CN110516851B - Source-load double-side thermoelectric combined random optimization scheduling method based on virtual power plant - Google Patents
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Abstract
The invention discloses a source-charge double-sided thermoelectric combined random optimization scheduling method based on a virtual power plant. The invention aims at the maximum expected economic benefit of the virtual power plant, optimizes the output of each power generation unit through multi-source complementation coordination of the power source side, and simultaneously effectively solves the uncertainty of wind and light output and obtains better economic benefit through the coordination and optimization of the source load double-side reserved rotary reserve capacity.
Description
Technical Field
The invention relates to the field of optimization of cogeneration systems, in particular to a source-charge double-side thermoelectric combined random optimization scheduling method based on a virtual power plant.
Background
The cogeneration unit has great development potential due to the advantages of high efficiency, energy conservation, environmental protection and the like. However, the thermoelectric unit is generally operated in a hot-fixed electricity mode, so that the adjusting capability of the thermoelectric unit is greatly limited, and the optimal output of the thermoelectric unit cannot be adjusted according to the real-time electricity price level, so that the thermoelectric unit can flexibly participate in the operation of an electric power market. Particularly in winter in the 'three north' region, wind power and photovoltaic power generation continuously and rapidly develop in recent years, and as the wind power and photovoltaic power generation has the characteristics of randomness, intermittence and difficulty in accurate prediction, a large number of thermoelectric units occupying the main place operate with heat fixed electricity, so that higher rotation reserve is reserved for coping with uncertainty of wind power and photovoltaic power generation, and maximization of economic benefit is difficult to obtain. Therefore, on one hand, the influence of wind-light output uncertainty is fully considered in a scheduling strategy, and on the other hand, flexible resources on two sides of a source load are fully excavated, so that the rotating standby requirement is met, and higher economic benefit is obtained.
In recent years, electric boilers are receiving attention and application gradually due to the fact that regional electric loads can be increased, waste wind is effectively utilized, and the thermoelectric unit is decoupled from the constraint of 'power on heat setting'. In addition, the load side flexible load can realize peak clipping and valley filling and provide auxiliary services, and is beneficial to safe and economical operation of a power grid and the absorption of new energy. However, due to the lack of support of a dispatching platform, the large-scale source-load double-side integrated dispatching operation is difficult to realize. At this time, the virtual power plant provides a new idea for solving the above problems as an effective resource integration means. Conventional power system scheduling generally reserves deterministic rotational reserve according to the percentage of wind-solar predicted output, and cannot fully characterize the influence of wind-solar output uncertainty, so that a scheduling strategy is inevitably conservative or impossible. Currently, the scenario method is mostly used for describing uncertainty of wind-light output, however, few reported documents relate to thermoelectric systems, and no real-time electricity price-based coordination load side flexible load participates in a rotary standby plan.
It is therefore desirable to have a source-load double-sided thermoelectric joint random optimization scheduling method based on virtual power plants that overcomes or at least alleviates the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The invention aims to provide a source-load double-side thermoelectric combined random optimization scheduling method based on a virtual power plant, which overcomes or at least alleviates the defects of the prior art.
In order to achieve the above purpose, the source-load double-side thermoelectric combined random optimization scheduling method based on the virtual power plant provided by the invention comprises the following steps:
1) Building a wind-light output multi-scene model: generating a typical scene set by the virtual power plant according to probability distribution of wind and light prediction output and prediction error by using a scene method based on pull Ding Chao cubic sampling so as to simulate uncertainty of wind and light prediction error;
2) Establishing an optimized dispatching mathematical model: under the principle of meeting the constraint condition of a system and the prior utilization of wind and light, reserving certain rotation for standby through coordination and optimization of a power generation side and a load side, so that the uncertainty of wind and light prediction errors is effectively treated, and meanwhile, a mathematical model of source-load double-side thermoelectric combined random optimization scheduling is established with the aim of maximizing expected economic benefits in a daily scheduling period of a virtual power plant;
3) Optimized operation principle of virtual power plant: when a next day output plan is formulated in the thermoelectric coordination scheduling system of the virtual power plant, firstly, the virtual power plant is considered to preferentially utilize wind power and photovoltaic power generation in the capacity range of the virtual power plant, then, the combined operation output of the thermoelectric unit and the electric boiler is formulated, and on the premise of jointly meeting the heat supply requirement, the thermoelectric unit can flexibly adjust the output according to the electricity price level; finally, on this basis, flexible load operation is further arranged to maximize the expected economic benefit of the virtual power plant;
4) Solving an optimal scheduling mathematical model: carrying out model solving by adopting a two-layer optimal scheduling method, searching the optimal rotation reserve capacity by the outer layer, and pre-distributing the rotation reserve capacity so as to pre-determine the next-day output plan of the virtual power plant; and on the premise that the next-day output plan of the virtual power plant is determined, the inner layer optimizes the next-day actual output of the virtual power plant in each scene so as to meet the next-day output plan, and multiplies the economic benefit value in each scene by the corresponding scene probability to obtain the expected economic benefit.
Preferably, the establishing of the wind-light output multi-scene model includes:
1) Scene generation: generating an initial sampling scene set of the wind and light output prediction error by using a Latin hypercube sampling method according to the probability distribution of the wind and light output prediction error;
(1) the wind-light output prediction errorObeying the Laplace normal mixed distribution:
wherein mu W,t 、σ W,t Respectively representing the expected and standard deviation of the wind-light output prediction deviation in the t period;the wind-light output predicted value of the t period is represented; epsilon W,t Representing the percentage of the wind-light output prediction deviation in the t period to the predicted value; a. b represents an intermediate parameter; t represents a time sequence, and the invention takes 0.5h as a scheduling period, namely t=1, 2, …, T, t=48;
(2) The photovoltaic output prediction errorObeys N (0, sigma) PV,t 2 ) Normal distribution of (c):
wherein the method comprises the steps ofRepresenting a predicted value of the photovoltaic output in a t period; sigma (sigma) PV,t Representing the standard deviation of the photovoltaic output prediction error in the t period; epsilon PV,t Representing the percentage of the photovoltaic output prediction error in the t period to the predicted value;
2) Scene ordering: the elements in the resulting initial sample scene set are randomly arranged with the correlation between the random variable sample values being random and uncontrollable. The smaller the correlation between the random variable sample values, the higher the accuracy that results. Therefore, the cholesky decomposition method is adopted to sort the scenes so as to reduce the correlation among sampling values of random variables;
3) Scene reduction: for a scene set with a large number of similar scenes, if computed one by one, efficiency can be significantly impacted. Therefore, on the premise of ensuring certain calculation precision and speed, the scene reduction is carried out on the ordered scenes by adopting synchronous back substitution subtraction, and the basic idea of the reduction is to minimize the probability distance between scene sets before and after the reduction. And finally, combining the reduced scene with the initial wind-light prediction output to obtain a final typical scene set.
Preferably, the optimized dispatching mathematical model comprises an objective function and constraint conditions;
1) The objective function of the optimized dispatching mathematical model considers a plurality of wind-light output scene sets after reduction, so that the objective is to maximize the expected economic benefit of the virtual power plant in one dispatching period:
f is the expected economic benefit of the virtual power plant in a scheduling period of 24 h; s represents a scene sequence, s=1, 2, …, S, s=50; pr(s) represents the probability of scene s occurrence; the remaining terms in the above formula have the following meanings:
①the total electricity and heat selling benefits of the day-ahead energy market are participated in for the t-period virtual power plant:
wherein α (t) represents the electricity rate of the t period; beta represents a heat price; p (P) t 、H t Respectively representing the electric and thermal output of the virtual power plant in the t period;
②fuel cost for the thermoelectric unit for the t period in scenario s:
wherein the method comprises the steps ofThe coal consumption of the thermoelectric unit in the scene s at the t period; c 0 ～c 5 Fitting a constant for the coal consumption characteristic of the thermoelectric unit; />The electric and thermal output of the ith thermoelectric unit in the t period under the scene s are respectively; phi is standard coal unit price;
③the operation maintenance cost of the thermal power plant is as follows:
wherein χ is the proportion of the running maintenance cost of the power plant in the total power generation cost; ρ C The unit capacity cost of the thermal power plant; p (P) C Is the installed capacity of the thermal power plant; n is n c Is the depreciated year of the thermal power plant; τ is the line loss rate between the power generation terminal and the electricity selling settlement point;
④The method is characterized in that the method comprises the following steps of:
wherein k is f 、k g The unit operation maintenance cost of wind-light power generation is respectively;the actual output of wind and light in the scene s at the t period is respectively;
⑤for the environmental cost of the virtual power plant in the t period under the scene s, because wind and light power generation belongs to clean energy power generation, only the environmental cost caused by pollutant emission of the thermoelectric unit is considered:
wherein m is the contaminant species; d, d Cj Pollutant discharge amount per unit coal consumption; upsilon (v) j 、ν j Environmental value and penalty criteria corresponding to the jth contaminant in units respectively;
⑥representing the cost of selling and purchasing power to the power grid due to unbalanced output of the virtual power plant in the t period of the scene s:
wherein alpha is up (t)、α down (t) respectively the up-and-down electricity prices of the power grid in the period t, if the actual output of the virtual power plant is lower than the declaration output before the day, the power is purchased at the up-and-down electricity price and is higher than the day before the dayReporting the output, and selling the electric power by regulating the electricity price;the unbalanced output is generated when the virtual power plant actually operates in a t period under the scene s; />The electric power consumed by the electric boiler in the t period under the scene s; n (N) H The number of users is flexible; />The power interruption and the power increase of the user in the t period k under the scene s are respectively;
⑦the flexible load scheduling cost is represented and consists of two parts, namely a spare capacity cost and a response electric quantity cost:
Wherein omega k 、The method comprises the steps of respectively obtaining an interruptible standby compensation coefficient and a unit scheduling cost coefficient of k users; sigma (sigma) k 、δ k The excitation standby compensation coefficient and the electricity price discount rate of k users are respectively; />Interruptible and stimulated reserve capacity provided for k users during period t, respectively;
⑧C EI investment cost for electric boiler construction:
wherein ρ is E Is an electric boiler equipmentCost per unit capacity; p (P) E The total capacity of the electric boiler equipment; n is n e Is the depreciated years of the electric boiler; r is annual rate;
⑨C EOM the operation and maintenance cost for the electric boiler is as follows:
wherein lambda is the proportionality coefficient of annual running cost of the electric boiler equipment to total investment cost;
2) The constraint conditions of the optimized dispatching mathematical model comprise:
(1) electric balance constraint:
(2) thermal equilibrium constraint:
(3) system rotation standby reliability opportunity constraints:
where Pr {. Cndot. } is the probability of event occurrence;positive and negative rotation spare capacities respectively provided for the t-period unit i; />The rotational reserve capacity provided by the user k of the excitation load can be interrupted and excited for the period t respectively; theta isA confidence level;
(4) maximum trade power constraint of power grid:
wherein eta Grid The electric quantity proportionality coefficient is traded with the power grid;
(5) output characteristic constraint of thermoelectric unit:
wherein the method comprises the steps ofThe upper limit and the lower limit of the power supply output of the ith thermoelectric unit are respectively provided; / >Maximum heat output of the ith thermoelectric unit; />The heating force corresponding to the i-th thermoelectric unit when the heating force is minimum; />The reduction of the power output under the condition of extracting more unit heat when the steam inlet of the steam turbine of the ith thermoelectric unit is unchanged, wherein +.>Is the corresponding value at maximum electric force, < >>Is the corresponding value under the minimum power output; />The ratio coefficient of the electric output and the thermal output when the ith thermoelectric unit runs in back pressure is set;
(6) thermoelectric unit ramp rate constraint:
wherein the method comprises the steps ofAnd->The upward and downward climbing rates of the ith thermoelectric unit are respectively;
(7) electric boiler electrothermal conversion constraint:
wherein ζ is the electric heat conversion efficiency of the electric boiler;
(8) flexible load constraint:
wherein the method comprises the steps ofThe upper and lower limits of the interruptible capacity of the interruptible load user k respectively; />The upper and lower limits of the capacity which can be increased for the exciting load user k are respectively;
preferably, the specific optimization operation principle of the virtual power plant includes:
1) Wind-light operation principle: wind power and photovoltaic power generation are used as clean energy sources for power generation, and virtual power plants are preferentially utilized in the capacity range;
2) The combined operation principle of the thermoelectric unit and the electric boiler is as follows: firstly, the thermoelectric unit and the electric boiler should meet the heat supply requirement together; then, according to the electricity price level, i) if the electricity price of the thermoelectric unit is higher than the electricity selling price, the electric boiler operates to convert part of wind and light power into heat, so that 'thermoelectric decoupling' of the thermoelectric unit is realized, and the thermoelectric unit reduces the output as much as possible to avoid loss; ii) if the generating cost of the thermoelectric unit is lower than the electricity selling price, stopping the electric boiler, and improving the generating output to the greatest extent by the thermoelectric unit to obtain benefits; iii) According to the price level of the power grid, the price level of the power grid and the actual wind and light output typical scene set of the next day, under the condition that the constraint condition of the system reliability is met, the expected economic benefit maximization is targeted, and a certain rotation standby is reserved for the thermoelectric unit so as to cope with the uncertainty of wind and light output;
3) Flexible load operation principle: the virtual power plant aims at maximizing expected economic benefit according to electricity price information, the electricity generation cost of the thermoelectric unit and flexible load compensation price, and the flexible load replaces the thermoelectric unit to bear part of rotation for standby.
Preferably, the established thermoelectric combined random optimization scheduling mathematical model relates to dynamic optimization of multiple variables, multiple constraints and multiple scenes, and the model solution of the virtual power plant source-load double-sided thermoelectric combined random optimization scheduling is solved by adopting a two-layer optimization scheduling method in consideration of the complexity and efficiency problems of the model: the outer layer searches the optimal rotary spare capacity, and pre-distributes the rotary spare capacity, so that the next day output plan of the virtual power plant is pre-determined; and on the premise that the next-day output plan of the virtual power plant is determined, the inner layer optimizes the next-day actual output of the virtual power plant in each scene so as to meet the next-day output plan, and multiplies the economic benefit value in each scene by the corresponding scene probability to obtain the expected economic benefit.
The two-layer optimal scheduling method comprises the following specific processes:
(1) inputting virtual power plant original data and algorithm parameters;
(2) selecting an initial search interval with precision epsilon >0 and a golden section method, namely a reserved rotation standby interval [ a, b ] of the virtual power plant;
(3) Calculating a heuristic point r 1 ＝a+0.382*(b-a)、r 2 ＝a+0.618*(b-a)；
(4) Will r 1 、r 2 Respectively substituting the target functions into a target function formula for maximizing the expected economic benefit of the virtual power plant;
(5) the thermoelectric unit and the flexible load jointly bear rotation for standby, and a virtual power plant next-day output plan is prefabricated;
(6) setting a scene i=1 on the premise of planning the next day of output of the virtual power plant;
(7) randomly generating an initial population;
(8) calculating the fitness function value of each individual of the population by taking the economic benefit of the next day operation of the virtual power plant in the scene i as a target;
(9) selecting regenerated individuals according to the fitness, wherein the individuals with high fitness have high probability of being selected, and the individuals with low fitness may be eliminated;
performing adaptive crossover and mutation operations on the individuals selected in step (9) to generate new individuals;
crossover probability P C Probability of variation P m The determination mode is as follows:
wherein f max Is the maximum fitness value in the population; f (f) avg Average fitness value for the population; f is the larger fitness value of the two individuals to be crossed; f' is the fitness value of the individual to be mutated; p (P) C1 、P C2 For hybridization constant, P m1 、P m2 Is a variation constant;
generating a new generation population by crossing and mutation, and updating the optimal solution of individuals and the population;
judging whether a termination condition is met, and if so, outputting an optimal solution f (i); if not, returning to the step (8);
Let i=i+1, determine if i > 50 is true, if so, turn +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, returning to the step (7);
calculate->If F (r) 1 )＜F(r 2 ) If true, turn->Otherwise turn->；
Let a=r 1 ，r 1 ＝r 2 ，r 2 =a+0.618 (b-a), trans->；
Let b=r 2 ，r 2 ＝r 1 ，r 1 =a+0.382 x (b-a), trans->；
If r 2 -r 1 If < epsilon, stopping calculation and outputting approximately optimal solution +.>Otherwise, turning to (4);
the virtual power plant source-load double-side combined heat and power random optimization scheduling method provided by the invention aims at the maximum expected economic benefit in the daily scheduling period of the virtual power plant, and can effectively cope with uncertainty of wind-light output and obtain better economic benefit by coordinating and optimizing the rotation reserve capacity of the power generation side and the load side.
Description of the drawings:
FIG. 1 is a flow chart of virtual power plant operation.
FIG. 2 is a flow chart of a two-layer optimized scheduling algorithm.
FIG. 3 is a graph of wind and light output prediction curves and thermal load demand values.
Fig. 4 is a graph of day-ahead electricity prices of virtual power plants and up-and-down electricity prices of the power grid.
FIG. 5 is a graph of the next day planned output of a virtual power plant formulated by different scheduling methods.
Fig. 6 is a diagram of rotational spare capacity reserved for different scheduling methods.
The specific embodiment is as follows:
in order to make the objects, technical solutions and advantages of the present invention become more apparent, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the invention. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
According to the broad embodiment of the invention, the method comprises the steps of building a wind-light output multi-scene model, building an optimized dispatching mathematical model, and solving an optimized operation principle and the optimized dispatching mathematical model of the virtual power plant;
the building of the wind-light output multi-scene model is that a virtual power plant generates a typical scene set by using a scene method based on pull Ding Chao cubic sampling according to probability distribution of wind-light prediction output and prediction error so as to simulate uncertainty of wind-light prediction error;
the establishment of the optimal scheduling mathematical model is to reserve a certain rotation reserve through coordination and optimization of a power generation side and a load side under the principle of meeting system constraint conditions and wind-solar priority utilization, so that the uncertainty of wind-solar prediction errors is effectively treated, and meanwhile, the mathematical model of source-load double-side thermoelectric combined random optimization scheduling is established with the aim of maximizing expected economic benefits in a daily scheduling period of a virtual power plant;
the optimal operation principle of the virtual power plant is that when a next day output plan is formulated in a thermoelectric coordination scheduling system of the virtual power plant, firstly, wind power and photovoltaic power generation are preferentially utilized by the virtual power plant in the capacity range of the virtual power plant, then, the combined operation output of a thermoelectric unit and an electric boiler is formulated, and on the premise of meeting the heat supply requirement together, the thermoelectric unit can flexibly adjust the output according to the electricity price level; finally, on this basis, flexible load operation is further arranged to maximize the expected economic benefit of the virtual power plant;
Because the thermoelectric combined random optimization scheduling mathematical model relates to the dynamic optimization of multiple variables, multiple constraints and multiple scenes, and the complexity and efficiency problems of the model are considered, the solution of the optimization scheduling mathematical model adopts a two-layer optimization scheduling method to solve: the outer layer searches the optimal rotary spare capacity, and pre-distributes the rotary spare capacity, so that the next day output plan of the virtual power plant is pre-determined; and on the premise that the next-day output plan of the virtual power plant is determined, the inner layer optimizes the next-day actual output of the virtual power plant in each scene so as to meet the next-day output plan, and multiplies the economic benefit value in each scene by the corresponding scene probability to obtain the expected economic benefit.
The virtual power plant source-load double-side combined heat and power random optimization scheduling method provided by the invention aims at the maximum expected economic benefit in the daily scheduling period of the virtual power plant, and can effectively cope with uncertainty of wind-light output and obtain better economic benefit by coordinating and optimizing the rotation reserve capacity of the power generation side and the load side.
The building of the wind-light output multi-scene model comprises the following steps:
1) Scene generation: generating an initial sampling scene set of the wind and light output prediction error by using a Latin hypercube sampling method according to the probability distribution of the wind and light output prediction error;
(1) The wind-light output prediction errorObeying the Laplace normal mixed distribution:
wherein mu W,t 、σ W,t Respectively representing the expected and standard deviation of the wind power output prediction deviation in the t period;representing a predicted value of the wind power output in a t period; epsilon W,t Representing the percentage of the wind power output prediction deviation in the t period to the predicted value; a. b represents an intermediate parameter; t represents a time sequence, and the invention takes 0.5h as a scheduling period, namely t=1, 2, …, T, t=48;
(2) the photovoltaic output prediction errorObeys N (0, sigma) PV,t 2 ) Normal distribution of (c):
wherein the method comprises the steps ofRepresenting a predicted value of the photovoltaic output in a t period; sigma (sigma) PV,t Representing the standard deviation of the photovoltaic output prediction error in the t period; epsilon PV,t Representing the percentage of the photovoltaic output prediction error in the t period to the predicted value;
2) Scene ordering: the elements in the resulting initial sample scene set are randomly arranged with the correlation between the random variable sample values being random and uncontrollable. The smaller the correlation between the random variable sample values, the higher the accuracy that results. Therefore, the cholesky decomposition method is adopted to sort the scenes so as to reduce the correlation among sampling values of random variables;
3) Scene reduction: for a scene set with a large number of similar scenes, if computed one by one, efficiency can be significantly impacted. Therefore, on the premise of ensuring certain calculation precision and speed, the scene reduction is carried out on the ordered scenes by adopting synchronous back substitution subtraction, and the basic idea of the reduction is to minimize the probability distance between scene sets before and after the reduction. And finally, combining the reduced scene with the initial wind-light prediction output to obtain a final typical scene set.
The optimized dispatching mathematical model comprises an objective function and constraint conditions;
1) The objective function of the optimized dispatching mathematical model considers a plurality of wind-light output scene sets after reduction, so that the objective is to maximize the expected economic benefit of the virtual power plant in one dispatching period:
f is the expected economic benefit of the virtual power plant in a scheduling period of 24 h; s represents a scene sequence, s=1, 2, …, S, s=50; pr(s) represents the probability of scene s occurrence; the remaining terms in the above formula have the following meanings:
①the total electricity and heat selling benefits of the day-ahead energy market are participated in for the t-period virtual power plant:
wherein α (t) represents the electricity rate of the t period; beta represents a heat price; p (P) t 、H t Respectively representing the electric and thermal output of the virtual power plant in the t period;
②fuel cost for the thermoelectric unit for the t period in scenario s:
wherein the method comprises the steps ofThe coal consumption of the thermoelectric unit in the scene s at the t period; c 0 ～c 5 Fitting a constant for the coal consumption characteristic of the thermoelectric unit; />The electric and thermal output of the ith thermoelectric unit in the t period under the scene s are respectively; phi is standard coal unit price;
③the operation maintenance cost of the thermal power plant is as follows:
wherein χ is the proportion of the running maintenance cost of the power plant in the total power generation cost; ρ C The unit capacity cost of the thermal power plant; p (P) C Is the installed capacity of the thermal power plant; n is n c Is the depreciated year of the thermal power plant; τ is the line loss rate between the power generation terminal and the electricity selling settlement point;
④the method is characterized in that the method comprises the following steps of:
wherein k is f 、k g The unit operation maintenance cost of wind-light power generation is respectively;the actual output of wind and light in the scene s at the t period is respectively;
⑤for the environmental cost of the virtual power plant in the t period under the scene s, because wind and light power generation belongs to clean energy power generation, only the environmental cost caused by pollutant emission of the thermoelectric unit is considered:
wherein m is the contaminant species; d, d Cj Pollutant discharge amount per unit coal consumption; upsilon (v) j 、ν j Environmental value and penalty criteria corresponding to the jth contaminant in units respectively;
⑥representing the cost of selling and purchasing power to the power grid due to unbalanced output of the virtual power plant in the t period of the scene s:
wherein alpha is up (t)、α down (t) respectively adjusting the power prices up and down of the power grid in the period t, and if the actual output of the virtual power plant is lower than the declared output before the day, purchasing power by the power price up to be adjusted, and is higher than the declared output before the day, selling power by the power price down to be adjusted;the unbalanced output is generated when the virtual power plant actually operates in a t period under the scene s; />The electric power consumed by the electric boiler in the t period under the scene s; n (N) H The number of users is flexible; / >The power interruption and the power increase of the user in the t period k under the scene s are respectively;
⑦the flexible load scheduling cost is represented and consists of two parts, namely a spare capacity cost and a response electric quantity cost:
wherein omega k 、The method comprises the steps of respectively obtaining an interruptible standby compensation coefficient and a unit scheduling cost coefficient of k users; sigma (sigma) k 、δ k The excitation standby compensation coefficient and the electricity price discount rate of k users are respectively; />Interruptible and stimulated reserve capacity provided for k users during period t, respectively;
⑧C EI investment cost for electric boiler construction:
wherein ρ is E The unit capacity cost of the electric boiler equipment is set; p (P) E The total capacity of the electric boiler equipment; n is n e Is the depreciated years of the electric boiler; r is annual rate;
⑨C EOM the operation and maintenance cost for the electric boiler is as follows:
wherein lambda is the proportionality coefficient of annual running cost of the electric boiler equipment to total investment cost;
3) The constraint conditions of the optimized dispatching mathematical model comprise:
(1) electric balance constraint:
(2) thermal equilibrium constraint:
(3) system rotation standby reliability opportunity constraints:
where Pr {. Cndot. } is the probability of event occurrence;positive and negative rotation spare capacities respectively provided for the t-period unit i; />The rotational reserve capacity provided by the user k of the excitation load can be interrupted and excited for the period t respectively; θ is the confidence level;
(4) maximum trade power constraint of power grid:
Wherein eta Grid The electric quantity proportionality coefficient is traded with the power grid;
(5) output characteristic constraint of thermoelectric unit:
wherein the method comprises the steps ofThe upper limit and the lower limit of the power supply output of the ith thermoelectric unit are respectively provided; />Maximum heat output of the ith thermoelectric unit; />The heating force corresponding to the i-th thermoelectric unit when the heating force is minimum; />The reduction of the power output under the condition of extracting more unit heat when the steam inlet of the steam turbine of the ith thermoelectric unit is unchanged, wherein +.>Is the corresponding value at maximum electric force, < >>Is the corresponding value under the minimum power output; />The ratio coefficient of the electric output and the thermal output when the ith thermoelectric unit runs in back pressure is set;
(6) thermoelectric unit ramp rate constraint:
wherein the method comprises the steps ofAnd->The upward and downward climbing rates of the ith thermoelectric unit are respectively;
(7) electric boiler electrothermal conversion constraint:
wherein ζ is the electric heat conversion efficiency of the electric boiler;
(8) flexible load constraint:
wherein the method comprises the steps ofThe upper and lower limits of the interruptible capacity of the interruptible load user k respectively; />The upper and lower limits of the capacity which can be increased for the exciting load user k are respectively;
as shown in fig. 1, the virtual power plant predicts the wind-solar power output on the next day first, and generates a typical scene set by using a scene method based on Ding Chao cubic sampling according to the probability distribution of wind-solar prediction output and prediction error thereof so as to simulate the uncertainty of wind-solar prediction error. And the power grid predicts the next-day power demand, determines the power price of each period of the day-ahead energy market and the up-down power price of the power grid according to the supply-demand relationship, and transmits the power price to the virtual power plant. And reserving a certain rotation reserve for standby by the coordination and optimization power generation side and the load side under the principle that the system constraint condition and the wind-solar priority utilization are met by the virtual power plant, optimizing the next-day output plan with the aim of maximizing the expected economic benefit, reporting to the power grid, and finally determining a feasible next-day output plan of the virtual power plant by the power grid.
When a next day output plan is formulated in the thermoelectric coordination scheduling system of the virtual power plant according to the electricity price level, the virtual power plant is considered to preferentially utilize wind power and photovoltaic power generation in the capacity range of the virtual power plant, then the combined operation output of the thermoelectric unit and the electric boiler is formulated, and the thermoelectric unit can flexibly adjust the output according to the electricity price level on the premise of jointly meeting the heat supply requirement. On the basis of this, the flexible load operation is further arranged. The specific optimization operation principle is as follows:
1) Wind-light operation principle: wind power and photovoltaic power generation are used as clean energy sources for power generation, and virtual power plants are preferentially utilized in the capacity range;
2) The combined operation principle of the thermoelectric unit and the electric boiler is as follows: first, the thermoelectric unit and the electric boiler should meet the heat supply requirement together. And then, according to the electricity price level, if i) the electricity generation cost of the thermoelectric unit is higher than the electricity selling price, the electric boiler operates to convert part of wind and light power into heat, so that 'thermoelectric decoupling' of the thermoelectric unit is realized, and the thermoelectric unit reduces the output as much as possible to avoid loss. ii) the generating cost of the thermoelectric unit is lower than the electricity selling price, the electric boiler is stopped, and the thermoelectric unit improves the generating output as much as possible to obtain benefits. iii) According to the price level of the power grid, the price level of the power grid and the actual wind and light output typical scene set of the next day, under the condition that the constraint condition of the system reliability is met, the expected economic benefit maximization is targeted, and a certain rotation standby is reserved for the thermoelectric unit so as to cope with the uncertainty of wind and light output;
3) Flexible load operation principle: the virtual power plant aims at maximizing expected economic benefit according to electricity price information, the electricity generation cost of the thermoelectric unit and flexible load compensation price, so that flexible load replaces the thermoelectric unit to bear part of rotation for standby;
the utility model relates to a dynamic optimization of multiple variables, multiple constraints and multiple scenes, and solves the problems of complexity and efficiency of the model by adopting a two-layer optimization scheduling method: the outer layer optimizes the rotary spare capacity by a golden section method of linear search, and pre-distributes the rotary spare capacity, so as to pre-determine the next day output plan of the virtual power plant; and on the premise that the next-day output plan of the virtual power plant is determined, optimizing the actual next-day output of the virtual power plant in each scene by adopting a self-adaptive genetic algorithm to meet the next-day output plan, and multiplying the economic benefit value in each scene by the corresponding scene probability to obtain the expected economic benefit.
As shown in fig. 2, the specific flow of the two-layer optimal scheduling method is as follows:
(1) inputting virtual power plant original data and algorithm parameters;
(2) selecting an initial search interval with precision epsilon >0 and a golden section method, namely a reserved rotation standby interval [ a, b ] of the virtual power plant;
(3) Calculating a heuristic point r 1 ＝a+0.382*(b-a)、r 2 ＝a+0.618*(b-a)；
(4) Will r 1 、r 2 Respectively substituting the target functions into a target function formula for maximizing the expected economic benefit of the virtual power plant;
(5) the thermoelectric unit and the flexible load jointly bear rotation for standby, and a virtual power plant next-day output plan is prefabricated;
(6) setting a scene i=1 on the premise of planning the next day of output of the virtual power plant;
(7) randomly generating an initial population;
(8) calculating the fitness function value of each individual of the population by taking the economic benefit of the next day operation of the virtual power plant in the scene i as a target;
(9) selecting regenerated individuals according to the fitness, wherein the individuals with high fitness have high probability of being selected, and the individuals with low fitness may be eliminated;
performing adaptive crossover and mutation operations on the individuals selected in step (9) to generate new individuals;
crossover probability P C Probability of variation P m The determination mode is as follows:
wherein f max Is the maximum fitness value in the population; f (f) avg Average fitness value for the population; f is the larger fitness value of the two individuals to be crossed; f' is the fitness value of the individual to be mutated; p (P) C1 、P C2 For hybridization constant, P m1 、P m2 Is a variation constant;
generating a new generation population by crossing and mutation, and updating the optimal solution of individuals and the population;
judging whether a termination condition is met, and if so, outputting an optimal solution f (i); if not, returning to the step (8);
Let i=i+1, determine if i > 50 is true, if so, turn +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, returning to the step (7);
calculate->If F (r) 1 )＜F(r 2 ) If true, turn->Otherwise turn->；
Let a=r 1 ，r 1 ＝r 2 ，r 2 =a+0.618 (b-a), trans->；
Let b=r 2 ，r 2 ＝r 1 ，r 1 =a+0.382 x (b-a), trans->；
If r 2 -r 1 If < epsilon, stopping calculation and outputting approximately optimal solution +.>Otherwise, turning to (4);
in one embodiment, the virtual power plant consists of 372MW thermal power plants (including two extraction thermoelectric units), 1 180MW wind farm and 1 100MW photovoltaic power station. The selling heat price of the virtual power plant is 90 yuan/MWh. The price of the standard coal is 548 yuan/t. The electric quantity proportionality coefficient of the virtual power plant and the electric network trade is 0.05. The unit operation maintenance cost of wind and light power generation is respectively 20 yuan/MWh and 30 yuan/MWh. The average relative error of wind-light output prediction is respectively 15% and 8%. For the electric boiler, a 10kV electrode type hot water boiler is adopted, and the electric heat conversion efficiency is 99.5%. In view of the characteristics of small capacity, dispersibility, uncertainty and the like of the flexible load at the load side, the invention assumes that various flexible load users are classified and integrated by a load aggregator and finally provided for a dispatching center to uniformly regulate and control, and flexible load parameter information provided by the load aggregator is shown in a table 1. The coal consumption characteristic and the operation characteristic parameter information of the thermoelectric unit are respectively shown in tables 2 and 3. The construction, operation and maintenance cost parameters of the thermal power plant and the electric boiler equipment are shown in table 4. The environmental value and penalty costs for each contaminant are shown in table 5.
TABLE 1 Flexible load parameter information
Table 2 coal consumption characteristic parameters of thermoelectric units
TABLE 3 operating characteristics parameters of thermoelectric units
TABLE 4 thermal power plant and electric boiler plant construction and operation maintenance cost parameters
TABLE 5 environmental value and penalty cost for each contaminant
The parameters of the adaptive genetic algorithm are set as follows: number of individuals np=50; maximum evolution algebra ng=500; hybridization constant P C1 ＝0.5，P C2 =0.9; variation constant P m1 ＝0.02，P m2 =0.06; the coding mode adopts binary coding, and the discrete precision eps=0.01.
The wind-light output prediction curve and the thermal load demand value curve are shown in fig. 3. The daily electricity selling price of the virtual power plant and the up-and-down electricity regulating price of the power grid are shown in fig. 4.
Substituting the data into a virtual power plant scheduling program compiled by Matlab language to obtain the optimal scheduling result shown in the following table 6:
table 6 comparison of optimal scheduling results for different scheduling methods
As can be seen from Table 6, compared with the conventional deterministic optimal scheduling method, the random optimal scheduling method provided by the invention has the advantages that the expected cost of purchasing electricity by the virtual power plant with higher electricity prices is lower, the expected income of selling electricity with lower electricity prices is lower, namely, the electricity quantity purchased by the virtual power plant with higher electricity prices is lower than the electricity quantity sold with lower electricity prices by base, so that the expected economic benefit is higher.
The planned output curve of the virtual power plant on the next day and the reserved rotation reserve capacity formulated by different scheduling methods are shown in fig. 5 and 6 respectively.
According to fig. 5 and 6, when the random optimal scheduling method provided by the invention is applied to make a virtual power plant next day output plan, the virtual power plant can reduce output and avoid loss in a period of lower electricity price; and in the period of higher electricity price, the virtual power plant can improve the output and increase the income. The random optimization scheduling method provided by the invention fully considers the situation of wind-light output prediction error and electricity price, and reserves the rotation reserve capacity together by coordinating and optimizing the flexible loads at the power generation side and the load side, so that the virtual power plant can flexibly adjust the output according to the electricity price level.
It will be appreciated by persons skilled in the art that the above examples of the invention are provided for clarity of illustration only and are not limiting of the embodiments of the invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. And obvious changes and modifications which come within the spirit of the invention are desired to be protected.
Claims (4)
1. A source-load double-side thermoelectric combined random optimization scheduling method based on a virtual power plant is characterized by comprising the following steps:
1) Building a wind-light output multi-scene model: generating a typical scene set by the virtual power plant according to probability distribution of wind and light prediction output and prediction error by using a scene method based on pull Ding Chao cubic sampling so as to simulate uncertainty of wind and light prediction error;
2) Establishing an optimized dispatching mathematical model: under the principle of meeting the constraint condition of a system and the prior utilization of wind and light, reserving certain rotation for standby through coordination and optimization of a power generation side and a load side, so that the uncertainty of wind and light prediction errors is effectively treated, and meanwhile, a mathematical model of source-load double-side thermoelectric combined random optimization scheduling is established with the aim of maximizing expected economic benefits in a daily scheduling period of a virtual power plant; the optimized dispatching mathematical model comprises an objective function and constraint conditions:
1) The objective function of the optimized dispatching mathematical model considers a plurality of wind-light output scene sets after reduction, so that the objective function is aimed at maximizing the expected economic benefit of the virtual power plant in one dispatching period, and the objective function is as follows:
f is the expected economic benefit of the virtual power plant in a scheduling period of 24 h; s represents a scene sequence, s=1, 2, …, S, s=50; pr(s) represents the probability of scene s occurrence; t represents a time sequence, taking 0.5h as a scheduling period, namely t=1, 2, …, T, taking t=48; the remaining terms in the above formula have the following meanings:
①The total electricity and heat selling benefits of the day-ahead energy market are participated in for the t-period virtual power plant:
wherein α (t) represents the electricity rate of the t period; beta represents a heat price; p (P) t 、H t Respectively representing the electric and thermal output of the virtual power plant in the t period;
②fuel cost for the thermoelectric unit for the t period in scenario s:
wherein the method comprises the steps ofThe coal consumption of the thermoelectric unit in the scene s at the t period; c 0 ～c 5 Fitting a constant for the coal consumption characteristic of the thermoelectric unit;the electric and thermal output of the ith thermoelectric unit in the t period under the scene s are respectively; phi is standard coal unit price;
③the operation maintenance cost of the thermal power plant is as follows:
wherein χ is the proportion of the running maintenance cost of the power plant in the total power generation cost; ρ C The unit capacity cost of the thermal power plant; p (P) C Is the installed capacity of the thermal power plant; n is n c Is the depreciated year of the thermal power plant; τ is the line loss rate between the power generation terminal and the electricity selling settlement point;
④for the operation maintenance cost of the wind-solar power generation at the t period under the scene s：
Wherein k is f 、k g The unit operation maintenance cost of wind-light power generation is respectively;the actual output of wind and light in the scene s at the t period is respectively;
⑤for the environmental cost of the virtual power plant in the t period under the scene s, because wind and light power generation belongs to clean energy power generation, only the environmental cost caused by pollutant emission of the thermoelectric unit is considered:
Wherein m is the contaminant species; d, d Cj Pollutant discharge amount per unit coal consumption; u (u) j 、ν j Environmental value and penalty criteria corresponding to the jth contaminant in units respectively;
⑥representing the cost of selling and purchasing power to the power grid due to unbalanced output of the virtual power plant in the t period of the scene s:
wherein alpha is up (t)、α down (t) respectively adjusting the power price up and down of the power grid in the period t, if the actual output of the virtual power plant is lower than the current output of the virtual power plantReporting the output, purchasing power with the upper power price, and selling power with the lower power price if the output is higher than the output reported before the day;the unbalanced output is generated when the virtual power plant actually operates in a t period under the scene s; />The electric power consumed by the electric boiler in the t period under the scene s; n (N) H The number of users is flexible; />The power interruption and the power increase of the user in the t period k under the scene s are respectively;
⑦the flexible load scheduling cost is represented and consists of two parts, namely a spare capacity cost and a response electric quantity cost:
wherein omega k 、The method comprises the steps of respectively obtaining an interruptible standby compensation coefficient and a unit scheduling cost coefficient of k users; sigma (sigma) k 、δ k The excitation standby compensation coefficient and the electricity price discount rate of k users are respectively; />Interruptible and stimulated reserve capacity provided for k users during period t, respectively;
⑧C EI investment cost for electric boiler construction:
wherein ρ is E The unit capacity cost of the electric boiler equipment is set; p (P) E The total capacity of the electric boiler equipment; n is n e Is the depreciated years of the electric boiler; r is annual rate;
⑨C EOM the operation and maintenance cost for the electric boiler is as follows:
wherein lambda is the proportionality coefficient of annual running cost of the electric boiler equipment to total investment cost;
2) The constraint conditions of the optimized dispatching mathematical model comprise:
(1) electric balance constraint:
(2) thermal equilibrium constraint:
(3) system rotation standby reliability opportunity constraints:
where Pr {. Cndot. } is the probability of event occurrence;positive and negative rotation spare capacities respectively provided for the t-period unit i; />Respectively t time periods can be interrupted and excitedThe spare capacity of rotation provided by the load user k; θ is the confidence level;
(4) maximum trade power constraint of power grid:
wherein eta Grid The electric quantity proportionality coefficient is traded with the power grid;
(5) output characteristic constraint of thermoelectric unit:
wherein the method comprises the steps ofThe upper limit and the lower limit of the power supply output of the ith thermoelectric unit are respectively provided; />Maximum heat output of the ith thermoelectric unit; />The heating force corresponding to the i-th thermoelectric unit when the heating force is minimum; />The reduction of the power output under the condition of extracting more unit heat when the steam inlet of the steam turbine of the ith thermoelectric unit is unchanged, wherein +.>Is the corresponding value at maximum electric force, < > >To minimum electric powerThe corresponding value below; />The ratio coefficient of the electric output and the thermal output when the ith thermoelectric unit runs in back pressure is set;
(6) thermoelectric unit ramp rate constraint:
wherein the method comprises the steps ofAnd->The upward and downward climbing rates of the ith thermoelectric unit are respectively;
(7) electric boiler electrothermal conversion constraint:
wherein ζ is the electric heat conversion efficiency of the electric boiler;
(8) flexible load constraint:
wherein the method comprises the steps ofThe upper and lower limits of the interruptible capacity of the interruptible load user k respectively; />Increased capacity for each excitation load user kUpper and lower limits of the amount; 3) Optimized operation principle of virtual power plant: when a next day output plan is formulated in the thermoelectric coordination scheduling system of the virtual power plant, firstly, the virtual power plant is considered to preferentially utilize wind power and photovoltaic power generation in the capacity range of the virtual power plant, then, the combined operation output of the thermoelectric unit and the electric boiler is formulated, and on the premise of jointly meeting the heat supply requirement, the thermoelectric unit can flexibly adjust the output according to the electricity price level; finally, on this basis, flexible load operation is further arranged to maximize the expected economic benefit of the virtual power plant;
4) Solving an optimal scheduling mathematical model: carrying out model solving by adopting a two-layer optimal scheduling method, searching the optimal rotation reserve capacity by the outer layer, and pre-distributing the rotation reserve capacity so as to pre-determine the next-day output plan of the virtual power plant; and on the premise that the next-day output plan of the virtual power plant is determined, the inner layer optimizes the next-day actual output of the virtual power plant in each scene so as to meet the next-day output plan, and multiplies the economic benefit value in each scene by the corresponding scene probability to obtain the expected economic benefit.
2. The virtual power plant-based source-load double-side thermoelectric joint random optimization scheduling method is characterized by comprising the following steps of: the building of the wind-light output multi-scene model comprises the following steps:
1) Scene generation: generating an initial sampling scene set of the wind and light output prediction error by using a Latin hypercube sampling method according to the probability distribution of the wind and light output prediction error;
(1) wind power output prediction errorObeying the Laplace normal mixed distribution:
wherein mu W,t 、σ W,t Respectively representing the expected and standard deviation of the wind power output prediction deviation in the t period;representing a predicted value of the wind power output in a t period; epsilon W,t Representing the percentage of the wind power output prediction deviation in the t period to the predicted value; a. b represents an intermediate parameter; t represents a time sequence, taking 0.5h as a scheduling period, namely t=1, 2, …, T, taking t=48;
(2) photovoltaic output prediction errorObeys N (0, sigma) PV,t 2 ) Normal distribution of (c):
wherein the method comprises the steps ofRepresenting a predicted value of the photovoltaic output in a t period; sigma (sigma) PV,t Representing the standard deviation of the photovoltaic output prediction error in the t period; epsilon PV,t Representing the percentage of the photovoltaic output prediction error in the t period to the predicted value;
2) Scene ordering: the elements in the obtained initial sampling scene set are arranged randomly, and the correlation among the random variable sampling values is random and uncontrollable; if the correlation between the random variable sampling values is smaller, the brought accuracy is higher; therefore, the cholesky decomposition method is adopted to sort the scenes so as to reduce the correlation among sampling values of random variables;
3) Scene reduction: for a scene set with a large number of similar scenes, if the scenes are calculated one by one, the efficiency is obviously affected; therefore, on the premise of ensuring certain calculation precision and speed, adopting synchronous back substitution reduction method to reduce the ordered scenes, wherein the basic idea of the reduction is to minimize the probability distance between scene sets before and after the reduction; and finally, combining the reduced scene with the initial wind-light prediction output to obtain a final typical scene set.
3. The virtual power plant-based source-load double-side thermoelectric joint random optimization scheduling method is characterized by comprising the following steps of: the specific optimization operation principle of the virtual power plant comprises the following steps:
1) Wind-light operation principle: wind power and photovoltaic power generation are used as clean energy sources for power generation, and virtual power plants are preferentially utilized in the capacity range;
2) The combined operation principle of the thermoelectric unit and the electric boiler is as follows: firstly, the thermoelectric unit and the electric boiler should meet the heat supply requirement together; then, according to the electricity price level, i) if the electricity price of the thermoelectric unit is higher than the electricity selling price, the electric boiler operates to convert part of wind and light power into heat, so that 'thermoelectric decoupling' of the thermoelectric unit is realized, and the thermoelectric unit reduces the output as much as possible to avoid loss; ii) if the generating cost of the thermoelectric unit is lower than the electricity selling price, stopping the electric boiler, and improving the generating output to the greatest extent by the thermoelectric unit to obtain benefits; iii) According to the price level of the power grid, the price level of the power grid and the actual wind and light output typical scene set of the next day, under the condition that the constraint condition of the system reliability is met, the expected economic benefit maximization is targeted, and a certain rotation standby is reserved for the thermoelectric unit so as to cope with the uncertainty of wind and light output;
3) Flexible load operation principle: the virtual power plant aims at maximizing expected economic benefit according to electricity price information, the electricity generation cost of the thermoelectric unit and flexible load compensation price, and the flexible load replaces the thermoelectric unit to bear part of rotation for standby.
4. The virtual power plant-based source-load double-side thermoelectric joint random optimization scheduling method is characterized by comprising the following steps of: solving the optimal scheduling mathematical model by adopting a two-layer optimal scheduling method, wherein the outer layer takes the rotation spare capacity as an optimizing variable, the expected economic benefit is maximized as a target, and the golden section method of linear search is adopted for optimizing; the inner layer adopts a self-adaptive genetic algorithm to optimize the actual output of the virtual power plant in each scene in the next day, and multiplies the economic benefit value in each scene by the corresponding scene probability to obtain the expected economic benefit;
the two-layer optimal scheduling method comprises the following specific processes:
(1) inputting virtual power plant original data and algorithm parameters;
(2) selecting an initial search interval with precision epsilon >0 and a golden section method, namely a reserved rotation standby interval [ a, b ] of the virtual power plant;
(3) calculating a heuristic point r 1 ＝a+0.382*(b-a)、r 2 ＝a+0.618*(b-a)；
(4) Will r 1 、r 2 Respectively substituting the target functions into a target function formula for maximizing the expected economic benefit of the virtual power plant;
(5) The thermoelectric unit and the flexible load jointly bear rotation for standby, and a virtual power plant next-day output plan is prefabricated;
(6) setting a scene i=1 on the premise of planning the next day of output of the virtual power plant;
(7) randomly generating an initial population;
(8) calculating the fitness function value of each individual of the population by taking the economic benefit of the next day operation of the virtual power plant in the scene i as a target;
(9) selecting regenerated individuals according to the fitness, wherein the individuals with high fitness have high probability of being selected, and the individuals with low fitness may be eliminated;
performing adaptive crossover and mutation operations on the individuals selected in step (9) to generate new individuals;
crossover probability P C Probability of variation P m The determination mode is as follows:
wherein f max Is the maximum fitness value in the population; f (f) avg Average fitness value for the population; f is the larger fitness value of the two individuals to be crossed; f' is the fitness value of the individual to be mutated; p (P) C1 、P C2 For hybridization constant, P m1 、P m2 Is a variation constant;
generating a new generation population by crossing and mutation, and updating the optimal solution of individuals and the population;
judging whether a termination condition is met, and if so, outputting an optimal solution f (i); if not, returning to the step (8);
let i=i+1, determine i>50, if so, turn ∈ - >If not, returning to the step (7);
calculate->If F (r) 1 )<F(r 2 ) If true, turn->Otherwise turn->
Let a=r 1 ，r 1 ＝r 2 ，r 2 =a+0.618 (b-a), trans->
Let b=r 2 ，r 2 ＝r 1 ，r 1 =a+0.382 x (b-a), trans->
If r 2 -r 1 <Epsilon, stopping calculation and outputting a near optimal solution +.>Otherwise, go to (4).
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