CN116843152A - Electric power-data service-oriented Internet data center double-layer planning method - Google Patents

Abstract

The invention provides an internet data center double-layer planning method for electric power-data service, and provides an IDC double-layer planning framework considering data user information demand response resources in an electric power market environment. First, a data load scheduling model is established that considers data service market (DS) -DR by in-depth analyzing different data load characteristics of data user requests, mining potential participation capabilities of data user information resource demand responses. Then, based on the interactive relation between IDC and electric power market and data service market, an IDC double-layer planning model is established. The upper layer is an IDC multi-domain resource collaborative planning model aiming at economy, respectively transmitting real-time power to lower layer independent system operators and designing DS-DR incentive prices for data users. The lower layer is an ISO economic dispatch model and a data user comprehensive utility decision model respectively. Aiming at a double-layer mixed integer nonlinear programming model with two problems of the lower layer, the KKT condition and the R & D algorithm are adopted to carry out accurate and efficient solving.

Description

Electric power-data service-oriented Internet data center double-layer planning method

Technical Field

The invention relates to the technical field of data processing, in particular to an internet data center double-layer planning method for electric power-data service.

Background

With the popularization of information industries such as cloud computing and big data technology, the demands of end users for various digital services are continuously rising. As data hubs and computing engines for carrying user service requests, IDC's are built in explosive growth situations in number and scale, which is an inevitable continuous surge in energy consumption and energy costs. It is estimated that the annual energy cost of a large IDC can reach tens of millions of dollars. However, it has been found that the computing device servers of the data center are unsaturated for a substantial portion of the time, simply to ensure resource availability during peak demand periods, which results in substantial resource wastage. Therefore, cost reduction, synergy and scientific planning have become urgent demands of data center operators.

Disclosure of Invention

The embodiment of the invention provides a double-layer planning method of an internet data center for electric power-data service, which is used for solving the technical problems existing in the prior art.

In order to achieve the above purpose, the present invention adopts the following technical scheme.

The electric power-data service-oriented Internet data center double-layer planning method comprises the following steps:

s1, establishing an IDC energy consumption model through a PUE index based on temperature sensing;

s2, modeling the interactive data load, the batch data load and constraint conditions capable of reducing the data load respectively to construct an IDC data load characteristic model;

s3, establishing an IDC multi-domain resource collaborative planning model based on a target of maximum net benefit of system annual investment operation; based on the target of minimum total power generation cost, combining the IDC energy consumption model to establish an ISO economic dispatch model; based on the relation characteristic between expected benefits and participation costs of DS-DR participation willingness of the data users, establishing a data user benefit model by combining the IDC data load characteristic model;

s4, taking the IDC multi-domain resource collaborative planning model as an upper model, taking the ISO economic scheduling model and the data user benefit model as a lower model, and constructing an IDC comprehensive planning model; and solving the IDC comprehensive planning model through KKT conditions and an R & D algorithm.

Preferably, step S1 comprises:

setting I epsilon I to represent IDC to be built, T epsilon T to represent each time period in a typical day, S epsilon S to represent a constructed scene, N epsilon N to represent nodes in a power network, B epsilon B to represent a power generation section of a thermal power unit, and passing through the formula

Establishing an IDC energy consumption model; wherein lambda is _i,s,t IDC data load arrival rate, μ at inode for period t _i For the server processing rate, u _i,s,t 、u ^max The cpu time period utilization and the maximum utilization respectively,starting up quantity and starting up quantity of server t time period respectivelyServer configuration quantity, +.>For server backup coefficients->Peak power when processing workload and silence power when idle for single server respectively, T _i,s,t An outdoor temperature of IDC, a _i /b _i /c _i Outdoor temperature coefficient of IDC of i node, ">Server power consumption and IDC total active power consumption, respectively.

Preferably, step S2 includes:

s21 migration balance constraint through IDL task, inter-IDC communication optical fiber bandwidth constraint and IDL migration total amount constraint

Establishing an interactive data load model; in the method, in the process of the invention,task amount before and after scheduling for interactive data load, respectively,/->For the amount of data migrated between two IDCs, w ^L For single data task capacity, +.>For the transmission delay of the communication line ii>Bandwidth limitation for communication line ii';

s22, balancing data load demands before and after transfer, restraining time transfer characteristics and restraining total load demand transfer

Establishing a batch processing data load model; in the method, in the process of the invention, Task amount before and after scheduling for batch data load respectively,/->The amount of data tasks transferred from time t to t';

s23 acceptable reduction ratio for reducing data load by kth class based on IDC i processingThrough type

Establishing a reducible data load model; in the method, in the process of the invention,to cut down the initial demand of the data load user;

s24 is based on formulas (7) to (13), by

Establishing an IDC data load characteristic model; in the method, in the process of the invention,for which the scheduled task amounts.

Preferably, step S3 includes:

s31 through type

max F ^IDC ＝Λ ^Ope -C ^Inv (15)

s.t.

Establishing an IDC multi-domain resource collaborative planning model; wherein F is ^IDC Net gain for IDC years; Λ type ^Ope The method is an IDC annual operation benefit; gamma ray ^ser /γ ^cool /γ ^pv /γ ^ess Annual coefficients of the installation costs of the server/refrigeration equipment/photovoltaic unit/energy storage equipment respectively; c ^si /c ^ci /c ^pvi /c ^ei The unit installation cost of the server/refrigeration equipment/photovoltaic unit/energy storage equipment is respectively;configuring capacity for refrigeration equipment/photovoltaic units/energy storage; ρ _s Probability of occurrence for the operational scene s; θ is the typical day of the year; pi _n,s,t LMP for node n time t; />The amount of electricity traded in the electricity market for IDC of i node whenRepresents the amount of electricity sold to the market when +.>Representing purchase of electricity to the market; delta ^data Servicing a unit price for the base data; c ^som /c ^com /c ^pvom /c ^eom The unit operation and maintenance cost of the server/refrigeration equipment/photovoltaic unit/energy storage equipment is respectively; />A state variable installed for the node to be addressed idc; />Maximum installation capacity of the server/refrigeration equipment/photovoltaic unit/energy storage equipment respectively; />The subsidy prices of the IDCi incentive data users participating in the BDL-DR and the RDL-DR and the upper price limit of the BDL-DR are respectively given; />Respectively photovoltaic actual output and predicted output;is the energy storage and charge quantity; epsilon ^ess Is self-discharge power>For charge/discharge power, eta ^c /η ^d For charge-discharge efficiency, SOC ^max /SOC ^min Is the upper/lower limit of state of charge, +.>Is a charge/discharge state variable, +.>Is the upper limit of charge/discharge power; />The rated capacity of the IDC transformer is set; />Respectively queuing time and processing time of data task, T ^max Maximum deferrable time for data tasks that are quality of service constrained;

s32 through type

s.t.

Establishing an ISO economic dispatch model; wherein C is ^G The total power generation cost of the system;the unit power generation cost; pi _n,s,t Is a dual variable of formula (34), the physical meaning of which is LMP, ++at node n time t>The unit active output cost of the generator set is set; />Interaction power of IDC for node n with market, +.>Load power at node n except IDC; p (P) _l,s,t Active power flowing for line l at time t, +. >An upper limit of active power capacity for line l; b _l Is the admittance of line l, alpha _n,s,t For the voltage phase angle of node n, +.>Maximum/minimum value of voltage phase angle; />Minimum output for the generator;

s33 through type

s.t.

Establishing a data user benefit model; wherein F is ^EDU Net benefit for the data user;benefit reduction for data users submitting BDLs; />The benefit of the data user submitting the RDL is cut; />(non-negative numbers) represent loss factors for class j BDL and class k RDL, respectively; />Acceptable cut-down ratios for the k-th reducible data load; d (D) _i,j A delay threshold acceptable for class j batch load; d (D) ^max A maximum delay threshold is set for IDC.

Preferably, in step S4, the KKT condition includes:

consistency constraint type

Complementary relaxation constraints

Converting formula (51) into a linear constraint type

In the formula (57), the amino acid sequence of the compound,is a constant, & gt>Is an auxiliary binary variable;

through type

Bilinear terms to be included in formula (18)Linearizing; in (1) the->The power interacting with the market for IDC at node n;

the R & D algorithm comprises the following steps:

converting the IDC comprehensive planning model into a matrix form

Wherein x is an upper layer 0/1 variable matrix, y is an upper layer continuous variable matrix, w is a lower layer continuous variable matrix, Z is a lower layer integer variable matrix, R represents a real number, and Z represents an integer; f, G, H, m, n, r, u, v, A, B, C, D, E, F, G, H, P and Q are respectively corresponding coefficient matrixes;

Resolving the reconstruction of equation (59) into a main problem MP

First sub-problem SP1

Second sub-problem SP2

The process of solving the IDC comprehensive planning model through the R & D algorithm includes:

s41 sets the upper bound LB = -infinity, lower bound ub= in the range of +++, iteration number l=0;

s42 solving the main problem MP, obtaining optimal x, y and updating ub=ψ;

s43 solving for SP1 based on given y, obtain

S44 is based on a given y sumSolving SP2 to obtain the optimal z and updating lb=max { LB, fy ^* +ψ ₀ (y ^* )}；

S45 stopping calculation if the absolute UB-LB absolute/UB is less than 0.01;

s46 setting z ^l+1 ＝z ^* And adds the following constraints to the MP;

-y ^T gw ⁰ -y ^T hz ⁰ +u ^T w ⁰ +v ^T z ⁰ ≥-y ^T gw ^r+1 -y ^T hz ^r+1 +u ^T w ^r+1 +v ^T z ^r+1

Pw ^r+1 ≤r-Qz ^r+1 ,P ^T σ ^r+1 ≥g ^T y+u

w ^r+1 ⊥(P ^T σ ^r+1 -g ^T y-u),σ ^r+1 ⊥(r-Qz ^r+1 -Pw ^r+1 )

w ^r+1 ,σ ^r+1 ∈R ⁺

s47 sets l=l+1, and returns to the execution substep S42.

According to the technical scheme provided by the embodiment of the invention, the invention provides the electric-Data service-oriented internet Data center double-layer planning method, aiming at the situation that large-scale construction of an internet Data center (Internet Data Center, IDC) serving a large number of terminal Data users (End Data users, EDUs) is in progress along with popularization of cloud computing, but the current huge energy consumption cost and low-utilization redundancy configuration situation are the difficult problems that the economic planning is needed to overcome urgently, and the time-space transferable characteristic of Data loads in the field of space-time changing electricity prices and information specific to the Data center in the power market environment in the energy field brings opportunities for IDC optimization construction. However, unlike conventional proprietary data centers, IDC does not have the problem of directly controlling the rights of all data loads. The invention provides an IDC double-layer planning framework considering data user information Demand Response (DR) resources in an electric power market environment from the energy-information coupling perspective. First, a data load scheduling model is established that considers data service market (DS) -DR by in-depth analyzing different data load characteristics of data user requests, mining potential participation capabilities of data user information resource demand responses. Then, based on the interactive relation between IDC and electric power market and data service market, an IDC double-layer planning model is established. The upper layer is an IDC multi-domain resource collaborative planning model targeting economy, delivering real-time power to lower layer independent system operators (Independent System Operator, ISO) and designing DS-DR incentive prices for data users, respectively. The lower layer is an ISO economic dispatch model and a data user comprehensive utility decision model respectively. Aiming at a double-layer mixed integer nonlinear programming model with two problems of the lower layer, the KKT condition and the R & D algorithm are adopted to carry out accurate and efficient solving.

Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a process flow diagram of a dual-layer planning method for an Internet data center for electric power-data services provided by the invention;

fig. 2 is a schematic diagram of IDC system architecture of an internet data center double-layer planning method for electric power-data service provided by the present invention;

FIG. 3 is a diagram of IDC double-layer mixed integer planning relationship of an Internet data center double-layer planning method for electric power-data service provided by the invention;

fig. 4 is a schematic flow chart of solving IDC comprehensive planning model through R & D algorithm in the internet data center double-layer planning method for electric power-data service.

Detailed Description

Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.

As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

For the purpose of facilitating an understanding of the embodiments of the invention, reference will now be made to the drawings of several specific embodiments illustrated in the drawings and in no way should be taken to limit the embodiments of the invention.

The invention provides an internet data center double-layer planning method for electric power-data service, which is used for solving the following technical problems in the prior art:

the most widely studied at present is to use the migratable properties of IDC in time and space dimensions over the information domain to achieve a space-time transfer of the electrical load, i.e. to transfer the data load to a time or place where the electricity price is cheaper. The literature [1] is based on the market price of electricity of the geographically dispersed IDCs, and the system researches the path and scheduling problem of batch data transmission among the data centers so as to reduce the energy cost of the data centers to the maximum extent; document [2] proposes a space-time load balancing method that minimizes energy costs of IDC in a deregulated power market. With respect to the flexible nature of information domains, there are also studies showing that: policy degradation quality of service (Quality of Service, qoS), i.e. the reduction of data load, may also reduce energy consumption and associated costs [3]. In addition, in the aspect of energy supply, a plurality of IDCs aim at utilizing the natural resource advantages of the region, integrate renewable energy sources and energy storage to reduce outsourcing energy cost, and promote the green sustainable development of the system. Document [4] studied the energy management problem of geographically dispersed data centers with renewable resources and stored energy, minimizing the cost of electricity and carbon emissions by exploiting the space-time diversity of system states. The document [5] considers the uncertainty of renewable energy sources and data loads, and provides an IDC intelligent energy management system based on a robust energy consumption optimization algorithm, so that the IDC operation cost is effectively reduced.

Under the above background, the direction of IDC comprehensive resource planning considering geographical dispersion of information and energy supply characteristics in market environment is also gradually rising, but only a small amount of research is performed at present, and according to our search, only three documents are found. The literature [6] provides a comprehensive planning method considering IDC and energy storage, and by reasonably utilizing the flexibility of the IDC under the time-of-use electricity price, the positions and the scales of the IDC and the energy storage are planned in a coordinated manner, so that the service quality, the reliability and the economy of the system are obviously improved. Document [7] proposes an optimized planning model for fixed-site IDC micro-grid, minimizing system planning cost by IDC space-time migration characteristics under time-varying electricity prices, and determining IDC calculation and capacity of energy devices. Document [8] proposes a hierarchical extended planning framework for data centers and data routes in data and power networks, IDC delivering the planning results to ISO, which issues the latest node marginal price (Locational Marginal Price, LMP). The above-mentioned studies have undoubtedly made much work, but there are still some disadvantages. Both the first two researches consider that the flexible characteristic of the IDC information field is utilized to carry out collaborative planning on hardware equipment and an energy supply system, and economic and reliable operation is realized, but the electricity price advantage of geographically dispersed IDC site selection in different areas cannot be fully mined during system planning, so that space transfer becomes more significant. In addition, similar to the documents [1] - [2] of energy optimization management of many IDCs, only market energy price signals are used as system fixed input parameters, default IDCs are only used as price acceptors, and the market price is not influenced. In fact, however, when IDC energy consumption is large, especially when a plurality of IDCs are in the same market environment, the market forces of the IDCs may cause electricity price fluctuation [9], and thus the IDC planning scheme may be changed. Document [10] also indicates that the transfer of IDC data load may also have an effect on LMP, and the third study just ignores this. Then the influence of IDC on the market is considered during planning, so that inaccuracy of site selection and volume determination can be further reduced, and economical efficiency of operation cost is ensured.

In fact, however, many documents on data load transfer issues do not address a problem: unlike traditional IDC proprietary to independent entities such as enterprises, which possess free scheduling rights for all data loads, public IDC which has just been exposed and developed rapidly in the future serves wide data users, cannot easily change user requests, and must strictly meet service level agreements (Service Level Agreement, SLA) with users, while available scheduling in the general SLA range is very poor in flexibility. Therefore, if the data service demand response (DS-DR) is not developed for the data users, the adjustment space of the information domain will be very limited, and no breakthrough can be made in the economical planning operation level. To also take advantage of the price of the space-time variation in the energy market, breaking this "incentive splitting" barrier, IDC is highly desirable to design incentive schemes in the information domain to encourage end users to participate in DS-DR, thus allowing flexibility. There is currently little research on the design of the excitation mechanism between IDC and user. Document [11] proposes a data service pricing model that calculates optimal prices for implementing data services based on dynamic energy costs and capital expenditures. Document [12] proposes an incentive subsidy mechanism based on usage pricing for deferrable data loads, which effectively reduces IDC peak energy consumption and energy consumption cost. Document [3] derives a mechanism for allocating economic margins between data center operators (Data Center Operator, DCO) and users that motivates users to cut loads to participate in emergency demand responses based on nash bargaining theory. It can be seen that the existing work design is complex, involves much information disclosure, and may not be easily implemented in practice. Meanwhile, users are mostly considered to be more passive, and no rational behavior selection is involved. In addition, the large variety is single, and the comprehensive requirement of IDC mining flexibility is not met.

Referring to fig. 1, the invention provides a dual-layer planning method of an internet data center facing to electric power-data service, which comprises the following steps:

s1, establishing an IDC energy consumption model through a PUE index based on temperature sensing;

s2, modeling an interactive data load, a batch data load and a reducible data load respectively to construct an IDC data load characteristic model;

s3, establishing an IDC multi-domain resource collaborative planning model based on a target of maximum net benefit of system annual investment operation; based on the target of minimum total power generation cost, combining an IDC energy consumption model to establish an ISO economic dispatch model; based on the relation characteristic between expected benefits and participation costs of DS-DR participation willingness of the data users, establishing a data user benefit model by combining with an IDC data load characteristic model;

s4, taking the IDC multi-domain resource collaborative planning model as an upper model, taking the ISO economic scheduling model and the data user benefit model as a lower model, and constructing an IDC comprehensive planning model; and solving the IDC comprehensive planning model through KKT conditions and an R & D algorithm.

The invention provides an IDC multi-domain full-element double-layer planning framework in the electric power-data service market. The method aims to promote data users to participate in data service demand response through a design excitation mechanism under the drive of space-time variation electricity price provided in the field of electric power markets so as to mine flexible resources of an information domain and meet the optimization demand of the energy domain, and then the IDC can be used for preparing an energy-information domain collaborative optimal planning scheme under the economic goal.

The key improvement of the invention is as follows:

1) An IDC double-layer planning framework is provided, and simultaneously energy-energy price interaction of IDC and a lower layer 1-electric power market and information-DR price interaction of IDC and a lower layer 2-data user are captured;

2) According to the data load characteristics, the comprehensive scheme that the DCO encourages users to participate in the DS-DR is considered, decision guidance of DS-DR participation will is provided for users with different characteristics according to the rational behavior selection of the users, and the win-win of benefits of the DCO and the data users is realized;

3) For the double-layer mixed integer nonlinear programming model (comprising two lower-layer problems) proposed herein, efficient solution is proposed by using a method of combining KKT with R & D reconstruction decomposition.

The following describes in detail the specific implementation of the method provided by the present invention.

Description of the problem

System architecture

Fig. 3 shows a basic architecture diagram of a typical IDC system, focusing on the internal device configuration, the communication network between IDCs and their interaction with external power markets and data users. It can be found that the IDC system mainly comprises a server inside the machine room, a refrigeration system, and an energy supply system such as photovoltaic and energy storage outside the machine room. The IDCs are subjected to overall data scheduling control by the cloud management platform, tasks are respectively issued to each IDC, and data transmission can be performed among the IDCs through an interconnection optical cable network.

Depending on self renewable energy power generation equipment and an energy storage system to flexibly charge and discharge, IDC is used as an electric energy producer, electricity can be purchased from an external electric power market when renewable energy resources are short or electricity price is low, and electricity can be sold to the outside when renewable energy sources are sufficient or electricity price is high, so that economic operation is realized on the basis of guaranteeing the internal power balance of the system. Meanwhile, the external power market side ISO also performs economic dispatching according to the interactive power between the IDC and the market, and timely adjusts power flow distribution of the power network, so that node marginal electricity price LMP information is provided for IDC electricity utilization strategies and data load distribution.

Furthermore, IDC's are the most important business to meet massive data load demands from different data users according to SLAs. In order to enable the IDC to have more flexible adjustment capability, the cost reduction and the efficiency enhancement are possible to the greatest extent, and the IDC issues a data service demand response excitation mechanism to a data user. Aiming at different data user types, DCO makes corresponding reasonable incentive measures to mobilize the enthusiasm of the data users to participate in demand response. Meanwhile, the data user comprehensively considers the relation between expected benefits and participation costs and then makes an effective decision to provide the IDC with the participation willingness of the data service DR. In order to simplify and effectively describe the participation willingness of the data user DR, the bidirectional decision of the DCO and the data user is facilitated, the user is charged with basic data service fee, and then subsidy is carried out according to the participation degree.

IDC planning framework

Based on the above analysis, from the DCO perspective, its interaction with ISO and data users can be seen as a master-slave gaming problem, i.e. DCO is the leader and ISO and data users are respectively different followers of the energy-information dimension. The comprehensive planning problem for IDC can then be constructed as a two-layer planning model comprising two underlying problems, as shown in fig. 3. The upper layer aims at maximizing the net benefit of IDC annual investment operation, determines the construction position of IDC in the power network, the installation capacity of each IDC energy supply device (photovoltaic/energy storage) and physical device (server/refrigeration system), optimizes the operation control strategy of IDC (including data load migration and reduction amount, server start-stop state, refrigeration device/photovoltaic output capacity, energy storage charge and discharge capacity and outsourcing electric quantity) in each period and the excitation patch unit price setting of DS-DR. The lower layer 1 is an ISO power system economic dispatch model considering IDC, and determines that the information of LMP in the system is transferred to DCO. The lower layer 2 is a comprehensive utility model of the participation DS-DR of the data users, and determines the quality requirement condition of the data load to be processed, namely DS-DR participation will, provided for IDC according to the DR incentive subsidy price set by DCO.

In addition, there are some non-negligible uncertainties during the system run-time. Random optimization methods based on scenes are used herein to capture uncertainties associated with the operation of various subjects in the system, including photovoltaic output, outdoor temperature, electrical load demand, data user request rate, and the like. Assuming that the data/electricity load requirements and the ambient temperature accord with truncated Gaussian distribution, the illumination intensity obeys Beta distribution, and scene generation is performed through a Monte-carlo simulation method. On the basis, a K-means method is further adopted to cluster generated scenes, information redundancy in the model is reduced, and the calculation efficiency of the problem is improved.

In the modeling process, the following parameters are set: i epsilon I represents IDC to be built, T epsilon T represents each time period in a typical day, S epsilon S represents a built scene, N epsilon N represents a node in a power network, and B epsilon B represents a power generation section of a thermal power unit.

IDC model

Equipment energy consumption model

IDC energy consumption mainly consists of a server for processing data load, a refrigeration system for maintaining indoor environment temperature, and a power supply and distribution system. Wherein the server and refrigeration system account for about 90% of the total IDC energy consumption. The power consumption of the server is mainly determined by the starting number of the server and the information task load in the current period. Under the working state of a large number of server clusters, it can be assumed that the data load in any period is equally distributed to all the starting servers, namely, when a plurality of servers operate, the overall CPU utilization rate is shown as a formula (1), and the total power consumption of the server clusters can be represented by a formula (2). Equations (3) and (4) are IDC server power-on number constraints and server CPU utilization constraints, respectively. In the existing domestic and foreign researches, the IDC total energy consumption is determined according to the IT equipment energy consumption by an empirical estimation method based on PUE (Power Usage Effectiveness) index. In fact, since the change of the IDC outdoor temperature may affect the energy efficiency of the refrigeration system (such as the machine room air conditioner) in real time and further affect the PUE value, the accuracy of the PUE estimation value determined empirically is low. Thus, embodiments of the present invention employ a PUE that takes into account temperature sensing to calculate IDC total power consumption. The dependence of the PUE on temperature is shown in formula (5), and the IDC total power consumption is shown in formula (6).

Wherein lambda is _i,s,t IDC data load arrival rate, μ at inode for period t _i For the server processing rate, u _i,s,t 、u ^max The cpu time period utilization and the maximum utilization respectively,the starting-up quantity and the server configuration quantity of the server t period are respectively +.>For server backup coefficients->Peak power when processing workload and silence power when idle for single server respectively, T _i,s,t An outdoor temperature of IDC, a _i /b _i /c _i Outdoor temperature coefficient of IDC of i node, ">Server power consumption and IDC total active power consumption, respectively.

Data load characteristic model

The data load in IDC can be roughly classified into 3 categories according to the request characteristics of the data user: interactive Data Load (IDL), batch Data Load (BDL), and reducible Data Load (Reduciable Data Load, RDL). The following models are made separately for various load characteristics.

Interactive data load

IDL refers to a data load that does not have processing delay but can be flexibly migrated between different geographic locations IDC as needed. In practical engineering, typical IDLs include user requests with high real-time requirements, such as market transactions, network services, online communications, and the like. Since IDC free scheduling of IDLs does not have a quality of service impact on the data users, i.e., there is no DS-DR potential, this class of data load is not considered an object of DS-DR. For IDL scheduling control, the relevant constraint is shown in formulas (7) - (9), and is respectively IDL task migration balance constraint, IDC communication optical fiber bandwidth constraint and IDL migration total amount constraint.

/>

In the method, in the process of the invention,task amount before and after scheduling for interactive data load, respectively,/->For the amount of data migrated between two IDCs, w ^L For single data task capacity, +.>For the transmission delay of the communication line ii',/>is the bandwidth limit of communication line ii'.

Batch processing data load

BDL refers to a data load with a fixed amount of tasks but a flexible and variable processing time within a user acceptable processing delay time. For IDC, common BDLs include data mining testing, task backup, etc. The larger the acceptable delay threshold provided by the BDL request of the user, the larger the time range that the IDC can flexibly schedule, wherein the BDL is taken as one of main objects of the IDC developing DS-DR. Since the batch requests of different data users differ in their sensitivity (degree of loss) to the delay processing, the delay thresholds provided differ, and the DCO subdivides the BDLs into j classes according to the sensitivity characteristics of the data users. Then, the maximum processing delay duration D of the j-th class batch data load based on IDC i processing _i,j IDC i may defer to [ t, t+d ] for the j-th class of batch data load demand generated at time t _i,j ]Processing within any period of time. The above process may be represented by equations (10) - (12), which are data load demand balancing, time transfer characteristic constraints, and load demand transfer aggregate constraints before and after transfer, respectively.

In the method, in the process of the invention,task amount before and after scheduling for batch data load respectively,/->For the amount of data tasks transferred from time t to t'.

Can cut down data load

RDL refers to a data load that can be reduced in quality of service and flexible in terms of reduction within a specified time frame, and mainly includes computational simulation, video playback, and the like. The lower the acceptable quality of service (i.e., the higher the cut-down ratio) requested by the RDL of the user, the greater the peak clipping and valley filling capability of IDC, and the RDL is taken as another important object of IDC development DS-DR. Similar to BDL, DCO subdivides RDL into k classes according to the sensitivity characteristics of data users, since the reducible requests of different data users are differently sensitive to reduced quality of service, the maximum acceptable reduction provided is also different. Then the kth class based on IDCi processing can cut down the acceptable cut-down proportion of the data loadThe RDL load characteristic expression is shown in formula (13).

After flexible adjustment of the data load according to equations (7) - (13), the total information load that each period IDC needs to handle is represented as follows:

in the method, in the process of the invention,to cut down the initial demand of the data load user, < >>For which the scheduled task amounts.

Problem modeling

Upper layer model: IDC multi-domain resource collaborative planning model

The upper IDC multi-domain resource collaborative planning model aims at maximizing the net benefit of the system year investment operation, and specific mathematical formulas are shown in (15) - (32). The formula (16) is the annual system investment cost, and comprises the installation of equipment such as a server, refrigeration equipment, a photovoltaic unit, energy storage and the like. Equation (17) is a system operation benefit, including benefits of participating in the electric wholesale market and the data service market, and operation and maintenance costs of each device and compensation costs of motivating users to participate in DR, and is specifically shown in equations (18) - (22), respectively. The DR compensation cost is detailed in section 4.3.

max F ^IDC ＝Λ ^Ope -C ^Inv (15)

s.t.

/>

Wherein F is ^IDC Net gain for IDC years; Λ type ^Ope The method is an IDC annual operation benefit; gamma ray ^ser /γ ^cool /γ ^pv /γ ^ess Annual coefficients of the installation costs of the server/refrigeration equipment/photovoltaic unit/energy storage equipment respectively; c ^si /c ^ci /c ^pvi /c ^ei The unit installation cost of the server/refrigeration equipment/photovoltaic unit/energy storage equipment is respectively;configuring capacity for refrigeration equipment/photovoltaic units/energy storage; ρ _s Probability of occurrence for the operational scene s; θ is the typical day of the year; pi _n,s,t LMP for node n time t; />The amount of electricity traded in the electricity market for IDC of i node, when +.>Represents the amount of electricity sold to the market when +.>Representing purchase of electricity to the market; delta ^data Servicing a unit price for the base data; c ^som /c ^com /c ^pvom /c ^eom The unit operation and maintenance cost of the server/refrigeration equipment/photovoltaic unit/energy storage equipment is respectively; / >A state variable installed for the node to be addressed idc; /> Maximum installation capacity of the server/refrigeration equipment/photovoltaic unit/energy storage equipment respectively; /> /δ ^BDL-max /δ ^RDL-max The subsidy prices of the IDCi incentive data users participating in the BDL-DR and the RDL-DR and the upper price limit of the BDL-DR are respectively given; />Respectively photovoltaic actual output and predicted output; />Is the energy storage and charge quantity; epsilon ^ess In order to be a self-discharge power,for charge/discharge power, eta ^c /η ^d For charge-discharge efficiency, SOC ^max /SOC ^min Is the upper/lower limit of state of charge, +.>Is a charge/discharge state variable, +.>Is the upper limit of charge/discharge power; />The rated capacity of the IDC transformer is set; />Respectively queuing time and processing time of data task, T ^max The maximum deferrable time for a data task that is a quality of service constraint.

Of the above constraints, equations (22) - (24) are system planning phase constraints, and equations (25) - (32) are system operating phase constraints. Wherein the constraints (22 a) - (22 d) are maximum installed capacity/number limits for the server, refrigeration equipment, photovoltaic unit, energy storage, respectively. Constraint (23) indicates that the configured capacity of the refrigeration appliance needs to meet the power relationship constraints at full server operation. Constraints (24) specify that the subsidy price for incentive data users to participate in the DR cannot exceed a certain upper limit. The constraint (25) is the output constraint of the photovoltaic unit. The operation constraint of the energy storage device is shown in formulas (26) - (29), and is respectively a power balance constraint, a charge-discharge state constraint, a continuity constraint for keeping consistent starting and ending capacity and a charge-discharge power constraint. The power balance constraint of IDC is shown by equation (30). Constraint (31) ensures that the IDC interaction power with the grid is within the transformer capacity range. It is assumed herein that all DC servers are of the same model and that data tasks are evenly delivered to active servers at run-time, based on M/M/1 queuing theory, quality of service constraints (32) for IDC data load handling are available.

Lower layer 1: ISO economic dispatch model

Generally, an economic dispatch issue for ISO is to minimize the overall cost of power generation, as shown in equation (33). The constraint conditions mainly consider active power balance constraint (34), grid tide constraint (35), voltage phase angle constraint (36) of the power system, line transmission active power constraint (37) and generator set active output constraint (38). Wherein pi _n,s,t The dual variable of formula (34) has the physical meaning of LMP at node n time t.

s.t.

Wherein C is ^G The total power generation cost of the system;the unit power generation cost; />The unit active output cost of the generator set is set; />Interaction power of IDC for node n with market, +.>Load power at node n except IDC; p (P) _l,s,t Active power flowing for line l at time t, +.>An upper limit of active power capacity for line l; b _l Is the admittance of line l, alpha _n,s,t For the voltage phase angle of node n, +.>Maximum/minimum value of voltage phase angle; />Minimum output for the generator. Variables noted after equations (34) - (38) are their corresponding dual variables, respectively.

Lower layer 2: data user benefit model

The DS-DR participation will of the data user is determined by the relation between the expected benefit and participation cost, and the comprehensive benefit mainly comprises incentive subsidies of DS-DR and basic DS payment reduction benefit, wherein DS benefit reduction is formed as shown in a formula (39). Equations (40) - (43) represent the data user DS-DR incentive patch functions providing BDL and RDL, respectively. Wherein, the liquid crystal display device comprises a liquid crystal display device, (non-negative numbers) represent the penalty factors for the j-th class BDL and the k-th class RDL, respectively, i.e., the higher the data user sensitivity, the greater the number. To prevent data user DR market arbitrage behavior, IDC sets a delay threshold not to exceed D ^max As shown in formula (44). The user-provided cutable ratio is between 0 and 1 as shown in equation (45). To ensure that each class of data user engagement DR is profitable at each time instant, constraints are shown in equations (46) and (47).

s.t.

/>

Wherein F is ^EDU Net benefit for the data user;benefit reduction for data users submitting BDLs; />The benefit of the data user submitting the RDL is cut; />Acceptable cut-down ratios for the k-th reducible data load; d (D) _i,j A delay threshold acceptable for class j batch load; d (D) ^max A maximum delay threshold is set for IDC.

Solving method

Solving process

The model presented herein is essentially a Bi-MINLP model with both continuous and discrete variables in the upper and lower problem that cannot be solved directly using existing commercial optimization solvers. The traditional method adopts an alternate iteration mode to solve by combining a genetic algorithm and a mixed integer nonlinear programming solver or a solving algorithm. However, such methods cannot find the optimal solution of the two-layer model, and the convergence of the algorithm cannot be guaranteed. The model is accurately solved by adopting KKT conditions and an R & D algorithm, meanwhile, the convergence is guaranteed, a solution flow diagram is shown in fig. 3, and a specific KKT solving process and an R & D algorithm process are respectively described in detail below.

KKT condition

First, the lower level problem 1-the power system economic dispatch model is a linear programming problem, and by replacing the lower level optimization model 1 with its KKT conditions (including consistency constraints and complementary relaxation conditions), the upper level optimization model and the lower level optimization model 1 can be converted into a single level optimization model first.

Consistency constraints

The consistency constraint requires that the derivative of the lagrangian function for all variables be 0, expressed as follows:

the variables involved in the consistency constraint are dual variables corresponding to equations (34) - (38).

Complementary relaxation constraints

The complementary relaxation constraint requires that the original constraint and the dual variable product be 0, expressed as follows:

the complementary relaxation constraints are nonlinear, can be linearized by a large M method, and can be converted into linear constraints (57) by equation (51), and equations (52) - (56) are similar.

Wherein, the liquid crystal display device comprises a liquid crystal display device,is a sufficiently large constant, +.>Is an auxiliary binary variable.

Bilinear term processing

The bilinear term associated with the lower problem is also contained in equation (18), i.e., the upper objective functionThe strong dual theorem can be used to linearize easily. Wherein (1)>Representing the power at which IDC at node n interacts with the market.

R & D algorithm

After the upper layer optimization model and the lower layer optimization model 1 are converted into a single layer optimization model, the current double-layer mixed integer programming model is written into the following compact matrix form for solving the subsequent problems:

Wherein x is an upper layer 0/1 variable matrix, and y is an upper layer continuous variable matrix. w is a lower continuous variable matrix, Z is a lower integer variable matrix, R represents a real number, and Z represents an integer. In addition, F, G, H, m, n, r, u, v, a, B, C, D, E, F, G, H, P, Q are respectively corresponding coefficient matrices.

Based on the R & D algorithm, the reconstruction (59) is decomposed into a Main Problem (MP) and two sub-problems (SP 1, SP 2), and the model can be solved by using the C & CG concept. MP, SP1, SP2 are represented by formulas (60) - (62), respectively.

/>

The R & D algorithm steps are as follows:

step 1: setting a lower bound LB= -infinity, an upper bound UB= -infinity, and the iteration number l=0;

step 2: solving MP to obtain optimal x, y and updating ub=ψ;

step 3: solving for SP1 based on a given y-x, resulting in

Step 4: based on given y sumSolving SP2 to obtain the optimal z and updating lb=max { LB, fy ^* +ψ ₀ (y ^* )}；

Step 5: if |UB-LB|/UB <0.01, stopping the calculation;

step 6: setting z ^l+1 ＝z ^* And adds the following constraints to the MP;

-y ^T gw ⁰ -y ^T hz ⁰ +u ^T w ⁰ +v ^T z ⁰ ≥-y ^T gw ^r+1 -y ^T hz ^r+1 +u ^T w ^r+1 +v ^T z ^r+1

Pw ^r+1 ≤r-Qz ^r+1 ,P ^T σ ^r+1 ≥g ^T y+u

w ^r+1 ⊥(P ^T σ ^r+1 -g ^T y-u),σ ^r+1 ⊥(r-Qz ^r+1 -Pw ^r+1 )

w ^r+1 ,σ ^r+1 ∈R ⁺

step 7: set l=l+1 and return to step 2.

In summary, the invention aims at the problem of economic planning of IDC under the future multi-domain fusion development, explores the potential effect of considering the energy price of space-time variation and the information resource demand response potential of data users on improving the system economy in the planning stage from the energy-information coupling view point, and provides an IDC multi-resource collaborative planning method comprehensively considering the electric market and the data service market under multi-domain uncertainty. According to the simulation result, the following main conclusion is obtained:

1) Compared with the traditional planning only in the fixed market electricity price and without considering the DS-DR environment of the data users, the IDC multi-resource collaborative planning provided by the invention can fully mine the flexibility value of information resource demand response so as to improve the optimization space of the energy domain, finally determine the development degree of the DR resource of the data load under the energy-information coupling and obtain obvious economic benefit;

2) In view of the influence that energy consumption volume and data load space-time migration and reduction of IDC can have on power network trend and further on market price, in order to achieve accurate location and volume selection of IDC, LMP cannot be simply used as a planning parameter, and energy-price interaction of IDC and the power market needs to be considered in a planning stage, so that the effectiveness of a final planning scheme is ensured;

3) Compared with single DS-DR, developing multiple DS-DR can reasonably excite participation degrees of users with different characteristics at lower subsidy price, optimize data load curve to a greater extent, and realize optimal economy;

4) The setting of the incentive price can influence the DS-DR participation willingness of users with different characteristics, thereby influencing the benefits of IDC and data users. Therefore, the incentive price and the user participation degree which are optimally designed by considering the rational behaviors of the users with different characteristics can capture the information-data price interaction of the IDC and the data users, and the win situation of the IDC and the data users is achieved.

The method comprises the following steps: prior art document names and authors of the foregoing citations

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Those of ordinary skill in the art will appreciate that: the drawing is a schematic diagram of one embodiment and the modules or flows in the drawing are not necessarily required to practice the invention.

From the above description of embodiments, it will be apparent to those skilled in the art that the present invention may be implemented in software plus a necessary general hardware platform. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the embodiments or some parts of the embodiments of the present invention.

In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, with reference to the description of method embodiments in part. The apparatus and system embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.

The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. The electric power-data service-oriented internet data center double-layer planning method is characterized by comprising the following steps of:

s1, establishing an IDC energy consumption model through a PUE index based on temperature sensing;

s2, modeling the interactive data load, the batch data load and constraint conditions capable of reducing the data load respectively to construct an IDC data load characteristic model;

s3, establishing an IDC multi-domain resource collaborative planning model based on a target of maximum net benefit of system annual investment operation; based on the target of minimum total power generation cost, combining the IDC energy consumption model to establish an ISO economic dispatch model; based on the relation characteristic between expected benefits and participation costs of DS-DR participation willingness of the data users, establishing a data user benefit model by combining the IDC data load characteristic model;

S4, taking the IDC multi-domain resource collaborative planning model as an upper model, taking the ISO economic scheduling model and the data user benefit model as a lower model, and constructing an IDC comprehensive planning model; and solving the IDC comprehensive planning model through KKT conditions and an R & D algorithm.

2. The method according to claim 1, wherein step S1 comprises:

setting I epsilon I to represent IDC to be built, T epsilon T to represent each time period in a typical day, S epsilon S to represent a constructed scene, N epsilon N to represent nodes in a power network, B epsilon B to represent a power generation section of a thermal power unit, and passing through the formula

Establishing an IDC energy consumption model; wherein lambda is _i,s,t IDC data load arrival rate, μ at inode for period t _i For the server processing rate, u _i,s,t 、u ^max The cpu time period utilization and the maximum utilization respectively,the starting-up quantity and the server configuration quantity of the server t period are respectively +.>For server standby coefficient, P _i ^peak 、P _i ^idle Peak power when processing workload and silence power when idle for single server respectively, T _i,s,t An outdoor temperature of IDC, a _i /b _i /c _i Outdoor temperature coefficient of IDC of i node, ">Server power consumption and IDC total active power consumption, respectively.

3. The method according to claim 2, wherein step S2 comprises:

S21 migration balance constraint through IDL task, inter-IDC communication optical fiber bandwidth constraint and IDL migration total amount constraint

Establishing an interactive data load model; in the method, in the process of the invention,task amount before and after scheduling for interactive data load, respectively,/->For the amount of data migrated between two IDCs, w ^L For single data task capacity, +.>For the transmission delay of the communication line ii>Bandwidth limitation for communication line ii';

s22, balancing data load demands before and after transfer, restraining time transfer characteristics and restraining total load demand transfer

Establishing a batch processing data load model; in the method, in the process of the invention,task amount before and after scheduling for batch data load respectively,/->The amount of data tasks transferred from time t to t';

s23 a reduction ratio θ acceptable for data load reduction by the kth class based on IDC i processing _i,k Through type

Establishing a reducible data load model; in the method, in the process of the invention,to cut down the initial demand of the data load user;

s24 is based on formulas (7) to (13), by

Establishing an IDC data load characteristic model; in the method, in the process of the invention,for which the scheduled task amounts.

4. A method according to claim 3, wherein step S3 comprises:

s31 through type

max F ^IDC ＝Λ ^Ope -C ^Inv (15)

s.t.

Establishing an IDC multi-domain resource collaborative planning model; wherein F is ^IDC Net gain for IDC years; Λ type ^Ope The method is an IDC annual operation benefit; gamma ray ^ser /γ ^cool /γ ^pv /γ ^ess Annual coefficients of the installation costs of the server/refrigeration equipment/photovoltaic unit/energy storage equipment respectively; c ^si /c ^ci /c ^pvi /c ^ei The unit installation cost of the server/refrigeration equipment/photovoltaic unit/energy storage equipment is respectively; p (P) _i ^cool /P _i ^pvi /E _i ^ei Configuring capacity for refrigeration equipment/photovoltaic units/energy storage; ρ _s Probability of occurrence for the operational scene s; θ is the typical day of the year; pi _n,s,t LMP for node n time t;IDC for i-node in power marketThe amount of electricity traded, when->Represents the amount of electricity sold to the market when +.>Representing purchase of electricity to the market; delta ^data Servicing a unit price for the base data; c ^som /c ^com /c ^pvom /c ^eom The unit operation and maintenance cost of the server/refrigeration equipment/photovoltaic unit/energy storage equipment is respectively; />A state variable installed for the node to be addressed idc; />Maximum installation capacity of the server/refrigeration equipment/photovoltaic unit/energy storage equipment respectively; />The subsidy prices of the IDCi incentive data users participating in the BDL-DR and the RDL-DR and the upper price limit of the BDL-DR are respectively given; />Respectively photovoltaic actual output and predicted output; />Is the energy storage and charge quantity; epsilon ^ess Is self-discharge power>For charge/discharge power, eta ^c /η ^d For charge-discharge efficiency, SOC ^max /SOC ^min Is the upper/lower limit of state of charge, +.>As a charge/discharge state variable, P _i ^cr /P _i ^dr To charge/discharge powerAn upper limit; />The rated capacity of the IDC transformer is set; />Respectively queuing time and processing time of data task, T ^max Maximum deferrable time for data tasks that are quality of service constrained;

s32 through type

s.t.

Establishing an ISO economic dispatch model; wherein C is ^G The total power generation cost of the system;the unit power generation cost; pi _n,s,t Is a dual variable of formula (34), the physical meaning of which is LMP, ++at node n time t>The unit active output cost of the generator set is set; />Interaction power of IDC for node n with market, +.>Load power at node n except IDC; p (P) _l,s,t Active power flowing for line l at time t, +.>An upper limit of active power capacity for line l; b _l Is the admittance of line l, alpha _n,s,t For the voltage phase angle of node n, +.>Maximum/minimum value of voltage phase angle; />Minimum output for the generator;

s33 through type

s.t.

Establishing a data user benefit model; wherein F is ^EDU Net benefit for the data user;benefit reduction for data users submitting BDLs; />The benefit of the data user submitting the RDL is cut; />(non-negative numbers) represent loss factors for class j BDL and class k RDL, respectively; θ _i,k Acceptable cut-down ratios for the k-th reducible data load; d (D) _i,j A delay threshold acceptable for class j batch load; d (D) ^max A maximum delay threshold is set for IDC.

5. A method according to claim 3, wherein in step S4, the KKT condition comprises:

consistency constraint type

Complementary relaxation constraints

Converting formula (51) into a linear constraint type

In the formula (57), the amino acid sequence of the compound,is a constant, & gt>Is an auxiliary binary variable;

through type

Bilinear terms to be included in formula (18)Linearizing; in (1) the->The power interacting with the market for IDC at node n;

the R & D algorithm comprises the following steps:

converting the IDC comprehensive planning model into a matrix form

Wherein x is an upper layer 0/1 variable matrix, y is an upper layer continuous variable matrix, w is a lower layer continuous variable matrix, Z is a lower layer integer variable matrix, R represents a real number, and Z represents an integer; f, G, H, m, n, r, u, v, A, B, C, D, E, F, G, H, P and Q are respectively corresponding coefficient matrixes;

resolving the reconstruction of equation (59) into a main problem MP

First sub-problem SP1

Second sub-problem SP2

The process of solving the IDC comprehensive planning model through the R & D algorithm includes:

s41 sets the upper bound LB = -infinity, lower bound ub= in the range of +++, iteration number l=0;

s42 solving the main problem MP, obtaining optimal x, y and updating ub=ψ;

s43 solving for SP1 based on given y, obtain

S44 is based on a given y sumSolving SP2 to obtain the optimal z and updating lb=max { LB, fy ^* +ψ ₀ (y ^* )}；

S45 stopping calculation if the absolute UB-LB absolute/UB is less than 0.01;

s46 setting z ^l+1 ＝z ^* And adds the following constraints to the MP;

-y ^T gw ⁰ -y ^T hz ⁰ +u ^T w ⁰ +v ^T z ⁰ ≥-y ^T gw ^r+1 -y ^T hz ^r+1 +u ^T w ^r+1 +v ^T z ^r+1

Pw ^r+1 ≤r-Qz ^r+1 ,P ^T σ ^r+1 ≥g ^T y+u

w ^r+1 ⊥(PTσ ^r+1 -g ^T y-u),σ ^r+1 ⊥(r-Qz ^r+1 -Pw ^r+1 )

w ^r+1 ,σ ^r+1 ∈R ⁺

s47 sets l=l+1, and returns to the execution substep S42.