CN107453407B - Intelligent micro-grid distributed energy scheduling method - Google Patents

Abstract

The invention provides an intelligent micro-grid distributed energy scheduling method, which comprises the steps of firstly analyzing an intelligent micro-grid distributed energy scheduling system and establishing a corresponding system model; then, analyzing the established system model, and deducing corresponding constraint conditions and a target function; according to the objective function and the constraint condition, carrying out cost optimization by scaling and using a Lyapunov framework and establishing long-time average constraint; carrying out distributed algorithm research on the target function; and finally, establishing an ADMM algorithm framework, and calculating to obtain the optimal solution of the distributed algorithm. The invention aims at optimizing the output cost of power energy scheduling to carry out real-time distributed scheduling, gradually optimizes along with the increase of storage capacity and the loosening of slope constraint of the traditional generator, can independently optimize each large cogeneration and aggregator, has fast convergence speed in distributed realization, and can realize nearly optimal performance in a wide storage capacity range.

Description

Intelligent micro-grid distributed energy scheduling method

Technical Field

The invention relates to a real-time distributed scheduling algorithm aiming at optimizing the output cost of power energy scheduling, and belongs to the technical field of intelligent micro-grid distributed energy scheduling.

Background

Energy is the foundation on which development and production can be realized in the world at present, and electric power resources are the most convenient and clean energy development form and are the important supporting points for developing economy in the current country. As environmental problems increase, more and more renewable energy sources, such as wind energy, solar energy, etc., are incorporated into the power grid. For example, the goal of the european union committee is: 20% of renewable energy is brought into the energy interests of the european union by the year 2020, and california plans to achieve 33% of the retail amount of renewable energy by the year 2020.

Renewable energy sources are often intermittent, have limited scheduling capabilities, and thus, their large-scale integration may upset the supply-demand balance, affecting the reliability of the system. Under such circumstances, many countries in the world are oriented to coherent technical categories such as distributed power generation using various renewable energy sources. An important feature of distributed power generation technology is that: flexibility: is economical and environment-friendly.

In terms of technology and feasibility of large cogeneration, it is required to meet large heat or cold demand, and it is required that the local demand for heat must be large enough to evaluate the scale of large cogeneration, and that the heat load is constant every season, so that it is ensured that the large cogeneration system can operate at full load most of the time. Efficiency must be reduced if operating at low load. Yet another requirement is that: the large-scale cogeneration needs to be consistent with the characteristics of heat load, and the fuel needs to have easy availability, mainly considering the uninterrupted supply characteristics of the fuel. Some countries in europe and some countries in north america are now widely used in large cogeneration systems for natural gas, and therefore the technology is relatively practicable and reliable. In the aspect of application, large-scale cogeneration needs to have a relatively proper price and be connected with a power grid, and the premise is that a supply position with a heat load demand has the power grid, so that the proper and expected prices of prepared power and supplemented insufficient power can be obtained, the flexibility of the large-scale cogeneration can be increased to a certain extent, excessive redundant power can be sold, the economic source can be increased, and the economy of the large-scale cogeneration can be improved.

The large-scale integration of cogeneration may cause unstable energy output and directly affect the reliability of the grid. In studying the power balance problem, the following problems are included: (1) supply management; (2) managing the demand; (3) battery storage management; (4) a random problem; (5) slope constraint; (6) a real-time algorithm; (7) a distributed algorithm. Considering a general power grid provided by a conventional generator and a plurality of large cogeneration systems, each large cogeneration system is connected to one heat storage tank and to an external power market. The aggregator operates the grid to ensure operation of the grid by coordinating the supply units, demand units and thermal storage tanks to maintain a power balance between supply and demand. Considering the problems of power balance, storage and flexible load of a common combined heat and power generation comprehensive power grid, how to reduce the long-term system cost as much as possible, get rid of the limitation on operation and improve the service quality of inflammable loads is a difficult problem which is solved by the technical personnel in the field.

Disclosure of Invention

The invention aims to solve the technical problems of power balance, storage and flexible load of a common combined heat and power generation comprehensive power grid, reduce the long-term system cost as much as possible when performing real-time distributed scheduling, loosen the limitation of the slope constraint requirement of the traditional generator and enable each large combined heat and power generation system and a aggregator to be independently optimized and controlled.

In order to solve the technical problem, the technical scheme of the invention is to provide an intelligent micro-grid distributed energy scheduling method, which is characterized by comprising the following 5 steps:

step 1: analyzing the intelligent micro-grid distributed energy scheduling system, and establishing a corresponding system model;

step 2: analyzing the established system model, and deducing corresponding constraint conditions and a target function;

and step 3: according to the objective function and the constraint condition, carrying out cost optimization by scaling and using a Lyapunov framework and establishing long-time average constraint;

and 4, step 4: carrying out distributed algorithm research on the target function;

and 5: and establishing an ADMM alternative direction multiplier algorithm framework, and calculating to obtain the optimal solution of the distributed algorithm.

Preferably, in step 1, the system model includes: the system comprises a traditional generator CG, a aggregator, a flexible load, a base load, a heat load, an external energy market and a plurality of cogeneration CHPs, wherein the aggregator is connected with the traditional generator, the flexible load, the base load, the external energy market and the plurality of cogeneration, the cogeneration is connected with an external natural gas supply and the heat load, and each cogeneration corresponds to a heat storage tank.

Preferably, in step 2, a power grid is considered to be composed of CG and N CHPs, N being a positive integer, each CHP being connected to an on-site heat storage tank, the power grid being connected to an external energy market and operated by an aggregator responsible for satisfying loads by managing energy from various sources; suppose the system operates in discrete time with time slots t e {0, 1, 2. }; for symbol simplicity, energy units are used instead of power units;

(1) loading: loads include foundation, compliance and thermal loads; the base load represents the base energy demand, which must be met once requested; the flexible load represents a controllable energy requirement which can be partially reduced when cost conditions are considered; at time slot t, by l_b，t∈[l_b，min，l_b，max]Represents the total amount of the base load of the request, and passes l_f，t∈[l_f，min，l_f，max]Representing the total amount of requested flexible load,/_b，min、l_b，maxRespectively representing the minimum and maximum values of the total amount of base load requested during a time slot t, l_f，min，l_f，maxRespectively representing the minimum value and the maximum value of the total amount of the flexible load requested during the time slot t; total amount l_b，tAnd l_f，tGenerated by the user based on his own needs and considered random; let the total amount of load satisfied during a time slot t be l_m，tWhich should satisfy

l_b，t≤l_m，t≤l_b，t+l_f，t(1)

The control of the flexible load needs to meet specific quality of service requirements; imposing an upper bound on the portion of the compliance load that is not satisfied, introducing a long-term time-averaged constraint

Where α E0, 1 is a preset threshold with a specific value indicating a strict quality of service requirement, where E indicates the desirability of the content within.

By a_w，tRepresenting the total amount of thermal load requested during time slot t, which should satisfy, due to the design and hardware constraints of the thermal storage tank:

l_h，min≤l_w，t≤l_h，max(3)

wherein l_h，minAnd l_h，maxMinimum and maximum values representing the total amount of thermal load requested, respectively;

(2) CHP and field heat storage tank: at the ith CHP, i is 1, 2, … …, N, during time slot t, by a_i，t∈[0，a_i，max]Represents a large cogeneration power generation amount, wherein a_i，maxIs the maximum energy produced; due to the stochastic nature of large cogeneration, a_i，tIs random;

the present invention assumes that each CHP corresponds to one on-site thermal storage tank unit that can be charged and discharged; during time slot t, with x representing the charge_i，t> 0 denotes the charging energy x of the ith battery_i，tBy x representing discharge_i，t< 0 indicates the discharge energy x of the ith cell_i，t(ii) a Due to battery design and hardware constraints, x_i，tThe values of (c) are bounded as follows:

x_i，min≤x_i，t≤x_i，max，(x_i，min＜0＜x_i，max) (4)

here, | x_i，minI and x_i，maxMaximum values representing total amounts of discharge and charge, respectively; for the ith cell, use s_i，tRepresents the energy state at the beginning of time slot t; due to charge-discharge operation, s_i，tThe equation of (c) can be given by:

s_i，t+1＝s_i，t+x_i，t(5)

furthermore, due to battery capacity and operating constraints, the energy state s is made_i，tThe upper and lower bounds of (A) are as follows:

s_i，mmin≤s_i，t≤s_i，max(6)

s_i，minrepresenting the minimum state of energy, s, allowed for the battery_i，maxRepresents the maximum energy state value allowed and may be used to indicate battery storage capacity; to simulate the cost of the battery, D was used_iTo express the charge or discharge quantity x_i，tAn associated degradation cost function;

during each timeslot, the CHP provides energy to the aggregator; by b_i，tTo represent the total amount of energy contributed by the ith CHP during time slot t; since the energy flow with respect to CHP should be balanced, there are:

b_i，t＝a_i，t-x_i，t，b_i，t＞0 (7)

in particular, if x_i，t> 0, the energy b contributed_i，tDirectly from large cogeneration; if x_i，t< 0, then b_i，tFrom large cogeneration power generation and batteries;

(3) CG: unlike CHP, the energy output of CG is controllable; by g_tRepresenting the energy output of the CG during time slot t, which satisfies:

0≤g_t≤g_max(8)

g_maxrepresents the maximum value of the energy output; due to the operating limitations of the CG, the change in output at two consecutive time slots is bounded, which typically reflects a ramp constraint on the CG output; assuming that the ramp-up and ramp-down constraints are the same, the overall ramp constraint is expressed as:

|g_t-g_t-1|≤rg_max(9) wherein the coefficient r ∈ [0, 1]]Representing the required tightness of the slope; for r-0, CG produces a fixed output over time, while for r-1, the slope requirement becomes invalid; further, the power generation cost function of CG is represented by C (·);

(4) external energy market: in addition to internal energy resources, the aggregator can resort to external energy markets as needed; in the case of energy shortage, the aggregator can buy energy from an external energy market, or sell energy to the market in the case of energy surplus; each using p_b，t∈[p_b，min，p_b，max]And p_s，t∈[p_s，min，p_s，max]Representing the unit price, p, for buying and selling energy to the external energy market at time slot t_w，t∈[p_w，min，p_w，max]Representing the unit price, p, of energy purchased from the external natural gas at time slot t_b，min、p_b，maxRespectively representing the minimum and maximum value of the unit price of energy purchased to the external energy market at time slot t, p_s，min、p_s，maxRespectively representing the minimum and maximum value of the unit price of energy sold to the external energy market at time slot t, p_w，min、p_w，maxMinimum and maximum values representing unit prices for purchasing energy from external natural gas at time slot t, respectively; to avoid energy arbitrage, assume that the purchase price is strictly greater than the sale price, i.e. p_b，t＞p_s，t(ii) a Price p due to unexpected market behavior_b，tAnd p_s，tAnd p_w，tIs random; respectively using e_b，tAnd e_s，tRepresents the total amount of energy purchased and sold by the external energy market during time slot t, wherein:

e_b，t≥0，e_s，t≥0 (10)

the balance requirements of the overall system are as follows:

e_w，trepresenting the total amount of energy supplied by the external natural gas during time slot t, the overall system meets the thermal load supply requirements as follows:

wherein the coefficient η_w∈[0，1]Indicating the extent to which CHP supply is required, for η_wCHP produces a fixed output to the polymerizer over time, 0, and for η_wThe CHP output to the polymerizer requirement becomes invalid at 1.

Preferably, in the step 3, a control action at a time slot t is defined:

wherein

The cost of the overall system at time slot t, including the cost of all CHPs and CGs and the cost of utilizing the external energy market, is given by:

based on the system model described previously, the problem of power balancing is formulated as a stochastic optimization problem

P1：

Wherein the expectation in the target and equation (2) depend on the randomness of the system state

And possible randomness of control actions, wherein

To keep the mathematical statements simple, cost functions C (-) and D are assumed_i(. is) a continuously differentiable convex function, using C ' (. and D ' respectively '_i(. represents C (-)And D_iDerivative of (g), on the assumption that the derivative C' (g) can be obtained_t)∈[C′_min，C′_max]，

And derivative D'_i(x_i，t)∈[D′_i，min，D′_i，max]，

In order to provide a real-time algorithm, a Lyapunov optimization method is adopted; the following problems are posed:

P2：

compared with P1, the energy state constraint formula (5) and formula (6) in P2 are replaced by a new time-averaged constraint formula (13), and the ramp constraint formula (9) is removed;

scaling certification process of P1 to P2:

with the energy state update in equation (5), the left side of resulting constraint equation (13) equals:

in the formula (14), if s_i，tAlways bounded, keeping constraint equation (6), then the right of equation (14) is equal to 0 and constraint equation (13) is also satisfied; thus, P2 is a scaling for the P1 problem;

the steps enable the invention to work under a standard Lyapunov optimization framework;

to satisfy constraint equation (2), a virtual queue backlog J is introduced_tThe evolution is as follows:

in equation (15), the virtual queue J_tAccumulate the portion of the compliant load that is not met, hold J_tIs equivalent to satisfy the constraint equation (2) by_tInitialized to J₀＝0；

At time slot t, a vector is defined

This vector is backlogged by the energy states of all thermal storage tank units and the virtual queue J_tComposition is carried out; by using theta_tDefining a Lyapunov function:

β therein_iIs a perturbation parameter designed to ensure the bounding of the energy states, i.e. a constraint (6); in addition to this, the present invention is,

defining the single-slot condition lyapunov offset as:

consider that

The offset given adds a cost function, instead of directly minimizing the system cost target, it is Δ (Θ)_t) And a weighted sum of the system cost at time slot t, where V is used as a weight;

in the algorithm design, an upper bound of an offset plus cost function is considered firstly, and then a real-time optimization problem is formulated so as to minimize the upper bound of the function under each time slot t; therefore, at each time slot t, there is the following optimization problem:

P3：

s.t.(1)，(4)，(7)-(11)

the design of the real-time problem P3 may yield some analytical performance guarantees; in addition, to ensure g_tThe step of obtaining P2 is taken and the ramp constraint equation (9) is moved back to P3;

due to C (-) and D_i(. h) is a convex function, P3 is a convex function optimization problem, which can be effectively solved by a standard convex optimization software package; the optimal solution for P3 at time slot t is represented as

At each time slot t, obtaining

Then, s is updated according to their evolution equation_i，t，

And J_t；

In the following proposition, it is demonstrated that despite relaxation to P2, by properly designing perturbation parameters β_iThe bounding of the energy states, and thus the control actions, can be ensured

Feasibility for P1;

proposition 1 for the ith battery cell, perturbation parameter β_iThe method comprises the following steps:

wherein V is (0, V)_max]，

Then, the control action derived by solving P3 at each time t

Is feasible for P1;

now analyze the solution provided by algorithm 1 with respect to P1; in algorithm 1, w is used to emphasize the dependency of the cost target value on the ramp coefficient r and the control parameter V^*(r, V) represents the cost target value achieved; from w^opt(r) represents the minimum cost target value of P1, which depends only on r, the main results are summarized in the following scheme;

theorem 1: assuming a random system state q of the grid_tAre independently and simultaneously distributed and are time-lapse; under algorithm 1, there are the following:

1)w^*(r，V)-w^opt(r)≤(1-r)g_maxmax{p_b，max，C′_max}+B/V

where B is a constant defined as:

2)w^opt(r)≥w^*(1，V)-B/V

assume battery capacity s_i，maxIs fixed, so to ensure the feasibility of the solution, the control parameter V should be such that

(21) Middle V_maxTo an upper bound, additionally, if the battery capacity can be designed, the question is what its value should be in order to achieve some desired performance; in the proposition below, by giving can be greater than V_maxOf any positive V energy state s_i，tI.e. the upper bound of the minimum required energy capacity, provides an answer to this question;

proposition 2: for any V > 0, the energy state s of the ith cell at time slot t_i，tBased on an algorithm₁Satisfies s_i，t∈[s_i，min，s_i，up]Wherein:

in the above formula with respect to s_i，upCan provide useful information and can reveal some beliefs about the dependence of the design of battery capacity on certain system parameters; first, s_i，upLinearly increases with the control parameter V; second, if the energy price is more subject to fluctuations or the marginal cost of degradation increases rapidly, s_i，upIs larger; finally, if there is p_b，max＝p_s，minAnd D'_i，max＝D′_i，minThen s_i，upIs given by x_i，max-x_i，min+s_i，minIt is given.

Other attributes regarding flexible loads and external transactions are summarized in the following propositions;

proposition 3: based on algorithm 1, the following holds:

(1) queue backlog J_tLimited uniformly from above to J_t≤Vp_b，maxl_f，max+1

(2) External transaction amount

And

satisfy the requirement of

In the current system model, one CG is incorporated to the supply side in addition to the CHP; if there are multiple CGs with the same characteristics, i.e. the same maximum output g_maxThe ramp coefficient r and the cost function C (-) which, for mathematical analysis, are combined into one generator; in this case, the current mathematical framework and performance analysis is applied directly to the combined generator, and then the output of each individual CG is obtained by distributing the output of the combined generator evenly over all the individual generators; on the other hand, if these CGs have heterogeneous characteristics, and thus cannot be combined into one,the proposed algorithm can still be used; in particular, in the original problem P1, for each individual generator, the total output of the generators in equations (8) and (9), (11) with the constraints is

And the total cost of the generator is

The resulting relaxation problem P2 will be similar to the current problem, with the ramp constraint removed for each individual CG (9); for real-time algorithms, the formulation of the optimization problem per time slot follows the current mathematical framework, and furthermore, the same approach proposed by the present invention can be used to develop distributed implementations of the algorithm.

Preferably, in step 4, for the convenience of algorithm development, first P3 is converted into an equivalent problem, and for the sake of symbolic simplicity, the time index t is discarded; defining a new optimization vector

By making y_i＝(1+η_w)x_iTo the optimization variables involved in P3, where 1 ≦ i ≦ N, y_N+1＝l_m，y_N+2＝-g，y_N+3＝-e_b，y_N+4＝e_s，y_N+5＝l_w，y_N+6＝-e_wThe target of P3 can be rewritten as each y_iOf a particular function of (A), which is represented by F_i(y_i) Represents; further, based on the constraint condition formula (7), b is set in the constraint of P3_iIs replaced by

Where 1 ≦ i ≦ N, therefore, P3 may be rewritten in the general form P4:

P4：

wherein, constraint set { gamma_iDerived from constraint equations (1), (4) and (7) - (12),

next, an auxiliary vector z is introduced as a copy of y, and further P4 is transformed into the equivalent problem:

P5：

s.t.y-z＝0 (18)

where 1 (-) is an indicator function, 0 if the event indicated is true, and infinity otherwise.

Preferably, in step 5, the equation in P5 is constrained (18) to bivariate following the general ADMM method

Is associated with and will

And

expressed as the respective variable values at the k-th iteration, these values will then be updated according to ADMM as follows:

where ρ > 0 is a penalty factor, ρ is adjusted to achieve good convergence performance.

The method provided by the invention overcomes the defects of the prior art, performs real-time distributed scheduling aiming at optimal output cost of power energy scheduling, gradually optimizes along with the increase of storage capacity and the loosening of slope constraint of the traditional generator, can independently optimize each large-scale cogeneration and aggregator, has fast convergence speed in distributed realization, and can realize nearly optimal performance in a wide storage capacity range.

Drawings

FIG. 1 is a schematic diagram of a system model for distributed energy scheduling of an intelligent micro-grid;

FIG. 2 is a graph of the average time system cost versus the average time system cost for various algorithms at various values of the control parameter V;

fig. 3 is a system cost versus system cost (in the case of a large load) for various algorithms at a ramp coefficient r.

Detailed Description

The invention will be further illustrated with reference to the following specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.

In order to reduce the long-term system cost as much as possible, the invention firstly provides a real-time centralized power balance solution, simultaneously considers the uncertainty, the load and the energy price of large-scale cogeneration, and provides a distributed implementation algorithm based on a Lyapunov optimization framework, and the algorithm can reduce the calculation complexity by controlling the charging and discharging amount of the battery to schedule the energy. The distributed algorithm provided by the invention is asymptotically optimized along with the increase of the storage capacity, the slope constraint requirement of the traditional generator is loosened, and the constraint condition requirement is not so tight. In addition, the distributed implementation has fast convergence speed and fast trend towards stable values, and each large cogeneration system and aggregator can be independently and optimally controlled, and near-optimal performance can be achieved in a wide range of storage capacity.

According to the intelligent micro-grid distributed energy scheduling method, the intelligent micro-grid distributed energy scheduling system is analyzed, and a corresponding system model is established; then, analyzing the established system model to deduce corresponding constraint conditions and a target function; then, a Lyapunov framework is used in a scaling mode according to the objective function and the constraint condition, and long-time average constraint is established so as to carry out cost optimization; then carrying out distributed algorithm research on the target function deduced in the previous step; and finally, establishing an ADMM algorithm framework so as to facilitate MATLAB simulation.

The invention provides a method for performing real-time distributed scheduling aiming at optimizing the output cost of power energy scheduling, which specifically comprises the following steps:

the method comprises the steps of firstly, analyzing an intelligent micro-grid distributed energy scheduling system, and establishing a corresponding system model.

As shown in fig. 1, the system model established by the present invention is a model with a conventional generator, an aggregator, flexible loads, base loads, thermal loads, external energy market, and multiple cogeneration CHPs and their respective heat storage tanks.

The definition of the corresponding primary symbols in the established system model is shown in the following table.

And secondly, analyzing the established system model to deduce corresponding constraint conditions and a target function.

The invention considers that a power grid is composed of a CG (traditional generator) and N CHPs (combined heat and power), wherein N is a positive integer. Each CHP is connected to one on-site thermal storage tank unit. The grid is connected to an external energy market and operated by an aggregator, which is responsible for meeting the load by managing energy from various sources. Suppose the system operates in discrete time with time slots t e {0, 1, 2. For symbol simplicity, in the present invention, the present invention uses units of energy rather than units of power.

(1) Loading: the loads include foundation, compliance and thermal loads. The base load represents the base energy demand, such as lighting, that must be met upon request. The flexible load here means some controllable energy demand, which can be partly reduced if the energy supply costs are high. At time slot t, by l_b，t∈[l_b，min，l_b，max]Represents the total amount of the base load of the request, and passes l_f，t∈[l_f，min，l_f，max]Representing the total amount of requested flexible load,/_b，min、l_b，maxRespectively representing the minimum and maximum values of the total amount of base load requested during a time slot t, l_f，min，l_f，maxRespectively representing the minimum and maximum values of the total amount of flex load requested during the time slot t. Total amount l_b，tAnd l_f，tGenerated by the user based on his own needs and considered random. Let the total amount of load satisfied during a time slot t be l_m，tWhich should satisfy

l_b，t≤l_m，t≤l_b，t+l_f，t(1)

The control of the flexible load needs to meet specific quality of service requirements. In the present invention, an upper bound is imposed on the portion of the flexural load that is not satisfied. In general, the present invention introduces a long-term time-averaging constraint

Where α ∈ [0, 1] is a preset threshold with a small value indicating a strict quality of service requirement, where E [ ] indicates a desire for the content within [ ].

By a_w，tRepresenting the total amount of heat load requested during time slot t, due to the provision of the heat storage tankAnd hardware constraints, which should satisfy:

l_h，min≤l_w，t≤l_h，max(3)

wherein l_h，minAnd l_h，maxRepresenting the minimum and maximum requested heat load totals, respectively.

(2) CHP and field heat storage tank: at the ith CHP, i is 1, 2, … …, N, during time slot t, by a_i，t∈[0，a_i，max]Represents a large cogeneration power generation amount, wherein a_i，maxIs the maximum energy produced. Due to the stochastic nature of large cogeneration, a_i，tIs random.

The present invention assumes that each CHP corresponds to an on-site thermal storage tank unit that can be charged and discharged. During time slot t, with x representing charging (and correspondingly discharging)_i，t> 0 (corresponding, x)_i，t<0) Representing the charging (corresponding, discharging) energy x of the ith cell_i，t. Due to battery design and hardware constraints, x_i，tThe values of (c) are bounded as follows:

x_i，min≤x_i，t≤x_i，max，(x_i，min＜0＜x_i，max) (4)

here, | x_i，minI and x_i，maxRepresenting the maximum values of the total amount of discharge and charge, respectively. For the ith cell, use s_i，tRepresenting the energy state at the beginning of time slot t. Due to charge-discharge operation, s_i，tThe equation of (c) can be given by:

s_i，t+1＝s_i，t+x_i，t(5)

furthermore, due to battery capacity and operating constraints, the energy state s is made_i，tThe upper and lower bounds of (A) are as follows:

s_i，min≤s_i，t≤s_i，max(6)

here, s_i，minRepresenting the minimum state of energy, s, allowed for the battery_i，maxRepresents the maximum energy state value allowed and may be used to indicate battery storage capacity. As is well known, quick charging orThe discharge may cause degradation of the battery, which may shorten the life of the battery. To simulate the cost of a battery, the invention uses D_iTo express the charge or discharge quantity x_i，tAn associated degradation cost function.

During each time slot, the CHP provides energy to the aggregator. For the invention b_i，tTo indicate the total amount of energy contributed by the ith CHP during time slot t. Since the energy flow with respect to CHP should be balanced, the present invention has:

b_i，t＝a_i，t-x_i，t，b_i，t＞0 (7)

in particular, if x_i，t> 0 (charging), the energy b contributed_i，tDirectly from large cogeneration; if x_i，t< 0 (discharge), b_i，tFrom large cogeneration power generation and batteries.

(3) CG: unlike CHP, the energy output of the CG is controllable. By g_tRepresenting the energy output of the CG during time slot t, which satisfies:

0≤g_t≤g_max(8)

here g_maxRepresenting the maximum value of the energy output. Due to the operating limitations of the CG, the change in output at two consecutive time slots is bounded. This typically reflects a ramp constraint on the CG output. Assuming that the ramp-up and ramp-down constraints are the same, the present invention represents the entire ramp constraint as:

|g_t-g_t-1|≤rg_max(9) wherein the coefficient r ∈ [0, 1]]Indicating the tightness required for the ramp. In particular, for r-0, CG produces a fixed output over time, while for r-1, the slope requirement becomes invalid. In addition, the present invention represents the cost function of power generation by CG by C (·).

(4) External energy market: in addition to internal energy resources, the aggregator can resort to external energy markets as needed. For example, the aggregator may purchase energy from an external energy market in the event of an energy deficit, or sell energy to the market in the event of an energy surplus. Each using p_b，t∈[p_b，min，p_b，max]And p_s，t∈[p_s，min，p_s，max]Representing the unit price, p, for buying and selling energy to the external energy market at time slot t_w，t∈[p_w，min，p_w，max]Representing the unit price, p, of energy purchased from the external natural gas at time slot t_b，min、p_b，maxRespectively representing the minimum and maximum value of the unit price of energy purchased to the external energy market at time slot t, p_s，min、p_s，maxRespectively representing the minimum and maximum value of the unit price of energy sold to the external energy market at time slot t, p_w，min、p_w，maxRespectively representing the minimum and maximum values of the unit price of energy purchased from the external natural gas at time slot t. To avoid energy arbitrage, assume that the purchase price is strictly greater than the sale price, i.e. p_b，t＞p_s，t. Price p due to unexpected market behavior_b，tAnd p_s，tAnd p_w，tUsually random. Respectively using e_b，tAnd e_s，tRepresents the total amount of energy purchased and sold by the external energy market during time slot t, wherein:

e_b，t≥0，e_s，t≥0 (10)

the balance requirements of the overall system are as follows:

e_w，trepresenting the total amount of energy supplied by the external natural gas during time slot t, the overall system meets the thermal load supply requirements as follows:

wherein the coefficient η_w∈[0，1]Indicating the extent to which CHP supply is required, particularly for η_wCHP produces a fixed output to the polymerizer over time, whereas for η_wThe CHP output to the polymerizer requirement becomes invalid at 1.

And thirdly, according to the objective function and the constraint conditions, carrying out cost optimization by using the Lyapunov framework in a scaling mode and establishing long-time average constraint.

The invention defines the control action at time slot t:

wherein

The cost of the overall system at time slot t, including the cost of all CHPs and CGs and the cost of utilizing the external energy market, is given by:

based on the system model described previously, the present invention makes the problem of power balancing a stochastic optimization problem

P1：

Wherein the expectation in the target and equation (2) depend on the randomness of the system state

And possible randomness of control actions, wherein

To keep the mathematical statements simple, the present invention assumes cost functions C (-) and D_i(. cndot.) is a continuously differentiable convex function, and this assumption is reasonable because many practical costs can be well approximated by such a function. From C ' (. cndot.) and D ' respectively '_i(. cndot.) represents C (. cndot.) and D_iThe derivative of (c) of the derivative of (c),based on this assumption, the present invention can obtain the derivative C' (g)_t)∈[C′_min，C′_max]，

And derivative D'_i(x_i，t)∈[D′_i，min，D′_i，max]，

In order to provide a real-time algorithm, the invention adopts a Lyapunov optimization method. Lyapunov optimization can be used to convert some long-term time-averaged constraints, such as equation (2), into queue stability constraints and provide efficient real-time algorithms for complex dynamic systems. However, the time coupling constraints equation (6) and equation (9) are not time averaging constraints but are hard constraints required at each slot, and therefore, the lyapunov optimization framework cannot be directly applied. In order to solve such a problem, the present invention proposes the following problems:

P2：

compared to P1, the energy state constraint equations (5) and (6) in P2 are replaced by a new time-averaged constraint equation (13), and the ramp constraint equation (9) is removed.

Scaling certification process of P1 to P2:

with the energy state update in equation (5), the present invention can obtain the constraint equation (13) with the left side equal to:

in the formula (14), if s_i，tAlways bounded, keeping constraint equation (6), then the right side of equation (14) is equal to0 and the constraint equation (13) is also satisfied. Thus, P2 is a scaling for the P1 problem.

The above steps are critical to enable the present invention to work under the standard lyapunov optimization framework, however, the present invention emphasizes that solving P2 is not an objective of the present invention. In contrast, the significance of P2 is presented to facilitate the design of real-time algorithms and performance analysis for P1. It is noted that the solution to P2 may not be feasible for P1, and for this reason, the present invention next provides a real-time algorithm that ensures that all constraints of P1 are satisfied.

In order to satisfy the constraint formula (2), the invention introduces a virtual queue backlog J_tThe evolution is as follows:

in equation (15), the virtual queue J_tThe portion of the unsatisfied compliant load is accumulated, and it can be seen that J is maintained_tIs equivalent to satisfy the constraint equation (2), the present invention puts J on_tInitialized to J₀＝0。

At time slot t, the invention defines a vector

This vector is backlogged by the energy states of all thermal storage tank units and the virtual queue J_tAnd (4) forming. By using theta_tThe invention defines a lyapunov function:

β therein_iIs a perturbation parameter, i.e. constraint (6), designed to ensure the bounding of the energy states. In addition to this, the present invention is,

the invention defines the single time slot condition Lyapunov offset as:

the invention is considered to consist of

The offset given adds a cost function instead of directly minimizing the system cost target. It is Δ (Θ)_t) And a weighted sum of the system cost at time slot t, where V is used as the weight.

In the algorithm design of the present invention, the present invention first considers an upper bound of the offset plus cost function and then formulates a real-time optimization problem to minimize the upper bound of the function at each time slot t. Therefore, at each time slot t, the present invention has the following optimization problem:

P3：

s.t.(1)，(4)，(7)-(11)

the design of the real-time problem P3 may yield some analytical performance guarantees. In addition, to ensure g_tThe invention takes the steps of obtaining P2 and moving ramp constraint equation (9) back to P3.

Since C (-) and Di (-) are convex functions, P3 is a convex function optimization problem that can be effectively solved by a standard convex optimization software package. The optimal solution for P3 at time slot t is represented as

At each time slot t, obtaining

The invention then updates s according to their evolution equation_i，t，

And J_t。

Below is providedIn proposition, the present invention demonstrates that despite relaxation to P2, by properly designing perturbation parameters β_iThe invention may ensure the bounding of energy states and thus control actions

Feasibility for P1.

Proposition 1 for the ith battery cell, perturbation parameter β_iThe method comprises the following steps:

wherein V is (0, V)_max]，

Then, the control action derived by solving P3 at each time t

This is possible for P1.

The invention now analyzes the solution provided by algorithm 1 with respect to P1. In algorithm 1, to emphasize the dependency of the cost target value on the ramp coefficient r and the control parameter V, the present invention uses w^*(r, V) represents the cost target value achieved. From w^opt(r) represents the minimum cost target value of P1, which depends only on r. The main results are summarized in the following schemes.

Theorem 1: assuming a random system state q of the grid_tAre independently co-distributed and over time. Under algorithm 1, the invention has the following:

2)w^*(r，V)-w^opt(r)≤(1-r)g_maxmax{p_b，max，C′_max}+B/V

where B is a constant defined as:

2)w^opt(r)≥w^*(1，V)-B/V

assume battery capacity s_i，maxIs fixed, so to ensure the feasibility of the solution, the control parameter V should be V in (21)_maxTo an upper bound, additionally, if the battery capacity can be designed, the question is what its value should be in order to achieve some desired performance. In the propositions below, the present invention can be greater than V by giving_maxOf any positive V energy state s_i，t(i.e., the upper bound of the minimum required energy capacity) provides an answer to this question.

Proposition 2: for any V > 0, the energy state s of the ith cell at time slot t_i，tSatisfies s based on Algorithm 1_i，t∈[s_i，min，s_i，up]Wherein:

in the above formula with respect to s_i，upCan provide useful information and can reveal some beliefs about the dependence of the design of battery capacity on certain system parameters. First, s_i，upIncreases linearly with the control parameter V. Second, if the energy price is more subject to fluctuations or the marginal cost of degradation increases rapidly, s_i，upAnd is larger. Finally, if there is p_b，max＝p_s，minAnd D'_i，max＝D′_i，minThen s_i，upIs given by x_i，max-x_i，min+s_i，minIt is given.

Other attributes regarding flexible loads and external transactions are summarized in the following propositions.

Proposition 3: based on algorithm 1, the following results hold.

(1) Queue backlog J_tLimited uniformly from above to J_t≤Vp_b，maxl_f，max+1

(2) External transaction amount

And

satisfy the requirement of

In the current system model, the present invention incorporates one CG to the supply side in addition to the CHP. If there are multiple CGs with the same characteristics, i.e. the same maximum output g_maxThe ramp coefficient r and the cost function C (-) which the present invention can combine into one generator for mathematical analysis. In this case, the current mathematical framework and performance analysis is applied directly to the combined generator, and then the output of each individual CG can be obtained by equally distributing the output of the combined generator over all individual generators. On the other hand, if these CGs have heterogeneous characteristics and therefore cannot be combined into one, the proposed algorithm can still be used. In particular, in the original problem P1, the present invention will have the total output of the generators in the constraint equations (8) and (9), (11) for each individual generator as

And the total cost of the generator is

The resulting relaxation problem P2 will be similar to the current problem, with the ramp constraint removed for each individual CG (9). For real-time algorithms, the formulation of the optimization problem per time slot follows the current mathematical framework, and furthermore, the same approach proposed by the present invention can be used to develop distributed implementations of the algorithm.

And fourthly, carrying out distributed algorithm research on the previously deduced objective function.

For ease of algorithm development, the invention first converts P3 into an equivalent problem, and for symbolic simplicity, the invention discards the time index t. The invention defines a new optimization vector

By making y_i＝(1+η_w)x_iTo the optimization variables involved in P3, where 1 ≦ i ≦ N, y_N+1＝l_m，y_N+2＝-g，y_N+3＝-e_b，y_N+4＝e_s，y_N+5＝l_w，y_N+6＝-e_wThe target of P3 can be rewritten as each y_iOf a particular function of (A), which is represented by F_i(y_i) The sections are omitted for brevity. Furthermore, based on the constraint condition equation (7), the present invention sets b in the constraint of P3_iIs replaced by

Where 1 ≦ i ≦ N, therefore, P3 may be rewritten in the general form P4:

P4：

wherein, constraint set { gamma_iDerived from constraint equations (1), (4) and (7) - (12),

next, the present invention introduces an auxiliary vector z as a copy of y and further translates P4 into the following equivalent problem:

P5：

s.t.y-z＝0 (18)

where 1 (-) is an indicator function, 0 if the event indicated is true, and infinity otherwise.

And fifthly, establishing an ADMM (alternating direction multiplier algorithm) algorithm framework so as to facilitate MATLAB simulation.

Following the general ADMM approach, the present invention constrains (18) the equation in P5 to bivariates

Is associated with and will

And

expressed as the respective variable values at the k-th iteration, these values will then be updated according to ADMM as follows:

where ρ > 0 is a penalty factor that needs to be carefully adjusted to obtain good convergence performance.

In experiments, the problem studied by the present invention is, mathematically, novel and different from all the problems previously proposed, which cannot be directly compared with the existing ones. To overcome this difficulty, the present invention employs two alternative algorithms and a lower bound on the minimum system cost obtained in theorem 1.2 for comparison.

The first alternative is a greedy algorithm that can only minimize the current system cost, and the optimization problem of the greedy algorithm at time slot t is as follows:

l_b，t+(1-α)l_f，t≤l_m，t≤l_b，t+l_f，t

-s_i，t≤x_i，t≤s_i，max-s_i，t

the second alternative is mainly to show the effect of the ramp constraint, especially at each slot t, except that without the ramp constraint (9), the invention solves the same optimization problem as P3, so the resulting CG output may not be feasible for P1, and in order to maintain feasibility, the aggregator only uses the external energy market to increase the CG output whenever it violates the ramp constraint. The invention is called as 'algorithm of nature'.

The specific implementation comprises the following contents:

in conjunction with fig. 2 and 3, each time slot is 15 minutes in length. Base load l_b，tAnd a flexible load l_f，tIs evenly distributed between 5 and 25kWh, the unsatisfied flexible load portion α is 0.07, assuming a CHP number of aggregator connections N-30, the present invention assumes a discharge and charge rate of 6.6kW for each corresponding field cell, and a maximum discharge and charge of 1.1kWh is set, since the model of the battery's degradation cost function is generally proprietary and unusable, so in the simulation, the present invention takes D as the value of_i(x)＝10x²For example. Large-scale cogeneration power generation amount a_i，tEvenly distributed between 0 and 1.1kWh, and for the traditional generator, the invention sets the generating cost function as C (x) 8x and the maximum output g_max50kWh, and the ramp coefficient r is 0.1. Unit price p of purchase electricity price_b，tUniformly distributed between 1.6 and 8.2 cents/degree, and the price unit p of the selling price of electricity_s，tUniformly distributed between 1.0 and 1.2 cents/degree, slightly lower than the price of purchasing electric power and the unit price p of the price of purchasing external natural gas_w，tEvenly distributed in 1.2 to 1.4 cents/kwh. The control parameter V is set to 1, s_i，min＝0。

While the invention has been described with respect to a preferred embodiment, it will be understood by those skilled in the art that the foregoing and other changes, omissions and deviations in the form and detail thereof may be made without departing from the scope of this invention. Those skilled in the art can make various changes, modifications and equivalent arrangements, which are equivalent to the embodiments of the present invention, without departing from the spirit and scope of the present invention, and which may be made by utilizing the techniques disclosed above; meanwhile, any changes, modifications and variations of the above-described embodiments, which are equivalent to those of the technical spirit of the present invention, are within the scope of the technical solution of the present invention.

Claims (4)

1. A distributed energy scheduling method for an intelligent micro-grid is characterized by comprising the following steps: the method comprises the following 5 steps:

step 1: analyzing the intelligent micro-grid distributed energy scheduling system, and establishing a corresponding system model; the system model includes: the system comprises a traditional generator CG, a aggregator, a flexible load, a base load, a heat load, an external energy market and a plurality of cogeneration CHPs, wherein the aggregator is connected with the traditional generator, the flexible load, the base load, the external energy market and the plurality of cogeneration, the cogeneration is connected with an external natural gas supply and the heat load, and each cogeneration corresponds to a heat storage tank;

step 2: analyzing the established system model, and deducing corresponding constraint conditions and a target function; in step 2, considering that a power grid is composed of a CG and N CHPs, N being a positive integer, each CHP is connected to a site heat storage tank, the power grid is connected to an external energy market and operated by a aggregator responsible for meeting the load by managing energy from various sources; suppose the system operates in discrete time with time slots t e {0, 1, 2. }; for symbol simplicity, energy units are used instead of power units;

(1) loading: loads include foundation, compliance and thermal loads; the base load represents the base energy demand, which must be met once requested; the flexible load represents the controllable energy demand, and the controllable energy can be partially reduced when the cost condition is consideredA quantity demand; at time slot t, by l_b，t∈[l_b,min，l_b,max]Represents the total amount of the base load of the request, and passes l_f，t∈[l_f,min，l_f,max]Representing the total amount of requested flexible load,/_b,min、l_b,maxRespectively representing the minimum and maximum values of the total amount of base load requested during a time slot t, l_f,min，l_f,maxRespectively representing the minimum value and the maximum value of the total amount of the flexible load requested during the time slot t; total amount l_b,tAnd l_f,tGenerated by the user based on his own needs and considered random; let the total amount of load satisfied during a time slot t be l_m,tIt should satisfy

L_b,t≤l_m,t≤l_b,t+l_f,t(1)

The control of the flexible load needs to meet specific quality of service requirements; applying an upper bound to the portion of the compliance load that is not satisfied, introducing a long term time averaging constraint;

wherein α ∈ [0, 1] is a preset threshold with a specific value indicating a strict quality of service requirement, where E [ ] represents de-expectation for content within [ ];

by a_w,tRepresenting the total amount of thermal load requested during time slot t, which should satisfy, due to the design and hardware constraints of the thermal storage tank:

l_h,min≤l_w,t≤l_h,max(3)

wherein l_h,minAnd l_h,maxMinimum and maximum values representing the total amount of thermal load requested, respectively;

(2) CHP and field heat storage tank: at the ith CHP, i is 1, 2, … …, N, during time slot t, by a_i,t∈[0，a_i,max]Represents a large cogeneration power generation amount, wherein a_i,maxIs the maximum energy produced; due to the stochastic nature of large cogeneration, a_i,tIs random;

assuming that each CHP corresponds to one on-site thermal storage tank unit capable of charging and discharging; during time slot t, with x representing the charge_i,t> 0 denotes the charging energy x of the ith battery_i,tBy x representing discharge_i,t< 0 indicates the discharge energy x of the ith cell_i,t(ii) a Due to battery design and hardware constraints, x_i,tThe values of (c) are bounded as follows:

x_i,min≤x_i,t≤x_i,max，(x_i,min＜0＜x_i,max) (4)

here, | x_i,minI and x_i,maxMaximum values representing total amounts of discharge and charge, respectively; for the ith cell, use s_i,tRepresents the energy state at the beginning of time slot t; due to charge-discharge operation, s_i,tThe equation of (c) can be given by:

s_i,t+1＝s_i,t+x_i,t(5)

furthermore, due to battery capacity and operating constraints, the energy state s is made_i,tThe upper and lower bounds of (A) are as follows:

S_i,min≤s_i,t≤s_i,max(6)

S_i,minrepresenting the minimum state of energy, s, allowed for the battery_i,maxRepresents the maximum energy state value allowed and may be used to indicate battery storage capacity; to simulate the cost of a battery, Di (-) is used to represent the charge or discharge amount x_i,tAn associated degradation cost function;

during each timeslot, the CHP provides energy to the aggregator; by b_i,tTo represent the total amount of energy contributed by the ith CHP during time slot t; since the energy flow with respect to CHP should be balanced, there are:

b_i,t＝a_i,t-x_i,t，b_i,t＞0 (7)

in particular, if x_i,t> 0, the energy b contributed_i,tDirectly from large cogeneration; if x_i,t< 0, then b_i,tFrom large cogeneration power generation and batteries;

(3) CG: in contrast to the CHP,the energy output of the CG is controllable; by g_tRepresenting the energy output of the CG during time slot t, which satisfies:

0≤g_t≤g_max(8)

g_maxrepresents the maximum value of the energy output; due to the operating limitations of the CG, the change in output at two consecutive time slots is bounded, which typically reflects a ramp constraint on the CG output; assuming that the ramp-up and ramp-down constraints are the same, the overall ramp constraint is expressed as:

|g_t-g_t-1|≤rg_max(9)

wherein the coefficient r belongs to [0, 1] to represent the compactness required by the slope; for r-0, CG produces a fixed output over time, while for r-1, the slope requirement becomes invalid; further, the power generation cost function of CG is represented by C (·);

(4) external energy market: in addition to internal energy resources, the aggregator can resort to external energy markets as needed; in the case of energy shortage, the aggregator can buy energy from an external energy market, or sell energy to the market in the case of energy surplus; each using p_b,t∈[p_b,min，p_b,max]And p_s,t∈[p_s,min，p_s,max]Representing the unit price, p, for buying and selling energy to the external energy market at time slot t_w,t∈[p_w,min，p_w,max]Representing the unit price, p, of energy purchased from the external natural gas at time slot t_b,min、p_b,maxRespectively representing the minimum and maximum values of the unit price of energy purchased to the external energy market at time slot t, p_s,min、p_s,maxRespectively representing the minimum and maximum value of the unit price of energy sold to the external energy market at time slot t, p_w,min、p_w,maxMinimum and maximum values representing unit prices for purchasing energy from external natural gas at time slot t, respectively; to avoid energy arbitrage, assume that the purchase price is strictly greater than the sale price, i.e. p_b,t＞p_s,t(ii) a Price p due to unexpected market behavior_b,tAnd p_s,tAnd p_w,tIs random; respectively using e_b,tAnd e_s,tRepresents the total amount of energy purchased and sold by the external energy market during time slot t, wherein:

e_b,t≥0，e_s,t≥0 (10)

the balance requirements of the overall system are as follows:

e_w,trepresenting the total amount of energy supplied by the external natural gas during time slot t, the overall system meets the thermal load supply requirements as follows:

wherein the coefficient η_w∈[0，1]Indicating the extent to which CHP supply is required, for η_wCHP produces a fixed output to the polymerizer over time, 0, and for η_wThe CHP output to the polymerizer request becomes invalid at 1;

and step 3: according to the objective function and the constraint condition, carrying out cost optimization by scaling and using a Lyapunov framework and establishing long-time average constraint;

and 4, step 4: carrying out distributed algorithm research on the target function;

and 5: and establishing an ADMM alternative direction multiplier algorithm framework, and calculating to obtain the optimal solution of the distributed algorithm.

2. The intelligent micro-grid distributed energy scheduling method of claim 1, wherein: in said step 3, a control action at time slot t is defined:

wherein

The cost of the overall system at time slot t, including the cost of all CHPs and CGs and the cost of utilizing the external energy market, is given by:

based on the system model described previously, the problem of power balancing is formulated as a stochastic optimization problem

P1：

Wherein the expectation in the target and equation (2) depend on the randomness of the system state

And possible randomness of control actions, wherein

To keep the mathematical statements simple, it is assumed that the cost functions C (-) and Di (-) are continuously differentiable convex functions, the derivatives of C (-) and Di (-) being represented by C '(. cndot.) and D' i (-) respectively, and based on this assumption, it is possible to

Obtaining a derivative

And derivative of

In order to provide a real-time algorithm, a Lyapunov optimization method is adopted; the following problems are posed:

P2:

compared with P1, the energy state constraint formula (5) and formula (6) in P2 are replaced by a new time-averaged constraint formula (13), and the ramp constraint formula (9) is removed;

scaling certification process of P1 to P2:

with the energy state update in equation (5), the left side of resulting constraint equation (13) equals:

in the formula (14), if s_i,tAlways bounded, keeping constraint equation (6), then the right of equation (14) is equal to 0 and constraint equation (13) is also satisfied; thus, P2 is a scaling for the P1 problem;

the steps work under a standard Lyapunov optimization framework;

in order to satisfy the constraint formula (2), the virtual queue backlog Jt is introduced to evolve as follows;

in equation (15), the virtual queue J_tAccumulate the portion of the compliant load that is not met, hold J_tIs equivalent to satisfy the constraint equation (2) by_tInitialized to J₀＝0；

At time slot t, a vector is defined

This vector is backlogged by the energy states of all thermal storage tank units and the virtual queue J_tComposition is carried out; by using the value of Θ t,defining a Lyapunov function:

where β i is a perturbation parameter designed to ensure the bounding of energy states, i.e. constraint (6), and further, defining the single-slot condition lyapunov offset as:

consider that

The offset given adds a cost function, instead of directly minimizing the system cost target, it is a weighted sum of Δ (Θ t) and the system cost at time slot t, where V is used as a weight;

in the algorithm design, an upper bound of an offset plus cost function is considered firstly, and then a real-time optimization problem is formulated so as to minimize the upper bound of the function under each time slot t; therefore, at each time slot t, there is the following optimization problem:

P3：

s.t.(1)，(4)，(7)-(11)

algorithm 1: real-time algorithm of power balancing: initialization J₀At each time slot t, the aggregator sequentially performs the following steps: 1) observing the system state q_tEnergy state s_i,t，

And the column backlog J_t；

2) Solving P3 and obtaining the optimal solution u^* _t；

3) Using u^* _tUpdating s according to equations (5), (15) respectively_i,t，

And J_t；

The design of the real-time problem P3 may yield some analytical performance guarantees; in addition, to ensure g_tThe step of obtaining P2 is taken and the ramp constraint equation (9) is moved back to P3;

since C (-) and Di (-) are convex functions, P3 is a convex function optimization problem, which can be effectively solved by a standard convex optimization software package; the optimal solution for P3 at time slot t is represented as

At each time slot t, obtaining

Then, s is updated according to their evolution equation_i,t，

And Jt;

in the following proposition, it is demonstrated that by properly designing the perturbation parameters β i, it is possible to ensure the bounding of the energy states, and therefore the control actions, despite the relaxation of P2

Feasibility for P1;

proposition 1 for the ith battery cell, the perturbation parameter β i is set as:

where V is (0, Vmax),

then, the control action derived by solving P3 at each time t

Is feasible for P1;

now analyze the solution provided by algorithm 1 with respect to P1; in algorithm 1, in order to emphasize the dependency of the cost target value on the ramp coefficient r and the control parameter V, the cost target value achieved is denoted by w (r, V); from w^opt(r) represents the minimum cost target value of P1, which depends only on r, the main results are summarized in the following scheme;

theorem 1: assuming a random system state q of the grid_tAre independently and simultaneously distributed and are time-lapse; under algorithm 1, there are the following:

3)w*(r，V)-w^opt(r)≤(1-r)g_maxmax{p_b,max，C′max}+B/V

wherein B is a constant defined as

2)w^opt(r)≥w*(1，V)-B/V

Assume battery capacity s_i,maxIs fixed, so to ensure the feasibility of the solution, the control parameter V should be bounded by Vmax in (21), and further, if the battery capacity can be designed, the question is what its value should be in order to achieve some desired performance; in the proposition below, by giving the energy state s of any positive V that can be greater than Vmax_i,tI.e. the upper bound of the minimum required energy capacity, provides an answer to this question;

proposition 2: for any V > 0, the energy state s of the ith cell at time slot t_i,tSatisfies s based on Algorithm 1_i,t∈[s_i,min，s_i,up]Wherein:

in the above formula with respect to s_i,upCan provide useful information and can reveal some beliefs about the dependence of the design of battery capacity on certain system parameters; first, s_i,upLinearly increases with the control parameter V; secondly, if canThe source price is more prone to fluctuation or the marginal degradation cost rapidly increases, then s_i,upIs larger; finally, if there is p_b,max＝p_s,minAnd D'_i,max＝D′_i,minThen s_i,upIs given by x_i,max-x_i,min+s_i,minGiving out;

other attributes regarding flexible loads and external transactions are summarized in the following propositions;

proposition 3: based on algorithm 1, the following holds:

(1) queue backlog J_tLimited uniformly from above to J_t≤Vp_b,maxl_f,max+1

(2) External transaction amount

And

satisfy the requirement of

In the current system model, one CG is incorporated to the supply side in addition to the CHP; if there are multiple CGs with the same characteristics, i.e. the same maximum output g_maxThe ramp coefficient r and the cost function C (-) which, for mathematical analysis, are combined into one generator; in this case, the current mathematical framework and performance analysis is applied directly to the combined generator, and then the output of each individual CG is obtained by distributing the output of the combined generator evenly over all the individual generators; on the other hand, if these CGs have heterogeneous characteristics and therefore cannot be combined into one, the proposed algorithm can still be used; in particular, in the original problem P1, for each individual generator, the total output of the generators in equations (8) and (9), (11) with the constraints is

And a generatorThe total cost of

The resulting relaxation problem P2 will be similar to the current problem, with the ramp constraint removed for each individual CG (9); for real-time algorithms, the formulation of the optimization problem per time slot follows the current mathematical framework, and furthermore, the same proposed method can be used to develop distributed implementations of the algorithm.

3. The intelligent micro-grid distributed energy scheduling method of claim 2, wherein: in the step 4, in order to facilitate algorithm development, P3 is first converted into an equivalent problem, and for simplicity of notation, the time index t is discarded; defining a new optimization vector

The optimization variables involved in P3 are linked by letting yi ≦ N, y ≦ i ≦ N, and (1+ η w) xi_N+1＝l_m，y_N+2＝-g，y_N+3＝-e_b，y_N+4＝e_s，y_N+5＝l_w，y_N+6＝-e_wThe target of P3 can be rewritten as each y_iOf a particular function of (A), which is represented by F_i(y_i) Represents; further, based on the constraint condition formula (7), b is set in the constraint of P3_iIs replaced by

Where 1 ≦ i ≦ N, therefore, P3 may be rewritten in the general form P4:

P4:

wherein the constraint set { gamma_iDerived from constraint equations (1), (4) and (7) - (12),

next, an auxiliary vector z is introduced as a copy of y, and further P4 is transformed into the equivalent problem:

P5:

s.t.y-z＝0 (18)

where 1 (-) is an indicator function, 0 if the event indicated is true, and infinity otherwise.

4. The intelligent micro-grid distributed energy scheduling method of claim 3, wherein: in step 5, following the general ADMM method, the equation in P5 is constrained (18) to bivariate

Is associated with and will

And

expressed as the respective variable values at the k-th iteration, these values will then be updated according to ADMM as follows:

where ρ > 0 is a penalty factor, ρ is adjusted to achieve good convergence performance.

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