Micro-grid energy storage frequency stabilization method based on battery energy storage planning

Abstract

The invention discloses a micro-grid energy storage frequency stabilization method based on battery energy storage planning, and the method comprises the steps: firstly, considering the effects of a synchronous generator, battery energy storage and emergency load shedding in frequency stabilization control, building a system frequency response model, and calculating the load shedding amount and the required frequency adjustment capability; on the basis, the uncertainty of interference is considered, and a multi-target opportunity constraint mixed integer nonlinear programming (MINLP) model taking the minimum investment cost and the maximum operation profit as targets is established. The chance constraint programming model is re-expressed as a processable deterministic form by using a linear weighting method, a piecewise linearization method based on a maximum affine function and Bernstein approximation, and multi-incision Benders decomposition iteration solution is adopted. According to the invention, uncertain interference can be effectively handled, and the load shedding amount is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronic converter control, and in particular relates to a microgrid energy storage frequency stabilization method based on battery energy storage planning. Background Art

[0002] As the share of renewable energy in the energy sector continues to increase, active power disturbances continue to occur, and power systems are more susceptible to frequency excursions. Synchronous generators are replaced by intermittent, non-dispatchable renewable energy sources, exacerbating the power imbalance in the power system. In addition, since renewable energy sources are connected to the power system through power electronic converters, they provide neither inertial regulation capabilities nor natural frequency regulation capabilities. Therefore, additional controllable resources are needed to prevent drastic frequency excursions and offset frequency instability under emergencies.

[0003] In response to the above problems, some scholars have designed a multi-level low-frequency load reduction strategy. According to the local measured frequency and load priority, a two-level low-frequency load reduction scheme is proposed to suppress rapid frequency deviation and achieve steady-state frequency recovery. Other scholars have considered the uncertainty of net load, analyzed the application of battery energy storage in frequency and peak regulation, established a frequency control and state of charge management model for battery energy storage considering the various stages of frequency regulation, and proposed a battery energy storage adaptive control strategy based on fuzzy logic to reduce frequency deviation and life loss. Generator low-frequency load reduction plays an important role in suppressing frequency deviation. However, low-frequency load reduction is the last resort to prevent system power outages and reduce large loads, and activation should be avoided. It can be seen that the use of a multi-level low-frequency load reduction strategy is not the best choice for steady-state frequency recovery. Summary of the invention

[0004] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a microgrid energy storage frequency stabilization method based on battery energy storage planning.

[0005] Technical solution: The present invention discloses a microgrid energy storage frequency stabilization method based on battery energy storage planning, which specifically includes the following steps:

[0006] Step 1: Establish a system frequency response model considering emergency load reduction and battery energy storage;

[0007] Step 2: Minimize the emergency load reduction ΔP e For this purpose, based on the system frequency response model and the frequency threshold f of the first level of underfrequency load shedding, u As boundary conditions, an NLP model for emergency load shedding optimization is established;

[0008] Step 3: Establish a multi-objective MINLP model based on the NLP model. Specifically, the minimization of the investment cost of battery energy storage is taken as the first optimization objective fv , taking the maximization of battery energy storage operating profit as the second optimization goal f p , and introduce the energy storage capacity constraints of the energy storage battery, the energy storage output power and charge state constraints of the energy storage battery, the generator load reduction opportunity constraints and the frequency stability constraints;

[0009] Step 4: Use the linear weighting method to convert the multi-objective function in the multi-objective MINLP model in step 3 into a single objective function, convert the nonlinear generator load reduction opportunity constraint in step 3 into a linear opportunity constraint, and then convert the linear opportunity constraint into a deterministic constraint;

[0010] Step 5: Take the single objective function in step 4, the deterministic constraints, the battery energy storage capacity constraints in step 3, the battery energy storage output power and state of charge constraints, and the frequency stability constraints as the battery energy storage planning model, express the battery energy storage planning model as a mixed integer linear programming problem, and solve it through the Benders decomposition algorithm to obtain the optimal planning strategy for the energy storage battery.

[0011] Furthermore, it is characterized in that the expression Δf(s) of the system frequency response model in step 1 is:

[0012]

[0013] Where s represents the frequency domain parameter of the model, τ is the time delay of emergency load reduction, ΔP L is the active power disturbance, H and D are the inertia coefficient and damping coefficient respectively; K m is the mechanical advantage coefficient, R G is the droop coefficient of the generator, T R is the reheat time constant, F H is the ratio coefficient of the high pressure turbine, T B is the time constant of the energy storage battery, S G,i is the capacity of the i-th synchronous generator, S B is the base capacity of the power system, R B is the droop coefficient of the energy storage battery.

[0014] Furthermore, the expression of the NLP model in step 2 is:

[0015]

[0016] Among them, f n Indicates the lowest frequency point, k t,1 is the safety margin factor, f N is the system rated frequency, Δf d,max is the maximum instantaneous frequency deviation, and Δf is the system frequency response.

[0017] Furthermore, the first optimization target f in step 3 is v The expression is:

[0018] minf v (x B )=minC v

[0019] Among them, x B represents the number of energy storage batteries deployed, where C v The expression is:

[0020] C v =x B ·(C c +C f +C m +C d )

[0021] Among them, C c , C f , C m , C d are the net present value of the capital cost, fixed operating cost, maintenance cost and disposal cost of the energy storage battery, C f , C m , C d The expressions are:

[0022]

[0023] Among them, n c represents life span, c d is the disposal cost of the energy storage battery, c f and c m are the annual fixed operating cost and maintenance cost of the energy storage battery, α and β are the interest rate and tax rate respectively;

[0024] The second optimization objective f p The expression is:

[0025] maxf p (P B,c,t,I ,P B,d,t,I )=maxC p

[0026] Where P B,c,t,I is the charging power of the energy storage battery at time t during the Ith operation cycle, P B,d,t,I is the discharge power of the energy storage battery at time t during the i-th operation cycle, C p The expression is:

[0027]

[0028] In the formula, Δt c is the time step of the operation cycle, T c is the length of the operating cycle, N o is the total number of operating cycles, p r,t is the usage time at time t, η B,c is the charging efficiency, η B,d is the discharge efficiency;

[0029] The energy storage capacity constraint of the energy storage battery is:

[0030] S' B，min ≤S' B ≤S' B，max

[0031] Among them, S' B Represents the energy storage capacity of the energy storage battery, S' B =x B S' B,r , where S' B,r is the rated power capacity of the energy storage battery, S' B，min is the minimum energy storage capacity, S' B，max is the maximum energy storage capacity;

[0032] The energy storage output power and state of charge constraints of the energy storage battery are:

[0033] 0≤P B,c,t,I ≤S' B

[0034] -S' B ≤P B,d,t,I ≤0

[0035] E B,1,I =x B E B,r R ini

[0036]

[0037] x B E B,r R min ≤E B,t,I ≤x B E B,r R max

[0038]

[0039] P res,t,I -P B,c,t,I -P B,d,t,I ≥P load,t,I

[0040] In the formula, E B,1,I is the energy stored in the battery at time t during the Ith operation cycle, E B,r is the rated energy capacity of the energy storage battery, R ini is the initial charge state, R min is the minimum state of charge, P res,t,I is the power of renewable energy at time t in the i-th operation cycle, P load,t,I is the power of the local load at time t in the i-th operating cycle;

[0041] The generator load shedding opportunity constraint is:

[0042] Pr{ΔP e ≤α c}≥1-γ c

[0043] Where Pr(.) is the probability of the event, α c is the preset emergency load reduction, γ c is the probability violation threshold, ΔP e Calculated by the NLP model;

[0044] The frequency stability constraint is:

[0045] S' B +P B,d,t,I ≥ΔP B,req

[0046] x B E B,r R max -E B,t,I ≥ΔE B,req

[0047] Among them, ΔP B,req is the preset frequency adjustment capability, ΔE B,req For preset energy reserve.

[0048] Furthermore, the expression of the single objective function f0 in step 4 is:

[0049] minf0=min(f v -ω a f p )

[0050] Among them, ω a is the weight coefficient.

[0051] Furthermore, in step 4, the opportunity constraint is converted into a deterministic constraint as follows:

[0052] Step 4.1: System frequency response model and NLP model, energy storage battery and emergency load shedding ΔP e and disturbance power ΔPL There is a nonlinear relationship between them. The hypersurface G is generated by using the step-by-step summation method. s (.):

[0053] ΔP e =G s (x B ,ΔP L )

[0054] Step 4.2: Based on the piecewise linearization method of the maximum affine function, a hyperplane is used to divide the parameter space of the hypersurface into Nm subspaces. The approximate function g of each subspace is h,j The expression of (·) is:

[0055] g h,j (x B,i1 ,ΔP L,i1 )=α a,j x B,i1 +α b,j ΔP L,i1 +β j

[0056] Where, j = 1, 2, ..., Nm; (x B,i1 ,ΔP L,i1 ) represents the il-th point in the j-th subspace of the hyperplane, il=1,2…,J, J represents the total number of points in the j-th subspace, all of which are located on the hypersurface, (x B,i1 ,ΔP L,i1 )∈C e , C e is the set of midpoints of the hypersurface, α a,j , α b,j and β j are the coefficients of the jth subspace, and α is solved by the following formula a,j , α b,j and β j :

[0057]

[0058] in, G m Represents the overall linearized hyperplane;

[0059] Step 4.3: Use auxiliary variable z h , we will solve α a,j , α b,j and β j The formula is transformed into a min structure to solve α a,j , α b,j and β j, the nonlinear generator load shedding opportunity constraint is transformed into a linear opportunity constraint represented by the maximum radiation function, and then the Bernstein approximation is used to transform the linear opportunity constraint into the following deterministic form:

[0060]

[0061] Among them, σ c Expressed by the disturbance power ΔP L The constant determined by the probability distribution of c is the preset emergency load reduction, γ c The violation threshold is the probability that the emergency load reduction exceeds the preset maximum value.

[0062] Furthermore, the step 5 is specifically as follows: using Benders decomposition to separate the constraints and the single objective function into a main problem M inv and two sub-problems S op and S fs ; Iterate the Benders decomposition until the preset termination condition is met to obtain the optimal planning strategy for the energy storage battery.

[0063] Furthermore, the main problem M inv The expression is:

[0064]

[0065] Among them, C inv is the coefficient vector, X inv ={x B}, x B represents the number of energy storage batteries deployed, q op is an auxiliary variable, A inv is the coefficient matrix, b inv is the coefficient vector, S opt is the Benders optimal set, S fea is the Benders feasibility set; T represents transposition;

[0066] Sub-problem S op The expression is:

[0067]

[0068] Among them, C op is the coefficient matrix, Y op = {P B,c,t,I ,P B,d,t,I} is the decision vector, P res,t,I is the power of renewable energy at time t in the i-th operation cycle, P load,t,I is the power of the local load at time t in the i-th operating cycle, A op,1 and Aop,2 is the coefficient matrix, A op,3 is the synergy matrix, b op,1 and b op,2 are coefficient vectors;

[0069] Sub-problem S fs The expression is:

[0070]

[0071] Among them, α fs is the slack variable, A fs is the coefficient matrix, b fs is the coefficient vector.

[0072] Furthermore, in the solution process, based on the main problem, the lower bound B of the optimization problem is low The expression is:

[0073] B low =max{B low ,C inv T X inv,s +q op,s}

[0074] Among them, X inv,s and q op,s is the optimal solution to the main problem;

[0075] During the solution process, if the subproblem S op The dual problem of is unbounded, that is, the subproblem S op Not feasible, in S fea Add a Benders feasibility cut:

[0076] λ op,f,1 T (b op,1 -A op,2 X inv )+λ op,f,2 T b op,2 ≤0

[0077] Among them, λ op,f,1 and λ op,f,2 It is a sub-problem S op The solution vector of the dual form of ;

[0078] If the subproblem S op is feasible, then in S opt Add a Benders optimal cut and update the original mixed integer linear programming B up The upper bound of :

[0079] λ op,f,1T (b op,1 -A op,2 X inv )+λ op,f,2 T b op,2 ≤q op

[0080] B up =min{B up ,C inv T X inv,s +λ op,f,1 T (b op,1 -A op,2 X inv )+λ op,f,2 T b op,2}

[0081] By solving the subproblem S fs The dual problem of calculating the slack variable α fs , and in the constraint set S fea Add a Benders feasibility cut to

[0082] λ fs T (b fs -A fs X inv,s )≤0.

[0083] Furthermore, the expression of the preset termination condition is:

[0084] B up -B low ≤ε c

[0085] where ε c is the convergence tolerance.

[0086] Beneficial effects: The present invention proposes a chance-constrained battery energy storage optimization method, which has good effects in improving the frequency minimum point and reducing the load shedding. The scheme can keep the load shedding within a predetermined range while achieving energy arbitrage. The method can coordinate synchronous generators, battery energy storage and emergency load shedding to prevent frequency deviation, and can prevent the activation of low-frequency load shedding even under extreme interference. DETAILED DESCRIPTION

[0087] This embodiment is based on the flexibility of the battery energy storage system, which can help the synchronous generator compensate for power imbalance and reduce load shedding. Therefore, this embodiment combines the low-frequency load shedding of the generator with the battery energy storage planning, and uses the flexibility of the battery energy storage system to reduce the low-frequency load shedding of the generator caused by frequency instability under emergencies.

[0088] The present invention provides a microgrid energy storage frequency stabilization method for battery energy storage planning, comprising the following steps:

[0089] (1) Establish a system frequency response model considering emergency load reduction and battery energy storage;

[0090] (2) Establish an NLP model to optimize the emergency load shedding strategy;

[0091] (3) Initialize the probability density function of the disturbance using the MLE method to form a multi-objective MINLP model with chance constraints;

[0092] (4) Use the linear weighting method to transform the investment minimization and operating profit maximization into a single objective form; based on the battery energy storage planning quantity x B and emergency load shedding ΔP e and disturbance power ΔP L There is a nonlinear relationship between them, and the hypersurface G is generated by the step-by-step summation method. s And estimate the required battery energy storage reserve, transform the hyperplane into a linearized form using the piecewise linearization method of the maximum affine function, bring the linearized hyperplane into the chance constraint formula and transform it into a deterministic form using the Bernstein approximation;

[0093] (5) The battery energy storage planning model is expressed as a mixed integer linear programming problem, and the optimal planning strategy of the energy storage battery is calculated through Benders decomposition.

[0094] The specific process of step (1) is as follows:

[0095] (101) The frequency response model Δf(s) describing the dynamic frequency response of the synchronous generator is expressed as:

[0096]

[0097] Where Δf is the frequency change of the system’s center of inertia, i.e., the frequency response, and ΔP G and ΔP S are the power changes of synchronous generator and secondary frequency control, H and D are the inertia coefficient and damping coefficient, T R is the reheat time constant, F H is the ratio coefficient of the high pressure turbine, K m is the mechanical advantage coefficient, R G is the droop coefficient of the generator; s represents the frequency domain parameter of the model.

[0098] (102) After a frequency disturbance occurs in the power system (usually a sudden load reduction causing a frequency increase), emergency load shedding is activated to prevent frequency deviation. Considering the time delay, the frequency domain response of emergency load shedding ΔPE(s) is expressed as: ΔP E (s) = ΔP e (s)·e -τs , where ΔP e (s) is the control command for emergency load shedding, and τ is the time delay of emergency load shedding. In practice, the value of the time delay τ is about 300ms. Therefore, the time delay unit is represented by the expansion of the first-order Taylor series around zero, and the transfer function of emergency load shedding can be restated as:

[0099] (103) The droop coefficient R of the energy storage battery B Normalized to the same basis as the frequency response model. The system basis of the frequency response model is the sum of the rated powers of the synchronous generators. Therefore, the output power of the energy storage battery P B Expressed as: P B (t) = P B (t e )+ΔP B (t), Where, t e is the disturbance time, ΔP B is the battery storage power change, S G,i is the capacity of the i-th synchronous generator, n s is the number of conventional generators; T B is the time constant of the energy storage battery.

[0100] (104) The frequency change of the system frequency response model is calculated as: Substituting steps (101), (102), and (103), the frequency response model of the system is expressed as: After a large disturbance, the secondary frequency modulation control is not started until the frequency reaches a quasi-steady state, so ΔP S (s) = 0. Active power disturbance and emergency load reduction control command can be expressed by step response: Substituting into the frequency response model, we get:

[0101] The specific process of step (2) is as follows:

[0102] (201) Synchronous generators, battery energy storage and emergency load shedding are coordinated to prevent frequency drops and prevent the initiation of underfrequency load shedding. When the droop coefficients of the generators and battery energy storage are equal, the amount of emergency load shedding ΔP e The frequency should be at the lowest point f n The frequency threshold f of the first level of under-frequency load shedding is not exceededu Therefore, the size of the battery energy storage depends on the emergency load reduction scheme, and the frequency threshold of the first level of low-frequency load reduction is used as a given boundary condition. According to the disturbance power ΔP L ,The NLP model for emergency load shedding optimization can be expressed as:

[0103]

[0104] The amount of emergency load reduction ΔP e is the decision variable, f N is the system rated frequency, k t,1 is the safety margin factor, Δf is the calculated frequency deviation (i.e., the frequency change of the system inertia center in step 1), and Δf d,max is the maximum instantaneous frequency deviation.

[0105] The specific process of step (3) is as follows:

[0106] (301) Disturbance power f c The probability density function can be expressed as:

[0107]

[0108] Among them, ΔP L,min Indicates ΔP L The lower bound of θ is the exponential parameter. Using maximum likelihood estimation, the scaling exponential parameter θ of the probability density function is calculated as:

[0109]

[0110] n d is the number of empirical data, ΔP L,i is the i-th empirical data.

[0111] (302) The first optimization objective is to minimize the investment cost of battery energy storage. Capital cost, fixed operating cost, maintenance cost and disposal cost are combined and the net present value method is used.

[0112] C v =x B ·(C c +C f +C m +C d )

[0113]

[0114] Among them, x B represents the number of energy storage batteries deployed, C c , C f , C m , C dare the net present value of the capital cost, fixed operating cost, maintenance cost and disposal cost of the energy storage battery, n c represents life span, c d is the disposal cost of the energy storage battery, c f and c m are the annual fixed operating cost and maintenance cost of the energy storage battery, α and β are the interest rate and tax rate, respectively. Therefore, the first objective function f of investment minimization is v Expressed as: minf v (x B )=minC v .

[0115] (303) The second optimization objective is to maximize the operating profit of battery energy storage. Taking into account the usage time, the operating profit of battery energy storage is calculated as the difference between the battery energy storage discharge profit and the battery energy storage charging cost:

[0116]

[0117] In the formula, Δt c is the time step of the operation cycle, T c is the length of the operating cycle, N o is the total number of operating cycles, p r,t is the usage time at time t, η B,c is the charging efficiency, η B,d is the discharge efficiency; P B,c,t,I is the charging power of the energy storage battery at time t during the Ith operation cycle, P B,d,t,I is the discharge power of the energy storage battery at time t during the i-th operating cycle; therefore, the second objective function f of maximizing operating profit p Expressed as: maxf p (P B,c,t,I ,P B,d,t,I )=maxC p .

[0118] (304) Due to environmental and financial constraints, installed battery storage capacity is subject to the following constraints:

[0119] S' B，min ≤S' B ≤S' B，max

[0120] Among them, S' B Represents the energy storage capacity of the energy storage battery, S' B =x B S' B,r , where S' B,r is the rated power capacity of the energy storage battery, S' B，min is the minimum energy storage capacity, S'B，max is the maximum energy storage capacity.

[0121] 305) Physical and operational limitations, battery energy storage output power and state of charge constraints are:

[0122] 0≤P B,c,t,I ≤S' B

[0123] -S' B ≤P B,d,t,I ≤0

[0124] E B,1,I =x B E B,r R ini

[0125]

[0126] x B E B,r R min ≤E B,t,I ≤x B E B,r R max

[0127]

[0128] P res,t,I -P B,c,t,I -P B,d,t,I ≥P load,t,I

[0129] In the formula, E B,1,I is the energy stored in the battery at time t during the Ith operation cycle, E B,r is the rated energy capacity of the energy storage battery, R ini is the initial charge state, R min is the minimum state of charge, P res,t,I is the power of renewable energy at time t in the i-th operation cycle, P load,t,I is the power of the local load at time t in the i-th operating cycle.

[0130] (306) Frequency Stability Constraint

[0131] The amount of emergency load shedding is calculated by the NLP model of (201), where the frequency deviation Δf is calculated by the frequency response model (104). Therefore, the remaining power is provided by the synchronous generator and the battery energy storage according to their equivalent droop coefficients R G and R B,e And the frequency deviation Δf is compensated. Considering the uncertainty of the disturbance, the probability constraint of the emergency load reduction exceeding the predefined maximum value (that is, the generator load reduction opportunity constraint, which is nonlinear) is:

[0132] Pr{ΔP e ≤α c}≥1-γ c

[0133] Where Pr(.) is the probability of the event, α c is the preset emergency load reduction, γ c is the probability violation threshold, 1-γ c is the confidence level.

[0134] In addition, the power and energy reserve of battery energy storage for frequency regulation should be kept within the feasible range. On this basis, the frequency stability constraint of battery energy storage is proposed to ensure that it has sufficient frequency regulation capability and a state of charge within the allowable range. The frequency stability constraint can be expressed as:

[0135] S' B +P B,d,t,I ≥ΔP B,req

[0136] x B E B,r R max -E B,t,I ≥ΔE B,req

[0137] Among them, ΔP B,req is the preset frequency adjustment capability, ΔE B,req For preset energy reserve.

[0138] The specific process of step (4) is as follows:

[0139] (401) The established battery energy storage planning model is a multi-objective MINLP problem with opportunity constraints. Then, the linear weighting method is used to reduce the number of objective functions, and the objective function can be expressed as:

[0140] minf0=min(f v -ω a f p )

[0141] where ω a is the weight coefficient.

[0142] (402) According to the frequency response model and the NLP model, the battery energy storage and the emergency load shedding amount ΔP e and disturbance power ΔP L There is a nonlinear relationship between them. Further, based on the step-by-step summation method, a hypersurface G can be generated. s (.) and is represented as:

[0143] ΔP e =Gs (x B ,ΔP L )

[0144] (403) A piecewise linearization method based on the maximum affine function is used to conservatively approximate the hypersurface with Nm hyperplanes. For a series of points (x B,i1 ,ΔP L,i1 ,ΔP e,i1 ), parameter space (x B,i1 ,ΔP L,i1 )∈C e It can be divided into Nm subspaces. In each subspace, the approximate function g h,j (·) is expressed as:

[0145] g h,j (x B,i1 ,ΔP L,i1 )=α a,j x B,i1 +α b,j ΔP L,i1 +β j

[0146] Where, j = 1, 2, ..., Nm; (x B,i1 ,ΔP L,i1 ) represents the il-th point in the j-th subspace of the hyperplane, il=1,2…,J, J represents the total number of points in the j-th subspace, all of which are located on the hypersurface, where α a,j , α b,j and β j is the coefficient that determines the jth hyperplane. Nm is the maximum affine function G of the approximate function h (·) can be expressed as:

[0147]

[0148] (404) According to (402)(403), α a,j , α b,j and β j It can be calculated by the following formula:

[0149]

[0150] Among them, G m Represents the overall linearized hyperplane.

[0151] The maximum affine function G h Substituting (·) into the formula of step (404), we get a min-max structure, using the auxiliary variable z h , convert the min-max structure into the following min form:

[0152]

[0153] Solve α using the min form a,j , α b,j and β j ;

[0154] The generator load shedding opportunity constraint in step (306) can be reformulated as:

[0155] Pr{G h (x B,i1, ,ΔP L,i1 )≤α c}≥1-γ c .

[0156] (405) In addition, Pr{G h (x B,i1, ,ΔP L,i1 )≤α c}≥1-γ c is reformulated in deterrence-minimum form by the Bernstein approximation. Based on the moment generating function Φ c (·), the above formula Pr{G h (x B,i1, ,ΔP L,i1 )≤α c}≥1-γ c can be restated as:

[0157]

[0158] Φ c (x) = ln[∫e xy dP c (y)]

[0159]

[0160] Among them, v c is the decision variable, x and y are independent variables, and Pc(·) is the disturbance power ΔP L The probability distribution of σ c is a constant determined by the probability distribution Pc(·), Substitution Get formula A:

[0161]

[0162] From the probability density function of step (301), it can be seen that the interference power ΔP L The expected μ c and variance It is expressed as:

[0163]

[0164] The interference power ΔP L The expected μ c and variance Substituting this into formula A, we get:

[0165]

[0166] The specific process of step (5) is as follows:

[0167] (501) Based on (401) to (405), the battery energy storage planning model is reformulated as a mixed integer linear programming problem. In order to solve the mixed integer linear programming more efficiently, multi-cut Benders decomposition is adopted. The mixed integer linear programming (constraints in step (3) and constraints in step (4) and single objective function) can be divided into a main problem M inv and two sub-problems S op and S fs Specifically, the main investment problem M inv Calculate the capacity of the battery storage. In subproblem S op In the process, the battery energy storage output power is optimized. By solving the frequency stability subproblem S fs To test whether battery energy storage satisfies the opportunity constraint.

[0168] (502) Investment Main Question M inv It can be concisely expressed as:

[0169]

[0170] The objective function C inv T X inv is minf0=min(f v -ω a f p ) v , C inv is the coefficient vector, T represents transpose; X inv ={x B}, q op is an auxiliary variable, A inv is the coefficient matrix, b inv is the coefficient vector, S opt is the Benders optimal set, S fea is the Benders feasibility set; the main problem M inv Determine the optimization problem B low The lower bound of can be expressed as:

[0171] B low=max{B low ,C inv T X inv,s +q op,s}

[0172] Among them, X inv,s and q op,s is the optimal solution to the main problem.

[0173] (503) Sub-problem S op It is expressed as:

[0174]

[0175] Among them, C op T Y op is minf0=min(f v -ω a f p ) a f p ; C op is the coefficient matrix, Y op = {P B,c,t,I ,P B,d,t,I} is the decision vector, A op,1 and A op,2 is the coefficient matrix, A op,3 is the synergy matrix, b op,1 and b op,2 are all coefficient vectors; the first constraint is the main problem M inv With subproblem S op The coupling constraints include the 1st, 2nd, 3rd, and 5th constraints in (305) and the constraint in (307); the second constraint includes the 4th, 6th, and 7th constraints in (305).

[0176] (504) Based on the strong duality theorem, subproblem S op The feasibility of is determined by its dual problem. If the dual problem is unbounded, then the original problem S op Not feasible, S fea Add a Benders feasibility cut to the constraint set, which is expressed as:

[0177] λ op,f,1 T (b op,1 -A op,2 X inv )+λ op,f,2 T b op,2 ≤0

[0178] where λ op,f,1 and λ op,f,2 It is a sub-problem Sop The extremum direction of the dual form of .

[0179] Otherwise, the original problem S op It is feasible. Under the set constraints S opt Add a Benders optimal cut to update the original mixed integer linear programming B up The upper bound of is expressed as:

[0180] λ op,f,1 T (b op,1 -A op,2 X inv )+λ op,f,2 T b op,2 ≤q op

[0181] B up =min{B up ,C inv T X inv,s +λ op,f,1 T (b op,1 -A op,2 X inv )+λ op,f,2 T b op,2}

[0182] where λ op,f,1 and λ op,f,2 It is a sub-problem S op The solution vector of the dual form of .

[0183] (505) established a slack variable α fs The frequency stability subproblem S of the vector fs , and compactly represent it as:

[0184]

[0185] The first constraint is the main problem M inv With subproblem S fs The relaxed coupling constraint of (405) contains the last definite constraint formula, A fs is the coefficient matrix, b fs is the coefficient vector.

[0186] (506) By solving the subproblem S fs The dual problem of calculating the slack variable α fs When α fs > 0, in the constraint set S fea Adding a Benders feasibility cut, it can be expressed as:

[0187] λ fs T (b fs -A fs X inv,s )≤0

[0188] Among them, λ fs It is a sub-problem S fs The solution vector of the dual subproblem of .

[0189] (507) The iteration of the multi-section Benders decomposition will continue until the termination condition is met, which can be expressed as:

[0190] B up -B low ≤ε c

[0191] where ε c is the convergence tolerance.

[0192] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

Claims

1. A microgrid energy storage frequency stabilization method based on battery energy storage planning, characterized in that: The specific steps include: Step 1: Establish a system frequency response model considering emergency load reduction and battery energy storage; Step 2: Minimize the emergency load reduction ΔP e For this purpose, based on the system frequency response model and the frequency threshold f of the first level of underfrequency load shedding, u As boundary conditions, an NLP model for emergency load shedding optimization is established; Step 3: Establish a multi-objective MINLP model based on the NLP model. Specifically, the minimization of the investment cost of battery energy storage is used as the first optimization objective f v , taking the maximization of battery energy storage operating profit as the second optimization goal f p , and introduce the energy storage capacity constraints of the energy storage battery, the energy storage output power and charge state constraints of the energy storage battery, the generator load reduction opportunity constraints and the frequency stability constraints; Step 4: Use the linear weighting method to convert the multi-objective function in the multi-objective MINLP model in step 3 into a single objective function, convert the nonlinear generator load reduction opportunity constraint in step 3 into a linear opportunity constraint, and then convert the linear opportunity constraint into a deterministic constraint; Step 5: Take the single objective function in step 4, the deterministic constraints, the battery energy storage capacity constraints in step 3, the battery energy storage output power and state of charge constraints, and the frequency stability constraints as the battery energy storage planning model, express the battery energy storage planning model as a mixed integer linear programming problem, and solve it through the Benders decomposition algorithm to obtain the optimal planning strategy for the energy storage battery.

2. A microgrid energy storage frequency stabilization method based on battery energy storage planning according to claim 1, characterized in that The expression Δf(s) of the system frequency response model in step 1 is: Where s represents the frequency domain parameter of the model, τ is the time delay of emergency load reduction, ΔP L is the active power disturbance, H and D are the inertia coefficient and damping coefficient respectively; K m is the mechanical advantage coefficient, R G is the droop coefficient of the generator, T R is the reheat time constant, F H is the ratio coefficient of the high pressure turbine, T B is the time constant of the energy storage battery, S G,i is the capacity of the i-th synchronous generator, S B is the base capacity of the power system, R B is the droop coefficient of the energy storage battery.

3. According to a method for stabilizing the energy storage frequency of a microgrid based on battery energy storage planning according to claim 1, it is characterized in that: The expression of the NLP model in step 2 is: Among them, f n Indicates the lowest frequency point, k t,1 is the safety margin factor, f N is the system rated frequency, Δf d,max is the maximum instantaneous frequency deviation, and Δf is the system frequency response.

4. According to a method for stabilizing the energy storage frequency of a microgrid based on battery energy storage planning according to claim 1, it is characterized in that: The first optimization objective f in step 3 v The expression is: minf v (x B )=minC v Among them, x B represents the number of energy storage batteries deployed, where C v The expression is: C v =x B ·(C c +C f +C m +C d ) Among them, C c , C f , C m , C d are the net present value of the capital cost, fixed operating cost, maintenance cost and disposal cost of the energy storage battery, C f , C m , C d The expressions are: Among them, n c represents life span, c d is the disposal cost of the energy storage battery, c f and c m are the annual fixed operating cost and maintenance cost of the energy storage battery, α and β are the interest rate and tax rate respectively; The second optimization objective f p The expression is: maxf p (P B,c,t,I ,P B,d,t,I )=maxC p Where P B,c,t,I is the charging power of the energy storage battery at time t during the Ith operation cycle, P B,d,t,I is the discharge power of the energy storage battery at time t during the i-th operation cycle, C p The expression is: In the formula, Δt c is the time step of the operation cycle, T c is the length of the operating cycle, N o is the total number of operating cycles, p r,t is the usage time at time t, η B,c is the charging efficiency, η B,d is the discharge efficiency; The energy storage capacity constraint of the energy storage battery is: S' B，min ≤S' B ≤S' B，max Among them, S' B Represents the energy storage capacity of the energy storage battery, S' B =x B S' B,r , where S' B,r is the rated power capacity of the energy storage battery, S' B，min is the minimum energy storage capacity, S' B，max is the maximum energy storage capacity; The energy storage output power and state of charge constraints of the energy storage battery are: 0≤P B,c,t,I ≤S' B -S' B ≤P B,d,t,I ≤0 E B,1,I =x B E B,r R ini x B E B,r R min ≤E B,t,I ≤x B E B,r R max P res,t,I -P B,c,t,I -P B,d,t,I ≥P load,t,I In the formula, E B,1,I is the energy stored in the battery at time t during the Ith operation cycle, E B,r is the rated energy capacity of the energy storage battery, R ini is the initial charge state, R min is the minimum state of charge, P res,t,I is the power of renewable energy at time t in the i-th operation cycle, P load,t,I is the power of the local load at time t in the i-th operating cycle; The generator load shedding opportunity constraint is: ΔP e ≤α c }≥1-γ c Where Pr(.) is the probability of the event, α c is the preset emergency load reduction, γ c is the probability violation threshold, ΔP e Calculated by the NLP model; The frequency stability constraint is: S' B +P B,d,t,I ≥ΔP B,req x B E B,r R max -E B,t,I ≥ΔE B,req Among them, ΔP B,req is the preset frequency adjustment capability, ΔE B,req For preset energy reserve.

5. According to a method for stabilizing the energy storage frequency of a microgrid based on battery energy storage planning according to claim 1, it is characterized in that: The expression of the single objective function f0 in step 4 is: minf0=min(f v -oh a f p ) Among them, ω a is the weight coefficient.

6. A microgrid energy storage frequency stabilization method based on battery energy storage planning according to claim 1, characterized in that: The conversion of the chance constraint into a deterministic constraint in step 4 is as follows: Step 4.1: Based on the system frequency response model and NLP model, the energy storage battery and the emergency load reduction ΔP e and disturbance power ΔP L There is a nonlinear relationship between them, and the hypersurface Gs(.) is generated by using the step-by-step summation method: ΔP e =G s (x B ,ΔP L ) Step 4.2: Based on the piecewise linearization method of the maximum affine function, a hyperplane is used to divide the parameter space of the hypersurface into Nm subspaces. The approximate function g of each subspace is h,j The expression of (·) is: g h,j (x B,i1 ,ΔP L,i1 )=a a,j x B,i1 +a b,j ΔP L,i1 +b j Where, j = 1, 2, ..., Nm; (x B,i1 ,ΔP L,i1 ) represents the il-th point in the j-th subspace of the hyperplane, il=1,2…,J, J represents the total number of points in the j-th subspace, all of which are located on the hypersurface, (x B,i1 ,ΔP L,i1 )∈C e , C e is the set of midpoints of the hypersurface, α a,j , α b,j and β j are the coefficients of the jth subspace, and α is solved by the following formula a,j , α b,j and β j : in, G m Represents the overall linearized hyperplane; Step 4.3: Use auxiliary variable z h , we will solve α a,j , α b,j and β j The formula is transformed into a min structure to solve α a,j , α b,j and β j , the nonlinear generator load shedding opportunity constraint is transformed into a linear opportunity constraint represented by the maximum radiation function, and then the Bernstein approximation is used to transform the linear opportunity constraint into the following deterministic form: Among them, σ c Expressed by the disturbance power ΔP L The constant determined by the probability distribution of c is the preset emergency load reduction, γ c The violation threshold is the probability that the emergency load reduction exceeds the preset maximum value.

7. A microgrid energy storage frequency stabilization method based on battery energy storage planning according to claim 1, characterized in that: The step 5 is specifically as follows: using Benders decomposition to separate the constraints and the single objective function into a main problem M inv and two sub-problems S op and S fs ; Iterate the Benders decomposition until the preset termination condition is met to obtain the optimal planning strategy for the energy storage battery.

8. A microgrid energy storage frequency stabilization method based on battery energy storage planning according to claim 7, characterized in that: Main Question M inv The expression is: Among them, C inv is the coefficient vector, X inv ={x B }, x B represents the number of energy storage batteries deployed, q op is an auxiliary variable, A inv is the coefficient matrix, b inv is the coefficient vector, S opt is the Benders optimal set, S fea is the Benders feasibility set; T represents transposition; Sub-problem S op The expression is: Among them, C op is the coefficient matrix, Y op = {P B,c,t,I ,P B,d,t,I } is the decision vector, P res,t,I is the power of renewable energy at time t in the i-th operation cycle, P load,t,I is the power of the local load at time t in the i-th operating cycle, A op,1 and A op,2 is the coefficient matrix, A op,3 is the synergy matrix, b op,1 and b op,2 are coefficient vectors; Sub-problem S fs The expression is: Among them, α fs is the slack variable, A fs is the coefficient matrix, b fs is the coefficient vector.

9. A microgrid energy storage frequency stabilization method based on battery energy storage planning according to claim 8, characterized in that: In the solution process, based on the main problem, the lower bound B of the optimization problem low The expression is: B low =max{B low ,C inv T X inv,s +q op,s } Among them, X inv,s and q op,s is the optimal solution to the main problem; During the solution process, if the subproblem S op The dual problem of is unbounded, that is, the subproblem S op Not feasible, in S fea Add a Benders feasibility cut: l op,f,1 T (b) op,1 -A op,2 X inv )+λ op,f,2 T b op,2 ≤0 Among them, λ op,f,1 and λ op,f,2 It is a sub-problem S op The solution vector of the dual form of ; If the subproblem S op is feasible, then in S opt Add a Benders optimal cut and update the original mixed integer linear programming B up The upper bound of : l op,f,1 T (b) op,1 -A op,2 X inv )+λ op,f,2 T b op,2 ≤q op B up =min{B up ,C inv T X inv,s +λ op,f,1 T (b) op,1 -A op,2 X inv )+λ op,f,2 T b op,2 } By solving the subproblem S fs The dual problem of calculating the slack variable α fs , and in the constraint set S fea Add a Benders feasibility cut to l fs T (b) fs -A fs X inv,s )≤0.

10. A microgrid energy storage frequency stabilization method based on battery energy storage planning according to claim 9, characterized in that: The expression of the preset termination condition is: B up -B low ≤ε c where ε c is the convergence tolerance.

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