Power scheme determination method and device based on inertia constraint and whale algorithm

Abstract

The invention provides an inertia constraint and whale algorithm-based power scheme determination method and device, and the method comprises the steps: carrying out the random combination and initialization processing of a pre-obtained first power scheme, obtaining a second power scheme, and enabling a capacity unit price a to comprise inertia supply cost; based on the power capacity S and the inertia time constant H, eliminating the second power scheme which does not meet the capacity constraint condition and the inertia constraint condition to obtain a third power scheme; and performing iterative optimization on the current power capacity S'of the third power scheme and the available quantity k 'of the power supply units according to the whale algorithm, a preset termination condition, the maximum supply quantity k and the capacity unit price a, and determining an optimal fourth power scheme. Based on the whale algorithm, a more stable, reliable, efficient and economical power scheme is formulated globally from multiple factors such as capacity adequacy, inertia adequacy and price in multiple dimensions, and a solid support is provided for long-term safe and stable operation of a power system and optimal configuration of resources.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of dispatching technology of power system, and particularly relates to a power scheme determination method and device based on inertia constraint and whale algorithm. BACKGROUND

[0002] In the power system, power capacity adequacy and power inertia adequacy can both affect the stability of power system frequency.

[0003] The existing power schemes have some problems, such as some of them only focus on the adequacy of capacity, some of them do not combine the inertia supply cost with the capacity price, some of them only consider the short-term adequacy of inertia, and some of them do not use whale algorithm but other algorithms to solve the power scheme result. In general, the existing power scheme determination method and device cannot realize the optimization of power capacity allocation scheme in terms of multi-dimensional coordination, cost mechanism innovation, whole cycle planning and use of advanced algorithm.

[0004] The above technical defects can lead to unreasonable power system capacity allocation scheme, and users face more frequent power supply interruption, frequency instability and other power quality problems. SUMMARY

[0005] Therefore, the present application provides a power scheme determination method and device based on inertia constraint and whale algorithm. The present application formulates a more stable and reliable, efficient and economic power scheme from capacity adequacy, inertia adequacy, price and other factors in multi-dimensions and globally based on whale algorithm, which provides a solid support for long-term safe and stable operation of power system and optimal allocation of resources.

[0006] According to a first aspect of the present application, a power scheme determination method based on inertia constraint and whale algorithm is provided, which comprises: S102: randomly combining and initializing a first power scheme obtained in advance to obtain a second power scheme, wherein the first power scheme comprises power capacity S of power supply unit, capacity unit price a, inertia time constant H and maximum supply quantity k, and the capacity unit price a includes inertia supply cost; S104: removing the second power scheme that does not meet the capacity constraint condition and the inertia constraint condition based on the power capacity S and the inertia time constant H to obtain a third power scheme; S106: iteratively optimizing the current power capacity S' of the third power scheme and the available quantity k' of power supply unit according to whale algorithm, a preset termination condition, the maximum supply quantity k and the capacity unit price a to determine an optimal fourth power scheme.

[0007] Further, the first power scheme further comprises power capacity S of power supply unit in different periods and different types, wherein the power capacity S comprises power rated capacity S 额 and power maximum available capacity S maxRated power capacity S 额 ≥ Maximum available power capacity S max The second power scheme includes all types of power supply units; both the second and third power schemes include the current power capacity S' and the available quantity k'; the current power capacity S' in the randomly initialized second power scheme is less than or equal to the rated power capacity S of the corresponding type of power supply unit. 额 In the second power scheme, the available number of power supply units k' is less than or equal to the maximum supply number k of the corresponding type of power supply units.

[0008] Further, S104 includes: S1042: eliminating the second power scheme that does not meet the capacity constraint condition to obtain the fifth power scheme, wherein the capacity constraint condition is based on the maximum available power capacity S of the power supply unit. max And the pre-obtained range of single-period system capacity requirements L b Determined; S1044: Eliminate the fifth power scheme that does not meet the inertia constraint condition to obtain the third power scheme, wherein the inertia constraint condition includes the frequency change rate constraint condition and the frequency minimum point constraint condition.

[0009] Further, S1042 includes: S10422: If the current power capacity S' of the power supply unit in the second power scheme is ≥ the maximum available power capacity S of the corresponding type of power supply unit. max If the second power scheme is eliminated, the sixth power scheme is obtained; S10424: If the sum of the current power capacities S' of the power supply units in the sixth power scheme is not within the predetermined single-phase system capacity demand range L b If the sixth power scheme is excluded, the fifth power scheme is obtained.

[0010] Further, S1044 includes: S10442: Based on the frequency change rate constraint, according to the rated power capacity S of all power supply units in the fifth power scheme. 额 S N The pre-obtained maximum system disturbance power ΔP L System rated frequency f, maximum frequency change rate RoCoF max Determine the minimum inertia requirement assessment value H based on the frequency change rate constraint. RoCoF S10444: Based on the minimum frequency constraint, according to the rated power capacity S of all power supply units in the fifth power scheme. 额 S N The pre-obtained maximum system disturbance power ΔP L The system's rated frequency f and the system's equivalent droop coefficient R G , First frequency modulation dead zone f1, lowest frequency value f nadirdetermining a minimum inertia demand evaluation value H based on a frequency minimum constraint nadir ; S10446: determining a minimum inertia demand evaluation value H based on a frequency change rate constraint RoCoF ; and determining a minimum inertia demand evaluation value H based on a frequency minimum constraint nadir ; and determining a minimum inertia demand constraint H of the fifth power scheme min ; S10448: eliminating the fifth power scheme whose overall system inertia H sys is less than H min , to obtain a third power scheme.

[0011] Further, in S10448, the overall system inertia H sys is determined based on the current power capacity S', the inertia time constant H, and the power rated capacity S 额 of each power supply unit of the fifth power scheme.

[0012] Further, S106 includes: S1062: randomly selecting a preset number of the third power schemes, and establishing an objective function and confirming an objective function value according to the current power capacity S', the available number k', and the capacity unit price a of the power supply units in the selected third power schemes; S1064: determining the third power scheme corresponding to the minimum objective function value as the current optimal power scheme; S1066: updating the current power capacity S' and the available number k' of the power supply units in the third power scheme according to the whale optimization algorithm to obtain a seventh power scheme, wherein the current power capacity S' in the seventh power scheme is less than or equal to the maximum available power capacity S max of the corresponding type of power supply unit, and the available number k' of the power supply units in the seventh power scheme is less than or equal to the maximum supply number k of the corresponding type of power supply unit; S1068: confirming the objective function value of the seventh power scheme, and updating the current optimal power scheme based on the objective function value of the seventh power scheme and the objective function value of the current optimal power scheme; S10610: determining whether the current optimal power scheme satisfies a preset termination condition, and if so, taking the current optimal power scheme as an optimal fourth power scheme, otherwise, performing S1066.

[0013] Further, S1066 further includes: randomly generating a coefficient vector A based on the whale algorithm; if the absolute value of the coefficient vector A is less than 1, updating the current power capacity S' and / or the available number k' of the power supply units based on the surround-prey or spiral method; otherwise, updating the current power capacity S' and / or the available number k' of the power supply units based on the random search method.

[0014] Further, different periods include spring, summer, autumn and winter; different types of power supply units include synchronous generator power supply units, wind power supply units, photovoltaic power supply units and energy storage power supply units.

[0015] According to a second aspect of the present application, a power scheme determination device based on inertia constraints and a whale algorithm is provided, which comprises: a first determination module, configured to randomly combine and initialize a first power scheme obtained in advance to obtain a second power scheme, wherein the first power scheme comprises power capacity S of a power supply unit, capacity unit price a, inertia time constant H and maximum supply quantity k; a second determination module, configured to eliminate the second power scheme that does not satisfy the capacity constraint condition and the inertia constraint condition based on the power capacity S and the inertia time constant H to obtain a third power scheme; and a third determination module, configured to iteratively optimize the current power capacity S' of the third power scheme and the available quantity k' of the power supply unit according to the whale algorithm, a preset termination condition, the maximum supply quantity k and the capacity unit price a to determine an optimal fourth power scheme.

[0016] The present application can obtain the following beneficial effects:

[0017] The present application is based on the whale algorithm, and a more stable, reliable, efficient and economic power scheme is globally and multidimensionally formulated from multiple factors such as capacity adequacy, inertia adequacy and price, thereby providing a solid support for long-term safe and stable operation of a power system and optimal configuration of resources. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 A flowchart of a power scheme determination method based on inertia constraints and a whale algorithm is provided for the present application;

[0019] Figure 2 A flowchart of another power scheme determination method based on inertia constraints and a whale algorithm is provided for the present application;

[0020] Figure 3 A flowchart of a power scheme determination method based on a whale algorithm is provided for the present application;

[0021] Figure 4 A schematic diagram of a power scheme determination device based on inertia constraints and a whale algorithm is provided for the present application. DETAILED DESCRIPTION

[0022] The present application is further described in detail below with the aid of the accompanying drawings and specific embodiments.

[0023] In the traditional power system, synchronous generators dominate, and their rotational inertia is sufficient. In the process of ensuring the balance between power supply and demand, the rotational inertia, as an "accessory" of synchronous generators, is naturally satisfied while meeting the capacity adequacy. In the modern power system, with the increasing penetration of new energy and power electronic devices in the power system, the risk of inertia shortage will become increasingly apparent, so it is urgent to guide the generation side of the system in advance to ensure inertia adequacy. Inertia is divided into two types: rotational inertia and virtual inertia.

[0024] The power capacity market is an important path to ensure the adequacy of installed generation capacity. The original intention of the design of the power capacity market is to provide stable expectation signals for power generation enterprises, thereby guiding investment and ensuring power capacity adequacy. In the traditional power capacity market, since the focus is on the adequacy of power capacity supply, it will be difficult to effectively address the inertia shortage problem when the inertia support of the regional power supply unit is insufficient.

[0025] In both traditional and modern power systems, if only the balance between power supply and demand is considered, and the inertia demand is ignored, the power system will face the risk of inertia shortage, leading to instability of the power system. If only the inertia adequacy is considered, a large number of power supply units need to be kept online to provide sufficient inertia to maintain high inertia. If the user's electricity demand is low, these power supply units must be operated at low load, which will result in poor efficiency, fuel waste, rising operating costs, and reduced service life of the power supply units.

[0026] Defects of the prior art:

[0027] Defect 1: The current mainstream capacity market mechanism is mainly designed around capacity adequacy to ensure sufficient generation capacity at peak load, and inertia adequacy is generally not included in the market framework.

[0028] Defect 2: The research on the inertia auxiliary service market is still in its infancy and focuses on short-term inertia regulation.

[0029] Defect 3: The transaction target only considers the rotational inertia provided by traditional synchronous generators, and does not consider the virtual inertia provided by new energy and energy storage, which cannot encourage new energy, energy storage, and other new types of subjects to provide inertia support.

[0030] Defect 4: Using other optimization methods to solve the power capacity scheme often encounters problems such as falling into local optimum, low computational efficiency, and parameter sensitivity.

[0031] Therefore, in order to address the lack of a long-term inertia sufficiency guarantee mechanism, it is urgent to propose a power scheme determination method and device based on inertia constraints and whale algorithm, guide the formation of a reasonable new power system structure, promote the optimal combination of new energy and conventional energy, guide the increase of the capacity of power generation units that can provide inertia or plan and construct equipment that can provide virtual inertia, and ensure the sufficiency of future system inertia.

[0032] Example 1

[0033] like Figure 1 As shown, this embodiment provides a method for determining power schemes based on inertia constraints and the whale algorithm. The method includes:

[0034] S102: The first power scheme obtained in advance is randomly combined and initialized to obtain the second power scheme. The first power scheme includes the power capacity S of the power supply unit, the unit price a of the capacity, the inertia time constant H and the maximum supply quantity k. The unit price a of the capacity includes the inertia supply cost.

[0035] Specifically, the first power scheme includes: the power capacity S of power supply units of different types and at different times, where S includes the rated power capacity S0. 额 Maximum available power capacity S max (Rated power capacity S) 额 ≥ Maximum available power capacity S max The unit price of capacity (a) and inertial time constant (H) are included, as well as the maximum supply quantity (k) of the available power supply units of different types. Different periods include spring, summer, autumn, and winter; different types of power supply units include synchronous generator power supply units, wind power power supply units, photovoltaic power supply units, and energy storage power supply units, with the maximum supply quantities (k) of the four types of units being i, j, m, and n, respectively.

[0036] Specifically, the first power supply plan is the original plan submitted by the supplier, in which the rated power capacity S... 额 Maximum available power capacity S max All values ​​are constants. The power capacity in the second power scheme after initialization, as well as in the subsequent third to seventh power schemes, is the processed capacity, denoted by S'. S' includes S... g S w S pv S es S' is a variable, and S'≤S 额 Similarly, the number of generating units supplied in the subsequent power plan is represented by k', where k' includes i', j', m', and n'. k' is a variable, and k' ≤ k.

[0037] S102 is twice the power scheme, the first processing is a single type of first power scheme for random combination, get the comprehensive power scheme, here the scheme of the power capacity S is equal to the corresponding type of S 额 , wherein the number of power supply units is also equal to k, and then the initialization processing is carried out again, that is, the S in the power scheme is changed, the number k of each power supply unit in the power scheme is changed, a large number of comprehensive schemes, that is, the second power scheme, is obtained; the power capacity S' in the second power scheme after random initialization is less than or equal to the power rated capacity S of the corresponding type of power supply unit 额 , the number k' of power supply units in the second power scheme is less than or equal to the maximum supply number k of the corresponding type of power supply unit, so the number of the second power scheme is theoretically infinite.

[0038] The first power scheme provided by a single supplier generally only includes one type of power supply unit in multiple periods, which cannot meet the needs of user diversity, so it is necessary to randomly combine the power supply units in different first power schemes to obtain a comprehensive second power scheme containing multiple types of power supply units,

[0039] Specifically, the supplier needs to provide the power rated capacity S 额 , the maximum available power capacity S max of each power supply unit of different types, generally, a supplier can only provide one single type of power supply unit. In addition, the capacity unit price a of different types of power supply units is also different, which also needs to be provided by the supplier, and the unit price a here includes the inertia supply cost. The inertia time constant H of different power supply units also needs to be provided.

[0040] Specifically, the first power scheme is equivalent to the content in the bidding scheme of the supplier (i.e. the power plant), the supplier needs to additionally report whether it has inertia support capability and the size of the inertia support capability and other information to participate in the bidding in addition to submitting the traditional capacity market bidding information, and the price needs to consider not only the capacity marginal cost but also the inertia supply cost.

[0041] The inertia provided by each type of power supply unit is usually quantified by the inertia time constant Hi. Based on the traditional control, the frequency of new energy power generation equipment and energy storage equipment is decoupled from the grid frequency, and lacks the ability to provide virtual inertia support, which brings serious challenges to grid safety. The control strategy of virtual synchronous machine can make new energy (wind power, photovoltaic) power supply units and energy storage power supply units have inertia response capability.

[0042] Here, the inertia is not priced separately, but the inertia cost is embodied in the capacity price here, that is, in a.

[0043] More specifically, generally speaking, one supplier can only provide one type of power supply unit, and the number of units is k, and the capacity of each unit in the final scheme is less than or equal to the maximum available capacity S declared by the unit max The final scheme also does not necessarily use all the power supply units of the supplier, that is, not all the power supply units can be successful in bidding. For example, the number of energy storage power supply units that a supplier can provide is k = 100, and finally only 60 units can be successful in bidding. The present application designs the most suitable comprehensive power scheme combined by different suppliers (that is, different types of power supply units) at different periods according to the user's demand.

[0044] Regarding the bid a, in addition to considering the capacity marginal cost of each type of power generator, the inertia supply cost also needs to be considered. The capacity price needs to recover a certain proportion of the fixed cost of the power market. The fixed cost of inertia service mainly includes power supply unit construction, equipment modification, etc. Such costs need to be recovered through long-term market. The inertia supply cost considered in this method is mainly the fixed cost of inertia service.

[0045] The inertia supply cost of traditional thermal power supply units (that is, synchronous rotating machines, that is, synchronous generator power supply units) is generally relatively fixed and already included in the regular cost accounting, and will not generate additional large costs due to providing inertia support. If new energy power supply units (wind power, photovoltaic) are required to provide stable inertia support, technical modification needs to be carried out, such as configuring energy storage equipment and using advanced control strategies, which will increase the additional costs of energy storage equipment procurement and converter modification. The inertia supply cost of energy storage power supply units depends on the energy storage configuration and operation control strategy, and the main additional cost is composed of the cost of energy storage equipment selection and converter modification. The above fees can be included in the bid a.

[0046] Regarding the power capacity, traditional thermal power (that is, traditional synchronous generator) needs to declare the effective capacity that can be stably dispatched, energy storage needs to declare the effective capacity that can be stably output within a certain duration, and new energy (that is, wind power + photovoltaic) power supply unit declares confidence capacity. New energy power supply unit needs to use equivalent capacity method or effective load capacity method to evaluate confidence capacity.

[0047] S104: Based on the power capacity S and the inertia time constant H, the second power scheme that does not meet the capacity constraint condition and the inertia constraint condition is eliminated, and a third power scheme is obtained.

[0048] S106: Based on the whale algorithm, the preset termination condition, the maximum supply quantity k and the capacity unit price a, the current power capacity S' and the available quantity k' of the power supply unit in the third power scheme are iteratively optimized to determine the optimal fourth power scheme.

[0049] The embodiment is based on the whale algorithm, and a more stable, reliable, efficient and economic power scheme is formulated from multiple factors such as capacity adequacy, inertia adequacy and price in multiple dimensions and globally, thereby providing a solid support for long-term safe and stable operation of the power system and optimal configuration of resources.

[0050] Embodiment two

[0051] As shown in Figure 2 and Figure 3 The embodiment provides a method for determining a power scheme based on inertia constraints and a whale algorithm, which is a specific description of the specific implementation of S104 and S106.

[0052] The method comprises the following steps:

[0053] S102: Randomly combining and initializing a first power scheme obtained in advance to obtain a second power scheme, wherein the first power scheme comprises power capacity S of a power supply unit, capacity unit price a, inertia time constant H and maximum supply quantity k, the capacity unit price a comprises inertia supply cost, and the second power scheme comprises current power capacity S' and available quantity k'.

[0054] S104: Removing the second power scheme that does not meet the capacity constraint condition and the inertia constraint condition to obtain a third power scheme.

[0055] S104 comprises the following steps:

[0056] S1042: Removing the second power scheme that does not meet the capacity constraint condition to obtain a fifth power scheme, wherein the capacity constraint condition is determined based on the maximum available capacity S of the power supply unit max and the single-period system capacity demand range L of each period obtained in advance. b

[0057] S1044: Removing the fifth power scheme that does not meet the inertia constraint condition to obtain a third power scheme, wherein the inertia constraint condition comprises a frequency change rate constraint condition and a minimum frequency constraint condition.

[0058] Specifically, in S104, first, the second power scheme that does not meet the capacity constraint condition of each unit is removed to obtain a sixth power scheme, then the scheme that does not meet the single-season system capacity demand constraint condition is removed to obtain a fifth power scheme, and finally, the scheme that does not meet the inertia constraint condition is removed to obtain a third power scheme.

[0059] ​Specifically, the capacity demand varies greatly between seasons, so the capacity demand is divided into four types. The inertia demand is mainly related to the maximum disturbance value of the system, the rated capacity of the system (the sum of the rated capacities of all power supply units), the maximum frequency change rate constraint and the minimum frequency constraint. Other values are related to the characteristics of the system and the relevant power regulations. Since the four seasons correspond to four types of power supply unit capacity bidding schemes, the rated capacity of the system is four, and the inertia demand is also four.

[0060] S1042 comprises:

[0061] S10422: If the current power capacity S' of the power supply unit in the second power scheme is greater than the maximum available power capacity S of the corresponding type of power supply unit max , the second power scheme is eliminated to obtain a sixth power scheme.

[0062] S10424: If the sum of the current power capacities S' of the power supply units in the sixth power scheme is not within the predetermined single-period system capacity demand range L b , the sixth power scheme is eliminated to obtain a fifth power scheme.

[0063] Specifically, S max is the maximum available power capacity of each unit, i.e. the effective capacity of each conventional synchronous generator that can be stably dispatched, the effective capacity of the energy storage unit that can be stably output within a certain duration, and the confidence capacity of the new energy (wind turbine or photovoltaic unit) power supply unit. The sixth power scheme needs to satisfy each unit power capacity S'≤S max . L b is the required power capacity demand range of the power system, which is obtained based on load historical data clustering and new capacity demand prediction. The maximum value of this range needs to be increased by 15% based on the predicted capacity demand value to avoid power capacity gaps due to prediction bias. The specific increase data can be adaptively changed according to user safety requirements, and the minimum value can be adaptively adjusted according to actual requirements. b represents the number of periods considered. If four seasons are considered, b=4. L b The required power system capacity demand range corresponding to the four seasons respectively.

[0064] Specifically, in addition to comparing whether the capacity of each unit meets the unit capacity constraint condition, it is also necessary to judge whether the system capacity demand in different periods (spring, summer, autumn and winter) is met. If both conditions are not met, the scheme is eliminated.

[0065] S1044 comprises:

[0066] S10442: Based on the frequency change rate constraint condition, the sum S 额 of the power rated capacities S of all power supply units in the fifth power scheme is calculated.N The pre-obtained maximum system disturbance power ΔP L System rated frequency f, maximum frequency change rate RoCoF max Determine the minimum inertia requirement assessment value H based on the frequency change rate constraint. RoCoF .

[0067]

[0068] S10444: Based on the minimum frequency constraint, according to the rated power capacity S of all power supply units in the fifth power scheme. 额 S N The pre-obtained maximum system disturbance power ΔP L The system's rated frequency f and the system's equivalent droop coefficient R G , First frequency modulation dead zone f1, lowest frequency value f nadir Determine the minimum inertia requirement assessment value H based on the minimum frequency point constraint. naidr .

[0069]

[0070] In the formula, the primary frequency modulation dead zone f1 can be set to 0.033Hz.

[0071] Because of the different power schemes, the power capacity S of each unit is different. 额 S N Different, so H RoCoF H nadir H min They are all different.

[0072] S10446: The minimum inertia requirement assessment value H based on the frequency change rate constraint is... RoCoF And the minimum inertia requirement assessment value H based on the minimum frequency point constraint nadir The larger value in the equation is used as the minimum inertia requirement constraint H that the fifth power scheme must satisfy. min .

[0073] H min =max{H RoCoF H nadir} (Formula 3).

[0074] S10448: Eliminate overall system inertia H sys Less than H min The fifth power scheme is used to obtain the third power scheme.

[0075] Firstly, the kinetic energy E provided by each power supply unit needs to be calculated. The kinetic energy E provided by each power supply unit is calculated according to the inertia time constant H and the current power capacity S' actually provided by the power supply unit. The relationship between the kinetic energy E provided by the power supply unit and the inertia time constant H is as follows:

[0076] E = H x S' (Formula 4);

[0077] wherein the H values of different types of power supply units are different, and the inertia time constants H of the same type of power supply unit are usually in the same numerical interval range, and the supplier needs to confirm the value, that is, the value needs to be embodied in the first power scheme; S' is the current power capacity actually provided by any power supply unit in the power scheme.

[0078] Here, because each power supply unit has different power capacity schemes in different seasons, different kinetic energies E are also obtained. The sum of the equivalent kinetic energies of the four types of power supply units, i.e., synchronous generator, wind power generator, photovoltaic power generator and energy storage power generator, is represented by E g , E w , E pv and E es respectively.

[0079] Then, the overall system inertia H sys of the fifth power scheme is calculated. The overall system inertia H sys is determined based on the current power capacity S', the inertia time constant H and the power rated capacity S 额 of each power supply unit of the fifth power scheme, and the specific calculation method is as follows:

[0080]

[0081] wherein H g , H w , H pv and H es are the inertia time constants of the synchronous generator power supply unit and the equivalent inertia time constants of the wind power supply unit, the photovoltaic power supply unit and the energy storage power supply unit respectively; S g , S w , S pv and S es represent the current power capacities of each type of power supply unit in the fifth power scheme, and i', j', m' and n' represent the actual number of each type of power supply unit in the fifth power scheme, i.e., the available number; and S N represents the sum of the power rated capacities S 额 of all power supply units in any fifth power scheme.

[0082] S106: iteratively optimize the current power capacity S' of the third power scheme and the available number k' of power supply units according to the whale algorithm, the preset termination condition and the capacity unit price a, to determine the optimal fourth power scheme.

[0083] The implementation process of the whale algorithm can refer to Figure 3 .

[0084] S106 includes:

[0085] S1062: randomly select a preset number of the third power schemes, and establish a target function according to the current power capacity S', the available number k' of power supply units and the capacity unit price a in the selected third power scheme and confirm the target function value, and randomly select x schemes in the third power scheme as new third schemes (x is usually between 20-100).

[0086] Specifically, the third scheme originally has an infinite number, but a limited x is randomly selected for the updating iteration of the whale algorithm.

[0087] f(x) = (∑ i' a g S g + ∑ j' a w S w + ∑ m’ a pv S pv + ∑ n' a es S es ) - d k × S N' (Formula 6);

[0088] ∑ i' S g + ∑ j' S w + ∑ m' S pv + ∑ n' S es = S N' (Formula 7);

[0089] Wherein, a g , a w , a pv , a es are the capacity unit prices a declared by the synchronous generator power supply unit, the wind power supply unit, the photovoltaic power supply unit and the energy storage power supply unit in the first power scheme, respectively, and different capacity unit prices correspond to different periods (seasons); d kThe clearing price of each type of power supply unit capacity and capacity price in the third scheme is determined according to a market marginal clearing mechanism; i', j', m', n' represent the actual number of each type of power supply unit in the third power scheme, i.e. the available number; S g w pv es S' represents the actual supply capacity of each type of power supply unit in the third power scheme, i.e. the current power capacity, S N' represents the sum of the current power capacity of all types of power supply units in any third power scheme.

[0090] S1064: determining the third power scheme corresponding to the minimum objective function value as the current optimal power scheme (i.e. Figure 2 the current global optimal solution).

[0091] Specifically, the x third power schemes are substituted into the objective function, and the third power scheme corresponding to the minimum objective function value is selected as the current optimal power scheme.

[0092] Specifically, referring to Figure 3 , steps S1062 and S1064 are specifically S1 initializing the population: generating x random individuals, satisfying the constraint condition, S2 calculating the objective function value of each individual, and determining the current global optimal solution.

[0093] S1066: updating the current power capacity S' and the available number k' of the power supply unit in the third power scheme according to the whale optimization algorithm, to obtain a seventh power scheme, wherein the current power capacity S' of each power supply unit in the seventh power scheme is less than the maximum available power capacity S max of the corresponding type of power supply unit, and the available number k' of each type of power supply unit in the seventh power scheme is less than the maximum supply number k of the corresponding type of power supply unit provided in the first power scheme, i.e. the number of the selected four types of power supply units in the final scheme is less than or equal to i, j, m and n.

[0094] Specifically, referring to Figure 3 , step S1066 is specifically S3 entering the loop, and S4 updating the position of the whale individual.

[0095] In S1066, the means of updating the scheme can also include updating the power scheme according to the absolute value size of the coefficient vector A. In the whale optimization algorithm, A is a core parameter for coordinating global exploration and local development, and its value is dynamically adjusted through a convergence factor and a random number.

[0096] ​​​When the absolute value of A is less than 1, the whale optimization algorithm is in a local development state, i.e. the third power scheme is updated to obtain the seventh power scheme by using a surrounding prey mechanism or a spiral update mechanism, and the probabilities of the two mechanisms are equal. When the absolute value of A is greater than or equal to 1, the whale optimization algorithm is in a global exploration stage, i.e. a scheme outside the third power scheme is randomly selected as a reference to update the next position by using a random search mechanism, so as to avoid falling into a local optimum. The reference Figure 3 Here, specifically, S5 is surrounding / spiral updating, and S6 is random search.

[0097] According to the size of the coefficient vector A in the whale algorithm, the surrounding prey, spiral updating or random search mechanism is selected, and the power supply capacity S' of each power supply unit in the x third power schemes is adjusted to obtain the seventh power scheme.

[0098] Specifically, according to the surrounding prey and spiral updating mechanisms of the whale algorithm, each seventh power scheme is related to the corresponding third power scheme and the current optimal power scheme, i.e. each third power scheme will obtain a corresponding seventh power scheme after updating iteration by the whale optimization algorithm. Overall, the current optimal power scheme in the third power scheme is the preliminary optimization direction of the third power scheme, and the seventh scheme is obtained after preliminary optimization. The surrounding prey and spiral updating mechanisms of the whale algorithm will cause the iteration to fall into a local optimum, because the current optimal power scheme in the third power scheme is only the optimal scheme in the x third power schemes, and is not necessarily the optimal scheme in all third power schemes. Therefore, the random search mechanism is used to adjust the optimization direction to avoid falling into a local optimum.

[0099] S1068: confirming the objective function value of the seventh power scheme, and updating the current optimal power scheme based on the objective function value of the seventh power scheme and the objective function value of the current optimal power scheme.

[0100] Specifically, each seventh power scheme is substituted into the objective function to obtain the objective function value corresponding to each scheme, and the current optimal power scheme is updated based on the objective function value of the seventh power scheme and the objective function value of the current optimal power scheme (the scheme with a smaller objective function value is taken as the current optimal power scheme). The power scheme and the current optimal power scheme are both updated in the iteration process, and the number of power schemes may be constantly reduced or unchanged in the iteration process because the power schemes that do not meet the capacity constraint condition and the inertia constraint condition are to be removed. Reference Figure 3 Specifically, step S1068 is S7, which calculates the objective function value of the new position, S8, which judges whether the new solution is better than the global solution, S9, which updates the global optimal solution, and S10, which keeps the current optimal solution.

[0101] S10610: judging whether the preset termination condition is met or not, if the preset termination condition is met, taking the current optimal power scheme of the last iteration as the final optimal power scheme, otherwise, performing S1066.

[0102] Specifically, referring to Figure 3 , step S10610 is specifically S11 checking the termination condition, S12 outputting the optimal capacity winning scheme.

[0103] Specifically, the termination condition includes whether the maximum iteration number reaches the preset number, whether the fitness value (i.e. the objective function value) converges, whether the convergence degree is within the preset threshold range, etc.

[0104] The implementation process of the whale optimization algorithm of S108 is as follows:

[0105] S108 adopts the whale optimization algorithm (WOA) to solve the power capacity market transaction model considering long-term adequacy of inertia, and four seasons correspond to four results. According to the final market clearing result and the capacity assessment result, the final settlement is carried out. The main idea of S108 is to first randomly generate different capacity winning schemes that meet the constraints, and then keep optimizing and iterating to update the optimal solution, and finally generate an optimal capacity winning scheme that meets various constraints and can make the objective function (formula 6) reach the minimum.

[0106] The specific scheme is as follows:

[0107] The power capacity market objective function meets the requirement of maximizing social welfare, i.e. minimizing the difference between transaction price and cost, and the transaction price covers the service cost. The objective function can be expressed as:

[0108] f(x)=(∑ i' a g S g +∑ j' a w S w +∑ m' a pv S pv +∑ n' a es S es )-d k ×S N' ;

[0109] ∑ i' S g +∑ j' S w +∑ m' S pv +∑ n' S es =S N' ;

[0110] Let each whale individual in the population represent a set of capacity bid X x = [S ix , S jx , S mx , S nx ].

[0111] For each season, generate an independent population, a total of 4 populations, corresponding to the four seasons. For a single population, initialize the population to generate x random individuals, and each individual (bid) is represented as a vector.

[0112] X x = [S ix , S jx , S mx , S nx ] ;

[0113] In the formula, X x represents the xth individual, S ix , S jx , S mx , S nx respectively represent the winning capacity of thermal power supply unit i, wind power supply unit j, photovoltaic power supply unit m, and energy storage supply unit n in the xth scheme. Each individual is uniformly distributed within the supply unit capacity range, ensuring that the initial solution meets the supply unit capacity constraint.

[0114] Substitute the randomly generated bid into the capacity adequacy constraint and inertia demand constraint to eliminate individuals that do not meet these two constraints.

[0115] Calculate and compare the objective function value of each individual (bid), that is, substitute each randomly generated and constraint-satisfied bid into the objective function to compare the size of the objective function value:

[0116] Select the optimal individual in the current population as the global optimal solution, that is, let the set of schemes X * with the smallest objective function value be the current best capacity bid.

[0117] According to the updating mechanism of the whale algorithm, the surrounding prey, spiral updating and random search mechanism are used to adjust the position of each individual, simulating the behavior of whales swimming in the search space.

[0118] The so-called position update is the continuous update of the bid capacity S. The position is the winning capacity of each power supply unit.

[0119] First, set the spiral shape parameter b = 1, the coefficient vector A = 2ar1-a, C = 2r2, where a linearly decreases from 2 to 0, r1, r2 ~ U(0, 1).

[0120] When |A|<1, the individual takes the surround-prey mechanism or the spiral update mechanism to update the position, and the probability of the two mechanisms is equal.

[0121] If the surround-prey mechanism is taken:

[0122] D = |CX * (t) - X(t) |;

[0123] X(t+1) = X * (t) - AD;

[0124] In the formula, X(t+1) is the updated position, and the position is the winning capacity S of each power supply unit.

[0125] If the spiral update mechanism is taken:

[0126] D' = |X * (t) - X(t) |;

[0127] X(t+1) = D' e bl cos(2πl) + X * (t);

[0128] In the formula, l is a spiral angle parameter, and l ~ U(-1, 1).

[0129] When |A|≥1, the individual takes the random search mechanism to randomly select an individual X r (t) in the population as a reference to update the next position, so as to avoid falling into a local optimum.

[0130] X(t+1) = X r (t) - A |CX r (t) - X(t) |;

[0131] For each updated individual (capacity winning scheme) X(t+1), the objective function value of the position is recalculated and compared, and whether the updated individual meets the three types of constraint conditions is checked, so as to obtain a new global optimal solution X * (t+1).

[0132] Iterate until the preset termination condition (maximum number of iterations, convergence or change of fitness value (here, the fitness value is the objective function value. In the whale algorithm, the term fitness value is generally used to express.) is less than a set threshold) is reached, and if the termination condition is met, the algorithm is terminated;

[0133] When the termination condition is met, the current optimal solution is output, and whether the constraint condition is met is checked, and if the constraint condition is met, the optimal capacity winning scheme is output

[0134] At this point, the final best power scheme is obtained.

[0135] At the end of each quarter, capacity effectiveness is assessed, and the maximum output of each power supply unit in that quarter is recorded. If the maximum output is less than the bid-winning capacity of that power supply unit in that quarter, a penalty is imposed on the capacity shortfall (bid-winning capacity - maximum output). For example, the final settlement amount for thermal power supply unit i is:

[0136] F i =S i d k -b i x;

[0137] In the formula, F i For the settlement amount of thermal power unit i, b i For thermal power generating unit i, the capacity deficit is represented by x, where x is the benchmark value for the penalty per unit capacity. The same principle applies to other generating units.

[0138] Confirm the single-period capacity demand range L for each period b The process is as follows:

[0139] The power dispatching agency conducts a centralized capacity auction market one year in advance, determining the capacity demand for four typical days of the following year by clustering historical load curves for spring, summer, autumn, and winter seasons and combining this with the planned new load for the following year. The capacity demand must include a reserve capacity margin R. Specifically:

[0140] 1) The power dispatching agency conducts a centralized capacity auction market one year in advance. Daily load data from the past year is collected, forming 365 samples, each a 24-dimensional vector: L d =[l1,l2,…,l 24 ] represents the hourly load value for a single day (the unit of load value is MW or kW, which represents the current active power consumed. When integrated over time, it represents the electrical energy consumed, with the unit being kWh / MWh). Abnormal data such as holidays and extreme weather days are removed, and missing data is supplemented by interpolation between adjacent days.

[0141] 2) The 365 samples were mapped to the corresponding seasons by date: spring (March-May), summer (June-August), autumn (September-November), and winter (December-February).

[0142] The K-means clustering method was used to independently cluster the datasets for each season, generating four typical daily load curves L for spring, summer, autumn, and winter. 春 (t), L 夏 (t), L 秋 (t), L 冬 (t).

[0143] Get the next year's new load schedule from the power development planning documents released by the government, local energy bureau, etc. According to the access time and load characteristics (power, duration) of the new load, generate the new load time sequence L new (t).

[0144] According to the influence characteristics of the new load, select the appropriate kernel function g(t), and convolve the new load time sequence with the kernel function. (This part is not the key, the role of the kernel function is to quantify the time domain influence characteristics of the new load on the power grid (such as instantaneous impact, sustained growth, decay effect, etc.). The selection of the kernel function: instantaneous load→rectangular kernel, impact load→exponential kernel, periodic load→Gaussian kernel, gradual load→linear kernel.) Get the modified increment ΔL(t):

[0145] ΔL(t)=L new (t)*(t);

[0146] Add ΔL(t) to the typical daily load curve to get:

[0147] L1(t)=L 春 (t)+ΔL(t);

[0148] L2(t)=L 夏 (t)+ΔL(t);

[0149] L3(t)=L 秋 (t)+ΔL(t);

[0150] L4(t)=L 冬 (t)+ΔL(t);

[0151] In the formula, L1(t), L2(t), L3(t), and L4(t) are the spring, summer, autumn, and winter typical daily load curves respectively, with the new load plan added.

[0152] 3) Capacity market needs to reserve a certain reserve capacity margin R based on system reliability targets (such as loss of load probability), new energy penetration rate, load forecast uncertainty, and other factors.

[0153] The lower the system loss of load probability (LOLP) value, the more reserve capacity the system needs to reserve. At the same time, the new energy penetration rate and the load forecast uncertainty are positively correlated with the reserve capacity margin R. In practical application, the joint distribution of multiple factors needs to be considered through Monte Carlo simulation or time sequence production simulation: generate a random field scenario of "new energy output-load-power supply unit outage", calculate the supply and demand balance under each scenario, and determine the minimum capacity margin that meets the LOLP target. Referring to the PJM power market in the United States, the margin is set to 15% to 20% of the predicted maximum load (peak load).

[0154] In practical applications, the joint distribution of multiple factors needs to be considered through Monte Carlo simulation or time series production simulation: generate a random scenario of "new energy output-load-power generating unit outage", calculate the supply and demand balance under each scenario, and determine the minimum capacity margin that meets the LOLP target. That is, simulation is needed to determine the appropriate capacity margin, and simulation needs to consider factors such as new energy penetration rate. However, the specific determination process of the reserve capacity margin is not the focus of the present application, so a determined value is selected from the PJM market to simplify the expression.

[0155] For each seasonal typical daily load curve, the reserve capacity margin can be set as:

[0156] R b = 0.15max(L b (t)), b = 1, 2, 3, 4.

[0157] In the formula, max(L b (t)) represents the peak value of the four typical daily load curves.

[0158] The capacity demand of the four typical days is:

[0159]

[0160] The present application relates to a kind of power capacity market transaction method considering inertia long-term adequacy.The method includes: power dispatching mechanism carries out centralized capacity auction market in advance one year, according to spring, summer, autumn, winter season clustering historical load curve, determines the capacity demand of four typical days of next year in combination with next year's new load plan, and capacity demand needs to include reserve capacity margin;Capacity supplier needs to additionally report whether it has inertia support capacity and the size of inertia support capacity and other information to participate in bidding in addition to submitting traditional capacity market bidding information, and the size of inertia supply cost needs to be considered in addition to capacity marginal cost in the aspect of offer;Inertia long-term adequacy is considered in the construction of power capacity market transaction model, and inertia safety constraint is added in constraint condition, and inertia safety constraint is obtained by minimum inertia demand evaluation method;Whale Optimization Algorithm (WOA) is used to solve the power capacity market transaction model considering inertia long-term adequacy, and four seasons correspond to four results.According to final market clearing result and capacity assessment result, final settlement is carried out.This method considers inertia safety constraint in traditional power capacity market transaction model, and inertia supply cost is reflected in offer, to guide to form reasonable new power system structure, promote to realize the optimization combination of new energy and conventional energy, and guarantee future system inertia adequacy.

[0161] The embodiments of the present application have the following beneficial effects:

[0162] 1. The power design scheme of the embodiment of the present application not only considers capacity constraints, but also considers inertia constraints, capacity unit prices including inertia supply costs, and adopts a whale algorithm to iteratively optimize the transaction model, thereby obtaining a more stable, reliable, efficient and economical power scheme, which provides a solid support for long-term safe and stable operation of the power system and optimal allocation of resources.

[0163] 2. By comprehensively considering different periods, long-term inertia adjustment can be performed.

[0164] 3. The rotational inertia and virtual inertia of various different types of power supply units are considered, so that the final power scheme is inertia-rich and more stable.

[0165] 4. The whale algorithm adjusts the capacity to achieve global optimization of the overall scheme. Specifically, by surrounding the prey, spiral updating, random search and other methods to update the capacity S of the power scheme, local optimal solution can be avoided and global optimal solution can be achieved.

[0166] 5. The reasonable new power system structure is formed, the optimal combination of new energy and conventional energy is promoted, the capacity of power supply units that can provide inertia is increased or devices that can provide virtual inertia are planned and constructed, and the future system inertia sufficiency is ensured.

[0167] 6. The final power scheme obtained by the present application is an optimal scheme obtained by comprehensively considering multiple suppliers (different suppliers provide different types of power supply units). The scheme considers different demands of users in different seasons, considers capacity prices including inertia costs, meets two capacity constraint conditions (unit capacity constraints and single period system capacity demand constraints), meets two inertia constraint conditions, and adjusts the supply capacity of each power supply unit and the supply quantity of the power supply unit to ensure that the benefits of the final capacity and inertia provided by each power supply unit can cover the cost of providing capacity and inertia, thereby ensuring the recovery of the cost of each power supply unit and encouraging power supply units to provide capacity and inertia services.

[0168] Embodiment three

[0169] As shown in Figure 4 , the embodiment of the present application provides a power scheme determination device based on inertia constraints and a whale algorithm, comprising:

[0170] A first determination module is configured to randomly combine and initialize a first power scheme obtained in advance to obtain a second power scheme, wherein the first power scheme includes power capacity S of a power supply unit, capacity unit price a, inertia time constant H and maximum supply quantity k, and the capacity unit price a includes inertia supply cost.

[0171] The second determining module is configured to eliminate the second power scheme that does not satisfy the capacity constraint condition and the inertia constraint condition based on the power capacity S and the inertia time constant H, to obtain a third power scheme.

[0172] The third determining module is configured to perform iterative optimization on the current power capacity S' of the third power scheme and the available number k' of power supply units according to a whale optimization algorithm, a preset termination condition, a maximum supply number k and a capacity unit price a, to determine an optimal fourth power scheme.

[0173] The power scheme determination device based on the inertia constraint and the whale optimization algorithm in the embodiment has the same beneficial effects as those of the above-described embodiments, and will not be described herein.

[0174] The above-described embodiments are merely examples for clear illustration, and are not intended to limit the embodiments. Based on the above description, other different forms of changes or variations can be made by those of ordinary skill in the art. Here, it is not necessary and impossible to enumerate all the embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A power scheme determination method based on inertia constraint and whale optimization algorithm, characterized in that, The method comprises: S102: randomly combining and initializing a pre-acquired first power scheme to obtain a second power scheme, wherein the first power scheme comprises power capacity S of a power supply unit, capacity unit price a, inertia time constant H, and maximum supply quantity k, and the capacity unit price a comprises inertia supply cost; S104: removing the second power scheme that does not satisfy the capacity constraint condition and the inertia constraint condition based on the power capacity S and the inertia time constant H to obtain a third power scheme; S106: iteratively optimizing the current power capacity S' of the third power scheme and the supplyable quantity k' of the power supply unit according to a whale optimization algorithm, a preset termination condition, the maximum supply quantity k, and the capacity unit price a to determine an optimal fourth power scheme.

2. The method of claim 1, wherein, The first power scheme also comprises: power capacity S of power supply units of different types and different periods, wherein the power capacity S comprises power rated capacity S 额 and power maximum available capacity S max , power rated capacity S 额 ≥ power maximum available capacity S max ; The second power scheme comprises all types of power supply units; The second power scheme and the third power scheme both comprise the current power capacity S' and the supplyable quantity k'; the current power capacity S' in the second power scheme after random initialization ≤ the power rated capacity S of the power supply units of the respective type 额 the available number k' of power supply units in the second power scheme ≤ the maximum supply number k of power supply units of the respective type.

3. The method of claim 2, wherein, S104 comprises: S1042: eliminate the second power scheme that does not meet the capacity constraint condition to obtain the fifth power scheme, wherein the capacity constraint condition is based on the maximum available capacity S of the power supply unit max and the pre-acquired single-period system capacity demand range L of each period b determined; S1044: removing the fifth power scheme that does not satisfy the inertia constraint condition to obtain the third power scheme, wherein the inertia constraint condition comprises a frequency change rate constraint condition and a frequency minimum point constraint condition.

4. The method of claim 3, wherein, S1042 comprises: S10422: if the current power capacity S' of the power supply unit in the second power scheme ≥ the maximum available power capacity S of the power supply unit of the corresponding type max then the second power scheme is rejected, and a sixth power scheme is obtained. S10424: if the sum of the current power capacity S' of the power units in the sixth power scheme is not within the predetermined single-period system capacity demand range L b , then the sixth power scheme is rejected, and a fifth power scheme is obtained.

5. The method of claim 4, wherein, S1044 comprises: S10442: based on the frequency change rate constraint condition, determining the minimum inertia demand evaluation value H based on the sum S of the power rated capacity of all power supply units in the fifth power supply scheme 额 N , the pre-acquired system maximum disturbance power ΔP L , the system rated frequency f, and the maximum frequency change rate RoCoF max determining the minimum inertia demand evaluation value H based on the frequency change rate constraint RoCoF ;​ S10444: determining the minimum inertia demand evaluation value H based on the frequency bottom constraint condition, according to the sum S of the power rated capacities of all power supply units in the fifth power scheme 额 N , the system maximum disturbance power ΔP obtained in advance L , the system rated frequency f, the equivalent droop coefficient R of the system G , the primary frequency modulation dead zone f1, the frequency bottom value f nadir determining the minimum inertia demand evaluation value H based on the frequency bottom constraint nadir ;​ S10446: the larger value of the minimum inertia requirement evaluation value H based on the frequency change rate constraint and the minimum inertia requirement evaluation value H based on the frequency bottom constraint is taken as the minimum inertia requirement constraint H that should be satisfied by the fifth power scheme RoCoF and the minimum inertia requirement evaluation value H based on the frequency bottom constraint nadir min ;​ S10448: eliminate the overall system inertia H sys less than H min The fifth power scheme is obtained by the third power scheme.

6. The method of claim 5, wherein, In S10448, the overall system inertia H sys is determined based on the current power capacity S' of the respective power supply units, the inertia time constant H and the power rating capacity S of the respective power supply units of the fifth power scheme 额 .

7. The method of claim 2, wherein, S106 comprises: S1062: randomly selecting a preset number of the third power schemes, and establishing a target function and confirming a target function value according to the current power capacity S', the supplyable quantity k', and the capacity unit price a of the power supply unit in the selected third power scheme; S1064: determining the third power scheme corresponding to the minimum target function value as the current optimal power scheme; S1066: updating the current power capacity S' and the available number k' of power supply units in the third power scheme according to the whale optimization algorithm to obtain a seventh power scheme, wherein the current power capacity S' in the seventh power scheme ≤ the maximum available power capacity S of the power supply units of the corresponding type max , and the available number k' of power supply units in the seventh power scheme ≤ the maximum supply number k of the power supply units of the corresponding type. S1068: confirming the target function value of the seventh power scheme, and updating the current optimal power scheme based on the target function value of the seventh power scheme and the target function value of the current optimal power scheme; S10610: determining whether the current optimal power scheme satisfies a preset termination condition, and if yes, taking the current optimal power scheme as the optimal fourth power scheme, otherwise, performing S1066.

8. The method of claim 7, wherein, S1066 further comprises: generating a coefficient vector A based on the whale optimization algorithm; if the absolute value of the coefficient vector A is less than 1, updating the current power capacity S' and / or the supplyable quantity k' of the power supply unit based on a surrounding prey or spiral method; otherwise, updating the current power capacity S' and / or the supplyable quantity k' of the power supply unit based on a random search method.

9. The method of claim 2, wherein, The different periods comprise spring, summer, autumn, and winter; The different types of power supply units comprise synchronous generator power supply units, wind power supply units, photovoltaic power supply units, and energy storage power supply units.

10. An inertia constraint and whale algorithm based power scheme determination apparatus, characterized in that, The device comprises: a first determination module configured to randomly combine and initialize a pre-acquired first power scheme to obtain a second power scheme, wherein the first power scheme comprises power capacity S of a power supply unit, capacity unit price a, inertia time constant H, and maximum supply quantity k, and the capacity unit price a comprises inertia supply cost; The second determining module is configured to eliminate the second power scheme that does not satisfy the capacity constraint condition and the inertia constraint condition based on the power capacity S and the inertia time constant H, to obtain a third power scheme; The third determining module is configured to perform iterative optimization on the current power capacity S' of the third power scheme and the available number k' of power supply units according to a whale optimization algorithm, a preset termination condition, a maximum supply number k and a capacity unit price a, to determine an optimal fourth power scheme.

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