A micro-grid energy storage frequency stabilization method based on battery energy storage planning

Abstract

The application discloses a kind of microgrid energy storage frequency stabilization method based on battery energy storage planning, first, the role of synchronous generator, battery energy storage and emergency load shedding in frequency stabilization control is considered, the system frequency response model is established, and the load shedding and required frequency regulation capability are calculated.On this basis, considering the uncertainty of disturbance, a multi-objective chance-constrained mixed-integer nonlinear programming (MINLP) model is established with the goal of minimizing investment cost and maximizing operating profit. Using linear weighting method, piecewise linearization method based on maximum affine function and Bernstein approximation, the chance-constrained programming model is reformulated into a tractable deterministic form, and solved using multi-cut Benders decomposition iteration. The application can effectively deal with uncertain disturbances and reduce load shedding.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power electronic converter control, and particularly relates to a micro-grid energy storage frequency stabilization method based on battery energy storage planning. BACKGROUND

[0002] With the increasing proportion of renewable energy in the energy field, active power disturbances are constantly emerging, and power systems are more susceptible to frequency deviation. Synchronous generators are replaced by intermittent and non-schedulable renewable energy, which exacerbates power imbalance in power systems. In addition, since renewable energy is connected to the power system through power electronic converters, neither inertia regulation nor natural frequency regulation is provided. Therefore, additional controllable resources are needed to prevent severe frequency deviation and offset frequency instability under sudden events.

[0003] In view of the above problems, some scholars have designed a multi-stage low-frequency load shedding strategy. According to the local measured frequency and load priority, a two-stage low-frequency load shedding scheme is proposed to suppress rapid frequency deviation and achieve steady-state frequency recovery. Some scholars have considered the uncertainty of net load, analyzed the application of battery energy storage in frequency modulation and peak regulation, established a frequency control and state of charge management model of battery energy storage considering various stages of frequency regulation, and proposed a fuzzy logic-based adaptive control strategy for battery energy storage to reduce frequency deviation and life loss. Generator low-frequency load shedding plays an important role in suppressing frequency deviation. However, low-frequency load shedding is the last resort to prevent system blackouts and reduce a large amount of load, and should be avoided. It can be seen that the multi-stage low-frequency load shedding strategy is not the optimal choice for steady-state frequency recovery. SUMMARY

[0004] The application aims to solve the problems existing in the prior art, and provides a micro-grid energy storage frequency stabilization method based on battery energy storage planning.

[0005] Technical scheme: The application discloses a micro-grid energy storage frequency stabilization method based on battery energy storage planning, and specifically comprises the following steps:

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

[0007] Step 2: Minimize the amount of emergency load shedding ΔP e , based on the system frequency response model and the frequency threshold f u as the boundary condition, an NLP model for emergency load shedding optimization is established;

[0008] Step 3: Based on the NLP model, a multi-objective MINLP model is established, specifically: the first optimization target fv maximize the operation profit of battery energy storage as the second optimization objective f p and introduce the energy storage capacity constraint of energy storage battery, the energy storage output power and state of charge constraint of energy storage battery, the generator load shedding opportunity constraint and the frequency stability constraint;

[0009] Step 4: convert the multi-objective function in the multi-objective MINLP model in step 3 into a single objective function by using the linear weighted method, convert the nonlinear generator load shedding 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 constraint, and the battery energy storage capacity constraint, the battery energy storage output power and state of charge constraint, and the frequency stability constraint in step 3 as the battery energy storage planning model, express the battery energy storage planning model as a mixed integer linear programming problem, and solve it by using the Benders decomposition algorithm, so as to obtain the optimal planning strategy of the energy storage battery.

[0011] Further, the expression of the system frequency response model in step 1 is Δf(s) = -K

[0012]

[0013] wherein s represents the frequency domain parameter of the model, τ is the time delay of emergency load shedding, ΔP L is the active power disturbance, H and D are the inertia coefficient and the damping coefficient respectively; K m is the mechanical gain coefficient, R G is the droop coefficient of the generator, T R is the reheating time constant, F H is the specific 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 reference capacity of the power system, R B is the droop coefficient of the energy storage battery.

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

[0015]

[0016] wherein f n represents the lowest point of the frequency, k t,1 is the safety margin coefficient, f N is the rated frequency of the system, Δf d,max is the maximum instantaneous frequency deviation, and Δf is the system frequency response.

[0017] Further, the first optimization objective f v in step 3 is expressed as:

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

[0019] where x B represents the number of energy storage battery deployments, and C v is expressed as:

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

[0021] where C c , C f , C m , C d are the net present values of the capital cost, fixed operating cost, maintenance cost and disposal cost of the energy storage battery respectively, and C f , C m , C d are expressed as:

[0022]

[0023] where n c represents the lifetime, 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 respectively, and a and b are the interest rate and tax rate respectively;

[0024] The second optimization objective f p is expressed as:

[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 in the i-th operating cycle, P B,d,t,I is the discharging power of the energy storage battery at time t in the i-th operating cycle, and C p is expressed as:

[0027]

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

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

[0030] S' B，min ≤ S' B ≤ S' B，max

[0031] where 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 constraint of the energy storage battery is:

[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 of the battery at time t in the first operating cycle, E B,r is the rated energy capacity of the energy storage battery, R ini is the initial state of charge, R min is the minimum state of charge, P res,t,I is the power of the renewable energy source at time t in the i th operating 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] In the formula, Pr(.) is the event probability, α c is the preset emergency load shedding, γ c is the probability violation threshold, ΔP e is 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] Where, ΔP B,req is the preset frequency regulation capability, ΔE B,req is the preset energy reserve.

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

[0049] minf0=min(f v -ω a f p )

[0050] Where, ω a is the weight coefficient.

[0051] Further, the conversion of the opportunity constraint to the deterministic constraint in step 4 is specifically:

[0052] Step 4.1: System frequency response model and NLP model, energy storage battery and emergency load shedding load shedding ΔP e and disturbance power ΔPL There is a nonlinear relationship between them, and the method of step-by-step summation is used to generate a hypersurface G 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, the parameter space of the hypersurface is divided into Nm subspaces by hyperplanes, and the expression of the approximate function g h,j (·) of each subspace 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 ilth point in the jth subspace of the hyperplane, il = 1, 2, …, J, J represents the total number of points in the jth subspace, and these points are located on the hypersurface, (x B,i1 ,ΔP L,i1 ) ∈ C e , C e is the set of points on the hypersurface, α a,j , α b,j and β j are the coefficients of the jth subspace, and α a,j , α b,j and β j are solved by the following formula:

[0057]

[0058] Where, G m represents the overall linearized hyperplane;

[0059] Step 4.3: Using auxiliary variable z h , the formula for solving α a,j , α b,j and β j is converted into a min structure, so as to solve α a,j , α b,j and β jThe nonlinear generator load shedding opportunity constraint is converted into a linear opportunity constraint represented by a maximum radiation function, and then the Bernstein approximation is used to convert the linear opportunity constraint into the following deterministic form:

[0060]

[0061] where σ c represents a constant determined by the probability distribution of the disturbance power ΔP L , α c is a preset emergency load shedding, γ c is a violation threshold of the probability that the emergency load shedding exceeds the preset maximum value.

[0062] Further, the step 5 is specifically: adopting Benders decomposition to divide the constraint condition and the single objective function into a master problem M inv and two sub-problems S op and S fs ; iterative calculation is performed on the Benders decomposition until a preset termination condition is met, and the optimal planning strategy of the energy storage battery is obtained.

[0063] Further, the expression of the master problem M inv is as follows:

[0064]

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

[0066] The expression of the sub-problem S op is as follows:

[0067]

[0068] where C op is a coefficient matrix, Y op ={P B,c,t,I , P B,d,t,I} is a decision vector, P res,t,I is the power of the renewable energy at t in the i-th operation period, P load,t,I is the power of the local load at t in the i-th operation period, 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] Subproblem 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 subproblem 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] The relaxation variable α fs is calculated by solving the dual problem of the subproblem S fs , and a Benders feasibility cut is added to the constraint set S fea :

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

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

[0084] B up -B low ≤ε c

[0085] Wherein, ε c is a convergence tolerance.

[0086] Beneficial effects: The application proposes an opportunity constraint battery energy storage optimization method, which has good effects in improving the lowest point of frequency and reducing the load shedding amount. The scheme can realize energy arbitrage while keeping the load shedding amount within the predetermined range. 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] The embodiment is based on the flexibility of the battery energy storage system, which can help the synchronous generator to compensate power imbalance and reduce load shedding. Therefore, the embodiment combines generator low-frequency load shedding and battery energy storage planning, and uses the flexibility of the battery energy storage system to reduce the generator low-frequency load shedding caused by frequency instability under emergency.

[0088] The application provides a micro-grid energy storage frequency stabilization method based on battery energy storage planning, comprising the following steps:

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

[0090] (2) establishing an NLP model for optimizing the emergency load shedding strategy;

[0091] (3) initializing the probability density function of the disturbance by the MLE method, forming a multi-objective MINLP model with chance constraints;

[0092] (4) converting the investment minimization and operation profit maximization into a single objective form by the linear weighting method; based on the battery energy storage planning amount x B and the emergency load shedding amount ΔP e and the disturbance power ΔP L there is a nonlinear relationship between them, and a step-by-step summation method is used to generate a hyper-surface G s and estimate the required battery energy storage reserve, and the hyperplane is transformed into a linear form by the piecewise linearization method of the maximum affine function, and the linearized hyperplane is brought into the chance constraint and transformed into a deterministic form by the Bernstein approximation;

[0093] (5) expressing the battery energy storage planning model as a mixed integer linear programming problem, and calculating the optimal planning strategy of the energy storage battery by Benders decomposition.

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

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

[0096]

[0097] In the formula, Δf is the frequency change of the system inertia center, that is, the frequency response, ΔP G and ΔP S are the power changes of the synchronous generator and the secondary frequency modulation control respectively, H and D are the inertia coefficient and the damping coefficient respectively, T R is the reheating time constant, F H is the specific coefficient of the high-pressure turbine, K m is the mechanical gain coefficient, R G is the droop coefficient of the generator; s represents the frequency domain parameter of the model.

[0098] (102) When 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 time delay τ is about 300ms. Therefore, the time delay unit is represented by a first-order Taylor series expansion 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 as a step response: Substituting into the frequency response model we can get:

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

[0102] (201) Synchronous generators, battery 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 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 does not exceed the first level of underfrequency load reductionu Therefore, the size of battery energy storage depends on the emergency load shedding scheme and takes the frequency threshold of the first stage of low frequency load shedding as the given boundary condition. According to the disturbance power ΔP L , the NLP model of emergency load shedding optimization can be expressed as:

[0103]

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

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

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

[0107]

[0108] where ΔP L,min represents the lower bound of ΔP L , and θ is the exponential parameter. The scale exponential parameter θ of the probability density function is calculated by maximum likelihood estimation as:

[0109]

[0110] n d is the number of empirical data, and 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. The capital cost, fixed operating cost, maintenance cost and disposal cost are combined by using the net present value method.

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

[0113]

[0114] where x B represents the number of energy storage battery deployments, C c , C f , C m , C dThe net present value of the capital cost, the fixed operation cost, the maintenance cost and the disposal cost of the energy storage battery, respectively, n c represents the lifetime, c d is the disposal cost of the energy storage battery, c f and c m are the annual fixed operation cost and the maintenance cost of the energy storage battery, respectively, and a and b are the interest rate and the tax rate, respectively. Therefore, the first objective function f v minimizing the investment is expressed as: min f v (x B ) = min C v .

[0115] (303) The second optimization objective is to maximize the operation profit of the battery storage. Considering the usage time, the operation profit of the battery storage is calculated as the difference between the discharging profit of the battery storage and the charging cost of the battery storage:

[0116]

[0117] wherein At c is the time step of the operation period, T c is the length of the operation period, N o is the total number of the operation periods, p r,t is the usage time at time t, h B,c is the charging efficiency, h B,d is the discharging efficiency; P B,c,t,I is the charging power of the energy storage battery at time t in the i-th operation period, P B,d,t,I is the discharging power of the energy storage battery at time t in the i-th operation period; therefore, the second objective function f p maximizing the operation profit is expressed as: max f p (P B,c,t,I , P B,d,t,I ) = max C p .

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

[0119] S' B，min ≤ S' B ≤ S' B，max

[0120] wherein S' B represents the energy storage capacity of the energy storage battery, S' B = x B S' B,r , wherein S' B,r is the rated power capacity of the energy storage battery, S' B，min is the minimum energy storage capacity, and S'B，max for maximum energy storage capacity.

[0121] 305) Physical and operational limits, 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] where E B,1,I is the energy of the battery energy storage at time t in the i-th operating cycle, E B,r is the rated energy capacity of the energy storage battery, R ini is the initial state-of-charge, R min is the minimum state-of-charge, P res,t,I is the power of the renewable energy source at time t in the i-th operating 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 constraints

[0131] The amount of emergency load shedding is calculated by the NLP model of (201), where the frequency deviation Af is calculated by the frequency response model (104). Therefore, the remaining power is compensated 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 Af. Considering the uncertainty of the disturbance, the probability constraint that the amount of emergency load shedding exceeds a predefined maximum value (i.e., the generator load shedding chance constraint, which is nonlinear) is:

[0132] Pr{ΔP e ≤α c}≥1-γ c

[0133] where Pr(.) is the probability of an event, α c is the preset emergency load shedding amount, γ c is the probability violation threshold, and 1-γ c is the confidence level.

[0134] In addition, the power and energy reserves of the battery energy storage for frequency regulation should be kept within a feasible range. On this basis, the frequency stability constraint of the 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] where ΔP B,req is the preset frequency regulation capability, and ΔE B,req is the preset energy reserve.

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

[0139] (401) The battery energy storage planning model established is a multi-objective MINLP problem with chance 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, there is a nonlinear relationship between the battery energy storage and the emergency load shedding amount ΔP e and the disturbance power ΔP L . Further, based on the step-by-step summation method, a hyper surface G s (.) can be generated and expressed as:

[0143] ΔP e =Gs (x B ,ΔP L )

[0144] (403)Using piecewise linearization method based on maximum affine function, the hyper-surface is conservatively approximated by Nm hyper-planes. For a series of points (x B,i1 ,ΔP L,i1 ,ΔP e,i1 ), the parameter space (x B,i1 ,ΔP L,i1 )∈C e can be divided into Nm subspaces. In each subspace, the approximated 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 ilth point in the jth subspace of hyper-planes, il = 1, 2, …, J, J represents the total number of points in the jth subspace, and these points are located on the hyper-surface, where α a,j , α b,j and β j are the coefficients that determine the jth hyper-plane. The maximum affine function G h (·) of Nm approximated functions can be expressed as:

[0147]

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

[0149]

[0150] where G m represents the overall linearized hyper-planes.

[0151] Substituting the maximum affine function G h (·) into the formula of step (404), a min-max structure is obtained, which is converted into the following min form by using auxiliary variable z h :

[0152]

[0153] Solving a by min form a,j , a b,j and β j ;

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

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

[0156] (405) Furthermore, Pr{G h (x B,i1, , ΔP L,i1 )≤ a c}≥ 1 - γ c is re-expressed in a deterrence-minimax form by Bernstein approximation. Based on the moment generating function Φ c (·), the above equation Pr{G h (x B,i1, , ΔP L,i1 )≤ a c}≥ 1 - γ c can be re-expressed as:

[0157]

[0158] Φ c (x) = ln[∫e xy dP c (y)]

[0159]

[0160] where v c is the decision variable, x, y are independent variables, Pc(·) is the probability distribution of the disturbance power ΔP L , σ c is a constant determined by the probability distribution Pc(·), and substituting into yields equation A:

[0161]

[0162] From the probability density function of step (301), the expectation μ L and variance of the disturbance power ΔP c are expressed as:

[0163]

[0164] The interference power ΔP L The expected μ c and variance are substituted into formula A, and the following is obtained:

[0165]

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

[0167] (501) Based on (401)-(405), the battery energy storage planning model is re-expressed as a mixed integer linear programming problem. In order to more effectively solve the mixed integer linear programming, a multi-cut Benders decomposition is adopted. The mixed integer linear programming (constraints in step (3) and constraints in step (4) and the single objective function) can be divided into a master problem M inv and two sub-problems S op and S fs .Specifically, the investment master problem M inv calculates the capacity of the battery energy storage. In the sub-problem S op , the output power of the battery energy storage is optimized. Whether the battery energy storage meets the opportunity constraint is checked by solving the frequency stability sub-problem S fs .

[0168] (502) The investment master problem M inv can be simply expressed as:

[0169]

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

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

[0172] where X inv,s and q op,s are the optimal solution of the master problem.

[0173] The subproblem S op is expressed as:

[0174]

[0175] where C op T Y op is minf0= min(f v - ω a f p ) in ω 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 are the coefficient matrix, A op,3 is the interaction matrix, b op,1 and b op,2 are the coefficient vectors; the first constraint is the coupling constraint of the master problem M inv and the subproblem S op , including the 1st, 2nd, 3rd, 5th constraints in (305) and the constraint in (307); the second constraint includes the 4th, 6th, 7th constraints in (305).

[0176] Based on the strong duality theorem, the feasibility of the subproblem S op is determined by its dual problem. If the dual problem is unbounded, the original problem S op is infeasible, and a Benders feasibility cut is added to the constraint set of S fea , 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 are the subproblem S op,f,1 and the dual problem of the master problem M T , respectively.op Dual form of the primal problem.

[0179] Otherwise, the primal problem S op is feasible. Add a Benders optimal cut to the set of constraints S opt and update the upper bound of the primal mixed integer linear programming B up , denoted 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 are the solution vectors of the dual form of the subproblem S op .

[0183] (505) Establish the frequency stability subproblem S fs in terms of the vector of slack variables α fs and compactly represent it as:

[0184]

[0185] where the first constraint is the relaxed coupling constraint of the master problem M inv and the subproblem S fs , containing the last determined constraint formula in (405), A fs is the coefficient matrix and b fs is the coefficient vector.

[0186] (506) Compute the slack variables α fs by solving the dual problem of the subproblem S fs . When α fs > 0, add a Benders feasibility cut to the set of constraints S fea , which can be denoted as:

[0187] λ fs T (b fs -A fs X inv,s )≤0

[0188] where λ fs is the solution vector of the dual subproblem of the subproblem S fs .

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

[0190] B up -B low ≤ε c

[0191] where ε c is a convergence tolerance.

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

Claims

1. A microgrid energy storage frequency stabilization method based on battery energy storage planning, characterized in that, Specifically comprising the following steps: Step 1: establishing a system frequency response model considering emergency load shedding and battery energy storage; Step 2: Minimize the amount of emergency load shedding For the purpose, based on the system frequency response model and the frequency threshold of the first level of low frequency load shedding As a boundary condition, an NLP model of emergency load shedding optimization is established; Step 3: Establishing a multi-objective MINLP model based on the NLP model, specifically: taking the minimization of the investment cost of battery energy storage as the first optimization objective taking the maximization of the operating profit of battery energy storage as the second optimization objective and introducing the energy storage capacity constraint of energy storage battery, the energy storage output power and state of charge constraint of energy storage battery, the load shedding opportunity constraint of generator and the frequency stability constraint; Step 4: converting the multi-objective function in the multi-objective MINLP model in step 3 into a single-objective function by using a linear weighting method, converting the nonlinear generator load shedding opportunity constraint in step 3 into a linear opportunity constraint, and then converting the linear opportunity constraint into a deterministic constraint; Step 5: taking the single-objective function in step 4, the deterministic constraint, and the battery energy storage capacity constraint, the battery energy storage output power and state of charge constraint, and the frequency stability constraint in step 3 as a battery energy storage planning model, expressing the battery energy storage planning model as a mixed integer linear programming problem, and solving the problem through a Benders decomposition algorithm to obtain an optimal planning strategy of the energy storage battery; The expression of the system frequency response model in step 1 is: ； where s represents a frequency domain parameter of the model, time delay for emergency load shedding, active power disturbance amount, H and D are inertia coefficient and damping coefficient, respectively; mechanical gain coefficient, droop coefficient of the generator, reheat time constant, ratio coefficient of the high-pressure turbine, T B time constant of the energy storage battery, , first synchronous generator capacity, reference capacity of the power system, R B droop coefficient of the energy storage battery.

2. The method of claim 1, wherein, The expression of the NLP model in step 2 is: ； wherein, represents the frequency minimum point, is a safety margin coefficient, is the system rated frequency, is the maximum instantaneous frequency deviation, is the system frequency response quantity.

3. The method of claim 1, wherein, The first optimization objective in step 3 The expression is: ； wherein, represents the number of energy storage battery deployments, wherein the expression for is: ； wherein, , , , are the net present values of the capital cost, fixed operating cost, maintenance cost and disposal cost of the energy storage battery, respectively, , , , respectively. ； wherein, represents the lifetime, is the disposal cost of the energy storage battery, and are the fixed operation cost and maintenance cost of the energy storage battery per year, respectively, and α and β are the interest rate and tax rate, respectively. A second optimization goal The expression for this is: ； In the formula, is the charging power of the energy storage battery at time t in the first operating cycle, is the discharging power of the energy storage battery at time t in the first operating cycle, is the discharging power of the energy storage battery at time t in the first operating cycle, The expression of is: ； wherein, is the time step of the running cycle, is the length of the running cycle, is the total number of running cycles, is the usage time at time t, is the charging efficiency, is the discharging efficiency; The energy storage capacity constraint of the energy storage battery is: ； wherein, represents the energy storage capacity of the energy storage battery, wherein is the rated power capacity of the energy storage battery, is the minimum energy storage capacity, is the maximum energy storage capacity; The energy storage output power and state of charge constraint of the energy storage battery is: ； wherein, is the energy stored in the battery at time t for the i-th cycle, is the rated energy capacity of the energy storage battery, is the initial state of charge, is the minimum state of charge, is the power of the renewable energy source at time t for the i-th cycle, is the power of the local load at time t for the i-th cycle. The generator load shedding opportunity constraint is: ； where Pr(.) is the probability of an event, is a preset emergency load shedding amount, is a probability violation threshold, calculated by the NLP model; The frequency stability constraint is: ； wherein, is a preset frequency adjustment capability, is a preset energy reserve.

4. The method of claim 1, wherein, The single-objective function in step 4 The expression is: ； wherein are weight coefficients.

5. The method of claim 1, wherein, The conversion of the opportunity constraint into the deterministic constraint in step 4 is specifically: Step 4.1: According to the system frequency response model and NLP model, there is a nonlinear relationship between the energy storage battery and the emergency load shedding load shedding amount and the disturbance power , a hyper-surface is generated by using the step-by-step summation method : ； wherein, represents the number of energy storage battery deployments; Step 4.2: Piecewise linearization method based on maximum affine function, using hyperplanes to divide the parameter space of hypersurfaces into Nmsubspaces, the approximation function of each subspace The expression is: ； where j = 1, 2,..., Nm; represents the jth point in the jth subspace in the hyperplane, J represents the total number of points in the jth subspace, and the points are located on the hyper-surface, , is a set of points in the hyper-surface, , and are coefficients of the jth subspace, and are solved by the following formula , and :​ ； wherein , represents the linearized hyperplane of the whole; Step 4.3: Using auxiliary variables The equations , and are transformed into min-structures, so that , and the non-linear generator underload opportunity constraints are transformed into linear opportunity constraints represented by max-radiation functions, which are then converted into deterministic form using Bernstein approximation: ； wherein, represents a constant determined by the probability distribution of the disturbance power , is a preset emergency load shedding amount, is a violation threshold of the probability that the emergency load shedding amount exceeds the preset maximum value.

6. The method of claim 1, wherein, The step 5 is specifically: adopting Benders decomposition to divide the constraint condition and the single objective function into a main problem and two sub-problems and ; Iterative calculation of the Benders decomposition is performed until a preset termination condition is met, and an optimal planning strategy of the energy storage battery is obtained.

7. The battery energy storage planning based microgrid energy storage frequency stabilization method of claim 6, wherein, Main problem The expression for the main problem is: ； wherein is a coefficient vector, , denotes the number of energy storage battery deployments, is an auxiliary variable, is a coefficient matrix, is a coefficient vector, is the Benders optimal set, is the Benders feasibility set; T denotes the transpose; Sub-problems The expression for the sub-problem is: ； where C op is a coefficient matrix, is a decision vector, is the power of the renewable energy at time t in the i-th operation cycle, is the power of the local load at time t in the i-th operation cycle, and is a coefficient matrix, is a cooperation matrix, and are both coefficient vectors; is the optimal solution of the main problem; Sub-problems The expression for the sub-problem is: ； wherein, is a slack variable, is a coefficient matrix, is a coefficient vector.

8. The battery energy storage planning based microgrid energy storage frequency stabilization method of claim 7, wherein, In the solving process, the lower bound of the optimization problem is based on the main problem The expression is: ； wherein and are the optimal solution of the main problem; If the subproblem is unbounded, i.e. the subproblem is infeasible, a Benders feasibility cut is added in : ； wherein and are the solution vectors of the dual form of the subproblem ; If the subproblem is feasible, then add a Benders optimal cut in and update the upper bound of the original mixed integer linear program : ； The relaxation variables are computed by solving the dual problem of the subproblem The relaxation variables are computed by solving the dual problem of the subproblem and adding a Benders feasibility cut to the constraint set and adding a Benders feasibility cut to the constraint set ； wherein is the solution vector of the dual subproblem of the subproblem .

9. The battery energy storage planning based microgrid energy storage frequency stabilization method of claim 8, wherein, The expression of the preset termination condition is: ； wherein is the convergence tolerance.

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