Processing method for estimating ownership of electric vehicles in power distribution area

Abstract

The embodiment of the invention relates to a processing method for estimating the ownership of an electric vehicle in a power distribution area, and the method comprises the steps: obtaining the daily mileage / initial charging moment probability distribution of the electric vehicle in the resident power distribution area, recording the daily mileage / initial charging moment probability distribution as first and second probability distribution, obtaining the regional transformer capacity range, and recording the regional transformer capacity range as a regional load range, obtaining a single-day load curve Sb, obtaining the number of real electric vehicles and recording the number as a first real quantity, and obtaining the vehicle quantity increasing speed and recording the vehicle quantity increasing speed as a first increasing speed; based on the first probability distribution, the second probability distribution, the single-day load curve Sb and the regional load range, the maximum value of the electric vehicle inventory is estimated and recorded as a first estimator; and based on the comparison relationship between the first real quantity and the first estimated quantity, the regional power supply regulation and control requirement is set to be regulation and control and sent to the power grid management interface. According to the invention, the stability and supportability of power grid operation can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a processing method for estimating the number of electric vehicles in a power distribution area. Background Art

[0002] If an electric vehicle (EV) charging pile is connected to the residential power distribution area, the power load component of the current area will change from the original daily power load to the superposition of the daily power load and the charging load. This superposition effect may lead to a significant increase in the power load, especially during the peak period of EV charging. If the theoretical value of the number of electric vehicles in the area (EV ownership) can be estimated, the transmission network can optimize the power supply planning of the area in advance according to the difference between the actual value and the theoretical value of the EV ownership. How to estimate the theoretical value of the EV ownership is a technical problem that needs to be solved by the present invention. Summary of the invention

[0003] The purpose of the present invention is to provide a method for estimating the number of electric vehicles in a power distribution area in view of the defects of the prior art. The present invention records any residential power distribution area as the first power distribution area in advance, and records the probability distribution of the daily mileage of electric vehicles in this area and the probability distribution of the starting charging time as the corresponding first and second probability distributions, and records the transformer capacity range corresponding to the main power grid access point in this area as the corresponding regional load range, and uses the daily average value curve of the daily power load in the recent specified time period in this area as the corresponding daily load curve S b , and record the actual number of electric vehicles in this area and the growth rate of the number as the first actual quantity and the first growth rate; then, based on the first probability distribution, the second probability distribution, and the single-day load curve S b and the regional load range to estimate the maximum value of the number of electric vehicles in the first distribution area to obtain the corresponding first estimated value; and when the first real value is greater than or equal to the first estimated value, the regional power supply regulation requirement is set to need regulation; and when the first real value is less than the first estimated value, the time length that the number of real electric vehicles exceeds the first estimated value is first estimated based on the first growth rate to obtain the first time length, and whether the first time length is lower than the preset time length threshold is identified, if so, the regional power supply regulation requirement is set to need regulation, otherwise, the regional power supply regulation requirement is set to not need regulation; finally, the obtained regional power supply regulation requirement is sent to the preset power grid management interface. Through the present invention, the power grid management side can optimize the power supply planning of the residential distribution area before the charging load conflicts with the daily power load.

[0004] To achieve the above object, an embodiment of the present invention provides a method for estimating the number of electric vehicles in a power distribution area, the method comprising:

[0005] Any residential power distribution area is recorded as the corresponding first power distribution area; the probability distribution of daily mileage of electric vehicles and the probability distribution of starting charging time corresponding to the first power distribution area are recorded as the corresponding first and second probability distributions; the transformer capacity range corresponding to the main power grid access point of the first power distribution area is recorded as the corresponding regional load range; and the daily average value curve of the daily power load of the first power distribution area in the most recent specified time period is recorded as the corresponding single-day load curve S b ; and the actual number of electric vehicles in the first power distribution area is counted to obtain the corresponding first actual quantity; and the growth rate of the actual number of electric vehicles in the first power distribution area is calculated to obtain the corresponding first growth rate; the load range of the area includes the minimum load s min and maximum load s max ; The most recent specified time period includes at least the most recent week, the most recent month, the most recent quarter and the most recent year;

[0006] Based on the first probability distribution, the second probability distribution, and the single-day load curve S b The maximum value of the number of electric vehicles in the first power distribution area is estimated based on the regional load range to obtain a corresponding first estimated value;

[0007] If the first real amount is greater than or equal to the first estimated amount, setting the corresponding regional power supply regulation requirement as requiring regulation;

[0008] If the first real amount is less than the first estimated amount, then the time length that the real number of electric vehicles exceeds the first estimated amount is estimated based on the first growth rate to obtain a corresponding first time length; and whether the first time length is lower than a preset time length threshold is identified; if so, the corresponding regional power supply regulation requirement is set to require regulation; if not, the corresponding regional power supply regulation requirement is set to not require regulation;

[0009] The obtained regional power supply regulation requirement is sent to a preset power grid management interface.

[0010] Preferably, the first probability distribution obeys a lognormal distribution, specifically:

[0011]

[0012] Where l is the mileage length, f 1 (l) is the probability corresponding to the mileage length l, μ 1 , σ 1are the preset mean and standard deviation parameters;

[0013] The second probability distribution obeys normal distribution, specifically:

[0014]

[0015] Among them, t s is the starting time of charging, f 2 (t s ) is the starting charging time t s The corresponding probability, μ 2 , σ 2 are the preset mean and standard deviation parameters.

[0016] Preferably, the single-day load curve S b The time length is 24 hours; the single-day load curve S b It is the average curve of the daily power load curves of all single days in the first power distribution area within the most recent specified time period.

[0017] Preferably, the first probability distribution, the second probability distribution, and the single-day load curve S b The method estimates the maximum number of electric vehicles in the first power distribution area based on the regional load range to obtain a corresponding first estimated value, specifically including:

[0018] Step 41, initializing the total number of vehicles C based on a preset initial total number;

[0019] Wherein, the initial total number is a preset positive integer;

[0020] Step 42, initializing the first counter to 1;

[0021] Step 43: randomly draw the mileage based on the first probability distribution to obtain the corresponding random mileage l rnd ;

[0022] Step 44: randomly draw a starting charging time based on the second probability distribution to obtain a corresponding random starting time t rnd ;

[0023] Step 45, based on the random mileage l rnd The total charging capacity is estimated to obtain the corresponding total charging capacity s all ;

[0024] Among them, s all = l rnd ×α, α is the preset power consumption per unit mileage;

[0025] Step 46, based on the total charging power sall , the random starting time t rnd and a preset charging power p to perform a charging load curve estimation to obtain a corresponding first charging load curve;

[0026] The time length of the first charging load curve is 24 hours; the time length from time 0 to the random starting time t rnd The charging load between is 0, starting from the random starting time t rnd At the end of charging time t end The charging load between is p, from the charging end time t end The charging load between the time when the curve ends is 0; the charging end time t end With the random starting time t rnd The time between the two is the charging time t ch =s all / p;

[0027] Step 47, adding 1 to the first counter; and identifying whether the first counter after adding 1 is greater than the total number of vehicles C; if so, superimposing the obtained C first charging load curves and using the superimposed curve as the corresponding total charging load curve S ev , and go to step 48; if not, return to step 43;

[0028] Step 48: the charging load total curve S ev With the single-day load curve S b Superimpose and use the superimposed curve as the corresponding regional load total curve S A ; and the total load curve S of the area A It is confirmed whether there is a curve segment exceeding the load range of the area; if it is confirmed that there is no curve segment, the total number of vehicles C is increased by 1 and the process returns to step 42; if it is confirmed that there is a curve segment, the total number of vehicles C minus 1 is used as the corresponding first estimation amount.

[0029] Furthermore, the mileage is randomly drawn based on the first probability distribution to obtain a corresponding random mileage l rnd , including:

[0030] From the mean value μ 1 , standard deviation is σ 1 Draw a random number r from a normal distribution 1 ; and the random number r 1 Perform exponential transformation to obtain the corresponding random mileage l rnd , l rnd =exp(r 1 ).

[0031] Furthermore, the random sampling of the starting charging time based on the second probability distribution obtains the corresponding random starting time t rnd , including:

[0032] Step 61, draw a random number r from the standard normal distribution 2 ;

[0033] Among them, the random number r 2 The value range of is [0,1];

[0034] Step 62, based on the random number r 2 , the standard deviation σ 2 and the mean μ 2 Calculate the corresponding random starting time t rnd ;

[0035] Among them, t rnd =mod((μ 2 +σ 2 *r 1 ),twenty four),

[0036] mod() is the modulus function, mod((μ 2 +σ 2 *r 1 ),24) is the pair (μ 2 +σ 2 *r 1 ) modulo 24.

[0037] The embodiment of the present invention provides a processing method for estimating the number of electric vehicles in a power distribution area. As can be seen from the above content, the embodiment of the present invention records any residential power distribution area as the first power distribution area in advance, and records the probability distribution of the daily mileage of electric vehicles in this area and the probability distribution of the starting charging time as the corresponding first and second probability distributions, and records the transformer capacity range corresponding to the main power grid access point in this area as the corresponding regional load range, and uses the daily average value curve of the daily power load in the recent specified time period in this area as the corresponding single-day load curve S b , and record the actual number of electric vehicles in this area and the growth rate of the number as the first actual quantity and the first growth rate; then, based on the first probability distribution, the second probability distribution, and the single-day load curve S band the regional load range to estimate the maximum value of the number of electric vehicles in the first distribution area to obtain the corresponding first estimated value; and when the first real value is greater than or equal to the first estimated value, set the regional power supply regulation requirement as requiring regulation; and when the first real value is less than the first estimated value, first estimate the time length that the number of real electric vehicles exceeds the first estimated value based on the first growth rate to obtain the first time length, and identify whether the first time length is lower than the preset time length threshold, if so, set the regional power supply regulation requirement as requiring regulation, otherwise set the regional power supply regulation requirement as not requiring regulation; finally, send the obtained regional power supply regulation requirement to the preset power grid management interface. Through the embodiment of the present invention, the power grid management side can optimize the power supply planning of the residential distribution area before the charging load conflicts with the daily power load, which not only improves the stable operation guarantee of the power grid, but also improves the timeliness and effectiveness of power capacity expansion. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic diagram of a processing method for estimating the number of electric vehicles in a power distribution area provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to make the purpose, 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. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] The embodiment of the present invention provides a method for estimating the number of electric vehicles in a distribution area for an intelligent power terminal or intelligent power system on the side of a residential distribution area (such as a distribution network node, a distribution station area, etc.). Figure 1 A processing method for estimating the number of electric vehicles in a power distribution area provided by an embodiment of the present invention is shown in a schematic diagram, which mainly includes the following steps:

[0041] Step 1: record any residential power distribution area as the corresponding first power distribution area; record the probability distribution of daily mileage of electric vehicles and the probability distribution of starting charging time corresponding to the first power distribution area as the corresponding first and second probability distributions; record the transformer capacity range corresponding to the main power grid access point of the first power distribution area as the corresponding regional load range; and record the daily average value curve of daily power load in the first power distribution area within the most recent specified time period as the corresponding daily load curve S b; and the actual number of electric vehicles in the first distribution area is counted to obtain the corresponding first real quantity; and the growth rate of the actual number of electric vehicles in the first distribution area is calculated to obtain the corresponding first growth rate.

[0042] Here, the probability distribution of daily mileage of electric vehicles and the probability distribution of starting charging time in the embodiment of the present invention are both big data statistical data obtained from the power grid management side; the power grid management side refers to the management system or platform of the power management agency to which the current residential power distribution area belongs;

[0043] The probability distribution of daily mileage of electric vehicles, i.e. the first probability distribution, follows the log-normal distribution, specifically:

[0044]

[0045] l is the mileage length, f 1 (l) is the probability corresponding to the mileage length l, μ 1 , σ 1 are the preset mean and standard deviation parameters;

[0046] The probability distribution of the start charging time, i.e., the second probability distribution, obeys the normal distribution, specifically:

[0047]

[0048] t s is the starting time of charging, f 2 (t s ) is the starting charging time t s The corresponding probability, μ 2 , σ 2 are the preset mean and standard deviation parameters.

[0049] The regional load range of the embodiment of the present invention includes the minimum load s min and maximum load s max .

[0050] The most recent specified time period in the embodiment of the present invention includes at least the most recent week, the most recent month, the most recent quarter, and the most recent year.

[0051] Single-day load curve S of the embodiment of the present invention b The time length is 24 hours, and the single-day load curve S b It is the average curve of the daily power load curves of all single days in the first distribution area within the most recent specified time period.

[0052] The first growth rate of the embodiment of the present invention is calculated as follows: first growth rate = total number of new vehicles in the most recent month / actual number of electric vehicles one month ago.

[0053] Step 2: Based on the first probability distribution, the second probability distribution, and the daily load curve S b and the regional load range to estimate the maximum value of the number of electric vehicles in the first distribution area to obtain a corresponding first estimated value;

[0054] Specifically, it includes: step 21, initializing the total number of vehicles C based on a preset initial total number;

[0055] Here, the initial total is a preset positive integer;

[0056] Step 22, initializing the first counter to 1;

[0057] Step 23: Randomly draw the mileage based on the first probability distribution to obtain the corresponding random mileage l rnd ;

[0058] Specifically: From the mean value to μ 1 , standard deviation is σ 1 Draw a random number r from a normal distribution 1 ; and for the random number r 1 Perform exponential transformation to obtain the corresponding random mileage l rnd , l rnd =exp(r 1 );

[0059] Step 24: randomly draw the starting charging time based on the second probability distribution to obtain the corresponding random starting time t rnd ;

[0060] Specifically, step 241, extracting a random number r from a standard normal distribution 2 ;

[0061] Here, the random number r 2 The value range of is [0,1];

[0062] Step 242, based on the random number r 2 , standard deviation σ 2 and mean μ 2 Calculate the corresponding random starting time t rnd ;

[0063] Here, t rnd =mod((μ 2 +σ 2 *r 1 ),twenty four);

[0064] Among them, mod() is the modulus function, mod((μ 2 +σ 2 *r 1 ),24) refers to (μ 2 +σ2 *r 1 ) modulo 24;

[0065] Step 25, based on random mileage l rnd The total charging capacity is estimated to obtain the corresponding total charging capacity s all ;

[0066] Here, s all = l rnd ×α, α is the preset power consumption per unit mileage;

[0067] Step 26, based on the total charge capacity s all , random starting time t rnd and a preset charging power p to perform a charging load curve estimation to obtain a corresponding first charging load curve;

[0068] Here, the time length of the first charging load curve of the embodiment of the present invention is 24 hours; the time length from time 0 to the random starting time t rnd The charging load between is 0, starting from the random starting time t rnd At the end of charging time t end The charging load between is p, and the charging end time is t end The charging load between the time when the curve ends is 0; the charging end time t end With random starting time t rnd The time between the two is the charging time t ch =s all / p;

[0069] Step 27, add 1 to the first counter; and identify whether the first counter after adding 1 is greater than the total number of vehicles C; if so, superimpose the obtained C first charging load curves and use the superimposed curve as the corresponding total charging load curve S ev , and go to step 28; if not, return to step 23;

[0070] Step 28, the total charging load curve S ev With the single-day load curve S b Superimpose and use the superimposed curve as the corresponding regional load total curve S A ; and the regional load total curve S A Whether there is a curve segment that exceeds the regional load range is confirmed; if it is confirmed that there is no curve segment, the total number of vehicles C is increased by 1 and the process returns to step 22; if it is confirmed that there is a curve segment, the total number of vehicles C minus 1 is used as the corresponding first estimation amount.

[0071] Step 3: If the first real value is greater than or equal to the first estimated value, the corresponding regional power supply regulation requirement is set to require regulation.

[0072] Step 4: If the first actual quantity is less than the first estimated quantity, the time length that the actual number of electric vehicles exceeds the first estimated quantity is estimated based on the first growth rate to obtain a corresponding first time length; and whether the first time length is lower than a preset time length threshold is identified; if so, the corresponding regional power supply regulation requirement is set to require regulation; if not, the corresponding regional power supply regulation requirement is set to not require regulation.

[0073] Here, the first time length=(first estimated amount-first true amount) / first growth rate; the time length threshold is a preset threshold parameter.

[0074] Step 5: Send the obtained regional power supply regulation requirement to the preset power grid management interface.

[0075] Here, the grid management interface is a data upload interface opened by the grid management side for the smart power terminals or smart power systems in each residential power distribution area.

[0076] In summary, the embodiment of the present invention provides a processing method for estimating the number of electric vehicles in a distribution area. As can be seen from the above content, the embodiment of the present invention records any residential distribution area as the first distribution area in advance, and records the probability distribution of daily mileage of electric vehicles in this area and the probability distribution of the starting charging time as the corresponding first and second probability distributions, and records the transformer capacity range corresponding to the main power grid access point in this area as the corresponding regional load range, and uses the daily average value curve of the daily power load in the recent specified time period in this area as the corresponding daily load curve S b , and record the actual number of electric vehicles in this area and the growth rate of the number as the first actual quantity and the first growth rate; then, based on the first probability distribution, the second probability distribution, and the single-day load curve S b and the regional load range to estimate the maximum value of the number of electric vehicles in the first distribution area to obtain the corresponding first estimated value; and when the first real value is greater than or equal to the first estimated value, set the regional power supply regulation requirement as requiring regulation; and when the first real value is less than the first estimated value, first estimate the time length that the number of real electric vehicles exceeds the first estimated value based on the first growth rate to obtain the first time length, and identify whether the first time length is lower than the preset time length threshold, if so, set the regional power supply regulation requirement as requiring regulation, otherwise set the regional power supply regulation requirement as not requiring regulation; finally, send the obtained regional power supply regulation requirement to the preset power grid management interface. Through the embodiment of the present invention, the power grid management side can optimize the power supply planning of the residential distribution area before the charging load conflicts with the daily power load, which not only improves the stable operation guarantee of the power grid, but also improves the timeliness and effectiveness of power capacity expansion.

[0077] The professionals should further realize that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to the function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0078] The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be implemented using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0079] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating the number of electric vehicles in a power distribution area, characterized in that: The method comprises: Any residential power distribution area is recorded as the corresponding first power distribution area; the probability distribution of daily mileage of electric vehicles and the probability distribution of starting charging time corresponding to the first power distribution area are recorded as the corresponding first and second probability distributions; the transformer capacity range corresponding to the main power grid access point of the first power distribution area is recorded as the corresponding regional load range; and the daily average value curve of the daily power load of the first power distribution area in the most recent specified time period is recorded as the corresponding single-day load curve S b ; and the actual number of electric vehicles in the first power distribution area is counted to obtain the corresponding first actual quantity; and the growth rate of the actual number of electric vehicles in the first power distribution area is calculated to obtain the corresponding first growth rate; the load range of the area includes the minimum load s min and maximum load s max ; The most recent specified time period includes at least the most recent week, the most recent month, the most recent quarter and the most recent year; Based on the first probability distribution, the second probability distribution, and the single-day load curve S b The maximum value of the number of electric vehicles in the first power distribution area is estimated based on the regional load range to obtain a corresponding first estimated value; If the first real amount is greater than or equal to the first estimated amount, setting the corresponding regional power supply regulation requirement as requiring regulation; If the first real amount is less than the first estimated amount, the time length that the real number of electric vehicles exceeds the first estimated amount is estimated based on the first growth rate to obtain a corresponding first time length; and whether the first time length is lower than a preset time length threshold is identified; if so, the corresponding regional power supply regulation requirement is set to require regulation; if not, the corresponding regional power supply regulation requirement is set to not require regulation; The obtained regional power supply regulation requirement is sent to a preset power grid management interface.

2. The method for estimating the number of electric vehicles in a power distribution area according to claim 1, characterized in that: The first probability distribution obeys the log-normal distribution, specifically: Where l is the mileage length, f1(l) is the probability corresponding to the mileage length l, μ1 and σ1 are the preset mean and standard deviation parameters; The second probability distribution obeys normal distribution, specifically: Among them, t s is the starting time of charging, f2(t s ) is the starting charging time t s The corresponding probability, μ2 and σ2 are the preset mean and standard deviation parameters.

3. The method for estimating the number of electric vehicles in a power distribution area according to claim 1, characterized in that: The single-day load curve S b The time length is 24 hours; the single-day load curve S b It is the average curve of the daily power load curves of all single days in the first power distribution area within the most recent specified time period.

4. The method for estimating the number of electric vehicles in a power distribution area according to claim 2, characterized in that: The method based on the first probability distribution, the second probability distribution, and the single-day load curve S b The method estimates the maximum number of electric vehicles in the first power distribution area based on the regional load range to obtain a corresponding first estimated value, specifically including: Step 41, initializing the total number of vehicles C based on a preset initial total number; Wherein, the initial total number is a preset positive integer; Step 42, initializing the first counter to 1; Step 43: randomly draw the mileage based on the first probability distribution to obtain the corresponding random mileage l rnd ; Step 44: randomly draw a starting charging time based on the second probability distribution to obtain a corresponding random starting time t rnd ; Step 45, based on the random mileage l rnd The total charging capacity is estimated to obtain the corresponding total charging capacity s all ; Among them, s all = l rnd ×α, α is the preset power consumption per unit mileage; Step 46, based on the total charging power s all , the random starting time t rnd and a preset charging power p to perform a charging load curve estimation to obtain a corresponding first charging load curve; The time length of the first charging load curve is 24 hours; the time length from time 0 to the random starting time t rnd The charging load between is 0, starting from the random starting time t rnd At the end of charging time t end The charging load between is p, from the charging end time t end The charging load between the time t and the end of the curve is 0; the charging end time t end With the random starting time t rnd The time between the two is the charging time t ch =s all / p; Step 47, adding 1 to the first counter; and identifying whether the first counter after adding 1 is greater than the total number of vehicles C; if so, superimposing the obtained C first charging load curves and using the superimposed curve as the corresponding total charging load curve S ev , and go to step 48; if not, return to step 43; Step 48: the charging load total curve S ev With the single-day load curve S b Superimpose and use the superimposed curve as the corresponding regional load total curve S A ; and the total load curve S of the area A It is confirmed whether there is a curve segment exceeding the load range of the area; if it is confirmed that there is no curve segment, the total number of vehicles C is increased by 1 and the process returns to step 42; if it is confirmed that there is a curve segment, the total number of vehicles C minus 1 is used as the corresponding first estimation amount.

5. The method for estimating the number of electric vehicles in a power distribution area according to claim 4, characterized in that: The mileage is randomly drawn based on the first probability distribution to obtain a corresponding random mileage l rnd , specifically including: A random number r1 is drawn from a normal distribution with a mean of μ1 and a standard deviation of σ1; and the random number r1 is subjected to an exponential transformation to obtain the corresponding random mileage l rnd , l rnd =exp(r1).

6. The method for estimating the number of electric vehicles in a power distribution area according to claim 4, characterized in that: The random sampling of the charging start time based on the second probability distribution obtains the corresponding random starting time t rnd , specifically including: Step 61, extracting a random number r2 from a standard normal distribution; Wherein, the value range of the random number r2 is [0,1]; Step 62, calculating the corresponding random starting time t based on the random number r2, the standard deviation σ2 and the mean μ2 rnd ; Among them, t rnd =mod((μ2+σ2*r1),24), mod() is the modulo function, mod((μ2+σ2*r1),24) is (μ2+σ2*r1) modulo 24.

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