Day-ahead optimization scheduling method considering system inertia supply out-of-limit risk

Abstract

The invention discloses a day-ahead optimal scheduling method considering a system inertia supply out-of-limit risk, and belongs to the technical field of day-ahead scheduling. Comprising the following steps: calculating to obtain a system inertia demand lower limit according to system frequency change rate constraint and frequency lowest point constraint, and calculating to obtain a system inertia demand upper limit by making a new energy station and an energy storage power station equivalent to a thermal power generating unit when the system is in the maximum load; the method comprises the following steps: considering inertia supporting capacities of a conventional unit, a wind power plant station and network construction energy storage, and constructing a risk driving index considering insufficient maximum inertia supply and excess minimum inertia supply of a system; constructing a two-stage stochastic optimization model according to the objective function and the constraint condition of the day-ahead stage and the objective function and the constraint condition of the real-time stage; and solving the two-stage stochastic optimization model, and verifying the economical efficiency of the scheduling scheme and the supply capability of the system inertia. According to the invention, the system is guaranteed to have sufficient inertia supply capability in the day-ahead stage, and the safety and economy of the system are guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of day-ahead scheduling, and in particular to a day-ahead optimization scheduling method considering the risk of system inertia supply exceeding a limit. Background Art

[0002] With the "dual carbon" goals being proposed, energy transition is accelerating. New energy generators, primarily wind and photovoltaic power, will gradually replace traditional thermal power generators and account for a larger proportion of the grid's total installed capacity. Unlike traditional synchronous generators, renewable energy generators are connected to the grid via power electronic converters. Their output power is decoupled from the grid frequency. Conventional control systems cannot actively provide inertia support to the system, resulting in excessively low system inertia. Low system inertia increases the initial frequency change rate and lowers the minimum frequency after a system active power surge. In severe cases, this can trigger the system's third line of defense, triggering the underfrequency load shedding device, causing the system to lose some load and even causing a system frequency collapse, posing significant challenges to safe and stable system operation. Virtual synchronous generators control the converter by simulating the rotor motion equations of synchronous generators. This allows the renewable energy generators and energy storage to provide inertia support, thereby increasing system inertia to a certain extent. High system inertia prolongs the recovery time after a disturbance, also detrimental to safe and stable system operation.

[0003] In power systems with a high proportion of renewable energy, the system inertia fluctuates greatly. It is necessary to establish a reasonable safety domain for the system inertia at the operational level to provide a basis for dispatching the system inertia. However, the demand assessment for system inertia in the existing technology only considers the minimum inertia demand of the system, and does not limit the maximum inertia demand of the system. In the existing technology, a dispatching model that considers multiple types of inertia resources such as conventional units, grid-connected energy storage, and new energy stations to regulate the system inertia has not yet been established for the safe and stable day-ahead dispatch of the system. In response to this situation, a day-ahead optimization dispatching method that considers the risk of exceeding the limit of the system inertia supply capacity is needed. By optimizing the startup plan of thermal power, the regulation capability of the system inertia can be guaranteed in the day-ahead stage, providing a basis for regulating the system inertia in the intraday and real-time stages. Summary of the Invention

[0004] The present invention aims to propose a day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit, comprising the following steps:

[0005] The lower limit of the system inertia requirement is calculated based on the system frequency change rate constraint and the frequency minimum point constraint. The upper limit of the system inertia requirement is calculated by equating the new energy stations and energy storage power stations at the maximum load of the system to thermal power units.

[0006] Considering the inertia support capacity of conventional units, wind farms, and grid-connected energy storage, and based on the conditional value at risk theory, a risk-driven indicator that considers the system's maximum inertia undersupply and minimum inertia oversupply is constructed.

[0007] A two-stage stochastic optimization model is constructed based on the objective function and constraints of the day-ahead phase and the objective function and constraints of the real-time phase.

[0008] The gurobi solver is used to solve the two-stage stochastic optimization model to verify the economic feasibility of this scheduling scheme and its ability to supply system inertia.

[0009] Furthermore, the lower limit of the system inertia requirement is the maximum value of the system minimum inertia requirement value obtained based on the frequency change rate and the lowest frequency point.

[0010] Furthermore, the calculation formula for the upper limit of system inertia requirement is:

[0011]

[0012] Where: H max is the maximum inertia requirement of the system, G is the set of thermal power units, n is the number of equivalent thermal power units of energy storage and new energy stations at maximum load, H g 、S g are the inertia constant and capacity of the thermal power unit g, H k 、S k are the inertia constant and capacity of the most used thermal power unit k in the system, It is the operating status of thermal power unit g at the moment of maximum load. When it is 1, it indicates operation, and when it is 0, it indicates non-operation.

[0013] Furthermore, risk-driven indicators include:

[0014]

[0015] Where H t CVaR,down is the penalty term for insufficient supply of the system's maximum inertia at time t, H max t,s is the maximum inertia supply of the system at time t under scenario s, H min is the lower limit of system inertia requirement, and is the auxiliary decision variable for calculating CVaR value, δ1 is the system inertia supply margin, c down H is the maximum inertia supply under-penalty cost; t CVaR,up is the penalty term for excess supply of the system minimum inertia at time t, H min t,s is the minimum inertia supply of the system at time t under scenario s, H max is the upper limit of system inertia demand, δ2 is the system inertia supply margin, c up is the minimum inertia oversupply penalty cost, ρs is the probability of scene s, S is the set of scenes, and α is the confidence level.

[0016] Furthermore, the two-stage stochastic optimization model includes:

[0017] Objective function:

[0018] min(C DA +C ERT +βC CVaR )

[0019]

[0020] Where: t, g, w, v, d, k, s are the identifiers of time period, thermal power unit, wind farm, photovoltaic farm, node load, energy storage, and real-time scene respectively; T, G, W s 、V s , D, K, and S are respectively the collection of time period, whole system thermal power units, wind farms, photovoltaic farms, node loads, energy storage, and real-time scenarios; C DA is the day-ahead cost; C ERT is the real-time cost; C CVaR Provides a risk penalty item for system inertia exceeding the limit; v g,t 、w g,t are binary variables for the start and stop of unit g during period t. When they are equal to 1, they indicate that unit g is started or stopped during period t. C(v g,t ,w g,t ) is the unit combination cost; P g,t is the active power output of thermal power unit g in period t during the day-ahead phase; C(P g,t ) is the power generation cost of the unit in the day-ahead stage; C g U 、C g D are the cost coefficients of increasing and decreasing the reserve capacity of unit g in the day-ahead phase; R g,t U 、R g,t D are the upward and downward reserve capacities of unit g in period t during the day-ahead phase; P g,t,s is the active power output of thermal power unit g during period t under real-time scenario s; C(P g,t,s ) is the power generation cost of the unit in the real-time scenario; C w cur 、C v cur 、C k cur are the penalty coefficients for wind curtailment, solar curtailment, and energy storage real-time readjustment deviation; ΔP w,t,s , ΔP v,t,sare the wind power curtailment and solar power curtailment of wind farm w and photovoltaic farm v in period t under scenario s, respectively; P k,t cha 、P k,t dis are respectively the charging and discharging power of energy storage k in period t during the day-ahead phase; P k,t,s cha 、P k,t,s dis are respectively the charging and discharging power of energy storage k in time period t under real-time scenario s; H t CVaR,down 、H t CVaR,up They are the risk penalty items of insufficient maximum inertia supply and excessive minimum inertia supply of the system in period t;

[0021] Constraints in the day-ahead phase:

[0022] Constraints on safe operation of thermal power units

[0023]

[0024] P g,t+1 -P g,t ≤SU g ·u g,t +(1-u g,t )·(P gmax +P gmin ) / 2

[0025] P g,t -P g,t+1 ≤SD g ·u g,t+1 +(1-u g,t+1 )·(P gmax +P gmin ) / 2

[0026] u g,t -u g,t-1 ≤v g,t ,u g,t-1 -u g,t ≤w g,t

[0027]

[0028]

[0029] Where: P g,max 、P g,min The upper and lower limits of the active power output of thermal power unit g; are the upper and lower limits of the spare capacity of unit g; SU g , SD gare the maximum upward and downward climbing rates of thermal power unit g respectively; are the minimum continuous start and stop time of thermal power unit g; m is the continuous on / off time of thermal power unit g; u g,t is the operating state variable of thermal power unit g at time t, which is 1 when it indicates operation and 0 when it indicates non-operation;

[0030] Node power balance and branch power flow constraints

[0031]

[0032] Where: G ij 、B ij are the real and imaginary parts of the node admittance matrix respectively; V i,t 、V j,t is the voltage amplitude of nodes i and j at time t in the day-ahead phase; θ i,t ,θ j,t is the voltage phase angle of nodes i and j at time t in the day-ahead phase; θ ij,t is the phase angle difference between nodes i and j at time t in the day-ahead phase; g ij 、b ij are the branch active power transmission upper limit, conductance and susceptance of branches i-j respectively;

[0033] Energy storage operation constraints

[0034]

[0035] Where: E k,t 、E kN are the capacity of energy storage k at time t and the rated capacity of energy storage k respectively; are the maximum charge and discharge power of energy storage k respectively; are the charge and discharge indicators of energy storage k at time t, respectively. When it is 1, it means that energy storage k is in the charge and discharge state at time t; is the energy storage SOC of energy storage k at time t; are the upper and lower limits of SOC respectively;

[0036] Constraints in the real-time phase:

[0037] Safe operation constraints of thermal power units under multiple scenarios

[0038] P g,(t+1),s -P g,t,s ≤SU g ·u g,t +(1-u g,t )·(P gmax +P gmin ) / 2

[0039] Pg,t,s -P g,(t+1),s ≤SD g ·u g,(t+1) +(1-u g,(t+1) )·(P gmax +P gmin ) / 2

[0040]

[0041] Where: P g,t,s is the active power output of thermal power unit g at time t under scenario s;

[0042] New energy power constraints in multiple scenarios

[0043]

[0044] Where: P w,t,s 、P v,t,s are the dispatching power of wind farm w and photovoltaic farm v at time t under scenario s, They are the predicted power of wind farm w and photovoltaic farm v at time t under scenario s.

[0045] The beneficial effects of the present invention are:

[0046] The method of the present invention can increase the number of system startup units when the system inertia supply is insufficient, and reduce the number of system startup units when the system inertia supply is excessive, thereby ensuring that the system has sufficient inertia supply capacity in the day-ahead stage, thereby ensuring the safety and economy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit, provided by the present invention;

[0048] Figure 2 Schematic diagram of the improved IEEE39 test system provided by the present invention;

[0049] Figure 3 2. It is a schematic diagram of the maximum inertia supply of the system under different wind power proportions according to the embodiment provided by the present invention;

[0050] Figure 4 2. This is a schematic diagram of minimum inertia supply of system inertia under different wind power proportions according to an embodiment of the present invention;

[0051] Figure 5 1. A diagram comparing the maximum inertia supply of the system in the scheduling scheme of the embodiment provided by the present invention that only considers economic efficiency and the scheduling scheme proposed by the present invention;

[0052] Figure 6This is a comparison chart of the system minimum inertia supply of the scheduling scheme that only considers economy in the embodiment provided by the present invention and the scheduling scheme proposed by the present invention. DETAILED DESCRIPTION

[0053] The present invention proposes a day-ahead optimization scheduling method that takes into account the risk of system inertia supply exceeding the limit. The present invention is further described below with reference to the accompanying drawings and specific embodiments.

[0054] Figure 1 FIG. 1 is a flow chart of a day-ahead optimization scheduling method considering the risk of exceeding the limit of the system inertia supply capacity according to an embodiment of the present invention. Figure 1 As shown, the method includes the following steps:

[0055] Step S101: Calculate the upper and lower limits of system inertia requirements

[0056] S101.1. Calculate the lower limit of the system inertia requirement using the frequency change rate and frequency minimum point constraints.

[0057] The frequency response of the system is described by the equivalent rotor motion equation:

[0058]

[0059] Where: H sys is the system inertia, f(t) is the system frequency at time t, f N is the system rated frequency, P mec (t), P ele (t) are the total mechanical power and the total electromagnetic power, respectively, D is the damping effect during the frequency response process, and Δf(t) is the frequency deviation.

[0060] At the moment of disturbance, the speed governor of the generator has not yet been activated. At this time, the unbalanced power and RoCoF are the largest. The rotor motion equation at the moment of disturbance is:

[0061]

[0062] Where: ΔP d is the disturbance power.

[0063] By limiting the RoCoF at the moment the disturbance occurs, the minimum inertia requirement of the system based on the RoCoF constraint can be obtained:

[0064]

[0065] Where: H RoCoF min is the minimum inertia requirement of the system based on RoCoF constraints, ΔP max RoCoF is the percentage of the system's maximum power deficit to the system's rated generating capacity.max The maximum frequency change rate allowed by the system.

[0066] Assume that the disturbance occurs at time t = 0. At the moment of disturbance, the synchronous generator with voltage source characteristics and the virtual synchronous generator automatically share the disturbance power, causing a sudden increase in electromagnetic power. The speed regulator has not yet been activated, and the mechanical power remains unchanged. The system inertia buffers the system unbalanced power by converting the rotor kinetic energy into electromagnetic power, and the system frequency decreases. When the system frequency exceeds the frequency regulation dead zone, that is, t = t db When the speed regulator starts to work, the mechanical power increases. When the mechanical power is equal to the electromagnetic power, the system frequency reaches the lowest point f NF , corresponding to time t NF After that, the prime mover continues to increase mechanical power, and cooperates with the system's secondary and tertiary frequency modulation to restore the system frequency to near the rated value.

[0067] Frequency minimum point f NF It is mainly related to the system inertia and primary frequency modulation. The lowest frequency point cannot be lower than the allowable limit:

[0068] f NF ≥f min (4)

[0069] Formula (4) is a nonlinear constraint, and the piecewise linearization technique is used to simulate the system frequency response process. db Integrating and neglecting the system damping yields:

[0070]

[0071] Where: f db , t db They are primary frequency modulation dead zone and action time respectively.

[0072] Using the primary frequency modulation rate R sys To indicate the time when the system frequency reaches the lowest point:

[0073]

[0074] For equation (1) from t = 0 to t = t NF Integrate and linearize, ignoring damping to obtain:

[0075]

[0076] Substituting equations (5) and (6) into equation (7), we can obtain the lowest frequency point f of the system: NF and the system minimum inertia requirement H based on the frequency minimum point constraint NF min They are:

[0077]

[0078] Equation (3) and Equation (9) are the system minimum inertia requirements based on RoCoF and the frequency minimum point constraint, respectively. The larger value of the two is taken as the system minimum inertia requirement:

[0079] H min =max(H RoCoF min ,H NF min ) (10)

[0080] S101.2. Equivalently treat the new energy stations and energy storage power stations at maximum load as thermal power units. Calculate the inertia provided by the existing thermal power and equivalent thermal power in the system to determine the upper limit of the system inertia requirement.

[0081] The equivalent number of thermal power units in energy storage and new energy stations at maximum load is:

[0082]

[0083] Where: P d max is the maximum load of the system in a day, is the power generated by thermal power unit g at maximum load, G is the set of thermal power units, S k is the capacity of the most used thermal power unit in the system, The symbol for rounding up.

[0084] The maximum inertia requirement of the system can be obtained by calculating the inertia provided by the existing and equivalent thermal power units in the system:

[0085]

[0086] Where: H max is the maximum inertia requirement of the system, H g 、S g are the inertia constant and capacity of the thermal power unit g, H k 、S k are the inertia constant and capacity of the most used thermal power unit k in the system, It is the operating status of thermal power unit g at the moment of maximum load. When it is 1, it indicates operation, and when it is 0, it indicates non-operation.

[0087] Step S102: Considering the inertia support capabilities of conventional units, wind farms, and grid-connected energy storage, based on the conditional value at risk theory, a risk-driven indicator is constructed that considers the maximum inertia supply shortage and the minimum inertia supply surplus of the system.

[0088] S102.1. Construction of system maximum and minimum inertia supply indicators

[0089] Controlling the converter through control strategies can provide energy storage and new energy units with inertia support capabilities. Based on the control strategy, these devices are primarily categorized as grid-following and grid-forming devices. Grid-following devices exhibit a current source response delay of approximately 100ms. They improve system power imbalance by varying output power, thereby reducing the rate of frequency change. This is essentially a power response and does not contribute inertia to the system. Grid-forming devices provide inertia support by simulating the rotor motion equations of synchronous generators. Their voltage source characteristics allow them to instantaneously share disturbance power, similar to synchronous machines, increasing the system's inertia.

[0090] The resources that can provide inertia for system inertia supply include thermal power units, grid-connected energy storage, and grid-connected wind turbines. Since photovoltaic units do not contain rotating components and have zero equivalent inertia, they require additional energy storage to provide inertia. Therefore, their contribution to system inertia is not considered for now.

[0091] The maximum inertia supply of the system considers the operation mode that can provide the maximum inertia for the system, that is, all wind turbines with the ability to switch to the grid are in the grid-building mode. All energy storage power stations with the ability to switch to the grid are in the grid-building mode and provide their maximum inertia to the system:

[0092]

[0093] Where: H max t,s is the maximum inertia supply of the system at time t under scenario s; H k,max 、H g 、H w are the maximum inertia constant that can be provided by the grid-type energy storage k, the inertia constant of the thermal power unit g, and the equivalent inertia constant of the wind farm w;

[0094] S k 、S g are the capacities of energy storage k and thermal power unit g respectively; are the predicted outputs of wind farm w and photovoltaic farm v at time t under scenario s; k GFM is the proportion of grid-type units in the wind farm, k switch is the proportion of wind farm units with grid switching capability; u g,t is the operating status of thermal power unit g at time t, 1 indicates operation, and 0 indicates shutdown; K', K, G, W s 、V s They are respectively a collection of energy storage that can be grid-connected and operated, a collection of full-system energy storage, thermal power units, wind farms, and photovoltaic farms.

[0095] The system's minimum inertia supply considers the operating mode that provides the system with the minimum inertia, that is, all wind turbines with the ability to switch to the grid are in the grid-following mode. All energy storage power stations with the ability to switch to the grid are in the grid-following mode, and only the grid-following energy storage provides its maximum inertia to the system:

[0096]

[0097] Where: H min t,s is the minimum inertia supply of the system at time t under scenario s; K” is the set of network energy storage.

[0098] S102.2. Construct risk-driven indicators for insufficient maximum inertia supply and excessive minimum inertia supply in the system

[0099] The risk-driven indicator is constructed using the conditional value at risk (CVaR) theory. Value at risk (VaR) is the maximum expected loss of a portfolio of financial assets under a certain confidence level and within a certain period. CVaR refers to the conditional expectation of the part of the loss that exceeds VaR, representing the average level of excess loss. CVaR makes up for the defect that VaR cannot reflect "tail risk" and does not meet the subadditivity. If the maximum inertia supply of the system is lower than the lower limit of the system inertia supply, the system will face the risk of insufficient maximum inertia supply. Low inertia will cause problems such as excessive frequency change rate after disturbance and too low frequency minimum point; if the minimum inertia supply of the system exceeds the upper limit of the system inertia supply, the system will face the risk of excessive minimum inertia supply. High inertia will cause the recovery time of the power system after disturbance to be prolonged, which is not conducive to the safe and stable operation of the system. The conditional value at risk theory is used to quantify the risks of insufficient maximum inertia supply and excessive minimum inertia supply of the system, as shown in formulas (15)-(16):

[0100]

[0101] Where: H t CVaR,down 、H t CVaR,up are the risk penalty items of the system’s maximum inertia undersupply and minimum inertia oversupply at time t; H t VaR,down and H t VaR,up is the auxiliary decision variable for calculating CVaR value; ρ s is the probability of scene s; S is the set of scenes; α is the confidence level; c down 、c up The penalty cost for exceeding the unit inertia supply limit; H max 、H minare the upper and lower limits of the system inertia requirements; δ1 and δ2 are the margins left for the maximum and minimum inertia supply of the system respectively; the expression [x] + =max{x,0};(H min ·(1+δ1)-H max t,s ) + 、(H min t,s -H max (1-δ2)) + They respectively represent the shortage of the system's maximum inertia supply and the surplus of the minimum inertia supply. They are not zero only when the system's maximum inertia supply is lower than the lower limit of the inertia supply and the minimum inertia supply is higher than the upper limit of the inertia supply.

[0102] Step S103: The unit power generation cost, start-up and shutdown cost, and standby cost are used as the objective function of the day-ahead phase, and the unit readjustment cost, the penalty item for abandoning new energy, and the penalty item for the risk of system inertia supply exceeding the limit are used as the objective function of the real-time phase. Meanwhile, the unit, energy storage, system operation constraints, and system inertia supply constraints are considered to construct a two-stage stochastic optimization model.

[0103] According to the day-ahead forecast of new energy, new energy scenarios are generated based on the autoregressive sliding average model, and clustered based on the improved k-means clustering algorithm to obtain a set of typical wind and solar scenarios as the operating scenarios in the real-time stage.

[0104] The two-stage stochastic optimization model consists of two phases: the day-ahead phase and the real-time phase. The day-ahead phase determines unit startup and output plans based on day-ahead forecasts of renewable energy and load. The real-time phase readjusts unit output based on real-time operating scenarios, with the amount of readjustment not exceeding the day-ahead reserve capacity. The two phases are interconnected and coupled. The real-time phase feeds back economic costs and risk penalties to the day-ahead phase in the form of expected adjustment costs, enabling day-ahead planning to account for real-time operational uncertainties, thereby improving system safety and economic efficiency.

[0105] The objective function of the two-stage stochastic optimization model includes day-ahead cost, real-time cost, and inertia supply over-limit penalty:

[0106] min(C DA +C ERT +βC CVaR ) (17)

[0107] The day-ahead cost includes unit start-up and shutdown costs, power generation costs, and spare capacity costs:

[0108]

[0109] Real-time costs include unit readjustment costs, abandoned renewable energy, load shedding penalties, and energy storage real-time readjustment deviation penalties:

[0110]

[0111] The inertia supply over-limit penalty items include the system maximum inertia supply insufficient and minimum inertia supply excess penalty items:

[0112]

[0113] Where: t, g, w, v, d, k, s are the identifiers of time period, thermal power unit, wind farm, photovoltaic farm, node load, energy storage, and real-time scene respectively; T, G, W s 、V s , D, K, and S are the collections of time periods, thermal power units in the entire system, wind farms, photovoltaic farms, node loads, energy storage, and real-time scenarios, respectively.

[0114] In formula (17), C DA is the day-ahead cost; C ERT is the real-time cost; C CVaR Provides a risk penalty for exceeding the limit for system inertia.

[0115] In formula (18), v g,t 、w g,t are binary variables for the start and stop of unit g during period t. When they are equal to 1, they indicate that unit g is started or stopped during period t. C(v g,t ,w g,t ) is the unit combination cost; P g,t is the active power output of thermal power unit g in period t during the day-ahead phase; C(P g,t ) is the power generation cost of the unit in the day-ahead stage; C g U 、C g D are the cost coefficients of increasing and decreasing the reserve capacity of unit g in the day-ahead phase; R g,t U 、R g,t D They are the upward and downward reserve capacities of unit g in period t during the day-ahead phase.

[0116] In formula (19), P g,t,s is the active power output of thermal power unit g during period t under real-time scenario s; C(P g,t,s ) is the power generation cost of the unit in the real-time scenario; C w cur 、C v cur 、C k curare the penalty coefficients for wind curtailment, solar curtailment, and energy storage real-time readjustment deviation; ΔP w,t,s , ΔP v,t,s are the wind power curtailment and solar power curtailment of wind farm w and photovoltaic farm v in period t under scenario s, respectively; P k,t cha 、P k,t dis are respectively the charging and discharging power of energy storage k in period t during the day-ahead phase; P k,t,s cha 、P k,t,s dis are respectively the charging and discharging power of energy storage k in period t under real-time scenario s.

[0117] In formula (20), H t CVaR,down 、H t CVaR,up are the risk penalty items for the system's maximum inertia undersupply and minimum inertia oversupply during period t, respectively, and can be obtained using equations (15)-(16).

[0118] The constraints in the day-ahead phase include:

[0119] (1) Constraints on safe operation of thermal power units

[0120]

[0121] P g,t+1 -P g,t ≤SU g ·u g,t +(1-u g,t )·(P gmax +P gmin ) / 2 (23)

[0122] P g,t -P g,t+1 ≤SD g ·u g,t+1 +(1-u g,t+1 )·(P gmax +P gmin ) / 2 (24)

[0123] u g,t -u g,t-1 ≤v g,t ,u g,t-1 -u g,t ≤w g,t (25)

[0124]

[0125] Where: P g,max 、P g,minThe upper and lower limits of the active power output of thermal power unit g; are the upper and lower limits of the spare capacity of unit g; SU g , SD g are the maximum upward and downward climbing rates of thermal power unit g respectively; are the minimum continuous on / off time of thermal power unit g, respectively. m is the continuous on / off time of thermal power unit g; u g,t is the operating state variable of thermal power unit g at time t. When it is 1, it indicates operation, and when it is 0, it indicates non-operation.

[0126] (2) Node power balance and branch power flow constraints

[0127]

[0128] Where: G ij 、B ij are the real and imaginary parts of the node admittance matrix respectively; V i,t 、V j,t is the voltage amplitude of nodes i and j at time t in the day-ahead phase; θ i,t ,θ j,t is the voltage phase angle of nodes i and j at time t in the day-ahead phase; θ ij,t is the phase angle difference between nodes i and j at time t in the day-ahead phase; g ij 、b ij are the branch active power transmission upper limit, conductance and susceptance of branches i-j respectively.

[0129] (3) Energy storage operation constraints

[0130]

[0131] Where: E k,t 、E kN are the capacity of energy storage k at time t and the rated capacity of energy storage k respectively; are the maximum charge and discharge power of energy storage k respectively; are the charge and discharge indicators of energy storage k at time t, respectively. When it is 1, it means that energy storage k is in the charge and discharge state at time t; is the energy storage SOC of energy storage k at time t; are the upper and lower limits of SOC respectively.

[0132] The constraints of the real-time phase include:

[0133] (1) Safe operation constraints of thermal power units under multiple scenarios

[0134] P g,(t+1),s -P g,t,s ≤SU g ·ug,t +(1-u g,t )·(P gmax +P gmin ) / 2(37)

[0135] P g,t,s -P g,(t+1),s ≤SD g ·u g,(t+1) +(1-u g,(t+1) )·(P gmax +P gmin ) / 2(38)

[0136]

[0137] Where: P g,t,s is the active power output of thermal power unit g at time t under scenario s.

[0138] (2) New energy power constraints in multiple scenarios

[0139]

[0140] Where: P w,t,s 、P v,t,s are the dispatching power of wind farm w and photovoltaic farm v at time t under scenario s, They are the predicted power of wind farm w and photovoltaic farm v at time t under scenario s.

[0141] The system inertia supply constraints are shown in Equations (13) to (16). In addition, it also includes node power balance constraints, branch power flow constraints, and energy storage operation constraints under multiple scenarios.

[0142] Step S104: Calculate the upper and lower limits of the system inertia demand, and use the Gurobi solver to solve the two-stage stochastic optimization model. Verify the economic efficiency of the proposed scheduling scheme and its improvement effect on the system inertia supply capacity through comparative examples.

[0143] Calculation of the upper and lower limits of system inertia requirements: ΔP max The maximum frequency change rate RoCoF is taken as the percentage of the maximum capacity thermal power unit in the system to the average rated power generation capacity of the system, which is 0.124; max Take it as 1Hz / s; the lower limit of the system inertia requirement H based on the frequency change rate constraint can be calculated by formula (3): RoCoF min 3.1s. One frequency modulation action time t db Take it as 0.25s; the system frequency modulation rate R sys Take it as 0.07; the lowest limit of system frequency f minTake it as 49Hz; the lower limit of the system inertia requirement H based on the frequency minimum point constraint can be calculated by formula (9): NF min The lower limit of the system inertia requirement is 3.49s. Equation (10) shows that the lower limit of the system inertia requirement based on the frequency change rate and the frequency minimum point constraint is 3.49s. Equations (11) and (12) equate the new energy stations and energy storage power stations at the maximum system load to four 600MW thermal power units, and the upper limit of the system inertia requirement is calculated to be 5.13s.

[0144] This embodiment adopts the improved IEEE39 node test system, such as Figure 2 As shown. The total installed capacity of thermal power is 7374MW, and the maximum load is 6000MW. Five wind farms with a capacity of 900MW and three photovoltaic power stations with a capacity of 500MW are added, and their locations are shown in the figure. Each wind farm is equipped with a 300MW energy storage power station, of which the energy storage at nodes 3 and 15 is grid-type energy storage, and the other energy storage is grid-following energy storage. In each wind farm station, 30% of the units are grid-type wind turbines, 20% of the units have the ability to switch to the grid, and 50% of the units are grid-following wind turbines, that is, k GFM is 0.3, k switch The penalty for curtailing renewable energy is 500 ¥ / MWh, and the system inertia supply margins δ1 and δ2 are set to 0.1. The equivalent inertia constant of the wind farm is 6 seconds, and the maximum inertia constant of grid-connected energy storage is 10 seconds. The capacity and inertia constant of the thermal power units are shown in the table below. A day is divided into 15-minute units, with T = 96. All calculations were performed on a computer with an AMD Ryzen 9 7945HX processor at 2.5 GHz and 16 GB of memory, using Python to call the Gurobi solver.

[0145] Table 1 Capacity and inertia constant of thermal power units

[0146]

[0147]

[0148] To compare and analyze the effectiveness of the method proposed in this embodiment, two results are compared:

[0149] Comparison result 1: Comparison of the difference between the two-stage stochastic optimization model that only considers economic efficiency and the model proposed in this invention in terms of ensuring the system inertia supply capacity.

[0150] Compare the maximum and minimum inertia supply capabilities of the system under different wind power installed capacity ratios, such as Figure 3As shown in Figure 2, when the total installed capacity of wind power exceeds 3000MW, the system maximum inertia supply is lower than the lower limit of the system inertia supply during the period from 0:00 to 6:00, which creates the risk of insufficient system maximum inertia supply. Figure 4 As shown in the figure, under different wind power proportions, the system minimum inertia supply of the dispatch scheme that only considers economic considerations exceeds the system inertia supply limit after 20:00, creating the risk of system minimum inertia oversupply. Analysis shows that between 0:00 and 6:00, wind power generation is high and thermal power generation is low, posing a risk of insufficient maximum inertia supply. After 20:00, wind power output is very low and thermal power generation is high, posing a risk of system minimum inertia oversupply. This shows that the day-ahead dispatch scheme that only considers economic considerations cannot guarantee sufficient system inertia supply capacity during the day-ahead period.

[0151] Under 4500MW of wind power installed capacity, the system inertia supply capacity of the day-ahead dispatching scheme that only considers economic efficiency is compared with the dispatching scheme proposed in this invention. Figure 5 As shown in the figure, at 0:00, the scheduling scheme that only considers economic efficiency starts up four units, namely unit 1, unit 5, unit 6, and unit 9, and the maximum inertia supply of the system is slightly lower than the lower limit. The scheduling scheme proposed in the present invention starts up four units, namely unit 1, unit 5, unit 6, and unit 8. By replacing unit 9 with an inertia constant of 3.8s with unit 8 with an inertia constant of 4.7s, the maximum inertia supply of the system is higher than the lower limit. During the period from 0:00 to 3:30, the wind power output gradually increased and reached its maximum value at 3:30. The scheduling scheme that only considers economic efficiency shuts down unit 6 at 1:15, further reducing the maximum inertia supply of the system. It was not until after 6:00 that the other units were started up one after another. After unit 2 was started at 7:30, the maximum inertia supply of the system was higher than the lower limit. The scheduling scheme proposed in the present invention does not shut down any units when the wind power output is high and gradually increases to the maximum value from 0:00 to 3:30. The four units that are in operation are still units 1, 5, 6, and 8. The maximum inertia supply of the system is always kept at a safe level. Figure 6 As shown in the figure, in the scheduling scheme that only considers economic efficiency, only unit 7 is not started after 20:00, and the system minimum inertia supply exceeds the system inertia supply upper limit. The scheduling scheme proposed in this invention shuts down unit 6 at 20:30 and unit 4 at 23:45, which reduces the system minimum inertia supply and does not exceed the upper limit.

[0152] Comparison Result 2: Comparison of the economic performance between the two-stage stochastic optimization model that only considers economic performance and the model proposed in this invention.

[0153] The economic comparison of the two solutions is shown in the following table:

[0154] Table 2 Economic comparison of the two plans

[0155]

[0156] Scheme 1 is a day-ahead dispatch scheme that considers only economic considerations, while Scheme 2 considers the risk of fluctuations in the system's inertia supply capacity. Neither scheme incurs any costs associated with curtailing renewable energy. As shown in the table, Scheme 2 has slightly higher startup and shutdown costs than Scheme 1, while its generation, standby, and re-regulation costs are slightly lower. Overall, the two schemes are similar in cost.

[0157] In summary, the day-ahead scheduling scheme that considers the risk of fluctuations in the system's inertia supply capacity can ensure that the system has sufficient inertia supply capacity in the day-ahead stage while taking into account economic efficiency by increasing the number of system operating units when the system inertia supply is insufficient and reducing the number of system operating units when the system inertia supply is excessive.

[0158] The embodiment of the present invention calculates the lower limit of the system inertia demand based on the frequency change rate constraint and the frequency minimum point constraint, and equates the new energy and energy storage at maximum load to the thermal power calculation system inertia demand upper limit. Based on the conditional risk value theory, a risk-driven indicator of insufficient maximum inertia supply and excessive minimum inertia supply of the system is constructed. The unit power generation cost, start-up and shutdown cost, and standby cost are used as the objective function of the day-ahead phase, and the unit readjustment cost, abandoned new energy cost, and system inertia supply over-limit risk cost are used as the objective function of the real-time phase. Taking the unit, energy storage, system operation constraints and system inertia supply constraints into consideration at the same time, a two-stage stochastic optimization model is constructed, and the Gurobi solver is called to solve the model. By comparing the differences between the two-stage day-ahead stochastic optimization model that only considers economic efficiency and the model proposed in the present invention in terms of ensuring the system inertia supply capacity and economic efficiency, it is verified that the scheduling scheme proposed in the present invention can take into account economic efficiency while ensuring that the system has sufficient inertia supply capacity in the day-ahead phase.

Claims

1. A day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit is characterized by: The following steps are involved: The lower limit of the system inertia requirement is calculated based on the system frequency change rate constraint and the frequency minimum point constraint. The upper limit of the system inertia requirement is calculated by equating the new energy stations and energy storage power stations at the maximum load of the system to thermal power units. Considering the inertia support capacity of conventional units, wind farms, and grid-connected energy storage, and based on the conditional value at risk theory, a risk-driven indicator that considers the system's maximum inertia undersupply and minimum inertia oversupply is constructed. A two-stage stochastic optimization model is constructed based on the objective function and constraints of the day-ahead phase and the objective function and constraints of the real-time phase. The gurobi solver is used to solve the two-stage stochastic optimization model to verify the economic feasibility of this scheduling scheme and its ability to supply system inertia.

2. The day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit according to claim 1 is characterized in that: The lower limit of the system inertia requirement is the maximum value of the system minimum inertia requirement value obtained based on the frequency change rate and the lowest frequency point.

3. The day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit according to claim 1 or 2 is characterized in that: The calculation formula for the upper limit of the system inertia requirement is: Where: H max is the maximum inertia requirement of the system, G is the set of thermal power units, n is the number of equivalent thermal power units of energy storage and new energy stations at maximum load, H g 、S g are the inertia constant and capacity of the thermal power unit g, H k 、S k are the inertia constant and capacity of the most used thermal power unit k in the system, It is the operating status of thermal power unit g at the moment of maximum load. When it is 1, it indicates operation, and when it is 0, it indicates non-operation.

4. The day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit according to claim 1 is characterized in that: The risk-driven indicators include: Where H t CVaR,down is the penalty term for insufficient supply of the system's maximum inertia at time t, H max t,s is the maximum inertia supply of the system at time t under scenario s, H min is the lower limit of system inertia requirement, and is the auxiliary decision variable for calculating CVaR value, δ1 is the system inertia supply margin, c down H is the maximum inertia supply under-penalty cost; t CVaR,up is the penalty term for excess supply of the system minimum inertia at time t, H min t,s is the minimum inertia supply of the system at time t under scenario s, H max is the upper limit of system inertia demand, δ2 is the system inertia supply margin, c up is the minimum inertia oversupply penalty cost, ρ s is the probability of scene s, S is the set of scenes, and α is the confidence level.

5. The day-ahead optimization scheduling method considering the risk of system inertia supply exceeding the limit according to claim 1 is characterized in that: The two-stage stochastic optimization model includes: Objective function: min(C DA +C ERT +βC CVaR ) Where: t, g, w, v, d, k, s are the identifiers of time period, thermal power unit, wind farm, photovoltaic farm, node load, energy storage, and real-time scene respectively; T, G, W s 、V s , D, K, and S are respectively the collection of time period, whole system thermal power units, wind farms, photovoltaic farms, node loads, energy storage, and real-time scenarios; C DA is the day-ahead cost; C ERT is the real-time cost; C CVaR Provides a risk penalty item for system inertia exceeding the limit; v g,t 、w g,t are binary variables for the start and stop of unit g during period t. When they are equal to 1, they indicate that unit g is started or stopped during period t. C(v g,t ,w g,t ) is the unit combination cost; P g,t is the active power output of thermal power unit g in period t during the day-ahead phase; C(P g,t ) is the power generation cost of the unit in the day-ahead stage; C g U 、C g D are the cost coefficients of increasing and decreasing the reserve capacity of unit g in the day-ahead phase; R g,t U 、R g,t D are the upward and downward reserve capacities of unit g in period t during the day-ahead phase; P g,t,s is the active power output of thermal power unit g during period t under real-time scenario s; C(P g,t,s ) is the power generation cost of the unit in the real-time scenario; C w cur 、C v cur 、C k cur are the penalty coefficients for wind curtailment, solar curtailment, and energy storage real-time readjustment deviation; ΔP w,t,s , ΔP v,t,s are the wind power curtailment and solar power curtailment of wind farm w and photovoltaic farm v in period t under scenario s, respectively; P k,t cha 、P k,t dis are respectively the charging and discharging power of energy storage k in period t during the day-ahead phase; P k,t,s cha 、P k,t,s dis are respectively the charging and discharging power of energy storage k in time period t under real-time scenario s; H t CVaR,down 、H t CVaR,up They are the risk penalty items of insufficient maximum inertia supply and excessive minimum inertia supply of the system in period t; Constraints in the day-ahead phase: Constraints on safe operation of thermal power units Q g,t+1 -P g,t ≤SU g u g,t +(1-u g,t )·(P gmax +P gmin ) / 2 Q g,t -P g,t+1 ≤SD g u g,t+1 +(1-u g,t+1 )·(P gmax +P gmin ) / 2 in g,t -in g,t-1 ≤v g,t ,in g,t-1 -in g,t ≤w g,t Where: P g,max 、P g,min The upper and lower limits of the active power output of thermal power unit g; are the upper and lower limits of the spare capacity of unit g; SU g , SD g are the maximum upward and downward climbing rates of thermal power unit g respectively; are the minimum continuous start and stop time of thermal power unit g; m is the continuous on / off time of thermal power unit g; u g,t is the operating state variable of thermal power unit g at time t, which is 1 when it indicates operation and 0 when it indicates non-operation; Node power balance and branch power flow constraints Where: G ij 、B ij are the real and imaginary parts of the node admittance matrix respectively; V i,t 、V j,t is the voltage amplitude of nodes i and j at time t in the day-ahead phase; θ i,t ,θ j,t is the voltage phase angle of nodes i and j at time t in the day-ahead phase; θ ij,t is the phase angle difference between nodes i and j at time t in the day-ahead phase; g ij 、b ij are the branch active power transmission upper limit, conductance and susceptance of branches i-j respectively; Energy storage operation constraints Where: E k,t 、E kN are the capacity of energy storage k at time t and the rated capacity of energy storage k respectively; are the maximum charge and discharge power of energy storage k respectively; are the charge and discharge indicators of energy storage k at time t, respectively. When it is 1, it means that energy storage k is in the charge and discharge state at time t; is the energy storage SOC of energy storage k at time t; are the upper and lower limits of SOC respectively; Constraints in the real-time phase: Safe operation constraints of thermal power units under multiple scenarios Q g,(t+1),s -P g,t,s ≤SU g u g,t +(1-u g,t )·(P gmax +P gmin ) / 2 Q g,t,s -P g,(t+1),s ≤SD g u g,(t+1) +(1-u g,(t+1) )·(P gmax +P gmin ) / 2 Where: P g,t,s is the active power output of thermal power unit g at time t under scenario s; New energy power constraints in multiple scenarios Where: P w,t,s 、P v,t,s are the dispatching power of wind farm w and photovoltaic farm v at time t under scenario s, They are the predicted power of wind farm w and photovoltaic farm v at time t under scenario s.

Images