1: Based on the probabilistic prediction corridor generated in Step 1, the market operator identifies two types of market participants: the set of synchronous generator units. (Such as coal-fired power, gas-fired power, hydropower) and virtual inertia supplier set (Including wind farms, photovoltaic power stations, and energy storage systems), the next operating day is divided into T time periods (e.g., T=96, corresponding to 15-minute intervals). All applications are based on this time sequence frame t=1,2,...,T. Predictive data is prepared for each virtual inertia supplier j: the electricity application benchmark is taken from the median curve of the prediction corridor. Its maximum power generation capacity is taken from the lower boundary curve. .

[0143] Step 2.2: To transform rapid frequency regulation capability into a tradable commodity, define the core technical standards for the "virtual inertia" product, whose supply capacity is determined by rapid power regulation capacity. and response time constant Quantitatively defined, rapid power regulation capacity refers to the maximum active power regulation range that supplier j can continuously provide during time period t through methods such as reserving backup load reduction operation and reserving charge and discharge margins, and its response time constant. This refers to the time constant required for supplier j's power control system to release 95% of its rated regulating power from detecting a frequency overshoot; based on the above parameters, this represents the equivalent virtual inertia capacity that supplier j can provide during time period t. The volume of its tradable core products is calculated using the following formula:

[0144] (12)

[0145] in, This is the system's rated frequency.

[0146] Step 2.3: All market entities must submit the day-ahead market declaration data and synchronize generator sets within the specified time. Declare its electricity price quotation curve and its inherent technical parameters, including inertia constant. The actual physical inertia it can provide In the clearing model, the unit start-up state variables will be used. Decide.

[0147] Virtual Inertia Supplier The submitted bid is a combined quote including electrical energy and virtual inertia products. For the electrical energy component, the quote must be based on the predicted median curve generated in step 1. Based on this, declare the amount of electrical energy it is willing to sell. and corresponding quotes Regarding virtual inertia, suppliers may choose whether to declare it. If they choose to declare it, they must provide a combination of parameters, including its fast power regulation capacity. Response time constant Equivalent virtual inertia capacity And the price of providing equivalent virtual inertia capacity services and promised to meet its requirements. ,in Contribute to the foundation of its plans and ensure the credibility of its capabilities.

[0148] After collecting and verifying all declared data, the market operation agency forms a structured market declaration dataset D that can be directly read by the optimization model:

[0149] (13)

[0150] Where J is the inertial constant vector of the synchronous generator set. This is a virtual inertia capacity declaration matrix. This is the set of all quotes; this dataset, along with the predicted corridors generated in step 1, is used as known parameters input into the subsequent optimization model.

[0151] Step 3 specifically involves:

[0152] Step 3.1: Based on the worst-case scenario, assess the minimum inertia required to maintain frequency stability; first, calculate the system net load under the extreme scenario (wind and solar power output taken as the lower boundary). :

[0153] (14)

[0154] in, This is the median of the load forecast. , This net load level serves as the lower bound for wind and solar power forecasts and is a benchmark for assessing inertia demand.

[0155] Based on the system frequency response model, the minimum inertia required by the system in time period t to meet frequency safety standards is calculated. This requirement necessitates simultaneously limiting the rate of frequency change and the minimum frequency drop at the initial moment of a fault. This ensures that, even under the most severe load scenarios and fault impacts, the system still possesses sufficient inertia buffer to maintain the frequency within a safe range. The calculation formula is as follows:

[0156] (15)

[0157] in, As the system's baseline capacity, The equivalent comprehensive frequency modulation coefficient of the system during time period t. It is a vector that changes over time. For the maximum allowable rate of frequency change, For the maximum allowable frequency deviation, This is the preset maximum power deficit for a single fault.

[0158] Step 3.2: Establish a probabilistic inertia safety constraint. This constraint requires that, in the market clearing outcome, the total equivalent inertia provided by all winning resources must meet the above robustness requirement in every time period. Its mathematical expression is:

[0159] (16)

[0160] in, It is a binary start-up state variable of synchronous generator set i in time period t (1 indicates start-up, 0 indicates shutdown). The virtual inertia supplier j's virtual inertia bidding status variable (a continuous variable between 0 and 1, representing the proportion of its bid capacity to the declared capacity) during time period t. (proportion);

[0161] To ensure the physical feasibility of virtual inertia suppliers' claims and prevent them from selling electrical energy and reserving regulation capacity that exceed their actual power generation limits, the following constraints are established:

[0162] (17)

[0163] (18)

[0164] in, It is the power of electrical energy won by virtual inertia supplier j in time period t. This is the power regulation capacity that needs to be reserved to provide the virtual inertia for winning the bid. It is the response time constant declared by the supplier.

[0165] Step 4: In the day-ahead joint clearing market model of electricity and inertia, the total generation-side cost is considered in the electricity trading and inertia service trading. Minimize this cost as the goal; this cost is the cost of clearing out the electricity market. With inertia market clearing costs The sum is cleared every 15 minutes:

[0166] (19)

[0167] (20)

[0168] (twenty one)

[0169] in, , , , These represent a collection of synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems, respectively. The prices listed are for synchronous generator sets, wind turbine sets, photovoltaic units, and energy storage systems, respectively. These represent the rated power of the electrical energy of the four types of generating units in time period t, respectively. For the set of virtual inertia suppliers, this set is , , A subset of this set includes only units that voluntarily declare virtual inertia services; if a unit does not declare, it is not included in this set. For synchronous generator set g, the start-stop state variable during time period t (1 indicates running, 0 indicates stopping); The no-load cost of providing physical inertia services for synchronous generator unit g; Quotation for virtual inertia services from virtual inertia provider j.

[0170] The constraint system is as follows:

[0171] System power balance constraints:

[0172] (twenty two)

[0173] Operating constraints of synchronous generator sets:

[0174] (twenty three)

[0175] (twenty four)

[0176] (25)

[0177] in, , The unit output limit; , This is the limit for the gradient rate;

[0178] Wind power / solar power unit operating constraints:

[0179] (26)

[0180] Energy storage system operating constraints:

[0181] (27)

[0182] (28)

[0183] (29)

[0184] (30)

[0185] in, , This refers to the charging / discharging power. The stored energy for time period t; , For charge / discharge efficiency; The duration of the time period; , Energy storage limit;

[0186] Virtual inertia reliability constraints:

[0187] To ensure the physical feasibility of the virtual inertia commitment, for each virtual inertia supplier, the sum of its contracted electrical power and the regulation power reserved for providing the virtual inertia must not exceed its maximum reliable power generation capacity:

[0188] (31)

[0189] Probabilistic inertia safety constraints:

[0190] The total available inertia of the system must meet the inertia requirements based on the worst-case scenario assessment:

[0191] (32)

[0192] The above model was solved using the commercial mathematical programming solver Gurobi.

[0193] Step 5: Based on the clearing results of Step 4, an improved mechanism considering the time value of money is adopted to fairly and efficiently allocate the total cost of system inertia services, forming the basis for final market settlement and realizing economic incentives for providing inertia support resources during critical periods. Specifically:

[0194] Step 5.1: To quantify the differentiated value of inertia support at different time periods, define a time value coefficient. This coefficient is positively correlated with the scarcity of system inertia or the risk of frequency instability in time period t, and its value is higher during periods of inertia tension, such as peak load and sharp drop in new energy output.

[0195] (33)

[0196] Calculate the time-weighted inertia contribution of each actual inertia provider, market participant a (including all synchronous generator units i and virtual inertia suppliers j). This contribution combines the "quantity" of the inertia it provides with the "value" of the time period in which it occurs:

[0197] (34)

[0198] in, The inertia actually provided by market participant a in time period t;

[0199] Step 5.2: Calculate the cost allocation ratio for each participant using the weighted contribution ratio method that considers time-series value. This method is an efficient and fair approximation of the classic Aumann-Shapley value method in continuous cooperative game scenarios:

[0200] (35)

[0201] Where Ω represents the set of all market participants that actually provide inertia, and the denominator is the weighted contribution W of all participants in the set Ω. j The sum of them satisfies This ensures that all costs are shared.

[0202] According to the sharing ratio Total cost of inertia services Calculate the final settlement amount that each market participant a should pay or receive. :

[0203] (36)

[0204] For synchronous generator sets, the settlement amount is generally positive, representing the fixed cost that should be recovered for providing physical inertia reserves to the system. For virtual inertia suppliers, the settlement amount is negative, and its absolute value is the economic compensation obtained for providing virtual inertia services.

[0205] Market application options for wind, solar and energy storage units, such as Figure 2 The diagram illustrates the difference in market optimization and clearing between wind, solar, and energy storage units when they choose to declare or not declare virtual inertia. When they choose not to declare virtual inertia, they act only as an energy supplier, and market clearing is optimized solely at the energy level. Their revenue depends entirely on electricity sales, and their rapid power regulation capabilities are not directly utilized by the system. However, when they choose to declare virtual inertia, they are explicitly defined as virtual inertia suppliers. The market optimizes their clearing through a joint energy and virtual inertia process, allowing them to generate additional revenue outside the energy market by quantifying their rapid regulation capabilities into "equivalent virtual inertia capacity" and selling it. This capability is also directly incorporated into system frequency security constraints, enhancing system robustness.

[0206] To verify the beneficial effects of this invention, scientific demonstration was conducted through experiments:

[0207] (1) Probabilistic prediction of corridors based on TCN-LSTM hybrid model and quantile regression technique;

[0208] First, using historical data from a provincial power grid as an example, the data is selected from 0:00 to 24:00 each day, sampled every 15 minutes, for a total of 96 sampling points per day. Next, a TCN-LSTM hybrid prediction model with powerful feature extraction and time-series modeling capabilities is constructed. The model is trained using a quantile regression loss function, allowing it to directly output probabilistic prediction results, such as... Figure 3 As shown, Figure 3 (a) represents the load forecast corridor. Figure 3 (b) represents the wind power forecast corridor. Figure 3 (c) represents the photovoltaic prediction corridor. The MAE (Mean Absolute Error) and RMSE (Root Mean Square Error) marked on the probabilistic prediction corridor diagram are two core indicators used to quantify the accuracy of the prediction model. Figure 3 In (a), MAE=37.1MW and RMSE=49MW, indicating that the load forecasting error is small in most periods and the model captures load trends and cyclical characteristics relatively accurately. Figure 3 In (b), MAE=22.3MW and RMSE=28.2MW, indicating that the wind power output fluctuates greatly, but the model can still characterize its uncertainty boundary well, especially in the extreme low output scenario. Figure 3 In (c), MAE = 4.8MW and RMSE = 8.4MW, indicating that the photovoltaic output is significantly affected by the solar cycle. The model has a smaller prediction error during the daytime and approaches zero at night, showing stable overall prediction performance. Table 1 shows the average values ​​for various resources: the average load prediction is 4567.9MW, the average wind power prediction is 243.0MW, and the average photovoltaic prediction is 89.1MW.

[0209] Table 1. Forecast Mean of Corridor

[0210]

[0211] (2) Market application and product quantitative analysis of virtual inertia suppliers;

[0212] Wind power, photovoltaic and energy storage systems are explicitly defined as "virtual inertia suppliers", and their rapid power regulation capabilities are quantified by equivalent inertia constants and are included in the recent market joint declaration.

[0213] Calculations from Tables 2 and 3 show that during the 96 simulated time periods, virtual inertia suppliers reported a total equivalent inertia capacity of 42,150 MW·s, accounting for 46.19% of the total reported inertia capacity, significantly expanding the sources of inertia supply. By applying for virtual inertia products, wind, solar, and energy storage resources can obtain additional inertia service revenue beyond electricity revenue, increasing their overall market revenue by an average of approximately 12.7%, effectively incentivizing flexible resources to participate in system frequency support.

[0214] Table 2. Market Clearing Results for Inertia

[0215]

[0216] Table 3. Results of Joint Market Clearing

[0217]

[0218] (3) Inertia requirement assessment and probabilistic safety constraint analysis based on worst-case scenarios;

[0219] As shown in Table 2, by introducing probabilistic inertia safety constraints and virtual inertia reliability constraints, the market clearing model ensures that the total equivalent inertia of the winning bid fully meets the dynamic requirements under the worst-case reliability scenario. After clearing, the system's inertia sufficiency rate stabilizes above 1.15, proving that this constraint mechanism can effectively guarantee the system's frequency safety baseline under the most unfavorable conditions.

[0220] As shown in Table 3, compared with the benchmark method that uses deterministic worst-case scenario constraints, the 80% confidence probabilistic corridor assessment method adopted in this invention reduces the inertia reserve cost by about 18.3%, achieving an optimal balance between safety and economy.

[0221] (4) Day-ahead electrical energy-inertia joint clearing market based on virtual inertia participation in market declaration;

[0222] Depend on Figure 4 It can be seen that the total planned electricity clearing amount is 438,520 MWh, with an electricity cost of 19.4484 million yuan, while the total planned inertia clearing amount is 74,876 MW·s, with an inertia service cost of 994,500 yuan. Analysis of the inertia-related results in Table 2 verifies that the "probabilistic prediction-inertia electricity joint clearing" mechanism possesses good economic efficiency while ensuring frequency security.

[0223] (5) Explanation of the time value coefficient variation diagram;

[0224] Figure 5 This demonstrates the pricing coefficients for inertia services based on time-period value differences, including the time value coefficient. It dynamically reflects the marginal value of inertia services at different time periods.

[0225] Simulation results show a significant increase in coefficients during peak hours, with coefficients generally exceeding 1.2 during the morning peak (8:00–11:00) and evening peak (17:00–21:00), reflecting a high risk of system frequency instability and strong inertia scarcity during these periods. During the nighttime off-peak period (0:00–6:00), the coefficient fluctuates around 1.0, indicating ample inertia and relatively stable value. The average time value coefficient is 1.0375, indicating that the overall system inertia value is slightly higher than the benchmark, and the incentive mechanism is moderately effective.

[0226] The above description is merely a preferred embodiment of the present invention and is not intended to further limit the present invention. All equivalent changes made based on the description and drawings of the present invention are within the protection scope of the present invention.

Claims

1. A probabilistic day-ahead market trading method considering time value and virtual inertia, characterized in that, Includes the following steps: Step 1: Collect historical load data and preprocess it. Use the TCN-LSTM hybrid model and quantile regression technology to generate a probabilistic prediction corridor that describes the uncertainty of the future. Step 2: If wind power, photovoltaic, and energy storage systems are selected as virtual inertia, then wind farms, photovoltaic power plants, and energy storage systems are defined as virtual inertia suppliers. The virtual inertia declaration method is defined, and they participate in the day-ahead market declaration for electrical energy and inertia capacity together with traditional synchronous generator sets; specifically: Divide the next day of operation into T time periods, t=1,2,...,T; The equivalent virtual inertia capacity that virtual inertia provider j can provide during time period t. Calculated by the following formula: （5） in, The system's rated frequency, For rapid power regulation capacity, The response time constant; This is a collection of virtual inertia providers, including only those generators that voluntarily declare their virtual inertia service; virtual inertia providers To predict the median curve of the corridor using probabilistic methods Based on this, declare the amount of electrical energy it is willing to sell. and corresponding quotes If a virtual inertia supplier chooses to declare virtual inertia, it should declare its fast power regulation capacity. Response time constant Equivalent virtual inertia capacity And the price of providing equivalent virtual inertia capacity services and promised to meet its requirements. ,in Contribute to the planned foundation of virtual inertia supplier j; Step 3: Evaluate the inertia requirements under adverse scenarios based on the lower boundary extreme scenarios in the probabilistic prediction corridor, and establish probabilistic inertia safety constraints and virtual inertia reliability constraints; Step 4: Taking the minimization of the total cost of the generation side considering electricity trading and inertia service trading as the objective function, and combining the constraints, construct and solve the day-ahead electricity-inertia joint clearing market model to determine the clearing result; Step 5: Based on the clearing results, the improved Aumann-Shapley value method, which takes into account the time value of money, is used to allocate inertia costs, so that virtual inertia providers who provide inertia services during critical periods can receive higher compensation. To quantify the differential value of inertia support at different time periods, a time value coefficient is defined. : (26) in, This represents the system inertia requirement during time period τ; It is a vector that changes over time; Calculate the time-weighted inertia contribution of each actual inertia provider, a, including synchronous generator i and virtual inertia supplier j. : (27) in, The inertia actually provided to market participant a during time period t.

2. The probabilistic day-ahead market trading method considering time value and virtual inertia according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: Collect historical data, including grid load power, total output of wind farm clusters, total output of photovoltaic power station clusters, and corresponding meteorological data and time labels. Using the predicted time point n as the benchmark, extract the historical sequence {X1, X2, ..., X} for the preceding T time periods. n } constitutes a set R n As input features, it predicts the feature sequence {Y1,Y2,...,Y} for T time periods in the future. n } as the prediction target F n The input features and the prediction target constitute the training samples (R). n ,F n ); perform max-min normalization on all input feature data and prediction target data, scaling them to the [0,1] interval; Step 1.2: Construct a TCN-LSTM hybrid prediction model, train the model using the quantile regression loss function, and generate probabilistic prediction corridors, including: Step 1.2.1: The TCN-LSTM hybrid prediction model includes a TCN module, a Long Short-Term Memory (LSTM) network, and a quantile regression output layer; The TCN module uses multi-layer dilated causal convolution to extract input features R. n The long-term cycle and trend characteristics are used to output the prediction target F. n : （1） Where n is the current time step, Let f be the feature value output after n convolution operations, f be the weight function of the convolution kernel, K be the size of the convolution kernel, d be the dilation factor, and k be the weight index within the convolution kernel. The input sequence is the value at historical time step nd·k; Predict the target The entire input is a Long Short-Term Memory (LSTM) network, which outputs feature vectors containing rich temporal context. ; Will The input quantile regression output layer simultaneously outputs predicted values ​​for multiple target quantiles at each prediction time interval t, forming the initial probabilistic prediction sequence. ; Step 1.2.2: For each target quantile Define the quantile loss function: （2） （3） Where u is the deviation between the predicted value and the actual value. ; y is the actual value; This represents the true value of the i-th training sample. For model output Quantile predicted value; N is the sample size; The total loss of the TCN-LSTM hybrid prediction model is the sum of the losses of multiple target quantiles: （4） Where Q represents the set of target quantile levels, and the total loss is minimized using the backpropagation algorithm and gradient descent optimizer. ; Step 1.2.3: Input feature data R corresponding to the prediction date. n Input the trained model and output the three-line prediction results for the next 24 hours, i.e., the lower boundary curve. Median curve Upper boundary curve Select the lower boundary curve With the upper boundary curve The area between them forms a probabilistic prediction corridor.

3. The probabilistic day-ahead market trading method considering time value and virtual inertia according to claim 2, characterized in that, In step 2, the synchronous generator set Declare its electricity price quotation curve and its inherent technical parameters, including inertia constant. The actual physical inertia it can provide In the clearing model, the unit start-up state variables will be used. Decide; The rated apparent capacity of unit i; A collection of synchronous generator sets; After collecting and verifying all declared data, the market operation agency forms the market declaration dataset D: （6） Where J is the inertial constant vector of the synchronous generator set. This is a virtual inertia capacity declaration matrix. For the set of all quotes.

4. The probabilistic day-ahead market trading method considering time value and virtual inertia according to claim 3, characterized in that, Step 3 specifically involves: Step 3.1: Based on the probabilistic prediction of the lower boundary extreme scenarios in the corridor, evaluate the minimum inertia required to maintain frequency stability, including: Calculate the net system load under extreme scenarios. : （7） in, This is the median of the load forecast. , The lower boundary is predicted for wind power and solar power; Calculate the minimum inertia required by the system in time period t to meet frequency safety standards. The calculation formula is: （8） in, As the system's baseline capacity, The equivalent comprehensive frequency modulation coefficient of the system during time period t. It is a vector that changes over time. For the maximum allowable rate of frequency change, For the maximum allowable frequency deviation, The maximum power deficit for a single fault is preset. Step 3.2: Establish probabilistic inertia safety constraints: （9） in, It is a binary start-up state variable of synchronous generator set i in time period t, where 1 indicates start-up and 0 indicates shutdown; This is the virtual inertia bid-winning status variable of virtual inertia supplier j in time period t, representing the proportion of its bid capacity to the declared capacity. The proportion; Establish virtual inertia credibility constraints: （10） （11） in, It is the power of electrical energy won by virtual inertia supplier j in time period t. This is the power regulation capacity that needs to be reserved to provide the virtual inertia for winning the bid.

5. The probabilistic day-ahead market trading method considering time value and virtual inertia according to claim 4, characterized in that, Step 4 is as follows: In the recent joint clearing market model of electricity and inertia, the total cost on the generation side is considered in relation to electricity trading and inertia service trading. Minimize the impact, clear out every 15 minutes: （12） （13） （14） in, To clear costs in the electricity market, Clearing out costs in the inertia market; , , , These represent the collections of synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems, respectively; g, w, pv, and e represent the synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems, respectively. The prices listed are for synchronous generator sets, wind turbine sets, photovoltaic units, and energy storage systems, respectively. These represent the rated power of electrical energy for synchronous generator sets, wind turbines, photovoltaic units, and energy storage systems during time period t. The no-load cost of providing physical inertia services for synchronous generator unit g; Quotation for virtual inertia services from virtual inertia provider j; The constraints are as follows: System power balance constraints: （15） Operating constraints of synchronous generator sets: （16） （17） （18） in, , The unit output limit; , This is the limit for the gradient rate; Wind power / solar power unit operating constraints: （19） Energy storage system operating constraints: （20） （21） （22） （23） in, , This refers to the charging / discharging power. The stored energy for time period t; , For charge / discharge efficiency; The duration of the time period; , Energy storage limit; Virtual inertia reliability constraints: （24） Probabilistic inertia safety constraints: （25）。 6. The probabilistic day-ahead market trading method considering time value and virtual inertia according to claim 1, characterized in that, Step 5 also includes: The cost allocation ratio for each participant is calculated using a weighted contribution ratio method that takes into account the time value. : （28） Where Ω represents the set of all market participants that actually provide inertia, and the denominator is the weighted contribution W of all participants in the set Ω. j The sum of them satisfies This ensures that all costs are shared. According to the sharing ratio and inertia market clearing costs Calculate the final settlement amount that each market participant a should pay or receive. : （29） For synchronous generator sets, the settlement amount is positive, representing the portion of the fixed cost that should be recovered for providing physical inertia reserves to the system. For virtual inertia suppliers, the settlement amount is negative, and its absolute value is the economic compensation they receive for providing virtual inertia services.

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