Flexible resource planning method based on time series operation simulation

Abstract

The application discloses a flexible resource planning method based on time sequence operation simulation, which comprises the following steps: S1, constructing a flexible resource planning model; S2, adjusting parameter values in the flexible resource planning model, so that the flexible resource planning model obtains a minimum value, and setting the parameters obtained when the planning model obtains the minimum value as optimal parameters of the flexible resource planning. The flexible resource planning method based on the time sequence operation simulation can accurately and reliably plan and analyze various flexible resources of different time scales in combination with different operation scenes, and provides a technical reference for scientific planning of the flexible resources.

Description

Technical Field

[0001] This invention relates to the field of power system planning, and more specifically to a flexible resource planning method based on time-series operation simulation. Background Technology

[0002] Currently, the flexible regulation of the power system is still mainly carried out by traditional thermal power units and hydropower units. With a high proportion of renewable energy integrated into the grid, the installed capacity and power generation share of thermal power units will continue to be replaced by wind and solar power, while the development of hydropower is limited by natural resources. In recent years, technologies for flexible resources such as energy storage, which are highly efficient and have strong regulation capabilities, have matured, and there is still room for breakthroughs in technology and consumption in the future. Therefore, considering the challenges of matching supply and demand for power system flexibility in the future, the rational planning of flexible resources such as energy storage is crucial.

[0003] Currently, energy storage types such as electrochemical energy storage used in power systems are mainly suitable for peak shaving and frequency regulation. However, with the gradual expansion of renewable energy grid integration, the source-load balance problem has become prominent over longer time scales, and daily, weekly, and seasonal power supply-demand mismatches pose challenges to the safety and stability of the power system. To meet the flexibility requirements at different time scales, power system planning needs to rationally plan various flexible resources, including short-term and long-term energy storage.

[0004] The regulation capability of energy storage largely depends on its planned capacity and maximum charge / discharge efficiency. Existing solutions extensively study capacity planning, primarily obtaining the energy storage configuration capacity for the corresponding planning year by solving optimization problems. On the planning timescale, existing planning methods typically consider a few typical or extreme scenarios. However, using a limited number of scenarios for planning cannot accurately account for the charging and discharging processes of flexible resources, nor can it account for the potential effects of flexible resources during operation. This is detrimental to the large-scale application of flexible resources such as energy storage, which have good peak-shaving and valley-filling effects.

[0005] Furthermore, due to the high penetration rate of renewable energy, the various flexible resources that need to be planned have different time characteristics. For example, the charging and discharging process of energy storage devices and the impact of lifespan degradation on their discharge power, as well as their faster load response speed compared to thermal power units with ramp constraints, all of these factors complicate the selection of typical scenarios. Given that both the source and load ends fluctuate over time, it is difficult to use typical scenarios to describe the future operation of the power system.

[0006] Therefore, a flexible resource planning method based on time-series simulation is needed to solve the above problems. Summary of the Invention

[0007] In view of this, the purpose of this invention is to overcome the deficiencies in the prior art and provide a flexible resource planning method based on time-series operation simulation. This method can accurately and reliably plan and analyze various flexible resources at different time scales in combination with different operation scenarios, providing a technical reference for the scientific planning of flexible resources.

[0008] The flexible resource planning method based on time-series simulation of the present invention includes the following steps:

[0009] S1. Construct a flexible resource planning model; the objective function of the flexible resource planning model is:

[0010] minC sys =C inv +C oper ;

[0011] Among them, C sys It is the total power system consumption; C inv It is the input and consumption of flexible resources; C oper It is the operating cost of the power system;

[0012] S2. Adjust the values ​​of each parameter in the flexible resource planning model to achieve the minimum value of the flexible resource planning model, and take the parameters set when the planning model achieves the minimum value as the optimal parameters for flexible resource planning.

[0013] Furthermore, the input and consumption C of flexibility resources is determined according to the following formula. inv :

[0014]

[0015] Where s1 is the power consumption coefficient of the flexible resource; s2 is the energy consumption coefficient of the flexible resource; It is the planned power capacity of the Class b flexible resources; γ is the planned energy capacity of the b-type flexible resource; γ is the operation and maintenance consumption conversion factor.

[0016] Furthermore, the operating consumption C of the power system is determined according to the following formula. oper :

[0017]

[0018] Among them, c t This represents the electricity consumption during time period t. and These are the charging and discharging efficiencies of the b-th type of flexibility resource in the t-th time period, respectively. and These represent the charging and discharging power of the b-th type of flexibility resource in the t-th time period; T is the total number of planned time periods; NG This is the total number of thermal power units; It is the power generation consumption coefficient of the g-th thermal power unit; C is the output of the g-th thermal power unit in the t-th time period; VoLL It is the load shedding penalty factor for the power system; N n It is the total number of nodes in the power system; C is the load shedding amount of the nth node in the tth time period; Cur N is the penalty coefficient for wind and solar power curtailment in the power system. W This is the total number of new energy generating units; It is the amount of renewable energy power abandoned by the wth renewable energy unit in the tth time period.

[0019] Furthermore, the flexible resource planning model includes energy strategy constraints;

[0020] The energy strategy constraints include:

[0021] New energy penetration rate requirements:

[0022]

[0023] Where T is the total number of planning time periods; N W This is the total number of new energy generating units; β is the output of the w-th renewable energy unit in the t-th time period; β is the renewable energy penetration rate requirement coefficient; N n D is the total number of nodes; n,t It represents the load demand of the nth node in the t-th time period;

[0024] Requirements for reducing renewable energy sources:

[0025]

[0026] in, This is the installed capacity of the wth new energy unit; γ is the available output coefficient of the w-th renewable energy unit in the t-th time period; γ is the renewable energy allowable reduction coefficient.

[0027] Load shedding limit requirements:

[0028]

[0029] in, α is the load shedding amount of the nth node in the tth time period; α is the load shedding ratio limit coefficient.

[0030] Furthermore, the flexible resource planning model includes systematic constraints;

[0031] The systemic constraints include:

[0032] Node power balancing:

[0033]

[0034] in, It is the output of the g-th thermal power unit in the t-th time period; It is the discharge power of the i-th type of flexibility resource in the t-th time period; is the charging power of the i-th type of flexibility resource in the t-th time period; b is the set of flexibility resources; It is the output of the w-th renewable energy unit in the t-th time period; w is the collection of renewable energy units; is the power transmitted by the l-th line in the power system during the t-th time period; lS represents the set of lines that transmit power from node n outwards; lE represents the set of lines that inject power into node n;

[0035] Node load shedding constraints:

[0036]

[0037] Line transmission capacity constraints:

[0038]

[0039]

[0040] Among them, F l max This is the maximum allowable transmission power for line l; It is the susceptance of line l; θ +,t θ is the phase angle of the first node of line l in the t-th time period; -,t It is the phase angle of the terminal node of line l in the t-th time period.

[0041] Furthermore, the flexible resource planning model includes generator-side constraints;

[0042] The generator-side constraints include:

[0043] Upper and lower limits of new energy output constraints:

[0044]

[0045] in, This is the maximum output of the wth new energy unit;

[0046] Upper and lower limits of thermal power unit output constraints:

[0047]

[0048] in, This is the lower limit of the output of the g-th thermal power unit; This is the upper limit of the output of the g-th thermal power unit;

[0049] Thermal power unit ramping constraints:

[0050]

[0051] in, and These refer to the uphill and downhill speeds of the thermal power unit, respectively.

[0052] Furthermore, the flexible resource planning model includes flexible resource-side constraints;

[0053] The flexibility resource-side constraints include:

[0054] Upper and lower limits of charge and discharge power constraints:

[0055]

[0056] in, It is the charging power of the type b flexibility resource during time period t; It is the discharge power of the type b flexibility resource during time period t; This represents the maximum capacity for input of type b flexibility resources;

[0057] Adjacent time period charge state coupling constraints:

[0058]

[0059] in, It is the state of charge of the type b flexibility resource in the t-th time period; It refers to the charging and discharging efficiency of the type b flexible resources;

[0060] Upper and lower limits of state of charge constraints:

[0061]

[0062] in, It is the continuous charging and discharging duration of the type b flexibility resource;

[0063] State-of-charge balance constraints within the cycle:

[0064]

[0065] in, N is the initial state-of-charge coefficient of the type b flexible resource; T It is a cycle.

[0066] Furthermore, the flexible resource planning model is solved using a multi-parameter programming algorithm, thereby minimizing the flexible resource planning model.

[0067] The beneficial effects of this invention are as follows: This invention discloses a flexible resource planning method based on time-series operation simulation. By constructing a flexible resource planning model with the objective function of minimizing the sum of various consumptions such as the input and operation of flexible resources, and under the constraints of energy strategy, power system instability, generator side constraints, and flexible resource side constraints, the planning model is solved and analyzed using multi-parameter programming theory. This enables the quantitative characterization of the analytical relationship between the penetration rate of new energy and the input of flexible resources in different operating scenarios, considering various time scales such as short-term and long-term. It can also quickly determine the optimal configuration capacity of flexible resources under future new energy consumption requirements. Attached Figure Description

[0068] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0069] Figure 1 This is a schematic diagram of the planning method of the present invention;

[0070] Figure 2 This is a schematic diagram of a typical daily load curve for the present invention;

[0071] Figure 3 This is a schematic diagram of a typical net load curve of the present invention;

[0072] Figure 4 This is a schematic diagram of the daily charging and discharging process of short-time energy storage according to the present invention;

[0073] Figure 5 This is a schematic diagram of the daily charging and discharging process of the long-term energy storage of the present invention;

[0074] Figure 6 This is a schematic diagram of the daily state of charge change process of short-term energy storage according to the present invention;

[0075] Figure 7 This is a schematic diagram of the daily state of charge change process of long-term energy storage according to the present invention;

[0076] Figure 8 This is a schematic diagram illustrating the relationship between the capacity of different types of flexible resource planning and the total system consumption according to the present invention;

[0077] Figure 9 This is a schematic diagram illustrating the analytical relationship between the total system consumption and the penetration rate of new energy sources in this invention. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings, as shown in the figures:

[0079] The flexible resource planning method based on time-series simulation of the present invention includes the following steps:

[0080] S1. Construct a flexible resource planning model; the objective function of the flexible resource planning model is:

[0081] minC sys =C inv +C oper ;

[0082] Among them, C sys It is the total power system consumption; C inv It is the input and consumption of flexible resources; C oper It is the operating cost of the power system;

[0083] S2. Adjust the values ​​of each parameter in the flexible resource planning model to achieve the minimum value of the flexible resource planning model, and take the parameters set when the planning model achieves the minimum value as the optimal parameters for flexible resource planning.

[0084] In this embodiment, the input consumption C of flexibility resources is determined according to the following formula. inv :

[0085]

[0086] Where s1 is the power consumption coefficient of the flexible resource; s2 is the energy consumption coefficient of the flexible resource; It is the planned power capacity of the Class b flexible resources; γ is the planned energy capacity of the b-type flexible resource; γ is the operation and maintenance consumption conversion factor.

[0087] The operating costs of the power system include the operating costs of thermal power units, the operating costs of flexible resources, load shedding penalties, and wind and solar curtailment penalties. The operating costs C of the power system are determined according to the following formula. oper :

[0088]

[0089] Among them, c t This represents the electricity consumption during time period t. and These are the charging and discharging efficiencies of the b-th type of flexibility resource in the t-th time period, respectively. and These represent the charging and discharging power of the b-th type of flexibility resource in the t-th time period; T is the total number of planned time periods; N G This is the total number of thermal power units; It is the power generation consumption coefficient of the g-th thermal power unit; C is the output of the g-th thermal power unit in the t-th time period; VoLL It is the load shedding penalty factor for the power system; N n It is the total number of nodes in the power system; C is the load shedding amount of the nth node in the tth time period; Cur N is the penalty coefficient for wind and solar power curtailment in the power system. W This is the total number of new energy generating units; This represents the amount of renewable energy curtailed by the w-th renewable energy unit during the t-th time period. The nodes in the power system are the busbars.

[0090] In this embodiment, the flexible resource planning model includes energy strategy constraints;

[0091] The energy strategy constraints include:

[0092] New energy penetration rate requirements:

[0093]

[0094] Where T is the total number of planning time periods; N W This is the total number of new energy generating units; β is the output of the w-th renewable energy unit in the t-th time period; β is the renewable energy penetration rate requirement coefficient; N n D is the total number of nodes; n,t It represents the load demand of the nth node in the t-th time period;

[0095] Requirements for reducing renewable energy sources:

[0096]

[0097] in, This is the installed capacity of the wth new energy unit; γ is the available output coefficient of the w-th renewable energy unit in the t-th time period; γ is the renewable energy allowable reduction coefficient.

[0098] Load shedding limit requirements:

[0099]

[0100] in, α is the load shedding amount of the nth node in the tth time period; α is the load shedding ratio limit coefficient.

[0101] The flexible resource planning model includes systematic constraints;

[0102] The systemic constraints involve constraints on all generating units within the power system, specifically including:

[0103] Node power balancing:

[0104]

[0105] in, It is the output of the g-th thermal power unit in the t-th time period; It is the discharge power of the i-th type of flexibility resource in the t-th time period; is the charging power of the i-th type of flexibility resource in the t-th time period; b is the set of flexibility resources; It is the output of the w-th renewable energy unit in the t-th time period; w is the collection of renewable energy units; is the power transmitted by the l-th line in the power system during the t-th time period; lS represents the set of lines that transmit power from node n outwards; lE represents the set of lines that inject power into node n;

[0106] Node load shedding constraints:

[0107]

[0108] Line transmission capacity constraints:

[0109]

[0110]

[0111] Among them, F l max This is the maximum allowable transmission power for line l; It is the susceptance of line l; θ +,t θ is the phase angle of the first node of line l in the t-th time period; -,t It is the phase angle of the terminal node of line l in the t-th time period.

[0112] The flexible resource planning model includes generator-side constraints;

[0113] The generator-side constraints include:

[0114] Upper and lower limits of new energy output constraints:

[0115]

[0116] in, This is the maximum output of the wth new energy unit;

[0117] Upper and lower limits of thermal power unit output constraints:

[0118]

[0119] in, This is the lower limit of the output of the g-th thermal power unit; This is the upper limit of the output of the g-th thermal power unit;

[0120] Thermal power unit ramping constraints:

[0121]

[0122] in, and These refer to the uphill and downhill speeds of the thermal power unit, respectively.

[0123] The flexible resource planning model includes flexible resource-side constraints;

[0124] The flexibility resource-side constraints include:

[0125] Upper and lower limits of charge and discharge power constraints:

[0126]

[0127] in, It is the charging power of the type b flexibility resource during time period t; It is the discharge power of the type b flexibility resource during time period t; This represents the maximum capacity for input of type b flexibility resources;

[0128] Adjacent time period charge state coupling constraints:

[0129]

[0130] in, It is the state of charge of the type b flexibility resource in the t-th time period; It refers to the charging and discharging efficiency of the type b flexible resources;

[0131] Upper and lower limits of state of charge constraints:

[0132]

[0133] in, It is the continuous charging and discharging duration of the type b flexibility resource;

[0134] State-of-charge balance constraints within the cycle:

[0135]

[0136] in, N is the initial state-of-charge coefficient of the type b flexible resource; T It is the cycle period, the N T Usually, 24 hours are taken.

[0137] In this embodiment, in step S2, the flexibility resource planning model is solved based on a multi-parameter planning algorithm so that the flexibility resource planning model obtains a minimum value; the parameters set when the planning model obtains a minimum value are taken as the optimal planning parameters for flexibility resources.

[0138] Among them, multi-parameter programming algorithms or theories can analyze the changes in the optimal solution set and feasibility of an optimization problem when one or more parameters in the problem change.

[0139] The optimization problem of the flexible resource planning model of this invention can be written in the following standard form:

[0140]

[0141] st

[0142] Ax≤Bw+D. (2)

[0143] In the formula: x is the optimization variable; w is the planning parameter; A and B are coefficient matrices; C and D are coefficient vectors.

[0144] For this standard form, the optimality conditions of the problem are first written out. Next, the constraints are categorized according to whether they are active or inactive, resulting in sets of active and inactive constraints. All active and inactive constraints are enumerated and substituted to obtain equivalent optimality conditions. The optimal solution (flexible resource planning) can be represented using planning parameters (such as new energy penetration rate) through the active constraints.

[0145] Substituting the above analytical representation into the objective function, we can obtain the analytical relationship between the objective function and the planning parameters. This allows for a quantitative analysis of the changes in the total system consumption when planning parameters such as the penetration rate of new energy sources change, thus providing technical support for a scientific, safe, and reasonable flexible resource planning scheme.

[0146] The specific solution is as follows:

[0147] First, define the optimal solution to optimization problems (1)-(2) as x. * Then the constraints in equation (2) can be divided into two categories: active constraints and inactive constraints.

[0148] Effective constraints:

[0149] A J x * =B J w+D J (3)

[0150] Ineffective constraints:

[0151] A K x * <B K w+D K (4)

[0152] Next, write out the optimality conditions for optimization problems (1)-(2), including:

[0153] Conditions for stationing:

[0154] C+A T λ=0, (5)

[0155] Complementary relaxation conditions:

[0156] λ⊥(Ax-Bw-D)=0, (6)

[0157] Feasibility conditions for the original problem:

[0158] Ax-Bw-D≤0. (7)

[0159] And the feasibility conditions for the dual problem:

[0160] λ≥0. (8)

[0161] Substituting the active and inactive constraints into the optimality conditions of the optimization problem, we obtain the equivalent optimality conditions:

[0162]

[0163] A J x * =B J w+D J (10)

[0164] λ K =0, (11)

[0165] A K x * <B K w+D K (12)

[0166] λ J ≥0, (13)

[0167] Through the equivalent optimality condition (10), the analytical representation relationship between the optimal solution and the planning parameters can be obtained:

[0168]

[0169] Substituting equation (14) into the objective function (1), we can obtain the analytical relationship between the objective function and the planning parameters:

[0170]

[0171] It should be noted that the multi-parameter programming algorithm or theory used above is existing technology. When solving the model, the parameters, variables, coefficient matrices, coefficient vectors, etc. involved can be replaced or set accordingly in combination with the specific flexible resource planning model, which will not be elaborated here.

[0172] To better understand the flexible resource planning method of this invention, the effectiveness of the method is verified using the IEEE-9 node system:

[0173] Considering two types of flexible resources: short-term energy storage with a continuous charge / discharge duration of 2 hours and long-term energy storage with a continuous charge / discharge duration of 24 hours, a 180MW renewable energy unit is installed at node 4, and its output is considered using renewable energy output prediction coefficients. The inputs for short-term and long-term energy storage are 3×102 respectively. 5 Yuan / MWh and 2×10 5 Yuan / MWh.

[0174] When the new energy penetration rate is set to 0.3, the planning capacity of two types of flexible energy storage resources, namely short-term and long-term energy storage, is obtained by applying the planning model proposed in this invention: 83.491MW for short-term energy storage and 10.8870MW for long-term energy storage.

[0175] The load and net load curves are as follows: Figure 2 and Figure 3 As shown, the charging and discharging power of different types of flexible resources is as follows: Figure 4 and Figure 5 As shown, the state of charge of different types of flexible resources is as follows: Figure 6 and Figure 7 As shown, Figure 8 This demonstrates the relationship between resource planning capacity with different flexibility and total system consumption.

[0176] Using a multi-parameter programming algorithm, the changes in total system consumption were quantitatively analyzed when the penetration rate of new energy sources varied from 0.1 to 0.8. Figure 9 As shown, system consumption initially decreases and then increases with the penetration of new energy sources. The initial decrease is because new energy sources have lower operating costs compared to conventional units; the subsequent increase is due to the excessive uncertainty brought about by high levels of new energy, which threatens the safe operation of the power system and thus requires more resources.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A flexible resource planning method based on time-series simulation, characterized in that: Includes the following steps: S1. Construct a flexible resource planning model; the objective function of the flexible resource planning model is: ； Among them, C sys It is the total power system consumption; C inv It is the input and consumption of flexible resources; It is the operating cost of the power system; The input and consumption of flexibility resources C are determined according to the following formula. inv : ； Where s1 is the power consumption coefficient of the flexible resource; s2 is the energy consumption coefficient of the flexible resource; It is the planned power capacity of the type b flexible resources; It is the planned energy capacity of Category b flexible resources; It is the conversion factor for operation and maintenance costs; The flexible resource planning model includes energy strategy constraints; The energy strategy constraints include: New energy penetration rate requirements: ； Where T is the total number of planning time periods; N W This is the total number of new energy generating units; This is the output of the wth new energy unit in the tth time period; This is the required coefficient for the penetration rate of new energy sources; N n D is the total number of nodes; n,t It represents the load demand of the nth node in the t-th time period; Requirements for reducing renewable energy sources: ； in, This is the installed capacity of the wth new energy unit; It is the available output coefficient of the w-th new energy unit in the t-th time period; It is the allowable reduction coefficient for new energy sources; Load shedding limit requirements: ； in, It is the load shedding amount of the nth node in the tth time period; It is the load shedding ratio limit factor; S2. Adjust the values ​​of each parameter in the flexible resource planning model to achieve the minimum value of the flexible resource planning model, and take the parameters set when the planning model achieves the minimum value as the optimal parameters for flexible resource planning.

2. The flexible resource planning method based on time-series simulation according to claim 1, characterized in that: The operating costs of the power system are determined using the following formula. : ； Among them, c t This represents the electricity consumption during time period t. and These are the charging and discharging efficiencies of the b-th type of flexibility resource in the t-th time period, respectively. and These represent the charging and discharging power of the b-th type of flexibility resource in the t-th time period; T is the total number of planned time periods; N G This is the total number of thermal power units; It is the power generation consumption coefficient of the g-th thermal power unit; It is the output of the g-th thermal power unit in the t-th time period; It is the load shedding penalty factor for the power system; N n It is the total number of nodes in the power system; It is the load shedding amount of the nth node in the tth time period; N is the penalty coefficient for wind and solar power curtailment in the power system. W This is the total number of new energy generating units; It is the amount of renewable energy power abandoned by the wth renewable energy unit in the tth time period.

3. The flexible resource planning method based on time-series simulation according to claim 1, characterized in that: The flexible resource planning model includes systematic constraints; The systematic constraints include: Node power balancing: ； in, It is the output of the g-th thermal power unit in the t-th time period; It is the discharge power of the i-th type of flexibility resource in the t-th time period; It is the charging power of the i-th type of flexibility resource in the t-th time period; It is a collection of flexible resources; This is the output of the wth new energy unit in the tth time period; It is a collection of new energy generating units; It is the transmission power of the l-th line in the power system during the t-th time period; This represents the set of lines that transmit power outward from node n; This represents the set of lines that inject power into node n; Node load shedding constraints: ； Line transmission capacity constraints: ； ； in, This is the maximum allowable transmission power for line l; It is the susceptance of line l; It is the phase angle of the first node of line l in the t-th time period; It is the phase angle of the terminal node of line l in the t-th time period.

4. The flexible resource planning method based on time-series simulation according to claim 3, characterized in that: The flexible resource planning model includes generator-side constraints; The generator-side constraints include: Upper and lower limits of new energy output constraints: ； in, This is the maximum output of the wth new energy unit; Upper and lower limits of thermal power unit output constraints: ； in, This is the lower limit of the output of the g-th thermal power unit; This is the upper limit of the output of the g-th thermal power unit; Thermal power unit ramping constraints: ； in, and These refer to the uphill and downhill speeds of the thermal power unit, respectively.

5. The flexible resource planning method based on time-series simulation according to claim 4, characterized in that: The flexible resource planning model includes flexible resource-side constraints; The flexibility resource-side constraints include: Upper and lower limits of charge and discharge power constraints: ； in, It is the charging power of the type b flexibility resource during time period t; It is the discharge power of the type b flexibility resource during time period t; This represents the maximum capacity for input of type b flexibility resources; Adjacent time period charge state coupling constraints: ； in, It is the state of charge of the type b flexibility resource in the t-th time period; It refers to the charging and discharging efficiency of the type b flexible resources; Upper and lower limits of state of charge constraints: ； in, It is the continuous charging and discharging duration of the type b flexibility resource; State-of-charge balance constraints within the cycle: ； in, It is the initial state of charge coefficient of the type b flexible resource; It is a cycle.

6. The flexible resource planning method based on time-series simulation according to claim 1, characterized in that: The flexible resource planning model is solved using a multi-parameter programming algorithm, thereby minimizing the flexible resource planning model.

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