Assessment Method for the Absorption Capacity of Intermittent Renewable Energy in Power Systems Considering Frequency Security

Abstract

An evaluation method for the consumption capacity of intermittent renewable energy in a power system considering frequency security, including obtaining the structural parameters, load data, synchronous generator set parameters, and intermittent renewable energy power plant parameters of the power system; constructing a linear frequency constraint of the system according to the first-order constant coefficient differential equation of the system frequency deviation dynamics; defining a robust feasible region for the output of intermittent renewable energy and establishing a system operation risk model, and then establishing an evaluation model for the consumption capacity of intermittent renewable energy in the power system considering frequency constraints; transforming the evaluation model into a solvable compact mathematical model, and using the Column and Constraint generation (C&CG) algorithm to solve it through a solver to obtain the evaluation result. Since the present invention considers frequency constraints, the frequency security of the system is ensured during the evaluation process, and the evaluation method has higher practicability and more reasonable evaluation results.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimal scheduling, and particularly relates to a method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security. Background Art

[0002] With the continuous increase in the proportion of the installed capacity of intermittent renewable energy represented by wind power and photovoltaic power, the problems of wind and light curtailment in the power grid are prominent. Therefore, it is particularly important to evaluate the robust feasible region of the output of intermittent renewable energy under the existing installed capacity of intermittent renewable energy in the power grid. In addition, in order to address energy and environmental issues, the proportion of the installed capacity of intermittent renewable energy in various countries in the power system is increasing continuously, further leading to a decline in the inertia originally provided by synchronous units. On the one hand, as an important index of frequency security, inertia, many existing scholars have conducted in-depth research on frequency constraint modeling, but mainly from the perspective of power system optimal operation and scheduling, and the frequency-related constraint problems have not been considered in the evaluation model of the consumption capacity of intermittent renewable energy in the power grid. Summary of the Invention

[0003] To solve the above technical problems, the present invention provides a method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security. By using this method, an intermittent renewable energy power plant equipped with a power electronic energy storage system can provide virtual inertia and primary frequency response reserve capacity for the system, effectively improving the inertia support and frequency modulation ability of the system.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security, comprising the following steps:

[0006] Step 1: Obtain the structural parameters, load data, synchronous generator set parameters, and intermittent renewable energy power plant parameters of the power system;

[0007] Step 2: Construct a programmable system frequency constraint according to the first-order constant coefficient differential equation of the system frequency deviation dynamics;

[0008] Step 3: Define the robust feasible region of the output of intermittent renewable energy, establish a system operation risk model, and then establish an evaluation model for the consumption capacity of intermittent renewable energy in the power system considering frequency constraints;

[0009] Step 4: Convert the evaluation model established in Step 3 into a solvable compact mathematical model, and use the C&CG algorithm to solve it through a solver to obtain the evaluation result.

[0010] In the said Step 1,

[0011] The structural parameters of the power system include: reactance parameters, the numbers of each node in the system, and line transmission capacity;

[0012] The load data includes the dispatching cycle load parameters of each node in the system;

[0013] The synchronous generator set parameters include: the numbers of each generator set, the numbers of the access nodes, installed capacity, unit ramp rate, start-stop time, minimum and maximum technical output, the inertia time constant of each unit, and the maximum reserve capacity;

[0014] The intermittent renewable energy power plant parameters include: the numbers of the access nodes of each power plant, predicted output, and installed capacity.

[0015] The said step 2 includes the following steps:

[0016] Step 2.1: The expression of the first-order constant coefficient differential equation of the system frequency deviation dynamics is as follows:

[0017]

[0018] In formula (1), is the aggregated inertia provided for the system time period t, with the unit of MWs / Hz; Δf(k) is the frequency deviation at time period k after the active power disturbance; is the load damping rate; P t L is the total load level of the system at time period t; N g is the total number of synchronous units; is the power adjustment provided by the conventional unit i at time period k; N re is the total number of controllable intermittent renewable energy power plants; is the power adjustment provided by the controllable intermittent renewable energy power plant at time period k; P t dis is the load disturbance at time period t, and the classical value is 5% or 10% of the active power load; i represents the number of the i-th synchronous unit; j represents the number of the j-th intermittent renewable energy; k represents the k-th time period.

[0019] Step 2.2: Assume that the primary frequency responses of the synchronous units and the controllable intermittent renewable energy power plants both increase linearly with time, and their adjustment times are the same; then the adjustment power constraint can be expressed as:

[0020]

[0021] In formula (2): k DB is the frequency dead zone time when droop control is adopted; K d is the response duration; is the primary frequency response reserve capacity provided by the synchronous unit i at time period t; Primary frequency response reserve capacity provided for the controllable intermittent renewable energy power plant at time period t of day j

[0022] Step 2.3: Construct the system frequency constraints, which include the rate of change of frequency constraint, frequency deviation constraint, and quasi-steady state frequency constraint

[0023] ①: Rate of change of frequency constraint

[0024] When k = 0 + At this time, the rate of change of the system frequency is the largest. Therefore, by combining Equation (1) and Equation (2), the rate of change of frequency constraint can be deduced as follows

[0025]

[0026] Where

[0027]

[0028] In Equation (3) and Equation (4), RoCoF max Is the maximum allowable rate of change of the system frequency Is the aggregated inertia provided for the system at time period t Is the aggregated inertia provided for the controllable intermittent renewable energy power plant at time period t of day j Is the inertia time constant (S) of synchronous generator set i; P i gmax Is the installed capacity of conventional generator set i; x i,t Is the operating state of synchronous generator set i at time period t Is the virtual inertia time constant that can be provided by the intermittent renewable energy power plant at time period t of day j Is the installed capacity of the intermittent renewable energy power plant of day j; u j,t Is the reserve state of the controllable intermittent renewable energy power plant at time period t of day j; f N Is the normal operating frequency of the system; T is the total dispatching time period

[0029] ②: Frequency deviation constraint

[0030] The lowest point of frequency occurs within time k DB ≤ k ≤ K d + k DB Integrate the system regulation power constraint into the differential equation and integrate with respect to k in the time period [0, k], we get

[0031]

[0032] In Equation (5): Δf DB Is the frequency dead zone using droop control; R t Is the total reserve capacity of the system at time period t; P t Lis the total system load level at time period t.

[0033] When the system reaches the lowest point of frequency; thus the time k when the lowest point of frequency is reached nadir is expressed as:

[0034]

[0035] Combining Equation (5) and Equation (6) gives the maximum frequency deviation |Δf nadir |:

[0036]

[0037] In Equation (7), Δf max is the allowable maximum frequency deviation.

[0038] For programmability, it is equivalent to:

[0039]

[0040] In Equation (8), α t is the introduced auxiliary constant, and α can be obtained by solving with the solve function t , since there is a multiplication of a 0-1 variable and a continuous variable, the above equation is equivalent to using the big M method as:

[0041]

[0042] In Equation (9), N g is the number of synchronous units; P i max represents the installed capacity of synchronous unit i; x i,t represents the operating state variable of synchronous unit i at time period t; N re represents the number of intermittent renewable energy power plants; represents the inertia time constant of intermittent renewable energy power plant j; represents the installed capacity of intermittent renewable energy power plant j; U j,t represents the auxiliary variable introduced by intermittent renewable energy power plant j at time period t; X i,t represents the auxiliary variable introduced by synchronous unit i at time period t; u j,t represents the binary variable indicating whether intermittent renewable energy power plant j provides reserve capacity and virtual inertia at time period t; M is a very large positive real number.

[0043] ③: Quasi-steady state frequency constraint:

[0044] When time k >> K d +k DB the rate of change of frequency and there is Kd +k DB ≤k, the system adjustment power constraint is substituted into the differential equation to obtain:

[0045]

[0046] In Equation (10): Δf qssf is the quasi-steady state frequency deviation; is the maximum allowable quasi-steady state frequency deviation.

[0047] Step 3 includes the following steps:

[0048] Step 3.1: Define the robust feasible region of the intermittent renewable energy output: When the boundary of the intermittent renewable energy output is determined, no matter how the intermittent renewable energy fluctuates within the feasible region, it will not cause losses to the system operation. If the output of the intermittent renewable energy is greater than the maximum allowable upper limit, curtailment of wind and solar power will occur to ensure the safe operation of the system; if the output of the intermittent renewable energy is less than the minimum allowable lower limit, load shedding will occur to ensure the safe operation of the system. Therefore, the following two-layer model is used for equivalence:

[0049]

[0050] In Equation (11), and are the state variables of the intermittent renewable energy power plant at the minimum and maximum output boundaries at time t in period j, respectively; respectively represent that in the worst case of the intermittent renewable energy power plant output, the curtailment of wind and solar power and the load shedding amount are minimized; is the curtailment of wind and solar power of the intermittent renewable energy power plant at time t in period j; N L is the total number of load nodes; is the load shedding power of load j at time t.

[0051] The constraint conditions of the robust feasible region model are as follows:

[0052] 1) The following formula is used as the uncertainty set U of the intermittent renewable energy output:

[0053]

[0054] In Equation (12), Γ T is the maximum uncertainty of the intermittent renewable energy in time; Γ S is the maximum uncertainty of the intermittent renewable energy in space.

[0055] The actual output of the intermittent renewable energy power plant

[0056]

[0057] In formula (13), is the actual power fed into the grid at time t in period j of the intermittent renewable energy power plant; is the upper bound of the output of the intermittent renewable energy power plant at time t in period j; is the lower bound of the output of the intermittent renewable energy power plant at time t in period j; is the predicted output of the intermittent renewable energy power plant at time t in period j.

[0058] 2) The following formula is used as the curtailment of wind and light and load shedding constraint:

[0059]

[0060] In formula (14), is the load prediction value of load d at time t.

[0061] 3) The following formula is used as the output constraint of the synchronous generator unit:

[0062]

[0063] In formula (15), P i,t is the output power of the synchronous generator unit at time t in period i; P i gmin is the minimum technical output of the synchronous generator unit at time t in period i.

[0064] 4) The following formula is used as the ramp rate constraint of the synchronous generator unit:

[0065]

[0066] In formula (16), is the maximum downhill power of the synchronous generator unit at time t in period i; is the maximum ramp rate power of the synchronous generator unit at time t in period i; P i,t+1 is the output of the synchronous generator unit i at time t + 1; represents the reserve capacity of the synchronous generator unit i at time t + 1; x i,t+1 is the operating status of the synchronous generator unit i at time t + 1.

[0067] 5) Power balance constraint:

[0068]

[0069] In formula (17), is the predicted value of load d at time t; is the load shedding amount of load d at time t.

[0070] 6) The following formula is used as the transmission power constraint of the transmission line:

[0071]

[0072] In Equation (18), B g , B re , B d are the network incidence matrices of the synchronous generator set, the intermittent renewable energy power plant, and the load, respectively; a l is the network offset factor vector of line l; P t G , P t re , ΔP t re , P t L , ΔP t L are the vectors of the synchronous generator set, the intermittent renewable energy power plant, curtailment of wind and light, the load prediction value, and load shedding, respectively; F l max is the maximum transmission power of line l. Step 3.2: Establish a system operation risk model:

[0073] The system operation risk is defined as the system loss caused by curtailment of wind and light and load shedding when the intermittent renewable energy generation exceeds or is lower than the robust feasible region of the intermittent renewable energy output allowed by the system; in the literature [1]: Hong.Tan, Zhouyang.Ren, Wei.Yan, Qiujie.Wang and Mohamed.A.Mohamed, A Wind Power Accommodation Capability Assessment Method for Multi-Energy Microgrids[J], IEEE Trans.Sustain.Energy, 2021, 12(4): 2482 - 2492., the system operation risk model has an integral form that is difficult to solve. Therefore, the present invention adopts the following discretization method for equivalence:

[0074] At any time period, the robust feasible region of the intermittent renewable energy output is bounded by the predicted value, is the lower bound, is the upper bound; furthermore, the lower bound and upper bound intervals are each equally divided into N l and N u risk units, and each risk unit contains two parameters: the upper bound risk unit contains the operation risk value RU and the corresponding intermittent renewable energy output WU; the lower bound risk unit contains the operation risk value RL and the corresponding intermittent renewable energy output WL.

[0075] According to the day-ahead predicted output of intermittent renewable energy and the above definition, the operating risk for the entire scheduling period can be obtained:

[0076]

[0077] In Equation (19), sor represents the minimum system operating risk for the entire scheduling period; Ω re is the cost of wind and light curtailment; Ω L is the cost of load shedding; RU j,t,b is the operating risk value of the b-th unit at the upper bound of the intermittent renewable energy power plant in period t of hour j; RL j,t,c is the operating risk value of the c-th unit at the lower bound of the intermittent renewable energy power plant in period t of hour j; is the state variable of the b-th unit at the upper bound of the intermittent renewable energy power plant in period t of hour j; is the state variable of the c-th unit at the lower bound of the intermittent renewable energy power plant in period t of hour j; N 1 represents the number of risk units at the lower bound of the intermittent renewable energy power plant; N u represents the number of risk units at the lower bound of the intermittent renewable energy power plant; b represents the b-th upper bound risk unit; c represents the c-th lower bound risk unit;

[0078] The boundary value of the intermittent renewable energy output can be expressed as:

[0079]

[0080] In Equation (20), is the upper bound of the intermittent renewable energy power plant in period t of hour j; is the lower bound of the intermittent renewable energy power plant in period t of hour j; WU j,t,b is the output power value of the b-th unit at the upper bound of the intermittent renewable energy power plant in period t of hour j; WL j,t,c is the output power value of the c-th unit at the lower bound of the intermittent renewable energy power plant in period t of hour j.

[0081] Step 3.3: Combining the frequency-related constraints in Step 2 with Steps 3.1 and 3.2 in Step 3, an evaluation model for the consumption capacity of intermittent renewable energy in a power system considering frequency constraints can be obtained:

[0082] The objective function is to minimize the operating risk and the amount of wind and light curtailment and load shedding during the total scheduling period under the worst scenario. Mathematically speaking, the proposed evaluation model is a two-stage robust optimization model. As follows:

[0083]

[0084] Among them, the following calculation formula is used as the unit commitment constraint:

[0085]

[0086] In Equation (22), y i,t is the start-up state variable of the synchronous generator set at time t in period i; z i,t is the shutdown state variable of the synchronous generator set at time t in period i; T i on is the time required for the start-up of the synchronous generator set i; T i off is the time required for the shutdown of the synchronous generator set i. x i,t-1 represents the operating state variable of the synchronous generator set i at time t - 1; is the start-up state variable of the synchronous generator set i at time t; is for the synchronous generator set i in period the shutdown state variable; represents the maximum value.

[0087] The system operation constraints include: the intermittent renewable energy output uncertainty set constraint Equation (12), the intermittent renewable energy output constraint Equation (13), the wind and light curtailment and load shedding constraint Equation (14), the synchronous generator set output constraint Equation (15), the synchronous generator set ramping constraint Equation (16), the power balance constraint Equation (17), and the transmission line power transfer constraint Equation (18).

[0088] In Step 4, the model in Step 3.3 of Step 3 is transformed into a solvable compact mathematical model, and the compact mathematical model is as follows:

[0089]

[0090] In Equation (23): Ω re T represents the transpose of Ω re ; Ω L T represents the transpose of Ω d ;

[0091] Ω re and Ω d are respectively the cost coefficient vectors of wind and light curtailment and load shedding; o + and o - are respectively the binary decision variable vectors of the boundary positions of the intermittent renewable energy output; RU and RL are respectively the operation risk value vectors of the upper and lower bounds of the intermittent renewable energy output; Z is the binary decision variable vector of the operating state of the synchronous generator set; R is the reserve capacity required for the system to respond to primary frequency regulation; P re\(P\) is the boundary variable of the intermittent renewable energy output to be optimized; \(v\) is the binary decision variable in the uncertainty set of the intermittent renewable energy output; \(y\) is the output of the synchronous generator set, the output of the intermittent renewable energy farm, the wind and light abandonment, and the load shedding variable;

[0092] \(\alpha, \beta, \delta,\) \(\varphi, A, B, D, E\) and \(S\) are the constant coefficient matrices of the variables under the corresponding constraints; \(C, Q, H, G\) and \(u\) are the constant coefficient vectors of the variables under the corresponding constraints; the symbol denotes that two matrices are in the form of Hadamard product.

[0093] The above compact model is a two-stage robust optimization model and cannot be solved directly. Therefore, the C&CG algorithm is used to divide the above original problem into a master problem and a sub-problem. The specific iterative solution process includes the following steps:

[0094] Step1: Solve the master problem according to the prediction scenario of the intermittent renewable energy output. It can be solved by using the commercial solver GUROBI or CPLEX, and the result is \(J_A(1)\). The operating state \(Z\) of the synchronous generator set obtained by solving the master problem * , the reserve capacity \(R\) required for primary frequency regulation * and the boundary of the intermittent renewable energy output \((P\) re ) * are substituted into the sub-problem to solve for \(v\) * and \(Y_A(1)\). The iteration number \(L = 1\). Let the iteration convergence value be \(\zeta\), and execute Step4;

[0095] Among them, the master problem can be expressed as:

[0096]

[0097] In Equation (24): \(y\) l is the \(l\)-th \(y\) variable; is the \(l\)-th \(v\) * constant coefficient vector.

[0098] The sub-problem can be expressed as:

[0099]

[0100] In Equation (25): \(v\) is the binary decision variable in the uncertainty set of the intermittent renewable energy output; \(y\) is the output of the synchronous generator set, the output of the intermittent renewable energy farm, the wind and light abandonment, and the load shedding variable;

[0101] Since the sub-problem is a max min problem and cannot be solved directly, the KKT conditions or the duality theory can be used to solve it. In the present invention, the duality theory is adopted to dualize the double-layer max min problem into a single-layer max problem;

[0102]

[0103] In Equation (26): B T is the transpose of the constant coefficient matrix B; λ is an auxiliary variable introduced using the duality principle;

[0104] There is a multiplication of non - linear terms in the objective function The present invention uses the big M method for linearization, then the dual sub - problem can be restated as:

[0105]

[0106] In Equation (27), Z * is the operating state of the synchronous generator set obtained by solving the master problem; ψ T represents the transpose of ψ;

[0107] ψ is an introduced auxiliary variable; q is an introduced constant coefficient vector; and the following formula is satisfied:

[0108]

[0109] In Equation (28), λ a represents the a - th variable of λ; v b represents the b - th variable of v; q a,b represents the element in the a - th row and b - th column of the constant coefficient matrix D.

[0110] Step2: After solving the sub - problem to obtain v * Return to the master problem, and the result is JA(L + 1);

[0111] Step3: Substitute Z * , R * and (P re ) * obtained by solving the master problem into the sub - problem to obtain v * and YA(L + 1);

[0112] Step4: If YA(L + 1)≥ζ, then return the v * obtained by solving the sub - problem to the master problem for continued iteration, update L = L + 1, and execute Step2; otherwise execute Step5;

[0113] Step5: End the iteration, and output sor = JA(L + 1) and the evaluation result.

[0114] An evaluation method for the consumption capacity of intermittent renewable energy in a power system considering frequency security has the following beneficial effects: 1) The evaluation method proposed in the present invention is for evaluating intermittent renewable energy, mainly wind farms and photovoltaic power plants. According to the evaluation results, no operation losses such as wind curtailment, light curtailment, and load shedding will occur regardless of the output of intermittent renewable energy within the robust feasible region. System operators can perform reasonable optimal dispatching based on the evaluation results.

[0115] 2) Since the evaluation method proposed in the present invention considers frequency constraints, compared with other evaluation methods, the present invention can obtain results that better meet the system operation requirements considering frequency security, and obtain the frequency-related conditions in each period and the required reserve capacity of the system.

[0116] 3) The present invention believes that controllable intermittent renewable energy power plants can provide virtual inertia and reserve capacity, which can reduce the inertia response and reserve capacity required by traditional synchronous units in the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] Figure 1 It is a graph of the predicted values of the output of intermittent renewable energy and load.

[0118] Figure 2 It is a graph of the optimization result of the robust feasible region of intermittent renewable energy power plant 1.

[0119] Figure 3 It is a graph of the optimization result of the robust feasible region of intermittent renewable energy power plant 2.

[0120] Figure 4 It is a graph of the combined operating conditions of synchronous units.

[0121] Figure 5 It is a graph of the system reserve operating conditions;

[0122] Figure 6 It is a graph of the system frequency change rate and the lowest point frequency operating conditions in each period;

[0123] Figure 7 It is a flow chart of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0124] An evaluation method for the consumption capacity of intermittent renewable energy in a power system considering frequency security includes obtaining the structural parameters, load data, synchronous generator set parameters, and intermittent renewable energy power plant parameters of the power system;

[0125] The structural parameters of the power system include: reactance parameters, the numbers of each node in the system, and the line transmission capacity; as shown in Table 1; the load data includes the dispatching period load parameters of each node in the system; as shown in Table 2;

[0126] The parameters of the synchronous generator sets include: the numbers of each generator set, the numbers of the access nodes, the installed capacity, the ramp power of the generator sets, the start-stop time, the minimum and maximum technical output powers, the inertia time constants of each generator set, and the maximum reserve capacity; as shown in Table 3;

[0127] The parameters of the intermittent renewable energy power plants include: the numbers of the access nodes of each power plant, the predicted output power and the installed capacity. As shown in Table 4.

[0128] Table 1 Power system structure parameters

[0129]

[0130] Table 2 Load parameters (MW)

[0131]

[0132]

[0133] Table 3 Synchronous generator set parameters

[0134]

[0135] Table 4 Intermittent renewable energy predicted output power data

[0136] Bus 1h 2h 3h 4h 5h 6h 7h 8h 10h 11h 12h 1 136.6 125.7 117.2 119.1 109.6 109.0 128.0 136.5 161.4 180.0 189.9 3 128.6 67.6 94.2 64.6 121.2 115.4 121.3 138.4 184.0 163.5 191.0 Bus 1h 2h 3h 4h 5h 6h 7h 8h 10h 11h 12h 1 212.8 206.9 191.7 171.5 187.3 181.1 140.4 122.7 109.7 109.6 111.4 3 201.4 178.9 150.9 151.0 149.3 126.8 126.1 131.9 130.0 126.1 126.7

[0137] According to the first-order constant coefficient differential equation of the system frequency deviation dynamics, the linear frequency constraint of the system is constructed; the robust feasible region of the intermittent renewable energy output is defined and the system operation risk model is established, and then the evaluation model of the intermittent renewable energy consumption capacity of the power system considering the frequency constraint is established; the evaluation model is transformed into a solvable compact mathematical model, and the Column and Constraint generation (C&CG) algorithm is used to solve it through a solver, and the evaluation result is obtained. Since the present invention considers the frequency constraint, the frequency safety of the system is ensured during the evaluation process, and the evaluation method has higher practicability and the evaluation result is more reasonable.

[0138] Embodiment:

[0139] An improved IEEE 9-node power system is used for simulation analysis. There are 5 conventional generator sets (G1, G1, G3, G4 and G5) in this system, and the total power generation is 1000 MW. The specific parameters are shown in Table 3. There are 2 intermittent renewable energy power plants (RE1 and RE2), and the total installed capacity is 500 MW. The proportion of the installed capacity of the intermittent renewable energy power plants is 33.33%. And it is assumed that the intermittent renewable energy power plants can all provide frequency support, and there are 3 node electrical loads. The curtailment cost coefficient of wind and light π w = 6$; the load shedding cost coefficient πd = 6$; The output and load prediction data of the intermittent renewable energy power plant are as Figure 1 shown. It is assumed that the maximum reserve capacity that the controllable intermittent renewable energy power plant can provide is 10% of the intermittent renewable energy output.

[0140] The system frequency - related parameter settings are as follows: The standard frequency f N = 50Hz, the maximum rate of change of frequency RoCoF max = 0.2Hz / s, the maximum frequency deviation is 0.8Hz (i.e., the minimum frequency is 49.2Hz), the quasi - steady - state frequency deviation is 0.2Hz, the frequency dead - band is 0.015Hz, the load damping D = 1% / Hz. When considering emergencies, it is assumed to be 5% of the predicted sudden increase in active load, and the response time T d = 10s.

[0141] Combined with Figure 1 the given prediction data, the optimization results of the robust feasible region of the intermittent renewable energy power plant output are as Figure 2 and Figure 3 shown, and the total system operation risk cost is 14676$. It can be seen from Figure 1 that from time period 8 to time period 18, it is in the "low - load intermittent renewable energy high - output" scenario. It can be seen from Figure 2 that compared with the lower bound of the robust feasible region of intermittent renewable energy in this time period, the upper bound of the output from time period 8 to time period 18 is closer to the predicted value of intermittent renewable energy output, which is likely to lead to a higher curtailment of wind and light. It can be seen from Figure 3 that the upper bound of the robust feasible region from time period 8 to time period 18 is closer to the predicted value of intermittent renewable energy output, which is likely to lead to a higher curtailment of wind and light. In addition, because this time period is in the "low - load intermittent renewable energy high - output" scenario, the synchronous generator unit G5 makes corresponding shutdown conditions, as Figure 4 shown. From time period 20 to time period 24, it is in the "high - load intermittent renewable energy low - output" scenario. Compared with the upper bound of the robust feasible region of intermittent renewable energy output in this time period, the lower bound of the robust feasible region in this time period is closer to the predicted value of intermittent renewable energy output, resulting in a higher load shedding.

[0142] Given that 5% of the predicted sudden increase in active load is an emergency, Figure 5 and Figure 6 are the frequency - related and system reserve capacity conditions after optimization respectively. Because primary frequency regulation is droop control, there is a situation where the active reserve in some time periods is less than the active disturbance. From time period 10 to time period 16 is the period when the intermittent renewable energy output is large. Therefore, the intermittent renewable energy power plant equipped with a power electronic controller can provide reserve capacity.

[0143] As Figure 5 shown, combined withFigure 4 For the unit combination situation, during time periods 9 to 13, unit G5 is in the shutdown state, resulting in a relatively low system inertia during this period, and the frequency change rate and frequency deviation are relatively prominent. However, it still meets the system frequency safety requirements. From time period 17 to time period 24, the load is at a relatively high level. Therefore, when a 5% load disturbance suddenly occurs, the frequency change rate and the maximum frequency deviation are relatively obvious. Therefore, the system inertia and the primary frequency regulation reserve capacity are important factors determining the system frequency change rate and the maximum frequency deviation. In addition, the present invention takes into account that the controllable intermittent renewable energy power plant can provide virtual inertia and frequency regulation reserve capacity, which can reduce the system's dependence on the inertia and frequency regulation capabilities of traditional synchronous units and improve the system's inertia support and frequency regulation capabilities.

Claims

1. Method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security, characterized in that it includes the following steps: Step 1: Obtain the structural parameters, load data, synchronous generator set parameters, and intermittent renewable energy power plant parameters of the power system; Step 2: Construct a programmable system frequency constraint according to the first-order constant coefficient differential equation of the system frequency deviation dynamics; The expression of the first-order constant coefficient differential equation of the system frequency deviation dynamics is as follows: In Equation (1), is the aggregated inertia provided for system time period t, with the unit of MWs / Hz; Δf(k) is the frequency deviation at time period k after the active power disturbance; is the load damping ratio; P t L is the total system load level at time period t; N g is the total number of synchronous generators; is the power adjustment provided by conventional generator i at time period k; N re is the total number of controllable intermittent renewable energy power plants; is the power adjustment provided by the controllable intermittent renewable energy power plant at time period k; P t dis is the load disturbance at time period t; i represents the number of the i-th synchronous generator; j represents the number of the j-th intermittent renewable energy; k represents the k-th time period; Step 3: Define the robust feasible region of the intermittent renewable energy output, establish a system operation risk model, and then establish an evaluation model for the consumption capacity of intermittent renewable energy in a power system considering frequency constraints; Step 3.1: Define the robust feasible region of the intermittent renewable energy output: When the output boundary of the intermittent renewable energy is determined, no matter how the intermittent renewable energy fluctuates within the feasible region, it will not cause losses to the system operation; If the output of the intermittent renewable energy is greater than the maximum allowable upper limit, phenomena of wind curtailment and light curtailment will occur to ensure the safe operation of the system; if the output of the intermittent renewable energy is less than the minimum allowable lower limit, load shedding phenomena will occur to ensure the safe operation of the system; Therefore, the following double-layer model is used for equivalence: In formula (11), and are the state variables when the intermittent renewable energy power plant takes the minimum output boundary and the maximum output boundary at time t in period j, respectively; respectively represent that when the output of the intermittent renewable energy power plant is in the worst case, the curtailment of wind and light and the minimum load shedding amount; is the curtailment power of wind and light of the intermittent renewable energy power plant at time t in period j; N L is the total number of load nodes; is the load shedding power of load j at time t in period j; P i,t is the output power of the synchronous generator set at time t in period i; Step 3.2: Establish a system operation risk model: The system operation risk is defined as the system losses caused by wind curtailment, light curtailment, and load shedding when the intermittent renewable energy generation exceeds or is lower than the robust feasible region of the intermittent renewable energy output allowed by the system; The following discretization method is used for equivalence: During any period, the robust feasible region of intermittent renewable energy output is bounded by the predicted value, which is the lower bound, and which is the upper bound; furthermore, the lower bound and upper bound intervals are each equally divided into N l and N u risk units, and each risk unit contains two parameters: the upper bound risk unit contains the operating risk value RU and the corresponding intermittent renewable energy output WU; the lower bound risk unit contains the operating risk value RL and the corresponding intermittent renewable energy output WL; According to the day-ahead predicted output of the intermittent renewable energy and the above definition, the operation risk of the entire scheduling period is obtained: In formula (19), sor represents the minimum system operation risk during the entire scheduling period; Ω re is the curtailment cost of wind and solar power; Ω L is the load shedding cost; RU j,t,b is the operation risk value of the b-th unit at the upper bound of the intermittent renewable energy power plant in period t of hour j; RL j,t,c is the operation risk value of the c-th unit at the lower bound of the intermittent renewable energy power plant in period t of hour j; is the state variable of the b-th unit at the upper bound of the intermittent renewable energy power plant in period t of hour j; is the state variable of the c-th unit at the lower bound of the intermittent renewable energy power plant in period t of hour j; N 1 represents the number of units with lower bound risk of the intermittent renewable energy power plant; N u represents the number of lower-bound risk units of the intermittent renewable energy power plant; b represents the b-th upper-bound risk unit; c represents the c-th lower-bound risk unit; Step 3.3: Combining the frequency-related constraints in Step 2 with Steps 3.1 and 3.2 in Step 3, an evaluation model for the consumption capacity of intermittent renewable energy in a power system considering frequency constraints can be obtained: as follows: WU j,t,b is the output power corresponding to the b-th risk unit in the upper bound of the intermittent renewable energy power plant j at time period t; Step 4: Convert the evaluation model established in Step 3 into a solvable compact mathematical model, and use the C&CG algorithm to solve it through a solver, and obtain the evaluation result.

2. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 1, characterized in that: In the said Step 1, The structural parameters of the power system include: reactance parameters, the numbers of each node of the system, and the line transmission capacity; The load data includes the dispatching period load parameters of each node of the system; The synchronous generator set parameters include: the numbers of each unit, the access node numbers, the installed capacity, the unit ramp power, the start-stop time, the minimum and maximum technical outputs, the inertia time constants of each unit, and the maximum reserve capacity; The intermittent renewable energy power plant parameters include: the access node numbers of each power plant, the predicted output, and the installed capacity.

3. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 1, characterized in that: In the said Step 2, assume that the primary frequency responses of the synchronous units and the controllable intermittent renewable energy power plants both increase linearly with time, and their adjustment times are the same; then the adjustment power constraint can be expressed as: In formula (2): k DB is the frequency dead zone time when droop control is adopted; K d is the response duration; is the primary frequency response reserve capacity provided by the synchronous unit at time t in period i; is the primary frequency response reserve capacity provided by the controllable intermittent renewable energy power plant at time t in period j; Construct a system frequency constraint, and the system frequency constraint includes a frequency change rate constraint, a frequency deviation constraint, and a quasi-steady state frequency constraint; ①: Frequency change rate constraint: When k = 0 + The system frequency change rate is the largest. By simultaneously solving equations (1) and (2), the frequency change rate constraint is derived as follows: Where: In Equation (3) and Equation (4), RoCoF max is the maximum allowable frequency change rate of the system; is the aggregated inertia provided by the system during time period t; is the aggregated inertia provided by the controllable intermittent renewable energy power plant during time period t; is the inertia time constant of synchronous generator i; P i gmax is the installed capacity of conventional generator i; x i,t is the operating status of synchronous generator i during time period t; is the virtual inertia time constant that can be provided by the intermittent renewable energy power plant j during time period t; is the installed capacity of the intermittent renewable energy power plant j; u j,t is the standby status of the controllable intermittent renewable energy power plant j during time period t; f N is the normal operating frequency of the system; T is the total dispatching time period; ②: Frequency deviation constraint: The lowest frequency point occurs at time k DB ≤ k ≤ K d + k DB Within, substitute the system adjustment power constraint into the differential equation and integrate with respect to k over the time period [0, k], we have: In formula (5): Δf DB is the frequency dead zone using droop control; R t is the total reserve capacity of the system at time period t; P t L is the total system load level at time period t; When the system reaches the lowest frequency point; thus, the time k to reach the lowest frequency point nadir is expressed as: Combining equation (5) and equation (6) gives the maximum frequency deviation |Δf nadir |: In Equation (7), Δf max is the maximum allowable frequency deviation; For programmability, it is equivalent to: In formula (8), α t is the introduced auxiliary constant, and α is obtained by solving with the solve function t , because there is a multiplication of a 0-1 variable and a continuous variable, the above formula is equivalently transformed into the following formula by the big M method: In Equation (9), N g is the number of synchronous generator sets; P i max represents the installed capacity of synchronous generator set i; x i,t represents the operating state variable of synchronous generator set i at time period t; N re is the number of intermittent renewable energy power plants; represents the inertia time constant of intermittent renewable energy power plant j; represents the installed capacity of intermittent renewable energy power plant j; U j,t represents the auxiliary variable introduced by intermittent renewable energy power plant j at time period t; X i,t represents the auxiliary variable introduced by synchronous generator set i at time period t; u j,t is a binary variable indicating whether intermittent renewable energy power plant j provides reserve capacity and virtual inertia at time period t; M is a very large positive real number; ③: Quasi-steady state frequency constraint: When time k >> K d +k DB At this time, the frequency change rate and there is K d +k DB ≤ k, then substitute the system adjustment power constraint into the differential equation to obtain: In formula (10): Δf qssf is the quasi-steady state frequency deviation; is the maximum allowable quasi-steady state frequency deviation.

4. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 1, characterized in that: In step 3.2, the value range of the output of intermittent renewable energy is expressed as: In formula (20), is the upper bound of the intermittent renewable energy power plant in period t of hour j; is the lower bound of the intermittent renewable energy power plant in period t of hour j; WU j,t,b is the output power corresponding to the b-th risk unit in the upper bound of the intermittent renewable energy power plant j in period t; WL j,t,c is the output power corresponding to the c-th risk unit in the lower bound of the intermittent renewable energy power plant j in period t; In step 3.3, the following formula is used as the unit commitment constraint: In formula (22), y i,t is the start state variable of the synchronous unit at time t of period i; z i,t is the shutdown state variable of the synchronous unit at time t of period i; T i on is the time required for the start-up of the synchronous unit i; T i off is the time required for the shutdown of synchronous unit i; x i,t-1 represents the operating state variable of synchronous unit i at time period t - 1; is the start-up state variable of synchronous unit i at time period ; is the shutdown state variable of synchronous unit i at time period .

5. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 4, characterized in that: In step 3.1, the constraint conditions of the robust feasible region model are as follows: 1) The following formula is used as the uncertainty set U of the output of intermittent renewable energy: In Equation (12), Γ T is the maximum uncertainty of intermittent renewable energy in terms of time; Γ S is the maximum uncertainty of intermittent renewable energy in terms of space. The actual output of the intermittent renewable energy power plant In formula (13), is the actual grid-connected power of the intermittent renewable energy power plant at time t in period j; is the upper bound of the output of the intermittent renewable energy power plant at time t in period j; is the lower bound of the output of the intermittent renewable energy power plant at time t in period j; is the predicted output of the intermittent renewable energy power plant at time t in period j; 2) The following formula is used as the wind curtailment, light curtailment and load shedding constraint: In formula (14), is the load prediction value for load d at time period t; 3) The following formula is used as the output constraint of synchronous generators: In Equation (15), P i,t is the output power of the synchronous unit at time t in period i; P i gmin is the minimum technical output of the synchronous unit at time t in period i; 4) The following formula is used as the ramp rate constraint of synchronous generators: In formula (16), is the maximum downhill power of the synchronous unit at time t of period i; is the maximum uphill power of the synchronous unit at time t of period i; P i,t+1 is the output of the synchronous unit i at time t + 1; represents the reserve capacity of the synchronous unit i at time t + 1; x i,t+1 is the operating status of the synchronous unit i at time t + 1; 5) Power balance constraint: In formula (17), is the predicted value of load d at time period t; is the load shedding amount of load d at time period t; 6) The following formula is used as the transmission power constraint of transmission lines: In Equation (18), B g , B re , B d are the network incidence matrices of the synchronous generator set, the intermittent renewable energy power plant, and the load, respectively; a l is the network offset factor vector of line l; P t G is the vector form of the output P i,t of the synchronous generator set; P t re is the vector form of the output of the intermittent renewable energy power plant; ΔP t re is the vector form of the curtailed wind and solar power ; P t L is the vector form of the load forecast value ; ΔP t L is the vector form of the load shedding amount ; F l max is the maximum transmission power of line l.

6. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 4, characterized in that: In step 4, the model in step 3.3 of step 3 is transformed into a solvable compact mathematical model, and the compact mathematical model is as follows: In formula (23): Ω re T represents the transpose of Ω re ; Ω L T represents the transpose of Ω d ; Ω re and Ω d are the curtailment of wind and solar power and load shedding cost coefficient vectors respectively; o + and o - are the binary decision variable vectors of the boundary positions of the intermittent renewable energy output respectively; RU and RL are the operation risk value vectors of the upper and lower bounds of the intermittent renewable energy output respectively; Z is the binary decision variable vector of the operation state of the synchronous generator sets; R is the reserve capacity required for the system to respond to primary frequency regulation; P re is the boundary variable of the intermittent renewable energy output to be optimized; v is the binary decision variable in the uncertainty set of the intermittent renewable energy output; y is the output of the synchronous units, the output of the intermittent renewable energy farm, the curtailment of wind and solar power and the load shedding variable; α, β, δ, φ, A, B, D, E, and S are constant coefficient matrices of variables under corresponding constraints; C, Q, H, G, and u are constant coefficient vectors of variables under corresponding constraints; the symbol denotes that two matrices are in the form of dot product (Hadamard product).

7. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 6, characterized in that: The C&CG algorithm is used to divide the original problem into a master problem and a sub-problem. The specific iterative solution process includes the following steps: Step1: Solve the master problem according to the intermittent renewable energy output prediction scenario. It can be solved using commercial solvers GUROBI or CPLEX, and the result is JA(1). Substitute the operating status Z of the synchronous generator set obtained from solving the master problem * , the reserve capacity R required for primary frequency modulation * and the intermittent renewable energy output boundary (P re ) * into the sub-problem to obtain v * and YA(1). The number of iterations L = 1. Set the iteration convergence value to ζ and execute Step4; Step2: Obtain v in the sub - problem solution * Return to the main problem, and the result is JA(L + 1); Step3: Substitute the Z obtained by solving the main problem * , R * and (P re ) * into the v obtained by solving the sub - problem * and YA(L + 1); Step4: If YA(L+1) ≥ ζ, then solve the sub-problem to obtain v * Return it to the main problem for continued iteration, update L = L + 1, and execute Step2; otherwise, execute Step5; Step5: The iteration ends, and sor = JA(L + 1) and the evaluation results are output.

8. The method for evaluating the consumption capacity of intermittent renewable energy in a power system considering frequency security according to claim 7, characterized in that: Among them, the master problem is expressed as: In formula (24): y l is the l-th y variable; is the l-th v * constant coefficient vector; The sub-problem is expressed as: In formula (25): v is the binary decision variable in the uncertainty set of the output of intermittent renewable energy; y is the output of synchronous generators, the output of intermittent renewable energy power plants, the variables of wind curtailment, light curtailment and load shedding; Using the duality theory, the double-layer max min problem is dualized into a single-layer max problem; In Equation (26): B T is the transpose of the constant coefficient matrix B; λ is an auxiliary variable introduced using the duality principle; There are multiplications of non - linear terms in the objective function Using the big - M method for linearization, the dual sub - problem can be restated as: In formula (27), Z * is the operating state of the synchronous generator set obtained by solving the main problem; ψ T represents the transpose of ψ. ψ is the introduced auxiliary variable; q is the introduced constant coefficient vector; and the following formula is satisfied: In Equation (28), λ a represents the ath variable of λ; v b represents the bth variable of v; q a,b represents the element in the ath row and bth column of the constant coefficient matrix D.

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