A Chance-Constrained Economic Dispatch Method with Explicit Accounting for AGC Fine-Grained Time-Scale Response Actions

Abstract

The present invention discloses an opportunity-constrained economic dispatch method that explicitly accounts for the fine-grained time-scale response actions of automatic generator sets (AGCs). The method comprises: constructing an AGC unit response action model within an opportunity-constrained framework based on changes in response output; constructing an opportunity-constrained economic dispatch model based on the refined AGC unit response action model and taking into account the AGC fine-grained time-scale response actions; and analytically transforming the opportunity-constrained economic dispatch model to achieve an explicit representation of the AGC fine-grained time-scale response actions. By solving the opportunity-constrained economic dispatch model that accounts for the AGC fine-grained time-scale response actions, the present invention can more rationally arrange unit dispatch plans and ensure the safe and economical operation of the power system.

Description

Technical Field

[0001] The present invention relates to the field of power systems and automation technologies thereof, and in particular to a chance-constrained economic dispatch method that explicitly takes into account AGC fine-grained time-scale response actions. Background Art

[0002] The inherent random volatility of renewable energy sources such as wind and solar power has led to a surge in uncertainty in the net load of the system. In order to cope with the growing uncertainty in the net load of the system, stochastic optimization methods such as multi-scenario method, robust optimization and chance constraint have been introduced into the economic dispatch of power systems and have achieved certain industrial applications. At the same time, Automatic Generation Control (AGC), as the main technical means for the power grid to smooth the uncertainty of net load, is also widely used in the above-mentioned stochastic optimization methods to construct a response model for AGC units to deal with net load uncertainty. However, traditional stochastic optimization economic dispatch only considers the output and reserved capacity of the AGC units at the dispatch time point, and does not take into account the actual response actions of the AGC units at a fine-grained time scale (generally 4 seconds to 3 minutes) during the dispatch period. Because existing dispatch methods ignore these factors, at the system operation level, economic dispatch models fail to account for the fine-grained timescale regulation needs of AGC units, threatening the economic and secure operation of the power grid. At the market clearing level, the correlation between fine-grained renewable energy uncertainty and frequency regulation reserve capacity is not reflected in economic dispatch models. This results in an inability to rationally allocate the ancillary service costs of frequency regulation reserve capacity provided by AGC units, hindering the market's resource regulation role. Therefore, it is necessary to explicitly account for the fine-grained timescale response of AGC units in stochastic optimization economic dispatch models to ensure system economic operation while providing a model foundation for market clearing of power systems with a high proportion of renewable energy.

[0003] Existing stochastic optimization methods are relatively mature for modeling the response of AGC units to net load uncertainty at a given dispatch time. Their core approach is to construct a linear mapping between the AGC unit's response output and the net load uncertainty characteristics using the AGC affine factor. This is used to determine the required frequency regulation reserve capacity for the AGC unit, which is then used as a constraint to construct the AGC unit response model. Based on the net load uncertainty characteristics, stochastic optimization methods can account for the frequency regulation reserve capacity required to mitigate net load uncertainty in economic dispatch models. Existing methods reserve regulation capacity for power balance and net load fluctuations at the dispatch time through optimized dispatch, and provide AGC signals to guide the units' real-time output adjustments to account for short-term net load fluctuations within the dispatch period. However, these methods only construct a mapping between the AGC unit's response output and net load uncertainty at the dispatch time, lacking detailed modeling of the AGC unit's response behavior at a fine-grained timescale. In fact, ignoring the actual response behavior of AGC units in economic dispatch can result in either excessive or insufficient reserved capacity, resulting in unnecessary economic losses.

[0004] The industry generally uses deterministic dispatch decision-making methods to implement AGC responses to net load uncertainty. The core idea is to set the frequency regulation reserve capacity required for each AGC unit based on operating experience before solving the economic dispatch model. The sum of the units' reserved reserve capacity is required to meet the frequency regulation needs of the net load during the dispatch period, ensuring that the system has sufficient operating margin to cope with net load uncertainty. This method is simple and easy to implement, but it fails to effectively account for the characteristics of net load uncertainty. Furthermore, this method essentially separates economic dispatch and AGC response into two independent processes, which is bound to cause unnecessary economic losses and potential safety hazards.

[0005] In summary, the existing economic dispatch methods for modeling AGC response actions still have the following problems: 1) The random optimization economic dispatch method can only construct the AGC response action model at the dispatch time point, and lacks the refined modeling of AGC response actions at a fine-grained time scale; 2) The existing economic dispatch method separates economic dispatch and AGC response, resulting in the economic dispatch results failing to take into account the AGC response action, threatening the economic and safe operation of the power grid. Summary of the Invention

[0006] The purpose of this invention is to address the current situation where the inherent random volatility of renewable energy sources such as wind and solar power leads to a surge in uncertainty in system net load, as well as the impact of this increasing uncertainty in system net load, thereby providing strong support for the safe and stable operation of the power grid. To this end, a chance-constrained economic dispatch method is proposed that explicitly accounts for the fine-grained timescale response of AGC.

[0007] The present invention discloses a chance-constrained economic dispatch method that explicitly takes into account the fine-grained time-scale response actions of AGC, which includes:

[0008] Step 1: Based on the change of response output, construct the AGC unit response action model under the opportunity constraint framework;

[0009] Step 2: Combined with the refined model of AGC unit response action, considering the AGC fine-grained time scale response action, a chance-constrained economic dispatch model is constructed;

[0010] Step 3: Analyze and transform the opportunity-constrained economic dispatch model to achieve explicit representation of the AGC fine-grained time-scale response actions.

[0011] Furthermore, the step 1 includes:

[0012] Step 11: Determine the total planned output of the AGC units within the dispatch time based on the fine-grained net load forecast curve and linear tracking mode;

[0013] Step 12: Construct the total system power deviation during the dispatch period considering the random fluctuation of net load and its uncertainty;

[0014] Step 13: Considering the dead zone of regulation demand, construct the AGC unit response action model.

[0015] Furthermore, the step 11 includes:

[0016]

[0017] Where, is the predicted power demand of net load i at the dispatch time point t; is the total planned output of the AGC units at the dispatching time t, which maintains power balance with the net load at the dispatching time; is the total planned output of the AGC units at the short time point k within the scheduling period t, which is determined by the linear tracking mode; K is the total number of time points in the next section of the scheduling period; I D is the collection of load nodes in the system.

[0018] Furthermore, the step 12 includes:

[0019]

[0020] Where, is the total system power deviation at the scheduling time point t; It represents the total system power deviation at short time point k within the scheduling period t; is the predicted power demand of net load i at short time point k within the dispatch period t; ΔD i,t,kis the deviation between the predicted power demand of net load i at short time point k within the scheduling period t and the actual power demand, that is, the net load uncertainty.

[0021] Furthermore, the step 13 includes:

[0022]

[0023] Where, ΔP i,t,1 represents the response output of AGC unit i at the dispatch time t, which is determined by the AGC adjustment factor β of AGC unit i i,t Total deviation from the system power at that moment Determine; ΔP i,t,k is the response output of AGC unit i at short time point k in the dispatch period t, and is related to ΔP i,t,1 Different, ΔP i,t,k The AGC unit will make corresponding adjustments only when the probability that the total system power deviation is higher than the dead zone DL is greater than the given probability value 1-ε.

[0024] Furthermore, in step 2, the objective function of the opportunity-constrained economic dispatch model includes system power generation cost and frequency regulation reserve cost; the objective function of the opportunity-constrained economic dispatch model is:

[0025]

[0026] Where, represents the planned output of AGC unit i at short-term time point k within the scheduling period t; and are the up / down frequency regulation reserve capacity of AGC unit i at dispatch time t; and I represents the power generation quotation and frequency regulation reserve capacity quotation of AGC unit i respectively; G is the set of thermal power units in the system; T is the total number of dispatch period t in economic dispatch;

[0027] In step 2, the operation constraints of the opportunity-constrained economic dispatch model include power balance constraints, unit planned output constraints, unit actual output constraints and net load actual power demand constraints, unit frequency regulation reserve capacity constraints, and line power flow constraints;

[0028] For the power balance constraint, assuming that all thermal power units are AGC units, at the dispatch time point, the system needs to ensure that the total planned output of all AGC units is equal to the total power demand predicted by the net load;

[0029]

[0030] Where, represents the planned output of AGC unit i at the scheduling time point t;

[0031] For the unit planned output constraint, according to the linear tracking mode of the AGC unit, its response output at the short time point k within the scheduling period t is Calculated by the following formula:

[0032]

[0033] Where, represents the planned output of AGC unit i at short-term time point k within the scheduling period t;

[0034] For the actual unit output constraint and the net load actual power demand constraint, the actual unit output is the sum of its planned output and the response output. Similarly, the net load actual power demand is the sum of its predicted power demand and its uncertainty, as shown in the following formula:

[0035]

[0036]

[0037] Where, P i,t,k represents the actual output of AGC unit i at short time point k within the dispatch period t; D i,t,k is the actual power demand of net load i at short time point k within the scheduling period t;

[0038] Regarding the unit frequency regulation reserve capacity constraint, the unit frequency regulation reserve capacity must meet the AGC unit adjustment demand at the short-term dispatch point within each dispatch period with a given probability of 1-ε, and the actual output of the AGC unit must be within the unit's physical output range. The specific constraints are as follows:

[0039]

[0040] Where, P i max and P i min Indicates the maximum / minimum output limit of AGC unit i;

[0041] For line flow constraints, the system line flow must ensure that it meets the line physical limit with a given probability of 1-ε at the short-term scheduling point within each scheduling period;

[0042]

[0043] Where, PTDF li is the power transfer distribution factor of branch l to node i.

[0044] Furthermore, the step 3 includes:

[0045] Step 31: Convert the discriminant in the AGC unit response action model into a set of logical discriminants related to opportunity constraints, and parse and transform the expression form of the opportunity constraints in the logical discriminant;

[0046] Step 32: Analyze and transform the logical discriminant judgment in the AGC unit response action model according to the expression form of the opportunity constraint after analysis and transformation;

[0047] Step 33: Analytically transform some constraints in the unit frequency regulation reserve capacity constraints and line power flow constraints of the opportunity-constrained economic dispatch model;

[0048] Step 34: Through steps 31 to 33, the opportunity-constrained economic dispatch model is transformed into a second-order cone-convex model, which can be directly solved by the solver. The objective function of the second-order cone-convex model is the same as that of the opportunity-constrained economic dispatch model, and the constraints are obtained through steps 2 and 33.

[0049] Furthermore, the step 31 includes:

[0050] The opportunity constraint of the opportunity-constrained economic dispatch model is expressed as follows:

[0051] Pr(g(x,0)+b(x) T ΔD≤g max )≥1-ε (18)

[0052] Where g(x,0) represents the system operating boundary function of the predicted operating point, that is, the system operating boundary when the net load power uncertainty is not considered; b() is the sensitivity matrix of g to the net load power uncertainty ΔD, which is essentially a linear function matrix of the power system control decision variable x; b(x) T ΔD represents the uncertainty of the system operation boundary caused by the uncertainty of net load power;

[0053] Assuming that the mean and standard deviation of the net load power uncertainty ΔD have been obtained from its historical or simulated data, the mean and standard deviation of the system operating boundary are calculated as follows:

[0054] μ(g(x,0)+b(x) T ΔD)=g(x,0)+b(x) T μ D (19)

[0055]

[0056] Where μ D and Σ DThey represent the mean vector and covariance matrix of the net load power uncertainty, respectively. The covariance matrix is ​​constructed by the standard deviation vector of the net load power uncertainty. Based on the literature opportunity constraint analysis, it is transformed into the following form:

[0057]

[0058]

[0059] Where, Γ ε is a constant, representing the transfer factor of the uncertainty standard deviation; UM g It is expressed as uncertainty boundary, which is essentially to determine the additional operating boundary margin reserved by the system under the given constraint exceeding probability; constraint (21) is a convex second-order cone constraint;

[0060] For the condition of the logical discriminant in formula (6) Transformed into a set of logical discriminant conditions related to opportunity constraints:

[0061]

[0062] For the two chance constraints in the logical discriminant, according to (18)-(22), it is analytically transformed into the following form:

[0063]

[0064] Where: Indicates N D dimensional unit column vector, N D is the number of load nodes; combined with formulas (23)-(24), the logical discriminant judgment, that is, formula (6), is transformed into the following form:

[0065]

[0066] Furthermore, the step 32 includes:

[0067] The analytical transformation of opportunity constraints (12) and (13) is:

[0068]

[0069] Where: b p,i (β i,t ) represents the sensitivity matrix of the response output of AGC unit i at the dispatch time t to the net load power uncertainty ΔD;

[0070] Similarly, the analytical transformation of opportunity constraints (16) and (17) is:

[0071]

[0072] Where: bl (β t ) represents the sensitivity matrix of the uncertainty power flow on branch l at dispatch time t to the uncertainty of net load power ΔD; PTDF l is the power transfer distribution factor vector of branch l to system nodes;

[0073] The step 33 includes:

[0074] The objective function of the second-order cone-convex model is formula (7), and the constraints are formulas (8)-(11), (14)-(15), and (25)-(31).

[0075] Furthermore, the second-order cone convex model calculates the uncertainty standard deviation transfer factor Г according to the net load distribution ε , to adapt to the net load power uncertainty distribution; if the net load power uncertainty obeys Gaussian distribution, then Г ε The expression is:

[0076] Γ ε =Ψ -1 (1-ε) (32)

[0077] Where Ψ is the probability density function of the Gaussian distribution.

[0078] Due to the adoption of the above technical solution, the present invention has the following advantages:

[0079] Without changing existing economic dispatch rules (which determine unit output and AGC response actions at the dispatch time), the proposed method provides a more economical and secure dispatch solution compared to existing chance-constrained economic dispatch methods. The effectiveness of the proposed method is demonstrated solely through the use of a chance-constrained stochastic optimization method. Because the proposed method is based on a mature stochastic optimization AGC response model, it is also applicable to the refined modeling of stochastic optimization AGC fine-grained timescale responses in multiple scenarios and robust optimization, demonstrating its universal applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments described in the embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0081] Figure 1 This is a schematic diagram of the response action of the AGC unit according to an embodiment of the present invention;

[0082] Figure 2 Schematic diagram of planned output and response output of an AGC unit according to an embodiment of the present invention;

[0083] Figure 3 A schematic diagram comparing total frequency modulation capacity according to an embodiment of the present invention;

[0084] Figure 4 The figure is a flow chart of an opportunity-constrained economic dispatch method that explicitly takes into account the fine-grained time-scale response actions of AGC according to an embodiment of the present invention. DETAILED DESCRIPTION

[0085] The present invention will be further described with reference to the accompanying drawings and embodiments. The embodiments described are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by those skilled in the art should fall within the scope of protection of the embodiments of the present invention.

[0086] This paper proposes an opportunity-constrained economic dispatch method that explicitly takes into account the fine-grained time-scale response actions of AGC, which has the following two aspects:

[0087] 1) A fine-grained time-scale AGC response model that considers net load uncertainty is constructed. Based on the actual AGC response strategy, this paper establishes a refined model of AGC unit response actions at a fine-grained time scale within a chance-constrained framework, revealing the correlation between AGC unit response actions and net load uncertainty characteristics.

[0088] 2) A method for opportunity-constrained economic dispatch with an explicit embedded AGC fine-grained time-scale response model is proposed. Based on the existing opportunity-constrained economic dispatch model, the AGC fine-grained time-scale response model is embedded into it, and an analytical model for opportunity-constrained economic dispatch with an embedded AGC fine-grained time-scale response model is constructed. This provides a model foundation for the safe and economic operation of the power system and the rational clearing of the power market.

[0089] See also Figure 4 The present invention provides an embodiment of a chance-constrained economic dispatch method that explicitly takes into account the fine-grained time-scale response actions of AGC, which includes the following steps:

[0090] S1: AGC unit response action model under the opportunity constraint framework according to the change of response output;

[0091] Traditional stochastic optimization economic dispatch only considers the response of AGC units at the dispatch time. However, in actual power system operation, AGC units must continuously adjust their output during the dispatch period to respond to random net load fluctuations and their uncertainties. This discrepancy between economic dispatch models and actual power system operation makes it difficult for dispatch decisions to account for the response of AGC units during the system dispatch period, impacting system economic efficiency. Insufficient frequency regulation reserve capacity may even prevent dispatch plans from meeting real-time operational requirements, compromising system security. To effectively account for random net load fluctuations and their uncertainties during the dispatch period, a refined model of AGC unit response at a fine-grained time scale is constructed within a chance-constrained framework. It should be noted that this refined model of AGC unit response does not change the inherent pattern of sending dispatch instructions at the dispatch time instant in existing economic dispatch. However, it enables the stochastic economic dispatch model to consider the output adjustments made by units during the dispatch period in response to random net load fluctuations and their uncertainties, thereby accounting for the adjustment costs of AGC response actions during the dispatch period and ensuring that unit dispatch plans effectively address random net load fluctuations during the dispatch period.

[0092] During the dispatch period, the AGC unit will adjust its output to respond to the random fluctuations in net load and its uncertainty. In order to fine-tune the response action of the AGC unit, a single dispatch period is subdivided into K short periods, and the time resolution of the unit AGC response short period is considered to be 4 seconds to 3 minutes (the specific time resolution depends on the actual situation of the response performance of different AGC units). In the real-time operation stage, the power system monitors the system power imbalance every short period. If the power imbalance exceeds a certain threshold (called the dead zone of regional regulation demand in industrial practice, which can avoid frequent adjustment of AGC units), the frequency regulation unit providing frequency regulation service will need to adjust its own output to rebalance the power, such as Figure 1 Otherwise, the unit does not need to adjust its own output. In addition, like the stochastic optimization economic dispatch model, the constructed model still considers the power balance at the beginning of the dispatch period.

[0093] The actual output of the AGC unit in operation is decomposed into planned output and response output. Figure 2As shown, the change in the actual output of the AGC unit includes the change in the planned output and the change in the response output. Among them, the change in planned output is caused by the unit tracking the scheduling plan, and the change in response output is caused by the response of the AGC unit. Its purpose is to deal with the deviation between the unit's planned output and the actual net load random fluctuation and its uncertainty during the scheduling period, so as to ensure the real-time power balance of the system. For the output change caused by the AGC unit tracking the scheduling plan, the present invention adopts a linear tracking mode to describe it, that is, the planned output within the scheduling period changes linearly with time, and its rate of change is determined by the output plan at adjacent scheduling time points. Although Figure 2 As shown, the AGC unit response output is also related to the unit scheduling plan tracking mode. However, the present invention's analysis of the relationship between random net load fluctuations and their uncertainty and AGC response actions is not limited to the linear tracking mode and is also applicable to other tracking modes. Therefore, the present invention constructs an AGC unit response action model based on the change in response output under the opportunity constraint framework. The specific steps are as follows:

[0094] 1) Determine the total planned output of the AGC units within the dispatch time based on the fine-grained net load forecast curve (which can determine the sum of the planned output of each unit at the clearing time point) and the linear tracking mode.

[0095]

[0096] Where, is the predicted power demand of net load i at the dispatch time point t; is the total planned output of the AGC units at the dispatching time t, which maintains power balance with the net load at the dispatching time; is the total planned output of the AGC units at the short time point k within the scheduling period t, which is determined by the linear tracking mode; K is the total number of time points in the next section of the scheduling period; I D is the collection of load nodes in the system.

[0097] It's worth noting that in the proposed method, the time resolution of the dispatch period t is the same as that of traditional economic dispatch, typically 1 hour or 15 minutes, depending on the specific dispatch method in practice. The total number of time points, K, in the lower portion of the dispatch period is determined based on the specific time resolution of the unit's AGC response period and the time resolution of the dispatch period t, also depending on the specific dispatch method and unit conditions.

[0098] 2) Construct the total system power deviation considering the random fluctuation of net load and its uncertainty during the scheduling period, as shown in formula (3).

[0099]

[0100] Where, is the total system power deviation at the scheduling time point t; It represents the total system power deviation at short time point k within the scheduling period t; is the predicted power demand of net load i at short time point k within the dispatch period t; ΔD i,t,k is the deviation between the predicted power demand of net load i at short time point k within the scheduling period t and the actual power demand, that is, the net load uncertainty.

[0101] 3) Considering the dead zone of regulation demand, the AGC unit response action model is constructed.

[0102]

[0103] Where, ΔP i,t,1 represents the response output of AGC unit i at the dispatch time t, which is determined by the AGC adjustment factor β of AGC unit i i,t Total deviation from the system power at that moment Determine; ΔP i,t,k is the response output of AGC unit i at short time point k in the dispatch period t, and is related to ΔP i,t,1 Different, ΔP i,t,k The AGC unit will make corresponding adjustments only when the probability that the total system power deviation is higher than the dead zone DL is greater than the given probability value 1-ε.

[0104] At this point, a refined model of AGC unit response behavior has been constructed based on fine-grained net load forecast curves. This effectively accounts for the AGC unit's response to random net load fluctuations and their uncertainties during the economic dispatch phase. This model is then embedded within a traditional stochastic optimization economic dispatch model to construct a chance-constrained economic dispatch model that considers the AGC's fine-grained timescale response behavior.

[0105] S2: Combined with the refined model of AGC unit response action, considering the AGC fine-grained time scale response action, an opportunity-constrained economic dispatch model is constructed;

[0106] (1) Objective function

[0107] The objective function of the opportunity-constrained economic dispatch model proposed in this invention consists of two parts: 1) system power generation cost; 2) frequency regulation and standby cost, as shown below:

[0108]

[0109] Where, represents the planned output of AGC unit i at short-term time point k within the scheduling period t; and are the up / down frequency regulation reserve capacity of AGC unit i at dispatch time t; and I represents the power generation quotation and frequency regulation reserve capacity quotation of AGC unit i respectively; G is the set of thermal power units in the system; T is the total number of scheduling periods t in economic scheduling.

[0110] (2) Operational constraints

[0111] a) Power balance constraints

[0112] In the present invention, it is assumed that all thermal power units are AGC units. Therefore, at the scheduling time point, the system needs to ensure that the total planned output of all AGC units is equal to the total power demand predicted by the net load.

[0113]

[0114] Where, It represents the planned output of AGC unit i at the scheduling time point t.

[0115] b) Unit planned output constraints

[0116] According to the linear tracking mode of the AGC unit, its response output at the short time point k within the dispatch period t is It can be calculated by the following formula.

[0117]

[0118] Where, It represents the planned output of AGC unit i at short time point k within the scheduling period t.

[0119] c) Constraints on actual unit output and actual net load power demand

[0120] The actual output of a unit is the sum of its planned output and its response output. Similarly, the actual power demand of the net load is the sum of its predicted power demand and its uncertainty, as shown in the following formula.

[0121]

[0122] Where, P i,t,k represents the actual output of AGC unit i at short time point k within the dispatch period t; D i,t,k is the actual power demand of net load i at short time point k within the scheduling period t.

[0123] d) Unit frequency regulation reserve capacity constraints

[0124] The unit frequency regulation reserve capacity must meet the AGC unit adjustment requirements at the short-term dispatch point within each dispatch period with a given probability of 1-ε, and the actual output of the AGC unit must be within the unit's physical output range. The specific constraints are as follows.

[0125]

[0126] Where, P i max and P i min Indicates the maximum / minimum output limit of AGC unit i.

[0127] e) Line flow constraints

[0128] The system line flow must ensure that it meets the line physical limit with a given probability 1-ε at the short-term scheduling point within each scheduling period.

[0129]

[0130] Where, PTDF li is the power transfer distribution factor of branch l to node i.

[0131] It should be noted that the present invention assumes that all thermal power units in the system are AGC units, which have the ability to quickly respond to random fluctuations in net load and its uncertainty. Therefore, the climbing constraints of the units are not considered. However, the method proposed in the present invention is still applicable to actual systems where only some units are AGC units.

[0132] Therefore, an opportunity-constrained economic dispatch model considering the fine-grained time-scale response of AGC is established. By considering the refined response of AGC units and the system operation constraints at fine-grained time scales in economic dispatch, the behavior of AGC units is further standardized and constrained to ensure the economic and safe operation of the system. The focus of this invention is how to formulate AGC instruction β i,t , so that the AGC unit can be based on the instructions and power mismatch information and The output is adjusted in real time to absorb the uncertainty of the net load of the system. The present invention does not consider the AGC control performance of the AGC unit itself, which is beyond the research scope of the present invention.

[0133] The model is a chance-constrained linear programming model, which will be analytically transformed later. Although the model takes into account the response output of the AGC unit at a fine-grained time scale, the final output of the model is still the planned output of the AGC unit at the dispatch time. And reserve frequency regulation capacity and Consistent with existing economic dispatch models.

[0134] S3: Analyze and transform the opportunity-constrained economic dispatch model to achieve explicit representation of the AGC fine-grained time-scale response actions.

[0135] The opportunity-constrained economic dispatch model established in S2 cannot be solved directly, and the opportunity constraints need to be analytically transformed.

[0136] Existing solutions to the opportunity-constrained economic dispatch problem revolve around determining the uncertainty boundary. When the power system operating boundary function is a linear function, the opportunity constraint uncertainty boundary can be obtained analytically. The opportunity constraint of the opportunity-constrained economic dispatch model can be expressed as follows:

[0137] Pr(g(x,0)+b(x) T ΔD≤g max )≥1-ε (18)

[0138] Where g(x,0) represents the system operating boundary function of the predicted operating point, that is, the system operating boundary when the net load power uncertainty is not considered; b() is the sensitivity matrix of g to the net load power uncertainty ΔD, which is essentially a linear function matrix of the power system control decision variable x; the term b(x) T ΔD represents the uncertainty of the system operation boundary caused by the uncertainty of net load power.

[0139] Assuming that the mean and standard deviation of the net load power uncertainty ΔD have been obtained from its historical or simulated data, the mean and standard deviation of the system operating boundary can be calculated as follows:

[0140] μ(g(x,0)+b(x) T ΔD)=g(x,0)+b(x) T μ D (19)

[0141]

[0142] Where μ D and Σ D They represent the mean vector and covariance matrix of the net load power uncertainty respectively. The covariance matrix can be constructed from the standard deviation vector of the net load power uncertainty. Based on the literature opportunity constraint, it can be analytically transformed into the following form:

[0143]

[0144]

[0145] Where, Γ ε is a constant, representing the transfer factor of the uncertainty standard deviation; UM g It is expressed as uncertainty bound, which is essentially to determine the additional operating margin reserved for the system under a given constraint violation probability. Constraint (21) is a convex second-order cone constraint and can be solved directly using commercial solvers.

[0146] For the condition of the logical discriminant in formula (6) Transformed into a set of logical discriminant conditions related to opportunity constraints:

[0147]

[0148] For the two chance constraints in the discriminant, they can be analytically transformed into the following form according to (18)-(22):

[0149]

[0150] Where: Indicates N D dimensional unit column vector, N D is the number of load nodes. Combining equations (23)-(24), equation (6) can be transformed into the following form:

[0151]

[0152] The analytical transformation of the opportunity constraints (12) and (13) is as follows:

[0153]

[0154] Where: b p,i (β i,t ) represents the sensitivity matrix of the response output of AGC unit i at the dispatch time t to the net load power uncertainty ΔD.

[0155] Similarly, the analytical transformation of opportunity constraints (16) and (17) is as follows:

[0156]

[0157] Where: b l (β t ) represents the sensitivity matrix of the uncertainty power flow on branch l at dispatch time t to the uncertainty of net load power ΔD; PTDF l is the power transfer distribution factor vector of branch l to system nodes.

[0158] Therefore, the opportunity-constrained economic dispatch model mentioned above can be transformed into a second-order cone-convex model, which can be directly solved by commercial solvers. The specific analytical model is as follows:

[0159] Objective function: (7)

[0160] Constraints: (8)-(11), (14)-(15), (25)-(31)

[0161] It should be noted that the analytical model can calculate the appropriate uncertainty standard deviation transfer factor Г according to the net load distribution.ε , to adapt to the net load power uncertainty distribution such as Gaussian distribution, symmetric distribution, unimodal distribution, student-t, and distributed robustness.

[0162] If the net load power uncertainty is assumed to follow Gaussian distribution, then Г ε The expression is as follows:

[0163] Γ ε =Ψ -1 (1-ε) (32)

[0164] Where Ψ is the probability density function of the Gaussian distribution.

[0165] In actual power system operation, historical data is often used to estimate the distribution of net load uncertainty, which can follow an arbitrary distribution. Given that this invention focuses on the refined modeling of the fine-grained timescale response of AGC units, the analytical transformation still uses the traditional chance-constrained analytical transformation method based on mean and variance.

[0166] It is important to note that the analytical transformation of stochastic optimization models is a natural advantage of applying chance-constrained stochastic optimization to power system economic dispatch problems. Within the framework of analytical economic dispatch models, the value of various system resources can be effectively measured using KKT conditions and Lagrange multipliers. Existing research has also developed node-based electricity pricing methods for renewable energy uncertainty based on chance-constrained economic dispatch models. Because the proposed method explicitly accounts for the response of AGC units at fine-grained time scales, it can also be used to obtain the ancillary service costs charged by AGC units in the power market for providing this type of service based on node-based electricity pricing methods.

[0167] For ease of understanding, the present invention provides a more specific embodiment:

[0168] (1) Collect data

[0169] The present invention is based on the net load forecast data of a provincial power grid in China on a certain day in May 2020. The data contains all net load forecast data with an interval of 15s within a day. In the example simulation, the total number of dispatch periods T is 24 periods considered by traditional economic dispatch; the total number of short moments K in a unit dispatch period is 240, that is, 1 hour is divided into 240 short periods of 15s. The net load data of the IEEE 30-node system and the 118-node system are scaled so that the net load data used for simulation matches the parameters of the test system. In order to take into account the uncertainty of the net load forecast, the mean and variance of the short-term node net load forecast error in each dispatch period are randomly generated.

[0170] (2) Constructing an opportunity-constrained economic dispatch model that considers the fine-grained time-scale response actions of AGC

[0171] A fine-grained time-scale response model for AGCs was constructed, taking into account net load uncertainty. Based on the actual AGC response strategy, the response patterns of AGC units to net load fluctuations and their uncertainties were constructed within a chance-constrained framework, achieving accurate modeling of the AGC unit response actions at a fine-grained time scale. A chance-constrained economic dispatch method was then proposed, embedding the AGC fine-grained time-scale response model. The fine-grained time-scale response actions of AGC units were considered within the chance-constrained economic dispatch model.

[0172] (3) Analytical transformation and solution of the opportunity-constrained economic dispatch model

[0173] The constructed opportunity-constrained economic dispatch model considering the fine-grained time-scale response action of AGC is analytically transformed into a second-order cone-convex model that is easy to solve, and is directly solved using a commercial solver.

[0174] (4) Simulation analysis

[0175] A case simulation was conducted using the IEEE 30 and IEEE 118 node systems as examples. The simulation results show that in the IEEE 118 standard test system, the economic dispatch plan obtained by the method proposed in the present invention has the lowest total operating cost, and the over-limit probability of the line flow and frequency regulation reserve constraints meet the set values. At the same time, it can still effectively ensure the economy and safety of the system in the larger test system of the IEEE 118 node system. In terms of calculation time, although the method of the present invention fully considers the AGC action at a fine-grained time scale, it can still guarantee a calculation time of minutes, which has certain feasibility. In summary, the method proposed in the present invention can provide a more economical and safer dispatching solution than the existing opportunity-constrained economic dispatch method.

[0176] The specific simulation results are as follows:

[0177] 1) Simulation data and example settings

[0178] The present invention is based on the net load forecast data of a provincial power grid in China on a certain day in May 2020. The data contains all net load forecast data with an interval of 15s within a day. Therefore, in the example simulation, the total number of dispatch periods T is still the 24 periods considered by traditional economic dispatch; the total number of short moments K in a unit dispatch period is 240, that is, 1 hour is divided into 240 short periods of 15s. The net load data of the IEEE 30-node system and the 118-node system are scaled so that the net load data used for simulation matches the parameters of the test system. In order to take into account the uncertainty of the net load forecast, the mean and variance of the short-term node net load forecast error in each dispatch period are randomly generated.

[0179] The following three methods are compared in the simulation:

[0180] M0: The opportunity-constrained economic dispatch method proposed in this invention explicitly considers the AGC fine-grained time-scale response action

[0181] M1: Chance-constrained economic dispatch method without considering AGC response action

[0182] M2: Chance-constrained economic dispatch method for determining AGC participation factors based on maximum unit output 2) Safety verification of the proposed method

[0183] To verify the security of the opportunity-constrained economic dispatch method proposed in this paper, which takes into account the fine-grained time-scale response action of AGC, the present invention takes Gaussian distribution as an example. Based on the mean and variance of the actual net load forecast data and the short-term node net load forecast error in each scheduling period, the Monte Carlo method is used to sample 5000 groups of samples for verifying the constraint violation probability of the economic dispatch result. The simulation results are shown in Table 1.

[0184] Table 1 Comparison of IEEE 30-node system security

[0185]

[0186]

[0187] This invention analyzes system security from two perspectives: the maximum probability of constraint violations and the average probability of constraint violations. The maximum probability of constraint violations reflects the potential probability of a system security issue, while the average probability of constraint violations reflects the overall security level of the system. It should be noted that it is normal for the average probability of constraint violations M0 to be less than the set threshold, as chance constraints only ensure that the probability of constraint violations for each constraint is less than the set threshold, not equal to it. Analysis of Table 1 leads to the following conclusions:

[0188] a) The method proposed in this invention can ensure that the probability of exceeding the system operation constraint meets the specified threshold;

[0189] b) Traditional opportunity-constrained economic dispatch methods cannot take into account the fine-grained time-scale response of AGC, making it difficult to ensure the operational safety of the system at every short moment during the entire dispatch period, and are prone to constraint violations.

[0190] c) Compared with the traditional opportunity-constrained economic dispatch method, the method of the present invention can effectively ensure that the constraint violation probability of the system at each short moment in the entire dispatch period is within a given threshold, thereby achieving safe operation of the system;

[0191] d) Comparing M1 and M2, it can be seen that for the economic dispatch method that only considers the response of AGC units to the random fluctuations of renewable energy and their uncertainties at the dispatch time point, the setting of its AGC participation factor has no obvious impact on the safety of the overall system. However, since neither M1 nor M2 can consider the response of AGC units at a fine-grained time scale, the constraint exceeding probability of their dispatch results is higher than the set value of 5%, which seriously affects the safe operation of the system.

[0192] 3) Economic verification of the proposed method

[0193] To verify the economic feasibility of the proposed opportunity-constrained economic dispatch method that takes into account the fine-grained time-scale response of the AGC, Table 2 compares the power generation cost, frequency regulation reserve cost, and total operating cost of the two opportunity-constrained economic dispatch methods, M0, M1, and M2. Figure 3 The comparison of the total frequency regulation reserve capacity required at each dispatch time for the three economic dispatch schemes is shown below.

[0194] Table 2 Comparison of economic efficiency of IEEE 30-bus system

[0195]

[0196] The following conclusions can be drawn from the analysis of Table 2:

[0197] a) Compared with M1 and M2, the scheduling scheme obtained by the method proposed in this invention has lower power generation cost, frequency regulation and standby cost, and total operating cost;

[0198] b) The costs of the economic dispatch solutions derived from the three models are relatively close. This is because economic dispatch requires power balance at the dispatch time. The power demand of the net load at each dispatch time is constant, so the power required to be provided by the two dispatch solutions is not much different.

[0199] c) Compared with M0 and M1, the reserve cost required by M2 is higher, which shows that considering the optimization of AGC participation factor in the economic dispatch model can effectively save the frequency regulation reserve cost of the system.

[0200] Depend on Figure 3 It can be seen that the frequency regulation reserve capacity given by the method proposed in this invention is higher than that of the traditional opportunity-constrained economic dispatch method. This shows that in order to ensure sufficient frequency regulation reserve capacity at a fine-grained time scale, the system needs to provide more frequency regulation reserve capacity to ensure the economic and safe operation of the power grid. Figure 3It can be seen that the scheduling scheme obtained by the method proposed in this invention requires more frequency regulation reserve capacity than M1 and M2, but the cost of frequency regulation reserve capacity is still lower than the traditional opportunity constrained economic scheduling method. This is because the model proposed in this invention takes into account the response action of AGC to net load uncertainty at a fine-grained time scale, which allows AGCs with lower frequency regulation reserve capacity bids to provide more frequency regulation reserve capacity, which can effectively save the overall operating cost of the system. In addition, analysis Figure 3 It can be seen that the frequency regulation reserve capacity obtained by optimization of M1 and M2 is exactly the same at all dispatching points, indicating that considering the AGC participation factor in the economic dispatch model does not affect the total frequency regulation reserve capacity of the system. This is because the net load uncertainty that needs to be smoothed by the AGC units of M1 and M2 at each dispatching time point is the same.

[0201] 4) Verification of the applicability of the proposed method in large systems

[0202] The present invention uses the IEEE 118-node standard test system to verify the applicability of the proposed method to larger power grids. Table 3 shows the simulation results of the three comparison methods on the IEEE 118-node system.

[0203] Table 3 Comparison of economic dispatch results of IEEE 118-bus system

[0204]

[0205] The following conclusions can be drawn from the analysis of Table 3:

[0206] a) In the IEEE 118 standard test system, the total operating cost of the economic dispatch plan obtained by the proposed method is the lowest compared with M1 and M2, and the over-limit probability of the line power flow and frequency reserve constraints meets the set values;

[0207] b) In larger systems, due to the large number of system constraints and relatively few constraints with over-limit risks, the average over-limit probability of the constraints obtained by the three methods is lower than that of the IEEE 30-bus system. However, the maximum over-limit probability of the M1 and M2 line flows and the frequency regulation reserve constraints shows that if only the system operation constraints at the scheduling time are considered, some severely congested constraints will not be able to meet the pre-set over-limit probability.

[0208] c) The method proposed in the present invention can effectively ensure the economy and security of the system in a large IEEE 118-node system test system;

[0209] d) In terms of computational time, as the number of factors considered in the chance-constrained economic dispatch model increases, so does the computational time. While the method of the present invention comprehensively considers the AGC operation at a fine-grained time scale, it still maintains a computational time of minutes, demonstrating its feasibility.

[0210] To address the difficulties faced by existing stochastic optimization economic dispatch methods in accounting for the actual response actions of AGC units at fine-grained time scales during the dispatch period, which threatens the safe and economic operation of the power grid and prevents the reasonable allocation of ancillary service costs, this paper proposes an opportunity-constrained economic dispatch method that explicitly accounts for the fine-grained time scale response actions of AGC units. Case analysis shows that the proposed method provides a more economical and secure dispatch solution than existing opportunity-constrained economic dispatch methods. This paper addresses the difficulty faced by existing stochastic optimization economic dispatch methods in adapting to the strong uncertainty in net load brought about by the large-scale integration of renewable energy sources. This paper proposes a refined modeling scheme for the economic dispatch problem, providing technical support for the economic and secure dispatch and market reform of new power systems.

[0211] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A chance-constrained economic dispatch method that explicitly takes into account the fine-grained time-scale response actions of AGC, characterized by: include: Step 1: Based on the change of response output, construct the AGC unit response action model under the opportunity constraint framework; Step 2: Combined with the refined model of AGC unit response action, considering the AGC fine-grained time scale response action, a chance-constrained economic dispatch model is constructed; Step 3: Analyze and transform the opportunity-constrained economic dispatch model to achieve explicit representation of the AGC fine-grained time-scale response action; In step 2, the objective function of the opportunity-constrained economic dispatch model includes the system power generation cost and the frequency regulation reserve cost; the objective function of the opportunity-constrained economic dispatch model is: Where, represents the planned output of AGC unit i at short-term time point k within the scheduling period t; and are the up / down frequency regulation reserve capacity of AGC unit i at dispatch time t; and I represents the power generation quotation and frequency regulation reserve capacity quotation of AGC unit i respectively; G is the collection of thermal power units in the system; T is the total number of dispatch periods t in economic dispatch; The step 3 comprises: Step 31: Convert the discriminant in the AGC unit response action model into a set of logical discriminants related to opportunity constraints, and parse and transform the expression form of the opportunity constraints in the logical discriminant; Step 32: Analyze and transform the logical discriminant judgment in the AGC unit response action model according to the expression form of the opportunity constraint after analysis and transformation; Step 33: Analytically transform some constraints in the unit frequency regulation reserve capacity constraints and line power flow constraints of the opportunity-constrained economic dispatch model; Step 34: Through steps 31 to 33, the opportunity-constrained economic dispatch model is transformed into a second-order cone-convex model, which can be directly solved by the solver. The objective function of the second-order cone-convex model is the same as that of the opportunity-constrained economic dispatch model, and the constraints are obtained through steps 2 and 33.

2. The method according to claim 1, characterized in that The step 1 comprises: Step 11: Determine the total planned output of the AGC units within the dispatch time based on the fine-grained net load forecast curve and linear tracking mode; Step 12: Construct the total system power deviation during the dispatch period considering the random fluctuation of net load and its uncertainty; Step 13: Considering the dead zone of regulation demand, construct the AGC unit response action model.

3. The method according to claim 2, characterized in that The step 11 comprises: Where, is the predicted power demand of net load i at the dispatch time point t; is the total planned output of the AGC units at the dispatching time t, which maintains power balance with the net load at the dispatching time; is the total planned output of the AGC units at the short time point k within the scheduling period t, which is determined by the linear tracking mode; K is the total number of time points in the next section of the scheduling period; I D is the collection of load nodes in the system.

4. The method according to claim 3, characterized in that The step 12 includes: Where, is the total system power deviation at the scheduling time point t; It represents the total system power deviation at short time point k within the scheduling period t; is the predicted power demand of net load i at short time point k within the dispatch period t; ΔD i,t,k is the deviation between the predicted power demand of net load i at short time point k within the scheduling period t and the actual power demand, that is, the net load uncertainty.

5. The method according to claim 4, characterized in that The step 13 comprises: Where, ΔP i,t,1 represents the response output of AGC unit i at the dispatch time t, which is determined by the AGC adjustment factor β of AGC unit i i,t Total deviation from the system power at that moment Determine; ΔP i,t,k is the response output of AGC unit i at short time point k in the dispatch period t, and is related to ΔP i,t,1 Different, ΔP i,t,k The AGC unit will make corresponding adjustments only when the probability that the total system power deviation is higher than the dead zone DL is greater than the given probability value 1-ε.

6. The method according to claim 5, characterized in that In step 2, the operation constraints of the opportunity-constrained economic dispatch model include power balance constraints, unit planned output constraints, unit actual output constraints and net load actual power demand constraints, unit frequency regulation reserve capacity constraints, and line power flow constraints; For the power balance constraint, assuming that all thermal power units are AGC units, at the dispatch time point, the system needs to ensure that the total planned output of all AGC units is equal to the total power demand predicted by the net load; Where, represents the planned output of AGC unit i at the scheduling time point t; For the unit planned output constraint, according to the linear tracking mode of the AGC unit, its response output at the short time point k within the scheduling period t is Calculated by the following formula: Where, represents the planned output of AGC unit i at short-term time point k within the scheduling period t; For the actual unit output constraint and the net load actual power demand constraint, the actual unit output is the sum of its planned output and the response output. Similarly, the net load actual power demand is the sum of its predicted power demand and its uncertainty, as shown in the following formula: Where, P i,t,k represents the actual output of AGC unit i at short time point k within the scheduling period t; D i,t,k is the actual power demand of net load i at short time point k within the scheduling period t; Regarding the unit frequency regulation reserve capacity constraint, the unit frequency regulation reserve capacity must meet the AGC unit adjustment demand at the short-term dispatch point within each dispatch period with a given probability of 1-ε, and the actual output of the AGC unit must be within the unit's physical output range. The specific constraints are as follows: Where, P i max and P i min Indicates the maximum / minimum output limit of AGC unit i; For line flow constraints, the system line flow must ensure that it meets the line physical limit with a given probability of 1-ε at the short-term scheduling point within each scheduling period; Where, PTDF li is the power transfer distribution factor of branch l to node i.

7. The method according to claim 1, characterized in that The step 31 includes: The opportunity constraint of the opportunity-constrained economic dispatch model is expressed as: Pr(g(x,0)+b(x) T ∆D≤g max )≥1-ε (18) Where g(x,0) represents the system operating boundary function of the predicted operating point, that is, the system operating boundary when the net load power uncertainty is not considered; b() is the sensitivity matrix of g to the net load power uncertainty ΔD, which is essentially a linear function matrix of the power system control decision variable x; b(x) T ΔD represents the uncertainty of the system operation boundary caused by the uncertainty of net load power; Assuming that the mean and standard deviation of the net load power uncertainty ΔD have been obtained from its historical or simulated data, the mean and standard deviation of the system operating boundary are calculated as follows: μ(g(x,0)+b(x) T ΔD)=g(x,0)+b(x) T m D (19) Where μ D and Σ D They represent the mean vector and covariance matrix of the net load power uncertainty, respectively. The covariance matrix is ​​constructed by the standard deviation vector of the net load power uncertainty. Based on the literature opportunity constraint analysis, it is transformed into the following form: Where, Γ ε is a constant, representing the transfer factor of the uncertainty standard deviation; UM g It is expressed as uncertainty boundary, which is essentially to determine the additional operating boundary margin reserved by the system under the given constraint exceeding probability; constraint (21) is a convex second-order cone constraint; For the condition of the logical discriminant in formula (6) Transformed into a set of logical discriminant conditions related to opportunity constraints: For the two chance constraints in the logical discriminant, according to (18)-(21), it is analytically transformed into the following form: Where: Indicates N D dimensional unit column vector, N D is the number of load nodes; combined with formulas (23)-(24), the logical discriminant judgment, that is, formula (6), is transformed into the following form:

8. The method according to claim 7, characterized in that The step 32 includes: The analytical transformation of opportunity constraints (12) and (13) is: Where: b p,i (β i,t ) represents the sensitivity matrix of the response output of AGC unit i at the dispatch time t to the net load power uncertainty ΔD; Similarly, the analytical transformation of opportunity constraints (16) and (17) is: Where: b l (β t ) represents the sensitivity matrix of the uncertainty power flow on branch l at dispatch time t to the uncertainty of net load power ΔD; PTDF l is the power transfer distribution factor vector of branch l to system nodes; The step 33 includes: The objective function of the second-order cone-convex model is formula (7), and the constraints are formulas (8)-(11), (14)-(15), and (25)-(31).

9. The method according to claim 7, characterized in that The second-order cone convex model calculates the uncertainty standard deviation transfer factor Г based on the net load distribution ε , to adapt to the net load power uncertainty distribution; if the net load power uncertainty obeys Gaussian distribution, then Г ε The expression is: C ε =Ψ -1 (1-e) (32) Where Ψ is the probability density function of the Gaussian distribution.

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