A Joint Optimization Method for Electric Energy, Inertia and Primary Frequency Regulation Considering EILS

Abstract

The present invention relates to a combined optimization method for electric energy, inertia and primary frequency regulation considering EILS, comprising the following steps: constructing an objective function of a continuous SCUC model; constructing conventional constraints of the continuous SCUC model; constructing frequency security constraints of the continuous SCUC model considering emergency interruptible loads, and writing the frequency lowest point constraint in the frequency security constraints in the form of a second-order cone, wherein the frequency lowest point constraint includes two cases; constructing a comprehensive evaluation index for the frequency lowest point constraint, and selecting the frequency lowest point constraint from the two cases based on the comprehensive evaluation index; constructing a Lagrangian function of the continuous SCUC model based on the objective function, conventional constraints and frequency security constraints, and solving the Lagrangian function to obtain the clearing prices of electric energy, inertia and primary frequency regulation. Compared with the prior art, the present invention has the advantages of comprehensive consideration and more practical optimization results, etc.

Description

Technical Field

[0001] The present invention relates to the field of optimal dispatching of power systems, and in particular to a method for jointly optimizing electric energy, inertia and primary frequency regulation considering EILS. Background Technique

[0002] To ensure the frequency security of the power system, researchers have begun to attach importance to the value of inertia and primary frequency regulation resources under large disturbance accidents. However, the existing models do not deeply study the coordinated optimization clearing of electric energy, inertia and primary frequency response (PFR) ancillary services in the spot market based on security-constrained unit commitment, and do not consider the impact of emergency interruptible load service (EILS) resources, resulting in inaccurate optimal dispatching results. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for jointly optimizing electric energy, inertia and primary frequency regulation considering EILS.

[0004] The purpose of the present invention can be achieved through the following technical solutions:

[0005] A method for jointly optimizing electric energy, inertia and primary frequency regulation considering EILS includes the following steps:

[0006] Step 1) Construct the objective function of the continuous SCUC model;

[0007] Step 2) Construct the conventional constraints of the continuous SCUC model;

[0008] Step 3) Construct the frequency security constraints of the continuous SCUC model considering emergency interruptible loads, and write the frequency nadir constraint in the frequency security constraints in the form of a second-order cone. The frequency nadir constraint includes two cases;

[0009] Step 4) Construct a comprehensive evaluation index for the frequency nadir constraint, and select the frequency nadir constraint from the two cases based on the comprehensive evaluation index;

[0010] Step 5) Construct the Lagrangian function of the continuous SCUC model based on the objective function, conventional constraints and frequency security constraints, and solve the Lagrangian function to obtain the clearing prices of electric energy, inertia and primary frequency regulation.

[0011] The objective function of the continuous SCUC model is:

[0012]

[0013] Among them, the subscripts HG, SG, and WG represent thermal power units, hydropower units, and wind power units respectively; N H , N S , and T represent the number of thermal power units, the number of hydropower units, and the scheduling time scale respectively; C HGi,t , C SGi,t , and C WG,t represent the electricity price quotations of thermal, hydro, and wind power units based on the operating cost, represents the scheduling cost of the emergency interruptible load resource, with the unit of $ / (MW·h); and represent the primary frequency regulation price quotations of thermal, hydro, and wind power units, with the unit of $ / (MW·h); P HGi,t , P SGi,t , and P WG,t represent the electricity winning bids of the units in the joint market, with the unit of MW; R HGi,t , R SGi,t , and R WG,t represent the PFR reserve capacity winning bids of the units under the anticipated large disturbance, with the unit of MW; represents the procurement quantity of the emergency interruptible load resource, with the unit of MW.

[0014] The conventional constraints of the continuous SCUC model include power balance constraints, unit output upper and lower limit constraints, and emergency interruptible load constraints.

[0015] The power balance constraint is:

[0016]

[0017] Among them, D t represents the load size in the t-th period predicted in advance;

[0018] The unit output upper and lower limit constraints are:

[0019]

[0020] Among them, and represent the upper and lower limits of the power generation of the unit; represents the power generation of the wind farm in the t-th period predicted in advance; represents the installed capacity of the wind power unit; U HGi,t and U SGi,t represent the start-stop variables of the unit, with the values of 0 or 1;

[0021] The emergency interruptible load constraint is:

[0022]

[0023] Among them, α% refers to the proportion of the purchased emergency interruptible load resources in the load.

[0024] The frequency security constraints include the frequency change rate constraint, the lowest frequency point constraint, and the quasi-steady state constraint.

[0025] The frequency change rate constraint is:

[0026]

[0027] Among them, H HGi and H SGi respectively refer to the inertia constants of thermal power units and hydropower units, with the unit of s; S HGi and S SGi refer to the rated capacities of thermal power units and hydropower units, with the unit of MW; U HGi,t and U SGi,t represent the start-stop variables of the units, taking values of 0 or 1; f0 is the nominal frequency of the system, with the unit of Hz; ΔP L refers to the pre-conceived large disturbance power, with the unit of MW; t is the response time, with the unit of s; is the frequency change rate threshold;

[0028] The lowest frequency point constraint includes two cases:

[0029] Case 1:

[0030]

[0031] Case 2:

[0032]

[0033] Among them, refers to the emergency interruptible load resources, T W is the primary frequency regulation time of wind turbines, T SH is the primary frequency regulation time of thermal and hydropower units, Δf maxc is the frequency deviation threshold;

[0034] The quasi-steady state constraint is:

[0035]

[0036] The second-order cone form of the lowest frequency point constraint is:

[0037] Case 1:

[0038]

[0039] Case 2:

[0040]

[0041] The steps for constructing the comprehensive evaluation index with the lowest frequency point constraint include the following:

[0042] Step 4-1) Determine the cost index A i : Normalize the cost, with the benchmark value being the lowest cost:

[0043]

[0044] Among them, i represents two cases of the lowest frequency point constraint, taking the value of 1 for case one and 2 for case two; F represents the total purchase cost of the power grid, that is, the objective function of the continuous SCUC model, and A i indicates that the lower the cost area, the higher the index value;

[0045] Step 4-2) Determine the inertia index B i : Normalize the inertia, with the benchmark value being the maximum inertia:

[0046]

[0047] Among them, M all represents the total inertia in the system. When the system encounters a pre-conceived disturbance, the slope of the frequency curve is related to the inertia in the system, and B i indicates that the more inertia there is, the flatter the frequency curve, and the higher the index value;

[0048] Step 4-3) Determine the effective PFR response ratio index Q i : Normalize the effective PFR response ratio, with the benchmark value being the maximum effective PFR response ratio:

[0049]

[0050] Among them, the superscripts HG, SG, and WG represent thermal power units, hydropower units, and wind power units respectively; E is the effective PFR response ratio, that is, the PFR reserve capacity R yx awarded to the unit through the clearing model, and the PFR resource R cq responded by the unit after the disturbance when the frequency drops from the start to the lowest frequency point. In fact, it is also the ratio of the time to reach the lowest frequency point in the frequency curve to the unit's frequency regulation time; is the time to reach the lowest frequency point in the frequency curve; Q i indicates that the larger the effective PFR response ratio, the higher the utilization rate of the PFR reserve, and the higher the index value;

[0051] Step 4-4) Determine the comprehensive evaluation index Y of the lowest frequency point constraint i :

[0052] Y i = aAi +bB i +cQ i

[0053] Among them, a, b, and c are the weight factors of the three components, and their value ranges are [0, 1], and a + b + c = 1 is satisfied.

[0054] The Lagrangian function of the continuous SCUC model is expressed as:

[0055]

[0056] Among them, and are the Lagrange multipliers of the power balance constraint, the frequency change rate constraint, and the quasi-steady state frequency constraint respectively; and μ t are the Lagrange multipliers of the frequency nadir constraint represented in the second-order cone form.

[0057] The clearing prices of electric energy, inertia, and primary frequency regulation are respectively:

[0058] A) Clearing price of electric energy

[0059]

[0060] B) Clearing price of inertia

[0061]

[0062] C) Clearing price of PFR of wind turbines

[0063]

[0064] D) Clearing price of PFR of hydro turbines

[0065]

[0066] E) Clearing price of PFR of thermal power units

[0067]

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] (1) The present invention deeply studies the joint optimization clearing of electric energy, inertia, and PFR ancillary services in the spot market based on security-constrained unit commitment, which can meet the frequency security of the system in the face of large disturbance accidents, and achieve the optimal allocation of resources and the minimum payment of costs.

[0070] (2) The present invention takes into account the impact of emergency interruptible load resources and can alleviate the system's demand for inertia and PFR ancillary services. At the same time, considering two cases of the frequency nadir constraint and the comprehensive evaluation index of the frequency nadir constraint, it can be more in line with the actual situation and obtain the optimal scheduling result. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is the flowchart of the method of the present invention;

[0072] Figure 2 is the predicted wind power and the predicted daily load value;

[0073] Figure 3 is the unit commitment result of the 4 scenarios described in the embodiment of the present invention;

[0074] Figure 4 is the total inertia clearing result of the 4 scenarios described in the embodiment of the present invention;

[0075] Figure 5 is the total PFR clearing result of the 4 scenarios described in the embodiment of the present invention;

[0076] Figure 6 is the RoCoF value under the 4 scenarios described in the embodiment of the present invention;

[0077] Figure 7 is the frequency nadir under the 4 scenarios described in the embodiment of the present invention;

[0078] Figure 8 is the electricity, inertia, and PFR clearing prices under the 3 scenarios described in the embodiment of the present invention;

[0079] Figure 9 is the total cost value of Scenario 4 with different α in the embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0080] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manner and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

[0081] This embodiment provides a combined optimization method for electricity, inertia, and primary frequency regulation considering EILS, as Figure 1 shown, including the following steps:

[0082] Step 1) Construct the objective function of the continuous SCUC model.

[0083] The objective function of the continuous SCUC model is:

[0084]

[0085] Among them, the subscripts HG, SG, and WG represent thermal power units, hydropower units, and wind power units respectively; N H , N S , and T represent the number of thermal power units, the number of hydropower units, and the scheduling time scale respectively; C HGi,t , C SGi,t , and C WG,t represent the electricity price quotes of thermal, hydro, and wind power units based on operating costs, represents the scheduling cost of emergency interruptible load resources, with the unit of $ / (MW·h); and represent the primary frequency response (PFR) price quotes of thermal, hydro, and wind power units, with the unit of $ / (MW·h); P HGi,t , P SGi,t , and P WG,t represent the electricity winning bids of the units in the joint market, with the unit of MW; R HGi,t , R SGi,t , and R WG,t represent the PFR reserve capacity winning bids of the units under the pre - conceived large disturbances, with the unit of MW; represents the procurement quantity of emergency interruptible load service (EILS) resources, with the unit of MW.

[0086] Step 2) Construct the conventional constraints of the continuous SCUC model.

[0087] The conventional constraints of the continuous SCUC model include power balance constraints, unit output upper and lower limit constraints, and emergency interruptible load constraints.

[0088] Step 2 - 1) Determine the power balance constraints:

[0089]

[0090] Among them, D t represents the load magnitude during the t - th period predicted in advance.

[0091] Step 2 - 2) Determine the unit output upper and lower limit constraints:

[0092]

[0093] Among them, and represent the upper and lower limits of the generating power of the unit; represents the generating power of the wind farm during the t - th period predicted in advance; Represents the installed capacity of the wind turbine; U HGi,t and U SGi,t represent the start-stop variables of the unit, taking values of 0 or 1.

[0094] Step 2-3) Determine the emergency interruptible load constraint:

[0095]

[0096] where α% refers to the proportion of the purchased emergency interruptible load resources in the load.

[0097] Step 3) Construct the frequency security constraint of the continuous SCUC model considering the emergency interruptible load, and write the frequency lowest point constraint in the frequency security constraint in the form of a second-order cone.

[0098] The frequency security constraint includes the rate of change of frequency constraint, the frequency lowest point constraint, and the quasi-steady state constraint.

[0099] Step 3-1) Determine the rate of change of frequency (RoCoF) constraint:

[0100]

[0101] where H HGi and H SGi are the inertia constants of thermal power units and hydropower units respectively, with the unit of s; S HGi and S SGi are the rated capacities of thermal power units and hydropower units respectively, with the unit of MW; U HGi,t and U SGi,t represent the start-stop variables of the unit, taking values of 0 or 1; f0 is the nominal frequency of the system, with the unit of Hz; ΔP L is the power of the anticipated large disturbance, with the unit of MW; t is the response time, with the unit of s; is the rate of change of frequency threshold.

[0102] Step 3-2) Determine the frequency lowest point constraint:

[0103] The frequency lowest point constraint includes two cases:

[0104] Case 1:

[0105]

[0106] Case 2:

[0107]

[0108] where, refers to the emergency interruptible load resources, T W is the primary frequency regulation time of the wind turbine, T SHis the primary frequency regulation time of the water and thermal power units, Δf maxc is the frequency deviation threshold;

[0109] The constraint of the lowest frequency point is written in the second-order cone form as:

[0110] Case 1:

[0111]

[0112] Case 2:

[0113]

[0114] Step 3-3) Determine the quasi-steady state constraint:

[0115]

[0116] Step 4) Construct a comprehensive evaluation index for the lowest frequency point constraint, and select the lowest frequency point constraint from the two cases based on the comprehensive evaluation index.

[0117] Step 4-1) Determine the cost index A i : Normalize the cost, and the benchmark value is the minimum cost:

[0118]

[0119] where i represents the two cases of the lowest frequency point constraint, taking the value of 1 for Case 1 and 2 for Case 2; F represents the total purchase cost of the power grid, that is, the objective function of the continuous SCUC model, A i indicates that the lower the cost area, the higher the index value.

[0120] Step 4-2) Determine the inertia index B i : Normalize the inertia, and the benchmark value is the maximum inertia:

[0121]

[0122] where M all represents the total inertia in the system. When the system encounters a pre-conceived disturbance, the slope of the frequency curve is related to the inertia in the system, B i indicates that the more inertia, the flatter the frequency curve and the higher the index value.

[0123] Step 4-3) Determine the effective PFR response ratio index Q i : Normalize the effective PFR response ratio, and the benchmark value is the maximum effective PFR response ratio:

[0124]

[0125] Among them, the superscripts HG, SG, and WG represent thermal power units, hydropower units, and wind power units respectively; E is the effective PFR response ratio, that is, the PFR reserve capacity R won by the unit through the clearing model yx and the PFR resource R responded by the unit from the start of the frequency drop to the lowest point of the frequency after the disturbance cq The ratio, which is actually also the ratio of the time to reach the lowest point of the frequency in the frequency curve to the frequency regulation time of the unit; is the time to reach the lowest point of the frequency in the frequency curve; Q i It means that the larger the effective PFR response ratio, the higher the utilization rate of the PFR reserve and the higher the index value.

[0126] Step 4-4) Determine the comprehensive evaluation index Y of the frequency lowest point constraint i :

[0127] Y i = aA i + bB i + cQ i

[0128] Among them, a, b, and c are the weight factors of the three components, and the value range is [0,1], and a + b + c = 1.

[0129] The comprehensive evaluation index of the frequency lowest point constraint can be further optimized by combining weather factors. For example, in bad weather, the weights of the frequency curve related indicators are increased, etc.

[0130] Step 4-5) Select the frequency lowest point constraint corresponding to the larger value of the comprehensive evaluation index from the two situations based on the comprehensive evaluation index, as one of the frequency security constraints for finally constructing the Lagrangian function.

[0131] Step 5) Construct the Lagrangian function of the continuous SCUC model based on the objective function, conventional constraints, and frequency security constraints, and solve the Lagrangian function to obtain the clearing prices of electric energy, inertia, and primary frequency regulation.

[0132] The Lagrangian function of the continuous SCUC model is expressed as:

[0133]

[0134] Among them, and are the Lagrangian multipliers of the power balance constraint, frequency change rate constraint, and quasi-steady state frequency constraint respectively; and μ t are the Lagrangian multipliers of the frequency lowest point constraint represented in the second-order cone form.

[0135] Then, solving the Lagrangian function gives the clearing prices as follows:

[0136] A) Electrical energy clearing price

[0137]

[0138] B) Inertia clearing price

[0139]

[0140] C) Clearing price of PFR of wind turbines

[0141]

[0142] D) Clearing price of PFR of hydro turbines

[0143]

[0144] E) Clearing price of PFR of thermal power units

[0145]

[0146] In this embodiment, it is assumed that the system includes 10 thermal power units, 5 hydro turbines and a wind farm with a 40MW supercapacitor and a capacity of 400MW, and a case study is carried out with appropriate adjustment of some unit parameters. For the unit bid ($ / (MW·h)), the operating cost of thermal and hydro units is approximately used to replace the electrical energy bid, and the detailed data are shown in Table 1 and Table 2. The electrical energy bid of the wind farm is 0, the frequency regulation bid is 10 $ / (MW·h), and the EILS resource call cost is 11 $ / (MW·h).

[0147] Table 1 Parameters of thermal power units

[0148]

[0149] Table 2 Parameters of hydro turbines

[0150]

[0151] Wind power predicted output and daily load are as Figure 2 shown. The system base frequency is 50Hz, the maximum value of RoCoF is set to 0.5Hz / s, and the limit of the lowest frequency point is set to 49Hz. EILS starts to detect the disconnection signal at 49.7Hz and fully responds after 0.5s.

[0152] To analyze the influence of frequency security constraints on the system's day-ahead clearing results, the pre-contingency large disturbance power ΔP for each time period LSet it to 10% of the load and compare the following four different scenarios.

[0153] Scenario 1: Without considering the frequency security constraint, the units set a fixed PFR reserve capacity according to the traditional reserve requirements. For example, the thermal power units are set to 6% of the unit capacity, and the hydropower and wind power units are set to 10% of the unit capacity.

[0154] Scenario 2: Considering the frequency security constraint, the PFR reserve capacity of the units is not compulsorily specified, and the participation of the fans in frequency regulation and the power response of the EILS resources are not considered.

[0155] Scenario 3: On the basis of Scenario 2, consider the participation of the fans in frequency regulation.

[0156] Scenario 4: On the basis of Scenario 3, consider purchasing EILS resources with a procurement limit of 5% of the load ratio for each time period.

[0157] This embodiment gives the unit start-stop conditions of the thermal and hydropower units for 24 hours under four scenarios, as Figure 3 shown; the inertia and PFR clearing results under the pre-conceived large disturbances are as Figures 4-5 shown; the RoCoF and the lowest frequency point for each time period are as Figures 6-7 shown.

[0158] From Figure 3 it can be seen that the electricity energy and PFR bids of thermal power units 1 and 2 are relatively high, and it is difficult to win the bid when the load demand is low; the number of started units in Scenario 1 is less than that in Scenarios 2 and 3 because the started units are only restricted by power balance and not affected by the frequency security constraint; Scenario 4 reduces the demand for inertia and PFR due to the consideration of EILS resources, and the number of started units is less. From Figure 4 it can be seen that in time periods 8 - 15, due to the high load demand, the number of started units is large and the inertia is relatively large; although Scenario 3 considers the fan frequency regulation compared with Scenario 2, the inertia difference for each time period is not significant.

[0159] Figure 5Indicates the PFR clearing capacity under four scenarios. It can be seen that the units in Scenario 1 have a fixed PFR clearing capacity according to the traditional reserve requirements, and compared with Scenarios 2 and 3, the overall clearing capacity is smaller; compared with Scenario 2, Scenario 3 has a smaller total PFR clearing capacity because the frequency regulation time of the wind turbines is less than that of the thermal and hydro power units, and the PFR of the same capacity responds more fully, so the required quantity is less; in Scenario 4, the participation of EILS resources in the response can reduce a large amount of PFR reserve capacity of thermal and hydro power units, and the procurement volume of EILS resources reaches the limit value at each time period, accounting for 5% of the load ratio. The total costs of the four scenarios are 853,622$, 854,966$, 847,537$ and 770,500$ respectively. Although Scenario 1 does not consider the frequency security constraint, some thermal power units with higher PFR bids are cleared as its marginal units, so the total cost is relatively high.

[0160] From Figure 6 it can be seen that the RoCoF values of the four scenarios in the embodiments do not exceed the limit, but the RoCoF values of Scenario 1 and Scenario 4 with smaller inertia are generally greater than those of Scenario 2 and Scenario 3. From Figure 7 it can be seen that only a few time periods in Scenario 1 meet the frequency minimum point requirement, and the minimum value occurs in Time Period 4, only 47.3 Hz; for the scenarios considering the frequency security constraint, the frequency minimum points are all greater than the limit value of 49 Hz. Although the PFR of the wind turbines in Scenario 3 replaces the PFR of some thermal and hydro power units in Scenario 2, the final effects of the two scenarios are similar; after considering the EILS resources in Scenario 4, the frequency minimum point is significantly higher than other scenarios.

[0161] Since the clearing result of Scenario 1 does not meet the frequency security requirements, only the resource marginal clearing prices of Scenarios 2 - 4 are discussed.

[0162] From Figure 8 it can be seen that during Time Periods 9 - 13 when the system load, inertia and PFR demand are relatively high, due to the higher - priced thermal power units being the marginal units, the clearing prices of the corresponding resources in Scenarios 2 and 3 are also higher. The electricity clearing price of Scenario 4 is high during this time period, but the inertia and PFR prices are low. The reasons are as follows: First, the system load demand is large but the wind energy is less, resulting in a large number of thermal and hydro power units in the system being started up, and the system inertia is sufficient, so that the RoCoF constraint does not work, and the corresponding Lagrange multiplier is 0. Second, after considering the EILS resources, the PFR resource demand of the system is reduced, and the limiting effect of the frequency minimum point constraint is reduced, and the corresponding multiplier value is also relatively small. By comparing the PFR prices of different types of units in the figure, it can also be obtained that the PFR price of the wind turbines with faster frequency regulation time is higher, about 1.87 times the price of the thermal and hydro power units in the corresponding time period, which is conducive to encouraging faster PFR resources to participate in the market.

[0163] Based on Scenario 4, the upper limit value α of the proportion of EILS in the load is changed from 0% to 5%, and the scheduling results show that the procurement volume of EILS in each period has reached the limit value. The size of the total cost of day-ahead clearing is as Figure 9 shown. It can be seen from Figure 9 that the more EILS resources are purchased, the lower the total cost shows a downward trend; compared with not purchasing EILS resources, when α is 5%, the total cost can be reduced by about 9%. And when the value of α changes from 2% to 3%, it will bring a sudden drop in the total cost value. This is because within this range, some expensive synchronous units can only be switched from on to off, without an intermediate state, resulting in cost changes.

[0164] Considering the frequency security constraint, the settlement costs of the method of the present invention (joint optimization method) are compared with those of the settlement costs using the separate sequential method model, and the results are shown in Table 3:

[0165] Table 3 Settlement Costs of Different Market Clearing Methods

[0166]

[0167] It can be seen from Table 3 that compared with the separate sequential method, the total settlement costs paid for electric energy, inertia, and PFR resources using the joint optimization method are lower. This is because the objective function of the separate sequential method is to minimize the payment of each resource in its respective market, and the clearing method is to clear in sequence according to the order of inertia, electric energy, and PFR resources. The three form relatively independent markets. The settlement price of the clearing model in each market is the unit price offer accepted from low to high. The clearing result only guarantees the lowest settlement cost for purchasing the corresponding resources in the current market. Since the coupling between markets is not considered, it cannot guarantee the lowest total settlement cost of resources; while the objective function of the joint optimization method is to ensure the lowest total payment of all resources, considering the coupling of the inertia, electric energy, and PFR markets, and using the continuous SCUC model to clear the three simultaneously, the clearing result can guarantee the lowest total payment of all resources.

[0168] The role of the comprehensive evaluation index of the frequency lowest point constraint is to analyze the clearing results after using different constraints in the day-ahead clearing stage and select the optimal scheduling plan from them. To illustrate the calculation process of this index, Table 4 gives the scheduling results when Scenario 3 is used to clear Period 5 and the frequency lowest point occurs in different regions (i.e., corresponding to different frequency lowest point constraints). Among them, Region 1 represents Case 1, and Region 2 represents Case 2.

[0169] Table 4 Scheduling Results in Different Regions where the Frequency Lowest Point Occurs

[0170]

[0171] Indicator A is an indicator related to cost, and both Indicator B and Q are indicators related to the frequency curve. In this embodiment, the weights are taken as a = 0.5, b = c = 0.25. Table 5 shows the calculation results of different indicators. It can be seen from this that the cost indicator when the lowest point of frequency occurs in Region 1 is better than that when it occurs in Region 2. However, after considering the indicators related to the frequency curve, the comprehensive evaluation indicator of the lowest point of frequency constraint deteriorates.

[0172] Table 5 Calculation Results of the Comprehensive Evaluation Indicator of the Lowest Point of Frequency Constraint

[0173]

[0174] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A combined optimization method for electric energy, inertia and primary frequency regulation considering EILS, characterized in that Including the following steps: Step 1) Construct the objective function of the continuous SCUC model: Among them, the subscripts HG, SG, and WG represent thermal power units, hydropower units, and wind power units respectively; N H , N S , and T represent the number of thermal power units, the number of hydropower units, and the scheduling time scale respectively; C HGi,t , C SGi,t , and C WG,t represent the electricity price quotes of thermal, hydro, and wind power units based on operating costs, represents the scheduling cost of emergency interruptible load resources, with the unit of $ / (MW·h); and represent the primary frequency regulation price quotes of thermal, hydro, and wind power units, with the unit of $ / (MW·h); P HGi,t , P SGi,t , and P WG,t represent the electricity winning bids of the units in the joint market, with the unit of MW; R HGi,t , R SGi,t , and R WG,t represent the PFR reserve capacity winning bids of the units under the anticipated large disturbances, with the unit of MW; represents the procurement quantity of emergency interruptible load resources, with the unit of MW; Step 2) Construct the general constraints of the continuous SCUC model, including power balance constraints, upper and lower limits of unit output constraints, and emergency interruptible load constraints; Step 3) Construct the frequency security constraints of the continuous SCUC model considering emergency interruptible loads, and write the frequency nadir point constraint in the frequency security constraints in the second-order cone form. The frequency nadir point constraint includes two cases: Case 1: Case 2: Among them, T W is the primary frequency regulation time of the wind turbine, T SH is the primary frequency regulation time of the hydro and thermal power units, Δf maxc is the frequency deviation threshold, ΔP L refers to the pre - imagined large disturbance power, f0 is the nominal frequency of the system, H HGi and H SGi respectively refer to the inertia constants of the thermal power unit and the hydro power unit, with the unit of s; S HGi and S SGi refer to the rated capacities of the thermal power unit and the hydro power unit, with the unit of MW; U HGi,t and U SGi,t represent the start - stop variables of the unit, taking values of 0 or 1; Step 4) Construct a comprehensive evaluation index for the frequency nadir point constraint, and select the frequency nadir point constraint from the two cases based on the comprehensive evaluation index; Step 5) Construct the Lagrangian function of the continuous SCUC model based on the objective function, general constraints, and frequency security constraints, and solve the Lagrangian function to obtain the clearing prices of electric energy, inertia, and primary frequency regulation.

2. The combined optimization method for electric energy, inertia, and primary frequency regulation considering EILS according to claim 1, characterized in that The power balance constraint is: Among them, D t represents the load magnitude within the t period predicted for the day ahead; The upper and lower limits of unit output constraints are: Among them, and represent the upper and lower limits of the generating power of the unit; represents the generating power of the wind farm within the t period predicted for the day before; represents the installed capacity of the wind turbine; U HGi,t and U SGi,t represent the start-stop variables of the unit, with values of 0 or 1; The emergency interruptible load constraint is: Where α% refers to the proportion of the purchased emergency interruptible load resources in the load.

3. A combined optimization method for electric energy, inertia, and primary frequency regulation considering EILS according to claim 2, characterized in that The frequency security constraints include frequency rate of change constraints, frequency nadir point constraints, and quasi-steady state constraints.

4. A combined optimization method for electric energy, inertia and primary frequency regulation considering EILS according to claim 3, characterized in that The frequency rate of change constraint is: Among them, H HGi and H SGi respectively refer to the inertia constants of thermal power units and hydropower units, with the unit of s; S HGi and S SGi refer to the rated capacities of thermal power units and hydropower units, with the unit of MW; U HGi,t and U SGi,t represent the start-stop variables of the units, taking values of 0 or 1; f0 is the nominal frequency of the system, with the unit of Hz; ΔP L refers to the power of the anticipated large disturbance, with the unit of MW; t refers to the response time, with the unit of s; is the threshold of the frequency change rate; The quasi-steady state constraint is:

5. A combined optimization method for electric energy, inertia and primary frequency regulation considering EILS according to claim 4, characterized in that The second-order cone form of the frequency nadir point constraint is: Case 1: Case 2:

6. The combined optimization method for electric energy, inertia, and primary frequency regulation considering EILS according to claim 5, characterized in that, The construction of the comprehensive evaluation index for the frequency nadir point constraint includes the following steps: Step 4-1) Determine the cost metric A i : Perform cost normalization, with the baseline value being the minimum cost: Among them, i represents two cases of the lowest frequency point constraint, with a value of 1 representing case one and a value of 2 representing case two; F represents the total purchase cost of the power grid, that is, the objective function of the continuous SCUC model, A i indicating that the lower the cost of the region, the higher the index value; Step 4-2) Determine the inertia index B i : Normalize the inertia, with the reference value being the maximum inertia: Among them, M all represents the total inertia within the system. When the system encounters a predicted disturbance, the slope of the frequency curve is related to the inertia within the system. B i indicates that the more inertia there is, the flatter the frequency curve and the higher the index value; Step 4-3) Determine the effective PFR response ratio index Q i : Normalize the effective PFR response ratio, with the reference value being the maximum effective PFR response ratio: Among them, the superscripts HG, SG, and WG represent thermal power units, hydropower units, and wind power units respectively; E is the effective PFR response ratio, that is, the PFR reserve capacity R won by the unit through the clearing model yx and the PFR resource R responded by the unit from the start of frequency drop to the lowest frequency point after the disturbance occurs cq The ratio, which is actually the ratio of the time to reach the lowest frequency point in the frequency curve to the frequency regulation time of the unit; is the time to reach the lowest frequency point in the frequency curve; Q i It means that the larger the effective PFR response ratio, the higher the utilization rate of the PFR reserve and the higher the index value; Step 4-4) Determine the comprehensive evaluation index Y for the lowest frequency point constraint i : Y i = aA i + bB i + cQ i Where a, b, and c are the weight factors of the three components, and the value range is [0, 1], and a + b + c = 1.

7. A combined optimization method for electric energy, inertia, and primary frequency regulation considering EILS according to claim 6, characterized in that The Lagrangian function of the continuous SCUC model is expressed as: Among them, and are the Lagrange multipliers of the power balance constraint, the rate of change of frequency constraint, and the quasi-steady state frequency constraint, respectively; and μ t are the Lagrange multipliers of the frequency nadir constraint represented in the second-order cone form.

8. A combined optimization method for electric energy, inertia, and primary frequency regulation considering EILS according to claim 7, characterized in that The clearing prices of electric energy, inertia, and primary frequency regulation are respectively: A) Electricity clearing price B) Inertial clearing price C) Clearing price of the PFR of the wind turbine unit D) Clearing price of the PFR of the hydropower unit E) Clearing price of the PFR of thermal power units

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