CN104734200A - Initiative power distribution network scheduling optimizing method based on virtual power generation - Google Patents

Abstract

The invention discloses a method for optimal dispatching of an active distribution network based on virtual power generation. Balance constraints, system spinning reserve constraints, technical output constraints of conventional units and demand-side resources, conventional unit ramp-up constraints, conventional unit minimum operating time and minimum downtime constraints, demand-side maximum continuous control time constraints, power consumption mode satisfaction (3) According to the optimal scheduling objective function and constraints and through the discrete particle swarm optimization algorithm based on heuristic rules to determine the start-stop status of all units one by one; (4) after completing the start-stop status of all units in each period After the calculation, on the basis of the known start-stop state, each unit is economically allocated on the basis of constraint conditions; thus realizing the optimal dispatch of the active distribution network.

Description

An Optimal Dispatch Method for Active Distribution Network Based on Virtual Power Generation

technical field

The invention belongs to the technical field of optimal dispatching of an active distribution network, and more particularly relates to an optimal dispatching method of an active distribution network based on virtual power generation.

Background technique

The large-scale access of distributed power sources, flexible loads and new energy storage systems, as well as the wide application of modern power electronic devices in the power grid, have brought about a series of changes in the system structure and operation mode of the distribution network. As a distribution network system that comprehensively controls distributed energy (DG, flexible loads and energy storage), the active distribution network manages distributed energy at the level of the entire distribution network, not only focusing on local autonomous control, but also on the entire distribution network. The overall optimization and coordination of the power grid provides a new idea for solving the large-scale centralized access of distributed energy. The coordination and cooperation of active distribution network source, network and load, how to effectively coordinate the schedulable resources on the generation side, grid side and load side, so as to achieve the optimal safety, economic and environmental benefits, and realize the safety of distribution network Reliable, high-quality and efficient operation is an urgent problem to be solved at present.

At present, the research on optimal dispatching of active distribution network is mostly for the dispatching research of distributed power generation, electric vehicle and energy storage system, or for the research of demand side response strategy alone. Individually studied the wind power consumption model based on demand side response and established a mixed integer programming model including the wind power system's day-ahead power generation plan, and used ILOG/CPLEX commercial software to solve it. Photovoltaic power generation), demand-side response and comprehensive optimization scheduling method of user satisfaction. The present invention proposes the comprehensive use of virtual power generation and active distribution network technology, and equivalates the demand response resources on the load side as virtual power generation resources, and participates in power balance adjustment as a virtual unit. At the same time, according to the output forecast curves of wind power and photovoltaic power generation, combined with conventional units, a multi-objective optimization model of integrated distributed power, demand-side resources and conventional units was established, and the scheduling problem was transformed into a unit combination problem, and the improved dual particle The group algorithm is solved. The calculation example shows that on the basis of satisfying high user satisfaction with electricity consumption, this scheduling method can effectively reduce the operating cost of power generation and environmental pollution in the distribution network, and can effectively reduce the peak-to-valley load difference.

Contents of the invention

In view of the above defects or improvement needs of the prior art, the present invention provides an optimal scheduling method for active distribution networks based on virtual power generation, the purpose of which is to use the idea of virtual power generation to equivalent the demand response resources on the load side to virtual power generation resources, Participate in power balance regulation as a virtual unit, and use the improved dual particle swarm optimization method to achieve the optimal allocation of resources in the active distribution network, thereby solving the problem of considering conventional units, distributed power sources, demand-side response and user consumption in the active distribution network. When the electricity satisfaction is satisfied, the optimization calculation speed is slow, which makes it difficult to quickly carry out the technical problem of scheduling control.

The present invention provides an active distribution network optimal dispatching method based on virtual power generation, comprising the following steps:

(1) Establish an optimal scheduling objective function; establish the first objective function F ₁ with the goal of the lowest system power generation operation cost, and establish the second objective function F ₂ with the goal of the minimum total equivalent number of pollutant discharge;

(2) Obtain the constraint conditions of the optimal scheduling objective function; the constraint conditions include: system load balance constraints, system spinning reserve constraints, technical output constraints of conventional units and demand-side resources, conventional unit climbing constraints, conventional unit minimum Running time and minimum outage time constraints, demand-side maximum continuous control time constraints, electricity consumption mode satisfaction constraints;

(3) The demand side response is equivalent to a virtual generator, and according to the optimal scheduling objective function and the constraints and through the discrete particle swarm optimization algorithm based on heuristic rules, the start and stop states of all units are obtained time by time ;

(4) According to the start-stop status of all units, and through the continuous particle swarm algorithm based on heuristic rules, each unit is economically allocated on the basis of the constraints; and according to the results of economic allocation and all units in each period The output of each unit is allocated according to the final start-stop status and output size of the power distribution network, so as to realize the optimal dispatch of the active distribution network.

Further, in step (1), the first objective function is: $\min f_1=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}[f_i\left(P_{\mathrm{Gi}}\left(t\right)\right)\×u_i\left(t\right)+S_i\left(t\right)\×(1-u_i(t-1))\×u_i\left(t\right)]+\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{f}_{\mathrm{DR}}\left(P_{\mathrm{DR}}\left(t\right)\right)\×u_{\mathrm{DR}}\left(t\right);$ The second objective function is: $\min f_2=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{g}_i\left(P_{\mathrm{Gi}}\left(t\right)\right)\×u_i\left(t\right);$

Among them, F ₁ represents the operating cost of system power generation; T represents the dispatch cycle time; N _G represents the total number of conventional units; f _i (P _Gi (t))=A _i ×P _Gi (t) ² +B _i ×P _Gi ( t)+C _i , f _i represents the operating cost of the i-th conventional unit; P _Gi represents the output power of the i-th conventional unit; S _i represents the start-stop cost of the i-th conventional unit; u _i (t) and u _i ( t-1) represent the start-stop status of unit i at the current moment and the previous moment respectively; f _DR represents the total amount of demand side response compensation; f _DR (P _DR (t))=d _DR ×P _DR (t), P _DR represents the regulated power on the demand side, that is, the virtual power generation; u _DR (t) represents the start-stop state of the virtual power generation at the current moment; A _i , B _i and C _i represent the operating parameters of the i-th conventional unit; $S_i\left(t\right)=\left\{\begin{array}{cc}{\mathrm{Sh}}_i& T_{i,\mathrm{off},\min }\≤T_{i,\mathrm{off}}\≤T_{i,\mathrm{cs}}\\ {\mathrm{sc}}_i& T_{i,\mathrm{off}}\&Greater\; Equal;T_{i,\mathrm{cs}}\end{array}\right.,$ Shi _i represents the hot start cost of the ith conventional unit; Sc _i represents the cold start cost of _{the i} The time that the i conventional unit has been shut down before a certain period of time, if the unit was on before, it is 0; T _i,cs represents the cold start time of the conventional unit i; d _DR is the reduction of electricity per kilowatt-hour on the demand side The amount of compensation; F ₂ represents the total equivalent amount of pollutant discharge; g _i (P _Gi (t))＝a _i ×P _Gi (t) ² +b _i ×P _Gi (t)+ci , _{g i represents} The pollutant emission equivalent of the i-th conventional unit; a _i , b _i and c _i represent the pollution emission coefficient of the i-th conventional unit.

Furthermore, in step (2), the system load balancing constraint is Among them, N _DG represents the number of distributed power sources; P _DGj (t) represents the output of the jth distributed power source at time t; P _L (t) represents the load power at time t; the system spinning reserve constraint is $\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{u}_i\left(t\right)P_{\mathrm{Gi},\max }+P_{\mathrm{DR},\max }\&Greater\; Equal;P_L\left(t\right)+P_{\mathrm{RL}}\left(t\right)+\underset{j=1}{\overset{N_{\mathrm{DG}}}{\mathrm{\Σ}}}{P}_{\mathrm{DG}}\left(t\right),$ Among them, P _Gi,max represents the maximum technical output of the i-th conventional unit; P _DR,max represents the maximum available demand side regulation load; P _RL represents the system spinning reserve demand; Indicates the newly added reserve capacity of the system to cope with the output uncertainty of the distributed generation, considering the uncertainty of the 100% probability interval of the distributed generation power, where P _DGj is the output of the jth distributed generation; the conventional The technical output of the unit and demand side resources is limited to $\left\{\begin{array}{c}{P}_{\mathrm{Gi},\min }\≤P_{\mathrm{Gi}}\left(t\right)\≤P_{\mathrm{Gi},\max }\\ 0\≤P_{\mathrm{DR}}\left(t\right)\≤P_{\mathrm{DR},\max }\end{array}\right.,$ P _Gi,min and P _Gi,max represent the minimum and maximum technical output of the i-th conventional unit respectively; the climbing constraint of the conventional unit is $\begin{array}{c}{P}_i\left(t\right)-P_i(t-1)\≤r_{\mathrm{ui}}T\\ P_i(t-1)-P_i\left(t\right)\≤r_{\mathrm{di}}T\end{array},$ Among them, P _i (t) and P _i (t-1) represent the output power of the i-th conventional unit at the current moment and the previous moment respectively; r _ui and r _di represent the power increase rate and decrease rate of the i-th conventional unit, respectively; The minimum running time and minimum downtime constraints of the conventional unit are $\begin{array}{c}{T}_{i,\mathrm{on}}\&Greater\; Equal;T_{i,\mathrm{on},\min }\\ T_{i,\mathrm{off}}\&Greater\; Equal;T_{i,\mathrm{off},\min }\end{array},$ Among them, T _i,on represents the continuous operation time of the i-th conventional unit; T _i,off represents the continuous outage time of the i-th conventional unit; T _i,on,min represents the minimum allowed continuous operation time of the i-th conventional unit; The maximum continuous controlled time constraint on the demand side is T _DR ≤ _{T DR, max} , where T _DR represents the controlled time on the demand side; T _{DR, max} represents the maximum continuous controlled time allowed by the demand side; the power consumption mode Satisfaction constraints are $\left\{\begin{array}{c}{m}_{\mathrm{the\; s}}\&Greater\; Equal;m_{\mathrm{the\; s},\min }\\ m_{\mathrm{the\; s}}=1-\frac{\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\left|\mathrm{\Δ}{q}_t\right|}{\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{q}_t}\end{array}\right.;$ Among them, m _s represents the satisfaction degree of electricity consumption mode; m _s,min represents the minimum allowable satisfaction degree of power consumption method, Indicates the sum of the absolute value of the change of electricity in each period before and after optimization within a scheduling period T; Indicates the total power consumption before optimization within a scheduling period T.

Further, it is characterized in that the discrete particle swarm optimization algorithm based on heuristic rules described in step (3) is specifically:

(3.1) Initialize each conventional unit, demand-side characteristic parameters, system predicted load size and distributed power generation predicted output size;

(3.2) Randomly initialize the start-stop status of each unit, and perform particle speed and position updates for a given number of times (preferably 100 times) according to the existing discrete particle swarm velocity update formula and position update formula, and complete the start-stop of the discrete particle swarm algorithm in the first period calculation of state;

The minimum continuous running time constraint, the minimum continuous outage time constraint, and the maximum continuous control time constraint that need to be dealt with in the discrete particle swarm optimization algorithm are heuristic correction methods: after a particle position is updated, if a unit is running or shutting down If the time does not meet the given constraints, the operating state of the unit is forcibly changed to meet the constraints. The heuristic correction method of the system spinning reserve constraint is as follows: firstly sort the units according to the order of operation economy from good to bad according to the priority method. Turn on non-operating units sequentially in order of economics from best to worst until the system spinning reserve constraint is satisfied;

At the same time, in order to prevent all units from running near the minimum output, the following heuristic correction is adopted: after a certain particle position update, if the sum of the minimum output limits of all conventional units in operation and the equivalent virtual generator is greater than the system load 0.9 times the difference from the total output of distributed power sources, the running units will be shut down according to the order of operating economy from bad to good, until the above inequality is satisfied, so as to further ensure the economic distribution of unit output;

(3.3) Determine the total number of time periods T (generally 24) in the scheduling cycle, and repeat step (3.2) until the calculation of the start and stop states of all time periods of the discrete particle swarm optimization algorithm is completed. Store the final start-stop status of each conventional unit and the equivalent virtual generator unit in each period.

Further, the continuous particle swarm optimization algorithm based on heuristic rules described in step (4) is specifically:

(4.1) According to the results of the above discrete particle swarm optimization algorithm, initialize the start-stop status information of each conventional unit and the equivalent virtual generator unit at each time period.

(4.2) Randomly initialize the output distribution of each conventional unit and the equivalent virtual generator unit in the first period. Using the existing continuous particle swarm velocity update formula and position update formula to update the particle velocity and position for a given number of times (preferably 100 times), and complete the calculation of the economic distribution of the output of each unit in the first period of the continuous particle swarm algorithm.

The heuristic correction method for the output of the technical output limit constraint and the climbing constraint that needs to be dealt with in the continuous particle swarm optimization algorithm is: after a certain particle position is updated, if the output of a certain unit is greater than the maximum output limit of the unit and the previous period The smaller value of the unit output value and the maximum unit time climb output of the unit, the unit output is forced to be the smaller value of the above two values; if the unit output is smaller than the unit minimum output limit and the previous If the difference between the output value of the unit during the time period and the maximum unit time drop output of the unit is larger, the output of the unit is forced to be the larger value of the above two values. The heuristic correction method for the satisfaction constraint of the user's electricity consumption mode is as follows: after a certain particle position is updated, if the user's electricity consumption mode satisfaction constraint is not satisfied, the output of the equivalent virtual generator is forcibly reduced until the user's electricity consumption mode is satisfied. degree constraints.

The system load balance constraint is dealt with by penalty function method. The processing method is: convert the constraint condition into a penalty function, and combine the penalty function and the objective function through the penalty factor to become a new fitness function to participate in the calculation of the algorithm. If the constraint condition is not satisfied, the function value of the penalty function is a positive number; if the constraint condition is satisfied, the function value of the penalty function is 0.

(4.3) Repeat the content of step (4.2) until the calculation of the economic distribution of the output of each conventional unit and the equivalent virtual generator unit in the continuous particle swarm optimization algorithm is completed. The discrete particle swarm optimization algorithm obtains the final start-stop state of each conventional unit and the equivalent virtual generator set at each period, and the continuous particle swarm optimization algorithm obtains the output of each conventional unit and the equivalent virtual generator unit at each period, which is the final combination of the unit. The result is also the optimized scheduling result described in the present invention.

Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

(1) Using the idea of virtual power generation, the resources on the demand side are equivalent to virtual power generation resources, and participate in the system power balance adjustment together with conventional units and distributed power sources, and transform the traditional optimal scheduling problem into the optimal combination of units, which can be more convenient and effective Unified deployment of demand-side resources. The calculation example shows that this dispatching method can effectively reduce system cost and environmental pollution, and at the same time satisfy high user satisfaction with electricity consumption.

(2) The improved dual particle swarm algorithm is used to make up for the shortcoming of the single continuous particle swarm algorithm that is difficult to determine the binary state of the unit's start and stop. At the same time, this algorithm decouples the discrete particle swarm and the continuous particle swarm, and adopts a period-by-period calculation method. The solution speed is greatly accelerated. The various heuristic corrections added in the algorithm can make the obtained solution fully satisfy all the constraints, and the introduction of the critical operator ensures that the particles are updated toward a better direction without losing diversity, thus ensuring that the algorithm satisfies higher While improving the accuracy, the solution speed can be effectively improved.

Description of drawings

Fig. 1 is a schematic diagram of the principle of optimal dispatching of an active distribution network according to an embodiment of the present invention;

Fig. 2 is a schematic diagram of optimal scheduling using the improved dual particle swarm optimization method according to an embodiment of the present invention;

Fig. 3 is the flow chart of the discrete particle swarm optimization algorithm based on heuristic rules of the embodiment of the present invention;

Fig. 4 is the flow chart of the continuous particle swarm optimization algorithm based on heuristic rules of the embodiment of the present invention;

Fig. 5 is the forecast curve of wind power generation provided by the embodiment of the present invention;

Fig. 6 is the ideal photovoltaic output prediction curve provided by the embodiment of the present invention;

Fig. 7 is the total system load curve provided by the embodiment of the present invention;

Fig. 8 is a comparison chart of system load curves before and after optimization provided by an embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.

The virtual power generation proposed by the embodiments of the present invention refers to using controllable demand-side resources as system backup power. When the grid load value is high, the power consumption of such resources is appropriately reduced, and corresponding power price compensation is performed to users. Since reducing the load is equivalent to increasing power generation, and the compensation price is equivalent to the cost of power generation, such demand-side resources can be equivalent to virtual power generation resources and actively participate in power grid regulation.

The active distribution network optimal scheduling method in the embodiment of the present invention includes the following steps:

(1) Establish optimal scheduling objective functions F ₁ and F ₂ .

S1: Establish the system power generation operation cost objective function:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\\ <span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; Sh</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; off</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; off</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; cs</span>}}\\ {\mathrm{<span\; class="notranslate">\; sc</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; off</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; cs</span>}}\end{array}\right.\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, F ₁ represents the operating cost of system power generation; T represents the dispatch cycle time; N _G represents the total number of conventional units; f _i represents the operating cost of the i-th conventional unit; P _Gi represents the output power of the i-th conventional unit _; Indicates the start-stop cost of the i-th conventional unit; u _i (t) and u _i (t-1) respectively indicate the start-stop status of the i-th unit at the current moment and the previous moment; f _DR indicates the total amount of compensation for demand side response; P _DR represents the regulated power on the demand side, that is, the virtual power generation; u _DR (t) represents the start-stop status of the virtual power generation at the current moment; A _i , Bi _and C _i represent the operating parameters of the i-th conventional unit; Sh _i represents the The hot start-up cost of the i-th conventional unit; Sc _i represents the cold-start cost of the i-th conventional unit; T _i.off.min represents the minimum continuous outage time allowed for the i-th conventional unit; T _i.off represents the i-th conventional unit The time that has been shut down before a certain period of time, if the unit was on before, it is 0; T _i,cs represents the cold start time of conventional unit i; d _DR is the amount of compensation for the reduction of electricity per kWh on the demand side .

S2: Establish the target function of pollutant discharge:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula, F ₂ represents the total equivalent number of pollutant discharge; g _i represents the pollutant discharge equivalent of the i-th conventional unit; a _i , b _i and c _i represent the pollution emission coefficient of the i-th conventional unit.

(2) Establish optimal scheduling constraints, including: system load balance constraints, system spinning reserve constraints, technical output constraints of conventional units and demand-side resources, conventional unit ramp constraints, conventional unit minimum operating time and minimum downtime constraints, The maximum continuous control time constraint on the demand side, and the satisfaction constraint of electricity consumption mode.

S3: Establish system load balancing constraints:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula, N _DG represents the number of types of distributed power generation; P _DGj (t) represents the output of the jth distributed power generation at time t; P _L (t) represents the load power at time t.

S4: Establish system spinning reserve constraints:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; RL</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, P _Gi,max represents the maximum technical output of the i-th conventional unit; P _DR,max represents the maximum available demand side regulation load; P _RL represents the system spinning reserve demand; Indicates the newly added reserve capacity of the system to deal with the output uncertainty of the distributed generation, considering the uncertainty of the 100% probability interval of the distributed generation power, where P _DGj is the output of the jth distributed generation.

S5: Establish technical output constraints of conventional units and demand-side resources:

P _Gi,min ≤P _Gi (t)≤P _Gi,max (5)

0≤P _DR (t)≤P _DR,max

In the formula, P _Gi,min and P _Gi,max represent the minimum and maximum technical output of the i-th conventional unit, respectively.

S6: Establish conventional unit ramp constraints:

P _i (t)-P _i (t-1)≤r _ui T (6)

P _i (t-1)-P _i (t)≤r _di T

In the formula, P _i (t) and P _i (t-1) represent the output power of the i-th conventional unit at the current moment and the previous moment respectively; r _ui and r _di represent the power increase rate and decline rate of the i-th conventional unit rate.

S7: Establish the minimum continuous operation time and minimum continuous outage time constraints allowed by conventional units:

T _i,on ≥ _{T i,on,min} (7)

T _i,off ≥ _{T i,off,min}

In the formula, T _i,on represents the continuous operation time of the i-th conventional unit; T _i,off represents the continuous outage time of the i-th conventional unit; T _i,on,min represents the minimum allowed continuous operation time of the i-th conventional unit .

S8: Establish the maximum continuous controlled time constraint allowed by the demand side (that is, the continuous running time constraint allowed by the virtual power supply):

T _DR ≤ _{T DR, max} (8)

In the formula, T _DR represents the controlled time of the demand side; T _DR,max represents the maximum continuous controlled time allowed by the demand side.

S9: Establish the satisfaction constraints of the user's electricity consumption mode:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; min</span>}}\\ {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; |</span>}{\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, m _s represents the satisfaction degree of power consumption mode; m _{s, min} represents the minimum allowable power consumption mode satisfaction degree, Indicates the sum of the absolute value of the change of electricity in each period before and after optimization within a scheduling period T; Indicates the total power consumption before optimization within a scheduling period T.

(3) The demand side response is equivalent to a virtual generator, and the start and stop states of all units are determined time by time through the discrete particle swarm algorithm based on heuristic rules.

S10: Initialize the characteristic parameters of each conventional unit, including: unit output limit, fuel characteristic coefficient, minimum start and stop time, cold start time, climbing limit, start-up cost, sewage characteristic coefficient, continuous operation/stop time; initialize the demand side Characteristic parameters, including: the maximum technical output of resources on the demand side, the maximum continuous control time allowed by the demand side; the predicted load size of the initialization system and the predicted output size of distributed power sources.

S11: Initialize the start-stop state of the conventional unit and the equivalent virtual generator set in a certain period of time; there are b _pop particles (generally an integer between [20,80]) that represent the start-stop state of the unit in a certain period of time, each The dimension of the particles is consistent with the sum of the conventional units and the equivalent virtual generator units in the system, and the value of each dimension of the particles represents the start-stop status of the corresponding units in the system. First, randomly initialize the start-stop status of all units to 0 or 1, where 0 means off and 1 means on. After that, first judge whether the initialized particles meet the allowable minimum continuous running time constraint and the minimum continuous downtime constraint, and correct the particle position. The correction formula is as follows:

In the formula, Indicates the value of the i-th dimension of the k-th particle in the 0th iteration, that is, the state of the unit after the initialization of the i-th conventional unit for a certain period of time. If at the moment of initialization, the i-th conventional unit was in the off state before, then T _i,on =0; if the i-th conventional unit was in the on-off state before, then T _i.off =0.

Each particle also needs to judge whether it meets the maximum continuous control time constraint on the demand side, and correct the particle position. The correction formula is as follows:

In the formula, Represents the kth particle, the 0th iteration, the value of the nth dimension, that is, the state of the virtual generator n after the initialization of a certain period of time. T _n,DR indicates the time that the nth virtual generator has been continuously powered on before a certain period of time, and it is 0 if the unit was shut down before. T _{n, DR, max} represents the maximum continuous control time allowed by the demand side, which is equivalent to the maximum continuous running time allowed by the nth virtual generator.

After detecting and correcting whether each particle satisfies the minimum running time constraint, the minimum downtime constraint and the maximum continuous control time constraint on the demand side, it is judged whether each particle satisfies the system spinning reserve constraint. The prioritization method is introduced to sort each conventional unit according to the order of operating economy from good to poor. The operating economy is judged by the average full-load cost AFLC (Average Full-LoadCost), the expression is as follows:

$\mathrm{<span\; class="notranslate">\; AFLC</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

f _i (P _Gi,max )＝A _i ×P _Gi,max ² +B _i ×P _Gi,max +C _i

In the formula, f _i (P _Gi.max ) represents the operating cost of the i-th conventional unit under full load. The smaller the average full load cost, the better the operating economy of the unit.

If a particle does not satisfy the system spinning reserve constraint, turn on the units that have not been turned on in order of operating economy from good to poor, and judge whether the particle satisfies the system spinning reserve constraint, until all particles satisfy the system spinning reserve constraint.

After that, heuristically correct the start-stop state of each particle to judge whether the start-stop state of each particle satisfies the following constraints:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0.9</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

In the formula, Indicates the sum of the output of the distributed power generation in the period t. N represents the sum of conventional units and equivalent virtual generators.

When the sum of the minimum technical output of all operating units at a certain moment is greater than 90% of the difference between the total load and the total output of distributed power, in order to meet the system load balance constraints, almost all units must operate at around the minimum output, which must not be economical Optimal, therefore, incorporates heuristic corrections to speed up convergence. Similarly, each conventional unit is sorted according to the order of operating economy from good to poor, and the index for judging the operation economy of conventional units is shown in formula (12). If a certain particle does not satisfy the constraint condition formula (13), shut down the units that have not been shut down in sequence according to the order of operating economy from bad to good, and judge whether the constraint condition formula (13) is satisfied, until all particles satisfy the constraint condition formula (13).

S12: Complete the single-step update of the discrete particle swarm. First, the speed is updated according to the discrete particle swarm algorithm based on heuristic rules. The speed update formula is as follows:

v _k (t+1)＝wv _k (t)+c ₁ r ₁ (P _k,best (t)-x _k (t))+c ₂ r ₂ (P _g (t)-x _k (t) ) (14)

In the formula, v _k (t) represents the velocity of the k-th particle after the t-th iteration, x _k (t) represents the position of the k-th particle after the t-th iteration, P _k,best (t) represents the k-th The historical optimal value of the particle, P _g (t) represents the global optimal value. w represents inertial weight (generally between [0.4,0.9]), c ₁ and c ₂ represent learning factors (generally 2 is acceptable), r ₁ and r ₂ are random numbers between [0,1].

After the speed update is completed, the position update is performed. The position update steps are as follows:

Firstly, judge whether the start-stop state of the unit satisfies the minimum running time constraint, the minimum downtime constraint and the maximum sustainable running time constraint. If so, then use the critical operator to update the position according to the position update formula of the standard discrete particle swarm; if If it is not satisfied, use (10) and (11) formulas to update. Among them, the introduction of the critical operator is to make the iterative process more optimal. Ordinary particle swarm optimization algorithm uses a random number λ. After the speed is converted into a number s between 0 and 1, if λ is too large or too small, the probability of the unit state changing to 0 or 1 is too high, which will seriously affect the iteration. the optimality. The critical operator 0.1<λ ₁ <0.4, 0.6<λ ₂ <0.9, narrows the range of the random number λ to [λ ₁ ,λ ₂ ], so as to ensure that the particles are updated towards a better direction without losing the diversity of particles .

The position update formula of discrete particle swarm is as follows:

$\mathrm{<span\; class="notranslate">\; Sigmoid</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}}}$

In the formula, x _k (t) represents the position of the kth particle after the tth iteration; rand is a random number between [0,1]; Sigmoid is a custom function.

Next, judge whether the particle satisfies the spinning reserve constraint, and update it. The update process is the same as that of the spinning reserve constraint in S11.

Finally, heuristic correction is performed on the start-stop state of each particle, and the correction process is the same as the heuristic correction process in S11.

After the update of the particle position is completed, each particle is brought into the fitness function to solve the fitness value and update the optimal value. The fitness function in this problem is the start-up cost of the unit, and the formula is as follows:

F＝S _i (t)×(1-u _i (t-1))

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; Sh</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; off</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; off</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; cs</span>}}\\ {\mathrm{<span\; class="notranslate">\; sc</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; off</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; cs</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

In the formula, F represents the start-up cost of the unit.

The steps to update the optimal value are: if the fitness value P _k (t) calculated by the k-th particle brought into the fitness function is smaller than the historical optimal value P _k,best (t) of the k-th particle, then let P _{k ,best} (t)=P _k (t), otherwise P _k,best (t) remains unchanged. If the global optimal value P _g,now (t) of the population after the current update is smaller than the previous global optimal value P _g (t), then set P _g,now (t)=P _g (t).

S13: Complete the calculation of the single-period start-stop state of the discrete particle swarm optimization algorithm; determine the number of iterations C _B to be iterated in each period (generally 100 times), first perform the S11 step, and then repeat the S12 step until the number of cycles reaches C _B times, get the start-stop status of the final certain period of time, and store the data.

S14: Completing the calculation of the start and stop states of the discrete particle swarm optimization algorithm for all time periods. After determining the total number of time periods T in a scheduling cycle (generally 24), the calculation of the start-stop status of each time period can be performed sequentially according to the method in step S13. Store the final start-stop status results of all units in various periods.

(4) After completing the calculation of the start-stop status of all units at each time period, on the basis of the known start-stop status, through the continuous particle swarm optimization algorithm based on heuristic rules, each unit is economically allocated on the basis of constraints , the specific implementation steps are as follows:

S15: Initialize the output distribution of each unit in a certain period of time. Set c _pop (generally a random integer between [20,80]) to represent the particles that all units produce in a certain period of time, and the dimension of each particle is consistent with the sum of the number of conventional units and the equivalent virtual generators in the system , the value of each dimension of the particle represents the output of the corresponding unit in the system. Within the range of the maximum and minimum output of each unit, the output of all units is randomly initialized.

S16: Complete the standard particle swarm single-step update. First update the velocity according to the standard particle swarm optimization algorithm, the velocity update formula is the same as that of discrete particle swarm optimization, see formula (14), and then update the position. The position update formula of continuous particle swarm optimization algorithm is:

x _k (t+1)=x _k (t)+v _k (t) (17)

After the position is updated, each particle needs to judge whether it meets the climbing constraint of the conventional unit, and correct the particle position. The correction formula is as follows:

In the formula, and Respectively represent the value of the i-th dimension of the k-th particle in the t period and the t-1 period, that is, the output of the i-th conventional unit in the t period and the t-1 period. UP ⁱ and DN ⁱ respectively represent the maximum output of the conventional unit i that can climb and the maximum output that can descend per unit time.

Each particle also needs to meet the satisfaction constraints of the user's electricity consumption mode, and the particle position must be corrected. The correction formula is as follows:

In the formula, Indicates the value of the n-th dimension of the k-th particle in the t-period, that is, the output of the n-th virtual generator in the t-period. _PL (t) represents the total system load for time period t.

After the position update is completed, each particle is brought into the fitness function to solve the fitness value and update the optimal value. The fitness function of this problem is composed of the operating cost of the unit, the equivalent price of system sewage discharge and the penalty function of the system load balance constraint. The fitness function formula is:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&times;</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; \&times;</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Gi</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DG</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; DR</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

In the formula, c represents the pollutant discharge price factor. λ represents the penalty factor. The last term of the polynomial represents the penalty function of the system load balancing constraints.

The steps of updating the optimal value are the same as the steps of updating the optimal value in S12.

S17: Completing the calculation of the economic distribution of the output of each unit in a single period; determine the number of iterations C _C (generally 100 times) that needs to be iterated in each period, first perform step S15, and then repeat step S16 until the number of cycles reaches C _C times, Obtain the economic distribution of the output of each unit in a certain period of time, and store the data.

S18: Completing the calculation of the economic distribution of the output of each unit in all periods of the standard particle swarm optimization algorithm; after determining the number of time periods T, the calculation of the economic distribution of units in each period can be performed sequentially according to the method of step S17. Store the final output of all units in each period.

S19: Obtain the final start-stop status and output of all units in each period, which is the final result of the unit combination. According to the results of the unit combination, the dispatching center allocates the output of each unit in a planned way to realize the optimal dispatch of the active distribution network.

In the embodiment of the present invention, in order to verify the effectiveness of the proposed optimal scheduling method, the proposed method is applied to the calculation of optimal scheduling of the active distribution network. The technical parameters of selected conventional thermal power units are shown in Table 1, the forecast curves of wind power and photovoltaic power generation output are shown in Figure 5 and Figure 6, respectively, and the total system load is shown in Figure 7. In the actual power grid, the types of demand-side resources are diverse. The user-side demand-side response needs to compensate the electricity price, while the demand-side resources such as energy storage only need to consider the maintenance cost without price compensation. In order to simplify the calculation of the model, the total size of all demand-side schedulable resources is set to 80MW, the equivalent average compensation amount per kWh is 0.016$, and the user satisfaction with electricity consumption is not less than 90%.

Table 1 Technical parameters of conventional thermal power units

Continued Table 1 Technical parameters of conventional thermal power units

The simulation results are as follows:

(a) Before optimal scheduling, only conventional units are used to supply load demand. At this time, the total cost of system operation within 24 hours is 426,300$, and the equivalent of pollutant discharge is 82,985kg.

(b) After adding distributed power and optimizing scheduling, the total cost of system operation within 24 hours is 390660$, which is 35640$ lower than that in case (a); 8552kg dropped.

(c) If distributed power and demand-side response are considered at the same time, after optimal scheduling, the total cost of system operation within 24 hours can be obtained as 370698$, which is 19962$ lower than that in case (b); the pollutant discharge equivalent is 72487kg , which is 1946kg lower than that in case (b). The comparison of load curves before and after optimal dispatching is shown in Figure 8. It can be seen that after considering the demand side response, the peak value of the load decreases significantly, effectively reducing the peak-to-valley difference of the load.

It can be seen from the calculation example that by adopting the optimal scheduling method proposed by the embodiment of the present invention, distributed power sources and demand-side resources participate in grid regulation at the same time, which can effectively reduce the operating cost of system power generation, reduce the load peak-to-valley difference, and reduce the environmental impact at the same time. Pollution is of positive significance to the optimal operation of the power grid.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (3)

1., based on an active distribution network Optimization Scheduling for virtual generating, it is characterized in that, comprise the steps:

(1) Optimized Operation target function is set up; First object function F is set up for target so that systems generate electricity operating cost is minimum ₁, set up the second objective function F so that pollutant emission total yield number is minimum for target ₂;

(2) described Optimized Operation bound for objective function is obtained; Described constraints comprises: system loading Constraints of Equilibrium, system spinning reserve retrains, the technology of conventional power unit and Demand-side resource is exerted oneself and is limited, conventional power unit Climing constant, conventional power unit minimum running time and the constraint of minimum idle time, the maximum continuous controllable period of time constraint of Demand-side, power mode satisfaction retrains;

(3) Demand Side Response is equivalent to a virtual synchronous generator, according to described Optimized Operation target function and described constraints and by the start and stop state of all units of acquisition that carry out the period one by one based on the discrete particle cluster algorithm of heuristic rule;

(4) according to the start and stop state of all units, and by the continuous particle cluster algorithm based on heuristic rule, on the basis according to described constraints, economic allocation is carried out to each unit; And allocate exerting oneself of each unit according to the result of economic allocation and the final start and stop state of all each periods of unit and size of exerting oneself, realize active distribution network Optimized Operation.

2. active distribution network Optimization Scheduling as claimed in claim 1, it is characterized in that, in step (1), described first object function is: $\min F_1=\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{N_G}{\mathrm{\&Sigma;}}}[f_i\left(P_{\mathrm{Gi}}\left(t\right)\right)\&times;u_i\left(t\right)+S_i\left(t\right)\&times;(1-u_i(t-1))\&times;u_i\left(t\right)]+\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}{f}_{\mathrm{DR}}\left(P_{\mathrm{DR}}\left(t\right)\right)\&times;u_{\mathrm{DR}}\left(t\right);$ Described second target function is: $\min F_2=\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{N_G}{\mathrm{\&Sigma;}}}{g}_i\left(P_{\mathrm{Gi}}\left(t\right)\right)\&times;u_i\left(t\right);$

Wherein, F ₁represent systems generate electricity operating cost; T represents time dispatching cycle; N _grepresent the total number of units of conventional power unit; f _i(P _gi(t))=A _i× P _gi(t) ²+ B _i× P _gi(t)+C _i, f _irepresent i-th conventional power unit operating cost; P _girepresent the power output of i-th conventional power unit; S _irepresent i-th conventional power unit start-up and shut-down costs; u _i(t) and u _i(t-1) the start and stop state of i-th unit current time and previous moment is represented respectively; f _dRrepresent that Demand Side Response compensates total amount; f _dR(P _dR(t))=d _dR× P _dR(t), P _dRrepresent Demand-side regulating power, i.e. virtual generated output; u _dRt () represents the start and stop state of virtual generating current time; A _i, B _iand C _irepresent the operational factor of i-th conventional power unit; $S_i\left(t\right)=\left\{\begin{array}{cc}{\mathrm{Sh}}_i& T_{i,\mathrm{off},\min }\&le;T_{i,\mathrm{off}}\&le;T_{i,\mathrm{cs}}\\ {\mathrm{Sc}}_i& T_{i,\mathrm{off}}\&GreaterEqual;T_{i,\mathrm{cs}}\end{array}\right.,$ Sh _irepresent i-th conventional power unit warm start cost; Sc _irepresent i-th conventional power unit cold start-up cost; T _i.off.minrepresent the minimum lasting idle time that i-th conventional power unit allows; T _i.offrepresenting that i-th conventional power unit continued the time of shutting down before certain period, if be open state before this unit, is then 0; T _{i, cs}represent the cold start-up time of conventional power unit i; d _dRfor Demand-side reduces the amount of money that every kilowatt hour electricity compensates; F ₂represent pollutant emission total yield number; g _i(P _gi(t))=a _i× P _gi(t) ²+ b _i× P _gi(t)+c _i, g _irepresent the pollutant emission equivalent of i-th conventional power unit; a _i, b _iand c _irepresent the disposal of pollutants coefficient of i-th conventional power unit.

3. active distribution network Optimization Scheduling as claimed in claim 1 or 2, it is characterized in that, in step (2), described system loading Constraints of Equilibrium is wherein, N _dGrepresent distributed power source species number; P _dGjt () represents that jth kind distributed power source t is exerted oneself; P _lt () represents the load power of t;

Described system spinning reserve is constrained to $\underset{i=1}{\overset{N_G}{\mathrm{\&Sigma;}}}{u}_i\left(t\right)P_{\mathrm{Gi},\max }+P_{\mathrm{DR},\max }\&GreaterEqual;P_L\left(t\right)+P_{\mathrm{RL}}\left(t\right)+\underset{j=1}{\overset{N_{\mathrm{DG}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{DGj}}\left(t\right),$ Wherein, P _{gi, max}represent that i-th maximum technology of conventional power unit is exerted oneself; P _{dR, max}represent that maximum available Demand-side regulates load; P _rLexpression system spinning reserve demand; expression system is exert oneself uncertainty and the newly-increased reserve capacity of reply distributed power source, considers the uncertainty of distributed electrical source power 100% probability interval, P herein _dGjbe jth kind distributed power source to exert oneself;

The technology of described conventional power unit and Demand-side resource is exerted oneself and is restricted to $\begin{array}{c}{P}_{\mathrm{Gi},\min }\&le;P_{\mathrm{Gi}}\left(t\right)\text{\&le;}{P}_{\mathrm{Gi},\max }\\ 0\&le;P_{\mathrm{DR}}\left(t\right)\&le;P_{\mathrm{DR},\max }\end{array},$ P _{gi, min}, P _{gi, max}represent that i-th minimum, maximum technology of conventional power unit is exerted oneself respectively;

Described conventional power unit Climing constant is $\begin{array}{c}{P}_i\left(t\right)-P_i(t-1)\&le;r_{\mathrm{ui}}T\\ P_i(t-1)-P_i\left(t\right)\&le;r_{\mathrm{di}}T\end{array},$ Wherein P _i(t) and P _i(t-1) power output of current time and previous moment i-th conventional power unit is represented respectively; r _uiand r _direpresent i-th conventional power unit power climbing speed and fall off rate respectively;

Described conventional power unit minimum running time and minimum idle time are constrained to $\begin{array}{c}{T}_{i,\mathrm{on}}\&GreaterEqual;T_{i,\mathrm{on},\min }\\ T_{i,\mathrm{off}}\&GreaterEqual;T_{i,\mathrm{off},\min }\end{array},$ Wherein, T _{i, on}represent i-th conventional power unit continuous operating time; T _{i, off}represent i-th conventional power unit continuous idle time; T _{i, on, min}represent the minimum continuous working period that i-th conventional power unit allows;

The maximum continuous controllable period of time of described Demand-side is constrained to T _dR≤ T _{dR, max}, wherein, T _dRrepresent Demand-side controllable period of time; T _{dR, max}represent the maximum continuous controllable period of time that Demand-side allows;

Described power mode satisfaction is constrained to $\left\{\begin{array}{c}{m}_s\&GreaterEqual;m_{s,\min }\\ m_s=1-\frac{\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\left|\mathrm{\&Delta;}{q}_t\right|}{\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}{q}_t}\end{array}\right.;$ Wherein m _srepresent power mode satisfaction; m _{s, min}represent the minimum power mode satisfaction allowed, represent in a dispatching cycle T, before and after optimizing each period electricity knots modification absolute value and; represent in a dispatching cycle T, power consumption total before optimizing.