CN114936453B - Photoelectric conversion system reliability assessment method based on Markov chain - Google Patents
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Abstract
The reliability evaluation method of the photoelectric conversion system based on the Markov chain comprises the following steps: establishing a temperature-irradiation Markov chain by carrying out state division on temperature and irradiation; establishing a photoelectric conversion system fault rate model, and then embedding the photoelectric conversion system fault rate into an established temperature-irradiation Markov chain to form a photoelectric conversion system fault rate Markov chain; the failure rate of the photoelectric conversion system is divided into three failure rate levels of high, medium and low, so that the average failure rate of the element and the system, the transition probability and frequency among the three failure rate levels are calculated, the reliability of the photoelectric conversion system is described from the angles of the failure rate and the frequency, the temperature and the irradiation elasticity coefficient of the average failure rate of the photoelectric conversion system are defined, and the sensitivity relation of the average failure rate of the photoelectric conversion system to two weather factors is quantized. The reliability model established by the method can be suitable for various meteorological environments, and can evaluate the influence of various meteorological factors on the reliability of the photoelectric conversion or wind power conversion system.
Description
Technical Field
The invention belongs to the field of reliability evaluation of photovoltaic power generation systems in power systems, in particular to a reliability evaluation method of a photovoltaic conversion system based on a Markov chain,
Background
The photovoltaic energy is rich, the photovoltaic power generation cost is low, and the development technology is mature. Wherein the photoelectric conversion system is an important device for converting solar energy into clean electric energy, and fig. 1 is a photovoltaic inverter topology structure, and comprises a photovoltaic array, a Boost converter, a DC-AC inverter and a filter. The photovoltaic array converts solar energy into direct-current electric energy, the direct-current electric energy is boosted by the Boost converter, the direct-current electric energy is converted into alternating-current electric energy by the inverter, and the alternating-current electric energy is connected to a load after filtering. The photoelectric conversion system is often arranged in a solar energy enrichment area, the junction temperature of each element is increased when the elements work while a large amount of energy is output, and the elements are prone to failure due to the high ambient temperature of the area, so that the overall reliability of the system is affected.
The prior literature researches the influence of meteorological factors on the reliability of a photoelectric conversion system from two directions, one is a reliability prediction manual based on experience criteria for analyzing the reliability of the element, and the other is a life model based on physical failure theory for researching the influence of meteorological factors on the reliability of the photoelectric conversion system. Most of the prior documents adopt a reliability prediction manual to evaluate the reliability of a photoelectric conversion system, and although the reliability prediction manual considers meteorological factors such as temperature, irradiation, wind speed and the like, the failure rate of elements under different power output levels of a photovoltaic array is analyzed, and finally the evaluation result is averaged, so that the evaluation result is relatively complete, but the failure rate of the elements calculated in this way cannot directly respond to the direct connection between the failure rate of the elements and the temperature, irradiation and wind speed. The current mainstream research mostly adopts a life model to analyze the life condition of the element under different meteorological conditions, firstly, the junction temperature of the element under the temperature and irradiation task section is calculated, then the junction temperature is processed by adopting a rain flow counting method, finally, the life of the element is estimated by applying the life model, the actual temperature and irradiation condition of each time period are fully considered in the process, the calculation result is relatively accurate, and the calculation process is relatively complex.
Based on the two methods, a plurality of students study the reliability of the photoelectric conversion system, but there are few studies on using Markov chains to describe the temperature-irradiation state, embedding a fault rate model in a single temperature-irradiation state into the temperature-irradiation Markov chain to form a fault rate Markov chain of the photoelectric conversion system, providing various reliability evaluation indexes, and providing a sensitivity analysis for evaluating the influence of the temperature and the irradiation on the average fault rate of the photoelectric conversion system by the quantitative indexes.
Disclosure of Invention
In order to accurately evaluate the influence of weather uncertainty on the reliability of a photoelectric conversion system, the invention provides a reliability evaluation method of the photoelectric conversion system based on a Markov chain.
The technical scheme adopted by the invention is as follows:
the reliability evaluation method of the photoelectric conversion system based on the Markov chain comprises the following steps:
Step 1: establishing a temperature-irradiation Markov chain by carrying out state division on temperature and irradiation;
step 2: establishing a photoelectric conversion system fault rate model, and embedding the photoelectric conversion system fault rate into the temperature-irradiation Markov chain established in the step 1to form a photoelectric conversion system fault rate Markov chain;
Step 3: the failure rate of the photoelectric conversion system is divided into three failure rate levels of high, medium and low, so that the average failure rate of the element and the system, the transition probability and frequency among the three failure rate levels are calculated, and the reliability of the photoelectric conversion system is described from the angles of the failure rate and the frequency.
In the step 1, a temperature-irradiation state dividing table is applied to divide an actual temperature-irradiation sample, and a temperature-irradiation Markov chain is determined according to the temperature-irradiation state dividing result of measured data.
In the step 1, the temperature-irradiation state is firstly scaled according to an experience criterion, and the transfer rate among the states of each group is as follows according to the temperature-irradiation state partitioning result of the measured data: mu ((j,k),(m,n))＝N((j,k),(m,n))/D(m,n), wherein: mu ((j,k),(m,n)) and N ((j,k),(m,n)) are respectively the transfer rate and the transfer frequency of the temperature irradiation state (j, k) to the temperature irradiation state (m, N); d (m,n) is the duration of the temperature irradiation state (m, n).
After the transfer rate among the temperature irradiation states of each group is calculated, a temperature irradiation state transfer rate matrix G is obtained as follows:
It is noted that the maximum dimension of G is 130×130, but in practice, the probability of occurrence of extreme temperatures or irradiation negligible, the dimension of G is usually lower than 130×130, and thus the number of temperature states and the number of irradiation states actually existing are denoted as N t(Nt. Ltoreq.10) and N r(Nr. Ltoreq.13), respectively.
The step 2 comprises the following steps:
s2.1: according to specific temperature irradiation, a photovoltaic cell output model is established, and photovoltaic cell output voltage V PV and current I PV under specific temperature-irradiation are obtained;
S2.2: calculating the power loss of a power device diode and an IGBT by using the photovoltaic cell output voltage V PV and the current I PV under specific temperature-irradiation;
S2.3: according to the element thermal model and the element power loss, the junction temperature of the element can be obtained, according to the method for calculating the element fault rate in the military manual MIL-HDBK-217F, the fault rate models of the power conversion device IGBT and the diode are established, and the fault rate models of the inverter, the boost converter and the photoelectric conversion system are obtained;
S2.4: and (3) embedding the fault rate model of the photoelectric conversion system into the temperature-irradiation Markov chain in the step (1) to obtain the fault rate Markov chain of the photoelectric conversion system. And the obtained transfer rate matrix of the failure rate Markov chain is the same as the transfer rate matrix of the temperature-irradiation Markov chain.
In the step 2.2 of the process described above,
Boost converter power loss at specific temperature-irradiance conditionsThe method comprises the following steps: /(I)
Wherein: And/> The power losses of the IGBT and the diode in the Boost converter are respectively;
wherein: And/> The IGBT conduction loss and the switching loss in the Boost converter are respectively, and I dc1 is the output current of the photovoltaic array; /(I)The turn-on threshold voltage of the IGBT; /(I)The IGBT on-resistance is adopted; d is the duty cycle of the converter;
Switching frequency for Boost converter;
And/> The energy consumption of each turn-on and turn-off of the IGBT is respectively; v dc2 is the Boost converter output voltage;
And/> The rated voltage and current values of the IGBT in the Boost converter are respectively.
Wherein: is the diode on-resistance; /(I) Energy consumption for each turn-off of the diode; /(I)And/>Respectively the rated voltage and the current value of the diode;
the inverter power loss is:
wherein: And/> The power losses of the IGBT and the diode in the inverter are respectively;
The power loss of the diodes in the inverter is calculated as follows:
wherein M is the modulation factor of the inverter; θ is the included angle between the output voltage and the current of the inverter; Is the diode on-resistance; i om is the inverter peak current; /(I) The threshold voltage is conducted for the diode; /(I)Switching frequency for the inverter; /(I)Energy consumption for each turn-off of the diode; i 0 is the output current of the inverter; /(I)And/>The rated voltage and current values of the diode, respectively.
The power loss of the IGBTs in the inverter is calculated as follows:
wherein: the turn-on threshold voltage of the IGBT; /(I) And/>Energy consumption of IGBT in each turn-on and turn-off respectively,/>And/>The rated voltage and the current value of the IGBT are respectively.
In the step 2.3, the junction temperature of the element is: t j(diode,IGBT)＝Ta+Rha×Ptotal+Rjh×Pdiode/IBGBT, wherein: t a、Rha and R jh are respectively the ambient temperature, the thermal resistance of the radiator to the environment, and the thermal resistance of the junction to the radiator;
P diode/igbt is the loss of a single diode or IGBT; p total is the total loss of the converter; using the military manual MIL-HDBK-217F, the IGBT and diode failure rates were:
λIGBT＝λb,IGBT×πQ×πA×πE×πT；
λdiode＝λb,diode×πQ×πE×πC×πS×πT，
Wherein: lambda b,IGBT and lambda b,diode are the fundamental failure rates of the IGBT and diode respectively, pi Q is the quality factor of the element, pi A is the application factor, pi E is the environmental factor of each partial quantification in the failure rate model, pi C is the relevant structural factor, pi S is the stress factor, pi T is the thermal factor, depending on the ambient temperature and junction temperature, as shown in the formula:
Wherein pi T,IGBT and pi T,diode are the thermal factors of the IGBT and the diode respectively;
T j,IGBT and T j,diode are junction temperatures of the IGBT and the diode respectively;
the failure rates of the boost converter and the inverter under the single temperature-irradiation state are respectively as follows:
Wherein: And/> The failure rates of the IGBT and the diode in the Boost converter are respectively;
And/> The failure rates of the IGBTs and diodes in the inverter, respectively.
The failure rate of the system is as follows: lambda SYS＝λINV+λBC.
The step 3 includes the following steps:
s3.1: all states are divided into four parts:
The failure rate of the low temperature scale (1-5) and the low irradiation scale (1-11) set state is lower, and the failure rate is marked as a low failure rate state lambda L;
The fault rate of the high temperature scale (6-10) and the high irradiation scale (8-13) in the aggregate state is higher, and the fault rate is marked as a high fault rate state lambda H;
The failure rate of the low temperature scale (1-5), the high irradiation scale (8-13), the high temperature scale (6-10) and the low irradiation scale (1-7) are in the two states, and the partial state is divided into a medium failure rate set lambda M;
The reliability of the photoelectric conversion system is evaluated by calculating probability indexes and frequency indexes of high, medium and low fault rate states.
S3.2: solving a photoelectric conversion system fault rate Markov chain to obtain probability P= [ P (1,1),p(1,2),…,p(j,k)…,p(10,13) ] of each fault rate state, wherein: p (j,k) is the occurrence probability of the failure rate state lambda (j,k), and j and k respectively represent a temperature state and an irradiation state;
From the above steps, the average failure rate of the converter and the system can be calculated;
The average failure rate of the system is as follows:
Wherein: n t is the temperature state number; n r is the number of irradiation states; p (i,j) is the failure rate state of the photoelectric conversion system Probability of occurrence,/>Is a system failure rate state at temperature-irradiance state (i, j).
Similarly, it willReplaced by/>And/>Average failure rate of inverter and Boost converter can be calculatedAnd/>The method comprises the following steps of:
Wherein, And/>Average failure rates of Boost converter and inverter in the respective states (i, j).
The occurrence probability of three types of fault rate levels of the photoelectric conversion system is represented by the sum of all state probabilities respectively belonging to respective sets, and the low fault rate probability is as follows:
wherein: subscript L is the low failure rate set and p (s,m) is the probability of belonging to the failure rate state (s, m) in the low failure rate set; similarly, the high failure rate probability p H and the medium failure rate probability p M can be calculated as:
wherein, subscripts M and H represent a medium failure rate set and a high failure rate set;
the occurrence frequency of three types of fault rate levels of the photoelectric conversion system can be obtained by combining the fault rate frequencies, and the low fault rate frequency is that
Wherein: p (u,k) is the probability of a state (u, k) in the low-failure-rate set L; h U M is a high and medium failure rate set; mu ](u,k),(x,y)] is the transition rate of state (u, k) to state (x, y); μ [(i,j),(m,n)] is the transition rate of state (i, j) to state (m, n) within set L, p (i,j) is the probability of state (i, j);
The same method can calculate that the high fault rate frequency f H and the medium fault rate frequency f M of the photoelectric conversion system are respectively
Wherein: m and H represent the medium and high failure rate sets, respectively.
In S3.3, the value of the scaling factor beta t,βt of the defined temperature is in the [0.1,2] interval, and the scaling factor beta t of the applied temperature is multiplied by all measured temperature data, for example: after temperature irradiation data (t 1,r1),(t2,r2),…,(tN,rN) of a certain area are multiplied by a scaling factor beta t, new temperature irradiation data (βtt1,r1),(βtt2,r2),…,(βttN,rN), are obtained, then the system failure rate of the area is reevaluated based on a Markov chain model of the failure rate of the photoelectric conversion system, and the failure rates before and after the scaling factor is applied are compared;
the temperature elastic coefficient defining the average failure rate of the photoelectric conversion system is as follows:
Wherein eta T is the elastic coefficient of the failure rate of the photoelectric conversion system when the temperature is changed, And the average failure rate of the photoelectric conversion system after the beta T is integrally changed for the actual temperature data.
Defining the scaling factor β r,βr of the irradiance to take value in the [0.1,2] interval, multiplying all measured irradiance data by β r, for example: after temperature irradiation data (t 1,r1),(t2,r2),…,(tN,rN) of a certain area are multiplied by a scaling factor beta r, new temperature irradiation data (t1,βrr1),(t2,βrr2),…,(tN,βrrN), are obtained, then the system failure rate of the area is reevaluated based on a Markov chain model of the failure rate of the photoelectric conversion system, and the failure rates before and after the scaling factor is applied are compared; the temperature elastic coefficient defining the average failure rate of the photoelectric conversion system is as follows:
Wherein: η R is the elastic coefficient generated when the failure rate of the photoelectric conversion system changes in irradiation, And the average failure rate of the photoelectric conversion system after the actual irradiation data is integrally changed by beta R, beta R is an irradiation scaling factor, and the value is [0.1,2].
The indexes are calculated, a program for influencing the reliability of the photoelectric conversion system by temperature irradiation is established, the reliability of the photoelectric conversion system can be evaluated, and the influence of two factors of temperature and irradiation on the reliability of the photoelectric conversion system can be determined to be larger.
The invention discloses a reliability evaluation method of a photoelectric conversion system based on a Markov chain, which has the following technical effects:
1) The invention adopts a new experience criterion to divide the temperature and the irradiation state, and can finely consider the influence of the temperature and the irradiation on the reliability of the photoelectric conversion system.
2) The Markov chain-based photoelectric conversion system fault rate calculation model provided by the invention can calculate indexes such as the average fault rate of the photoelectric conversion system, so as to evaluate the reliability of the system; secondly, the fault rate of the power device in the photoelectric conversion system can be distinguished, and the fault rate of the inverter is found to be higher than that of the boost converter in the invention.
3) The invention divides the failure rate of the photoelectric conversion system into the transition probability and the frequency index, can evaluate the failure rate condition of a single region, and simultaneously uses the model calculation of the invention for a plurality of regions, thereby being beneficial to the site selection work of the photovoltaic power station.
4) The temperature elasticity index of the failure rate and the irradiation elasticity index of the failure rate provided by the invention can obviously show the influence condition of temperature and irradiation change on the failure rate of the system, and can distinguish what meteorological factors have greater elasticity on the failure rate of the photoelectric conversion system.
5) The reliability model of the invention can be suitable for various meteorological environments, and can be extended to influence various meteorological factors on the reliability of the photoelectric conversion or wind power conversion system.
Drawings
FIG. 1 is a diagram of a photovoltaic grid-tie structure
Fig. 2 is an equivalent circuit diagram of a photovoltaic cell
Fig. 3 is a schematic diagram of a Markov chain of failure rates of a photoelectric conversion system.
FIG. 4 is a diagram of a site distribution at 6 North Dakota
FIG. 5 (a) is a graph showing the change in the failure rate of the Boost converter in the temperature irradiation state;
Fig. 5 (b) is a graph showing a change in the failure rate of the inverter in the temperature irradiation state;
Fig. 5 (c) is a graph showing a change in the failure rate of the photoelectric conversion system in the temperature irradiation state.
FIG. 6 (a) is a graph of failure rate as a function of temperature;
fig. 6 (b) is a graph of elasticity as a function of temperature.
FIG. 7 (a) is a graph of failure rate as a function of irradiance;
Fig. 7 (b) is a graph of failure rate as a function of irradiance.
Detailed Description
The method for evaluating the reliability of the photoelectric conversion system based on the Markov chain comprises the steps of dividing temperature-irradiation states by using an empirical rule to obtain the Markov chain, and calculating the failure rate of the photoelectric conversion system under each group of temperature-irradiation states according to a stress analysis method and the reliability serial-parallel relationship between elements to form the failure rate Markov chain of the photoelectric conversion system. Therefore, reliability indexes such as the average failure rate of the system and the like are calculated, and the defined temperature and the irradiation elasticity coefficient are used for quantifying the influence relationship of two meteorological factors on the failure rate of the system. The measured temperatures and irradiation data of multiple observation stations in North Dakota state in U.S. are collected, as shown in table 3, reliability indexes of a commercial photoelectric conversion system at different observation stations are evaluated, and the results show that the average failure rate of the photoelectric conversion system of the low-latitude observation station is higher, the irradiation elasticity coefficient is higher than the temperature elasticity coefficient, and the average failure rate of the system is more sensitive to irradiation change.
The method comprises the following steps:
Step one: taking into consideration the influence of temperature and irradiation on the reliability of a photoelectric conversion system, collecting measured temperature-irradiation samples of the photovoltaic power station pre-site area for 10 years per hour, wherein the samples are recorded as (t 1,r1),(t2,r2),…,(tN,rN) N groups of measured temperature irradiation data, and the (t i,ri) i (i=1, 2, …, N) th groups of measured temperature irradiation data, so as to prepare for constructing a temperature-irradiation Markov chain.
Step two: the temperature and the irradiation are subjected to scale division by using a temperature and irradiation experience division criterion, and a temperature and irradiation scale table is obtained:
TABLE 1 temperature State division criteria
TABLE 2 irradiation State division criteria
According to tables 1 and 2, the measured temperature irradiation data can be divided into at most 10×13=130 sets of temperature-irradiation states, which are denoted as (1, 1), (1, 2), …, (10, 13), where (j, k) represents that the temperature and the irradiation belong to the j-th set of temperature states and the k-th set of irradiation states, respectively. According to the temperature-irradiation state division result of the measured data, the transfer rate among the states of each group is as follows: mu ((j,k),(m,n))＝N((j,k),(m,n))/D(m,n),μ((j,k),(m,n)) and N ((j,k),(m,n)) are the transfer rate and the transfer frequency of the temperature irradiation state (j, k) to the temperature irradiation state (m, N), respectively, and D (m,n) is the duration of the temperature irradiation state (m, N).
After the transfer rate among the temperature irradiation states of each group is calculated, a temperature irradiation state transfer rate matrix G can be obtained as follows:
It is noted that the maximum dimension of G is 130×130, but in practice, the probability of occurrence of extreme temperatures or irradiation negligible, the dimension of G is usually lower than 130×130, and thus the number of temperature states and the number of irradiation states actually existing are denoted as N t(Nt. Ltoreq.10) and N r(Nr. Ltoreq.13), respectively.
Step three: applying a photovoltaic cell engineering output model to obtain photovoltaic cell output voltage (V PV) and current (I PV) under specific temperature-irradiation;
step four: the power loss of the element is calculated from the output voltage and current of the photovoltaic cell at a specific temperature-irradiation state: boost converter power loss The method comprises the following steps: /(I)
In the middle ofAnd/>The power losses of the IGBT and the diode in the Boost converter are respectively; in/> AndThe IGBT conduction loss and the switching loss in the Boost converter are respectively, and I dc1 is the output current of the photovoltaic array; /(I)The turn-on threshold voltage of the IGBT; /(I)The IGBT on-resistance is adopted; d is the duty cycle of the converter; /(I) Switching frequency for Boost converter; /(I)And/>The energy consumption of each turn-on and turn-off of the IGBT is respectively; v dc2 is the Boost converter output voltage; /(I)AndThe rated voltage and current values of the IGBT in the Boost converter are respectively.In/>And/>Conduction loss and switching loss of diodes in Boost converter, respectively,/>The threshold voltage is conducted for the diode; /(I)Is the diode on-resistance; /(I)Energy consumption for each turn-off of the diode; /(I)And/>Respectively the rated voltage and the current value of the diode;
the inverter power loss is: in/> And/>The power losses of the IGBT and the diode in the inverter are respectively; the power loss of the diodes in the inverter is calculated as follows:
m is the modulation factor of the inverter; θ is the included angle between the output voltage and the current of the inverter; Is the diode on-resistance; i om is the inverter peak current; /(I) The threshold voltage is conducted for the diode; /(I)Switching frequency for the inverter; /(I)Energy consumption for each turn-off of the diode; i o is the output current of the inverter; /(I)And/>The rated voltage and current values of the diode, respectively.
The power loss of the IGBTs in the inverter is calculated as follows:
In the middle of The IGBT on-resistance is adopted; /(I)The turn-on threshold voltage of the IGBT; /(I)And/>Energy consumption of IGBT in each turn-on and turn-off respectively,/>And/>The rated voltage and the current value of the IGBT are respectively.
The junction temperature of the component can be obtained according to the thermal model of the component: t j(diode,IGBT)＝Ta+Rha×Ptotal+Rjh×Pdiode/IBGBT, wherein: t a、Rha and R jh are respectively the ambient temperature, the thermal resistance of the radiator to the environment, and the thermal resistance of the junction to the radiator;
P diode/igbt is the loss of a single diode or IGBT; p total is the total loss of the converter; using the military manual MIL-HDBK-217F, the IGBT and diode failure rates were: lambda IGBT＝λb,IGBT×πQ×πA×πE×πT;
lambda diode＝λb,diode×πQ×πE×πC×πS×πT, wherein: lambda b,IGBT and lambda b,diode are the fundamental failure rates of the IGBT and diode respectively, pi Q is the quality factor of the element, pi A is the application factor, pi E is the environmental factor of each partial quantification in the failure rate model, pi C is the relevant structural factor, pi S is the stress factor, pi T is the thermal factor, depending on the ambient temperature and junction temperature, as shown in the formula:
wherein pi T,IGBT and pi T,diode are thermal factors of the IGBT and the diode respectively, and T j,IGBT and T j,diode are junction temperatures of the IGBT and the diode respectively.
The failure rates of the boost converter and the inverter under the single temperature-irradiation state are respectively as follows: in/> And/>For failure rate of IGBT and diode in Boost converter,/>And/>Is the failure rate of the IGBTs and diodes in the inverter.
The failure rate of the system is as follows: lambda SYS＝λINV+λBC.
Step five: embedding the photoelectric conversion system fault rate model obtained in the step four into the temperature-irradiation Markov chain in the step 2, so that the photoelectric conversion system fault rate Markov chain can be obtained, and the transfer rate matrix of the fault rate Markov chain is the same as the transfer rate matrix of the temperature-irradiation Markov chain;
Step six: dividing all states into four parts, wherein the failure rate of the low-temperature scale (1-5) and low-irradiation scale (1-11) aggregate state is lower, and marking the low-failure rate state as a low-failure rate state (lambda L); the fault rate of the high temperature scale (6-10) and the high irradiation scale (8-13) in the aggregate state is higher, and the fault rate is marked as a high fault rate state (lambda H); the failure rate of the low temperature scale (1-5), the high irradiation scale (8-13), the high temperature scale (6-10) and the low irradiation scale (1-7) are in the two states, the partial state is divided into a medium failure rate set (lambda M), and the reliability of the photoelectric conversion system is evaluated by calculating the probability index and the frequency index of the high, medium and low failure rate states.
Step seven: the probability P= [ P (1,1),p(1,2),....,p(10,13) ] of each fault rate state can be obtained by solving a fault rate Markov chain of the photoelectric conversion system, wherein: p (j,k) is the failure rate state, probability of lambda (j,k) in the transition process; the average failure rate of the converter and the system can be calculated by the steps, and the average failure rate of the system is as follows:
Wherein: n t is the temperature state number; n r is the number of irradiation states; p (i,j) is the failure rate state of the photoelectric conversion system Probability of occurrence,/>Is the average failure rate of the system in state (i, j). Similarly, will/>Replaced by/>And/>Average failure rate/>, of inverter and Boost converter can be calculatedAnd/>Respectively/>AndWherein/>And/>Is the average failure rate of the Boost converter and inverter in state (i, j).
The occurrence probability of three types of fault rate levels of the photoelectric conversion system is represented by the sum of all state probabilities respectively belonging to respective sets, and the low fault rate probability is as follows: Wherein: subscript L is the low failure rate set and p (s,m) is the probability of belonging to the failure rate state (s, m) in the low failure rate set; similarly, the high fault rate probability p H and the medium fault rate probability p M can be calculated as And/>Wherein subscripts M and H represent a medium failure rate set and a high failure rate set; the occurrence frequency of three types of fault rate levels of the photoelectric conversion system can be obtained by combining the fault rate frequencies, and the low fault rate frequency is/>
Wherein: p (u,k) is the probability of a state (u, k) in the low-failure-rate set L; h U M is a high and medium failure rate set; mu [(u,k),(x,y)] is the transition rate of state (u, k) to state (x, y); μ [(i,j),(m,n)] is the transition rate of state (i, j) to state (m, n) within set L, p (i,j) is the probability of state (i, j); the same method can calculate that the high fault rate frequency f H and the medium fault rate frequency f M of the photoelectric conversion system are respectively
Wherein: m and H represent the medium and high failure rate sets, respectively.
Step eight: the scaling factor β t,βt defining the temperature takes the value in the [0.1,2] interval, and the scaling factor β t of the temperature is applied to multiply all measured temperature data, for example: after temperature irradiation data (t 1,r1),(t2,r2),…,(tN,rN) of a certain area are multiplied by a scaling factor beta t, new temperature irradiation data (βtt1,r1),(βtt2,r2),…,(βttN,rN), are obtained, then the system failure rate of the area is reevaluated based on a Markov chain model of the failure rate of the photoelectric conversion system, and the failure rates before and after the scaling factor is applied are compared; the temperature elastic coefficient defining the average failure rate of the photoelectric conversion system is as follows: Wherein η T is the elastic coefficient generated when the failure rate of the photoelectric conversion system changes at the temperature,/> And the average failure rate of the photoelectric conversion system after the beta T is integrally changed for the actual temperature data.
Defining the scaling factor β r,βr of the irradiance to take value in the [0.1,2] interval, multiplying all measured irradiance data by β r, for example: after temperature irradiation data (t 1,r1),(t2,r2),…,(tN,rN) of a certain area are multiplied by a scaling factor beta r, new temperature irradiation data (t1,βrr1),(t2,βrr2),…,(tN,βrrN), are obtained, then the system failure rate of the area is reevaluated based on a Markov chain model of the failure rate of the photoelectric conversion system, and the failure rates before and after the scaling factor is applied are compared; the temperature elastic coefficient defining the average failure rate of the photoelectric conversion system is as follows: Wherein eta R is the elastic coefficient generated when the failure rate of the photoelectric conversion system changes due to irradiation, and is/( And the average failure rate of the photoelectric conversion system after the actual irradiation data is integrally changed by beta R, beta R is an irradiation scaling factor, and the value is [0.1,2].
And calculating the index to establish a program for influencing the reliability of the photoelectric conversion system by temperature irradiation, namely evaluating the reliability of the photoelectric conversion system, and determining that the two factors of temperature and irradiation influence the reliability of the photoelectric conversion system more.
Examples:
An Aster photovoltaic plate is selected, the model is CS1H330MS, the power of each photovoltaic plate is 330W, 15 photovoltaic plates are connected in series, two photovoltaic plates are connected in parallel, and a photoelectric conversion system with the capacity of 9.9kW is simulated. Some of which vary depending on the operating environment of the component. The type of the converter is F50R12RT4, the type of the inverter is FS25R12W1T 4B 11, and the photoelectric conversion system adopted by the invention is shown in FIG. 1.
The open weather database NDAWN (North Dakota agricultural weather network) is accessed and measured temperature-irradiance samples are collected every hour between six observation stations 2010 through 2019, the names and locations of which are shown in fig. 4.
TABLE 3 North Dakota site base data
Table 3 shows the characteristics of temperature irradiation of each site, and it can be seen that the irradiation mean values of Wishek and Watford City observation stations in low latitude areas are higher, which indicates that the solar energy resources are rich, and the irradiation and temperature mean values of Crosby and Rugby observation stations in high latitude areas are lower, which indicates that the solar energy resources are deficient. This indicates that the solar resources are different from station to station, and thus, there is a difference in reliability of the same type of photoelectric conversion system of different stations, which will be analyzed in detail in the next section.
(One), evaluation of reliability of a photoelectric conversion system of the cross observation station:
assuming that the photoelectric conversion system shown in fig. 1 is installed in a cross observation station, the reliability of the photoelectric conversion system of the six observation stations is evaluated by using a 3 rd section photoelectric conversion system failure rate Markov chain model, wherein three-dimensional relation diagrams of the average failure rate of the photoelectric conversion system and the average failure rate of the Boost converter of the cross observation station and the average failure rate of the inverter with temperature and irradiation states are shown in fig. 5 (a) to 5 (c). The following phenomena can be seen: 1) As the temperature increases, the average failure rate of the Boost converter, the inverter and the photoelectric conversion system increases; 2) As irradiation increases, the average failure rate of the Boost converter, the inverter and the photoelectric conversion system increases; 3) Comparing the three figures shows that the failure rate of the Boost converter is much smaller than that of the inverter. The phenomenon shows that the temperature and irradiation increase can increase the failure rate of the photoelectric conversion system, and the failure rate of the photoelectric conversion system is mainly influenced by the failure rate of the inverter.
(II), influence of mounting position on reliability of photoelectric conversion system:
Assuming that the photoelectric conversion system shown in fig. 1 is installed at the remaining five observation stations in fig. 4, the failure rate Markov chain model of the photoelectric conversion system is applied to evaluate the system and the average failure rate of the elements, and the results are shown in table 4.
Table 4 average failure rate index of photoelectric conversion system
The following phenomena can be seen: 1) With the same longitude, as the latitude decreases (solar resources increase), the failure rate of the elements and systems increases; 2) At the same latitude, as the western longitude increases (solar resources decrease), the failure rate of elements and systems increases; the phenomenon shows that the average failure rate of the regional system and the element with abundant low latitude and high longitude solar energy resources is higher, and the average failure rate of Mavie observation stations is the lowest and the Watford City observation stations are the highest under the condition that only the influence of the average failure rate is considered.
TABLE 5 probability of failure rate and frequency index
Table 5 shows the probability and frequency of occurrence of three types of high, medium and low failure rate levels for the photoelectric conversion systems of different observation stations. The following phenomena can be seen: 1) Under the same longitude, the areas with lower latitude have rich solar energy resources, the higher the probability and the frequency index of the high fault rate are, and the probability and the frequency index of the low fault rate are lower; 2) Under the same latitude, the larger the Western longitude is, the more the solar energy resources are enriched, the higher the probability and the frequency index of the high fault rate are, and the probability and the frequency index of the low fault rate are lower; the phenomenon shows that the regional system with abundant solar energy resources with low latitude and high longitude has high probability and frequency of high fault rate, and the fault rate of Mavie observation stations is lower under the condition that only three types of probability and frequency influence are considered; mavie observation stations are higher in reliability, more suitable for building photovoltaic power stations, and the Watford City observation stations are lowest in reliability and not suitable for building photovoltaic power stations.
(III), temperature elasticity of failure rate:
To analyze the influence of temperature variation on the average failure rate of the photoelectric conversion system, the temperature elasticity indexes of the failure rates of six observation stations are calculated, and the failure rates and the elasticity curves thereof along with the temperature variation are drawn, as shown in fig. 6 (a) and 6 (b). The following phenomena can be seen: 1) The magnitude relation between the average fault rates of the photoelectric conversion systems of the six observation stations is unchanged along with the temperature amplification and the temperature reduction, and the magnitude relation is increased and reduced along with the temperature amplification and the temperature reduction; 2) Along with the temperature amplification, the temperature elastic coefficient of the average failure rate of the photoelectric conversion system of the six observation stations is increased along with the temperature amplification, but the overall change is smaller; 3) The temperature elastic coefficients of the average failure rates in Harvey and Wishek regions are relatively close. The above phenomenon shows that the failure rate increases with an increase in temperature, and that the larger the temperature is, the larger the influence on the failure rate is, and the temperature elastic coefficient of which the temperature average value is close to the failure rate is also close.
(IV), irradiation elasticity of failure rate:
To analyze the influence of irradiation variation on the average failure rate of the photoelectric conversion system, irradiation elasticity indexes of failure rates of six observation stations are calculated, and failure rates and elasticity curves thereof according to irradiation variation are drawn, as shown in fig. 7 (a) and 7 (b). The following phenomena can be seen: 1) Along with irradiation amplification and reduction, the average fault rate of the photoelectric conversion system of the six observation stations is increased and reduced along with the original sequence; 2) Along with irradiation amplification, the temperature elastic coefficient of the average failure rate of the photoelectric conversion system of the six observation stations is gradually increased; 3) And comparing the temperature elastic curve of the failure rate, wherein the irradiation elastic curve of the failure rate expands more. The above phenomenon shows that the failure rate increases with increasing irradiation, and the larger the irradiation is, the greater the effect on the failure rate, and the effect of irradiation on the failure rate is greater than the temperature.
In summary, the invention provides a Markov chain-based photoelectric conversion system reliability evaluation model, which divides the temperature-irradiation state to obtain a plurality of state photoelectric conversion system fault rate models, and divides the states of the system multi-state fault rate again to calculate the element and system average fault rate index, and the transition probability and frequency index between different fault rates. The model can be applied to different photovoltaic power stations, and the region with the highest reliability can be judged by analyzing the reliability influence index of the temperature-irradiation to the photoelectric conversion system. Through data analysis and elasticity test in north dakota, the following conclusion is drawn: ① The higher the temperature and the stronger the irradiation, the richer the solar energy resources are, the higher the failure rate index of the photoelectric conversion system is, and the higher the high failure rate probability and the frequency index are; ② And compared with the influence of temperature on the failure rate, the influence of irradiation on the failure rate is more obvious, and the average failure rate of the system is more sensitive to irradiation change.
Claims (1)
1. The reliability evaluation method of the photoelectric conversion system based on the Markov chain is characterized by comprising the following steps of:
Step 1: establishing a temperature-irradiation Markov chain by carrying out state division on temperature and irradiation;
step 2: establishing a photoelectric conversion system fault rate model, and embedding the photoelectric conversion system fault rate into the temperature-irradiation Markov chain established in the step 1to form a photoelectric conversion system fault rate Markov chain;
Step 3: dividing the failure rate of the photoelectric conversion system into three failure rate levels of high, medium and low, so as to calculate the average failure rate of the element and the system, and the transition probability and frequency among the three failure rate levels, and describing the reliability of the photoelectric conversion system from the angles of the failure rate and the frequency;
in the step 1, a temperature-irradiation state dividing table is applied to divide an actual temperature-irradiation sample, and a temperature-irradiation Markov chain is determined according to a temperature-irradiation state dividing result of measured data;
In the step 1, the temperature-irradiation state is firstly scaled, and the transfer rate among the groups of states is as follows according to the temperature-irradiation state dividing result of the measured data: ，
Wherein: And/> The transfer rate and the transfer frequency of the temperature irradiation state (j, k) to the temperature irradiation state (m, n) are respectively; /(I)For the duration of the temperature irradiation state (m, n);
After the transfer rate among the temperature irradiation states of each group is calculated, a temperature irradiation state transfer rate matrix G is obtained as follows: ；
The step 2 comprises the following steps:
s2.1: according to specific temperature irradiation, a photovoltaic cell output model is established, and photovoltaic cell output voltage V PV and current I PV under specific temperature-irradiation are obtained;
S2.2: calculating the power loss of a power device diode and an IGBT by using the photovoltaic cell output voltage V PV and the current I PV under specific temperature-irradiation;
s2.3: according to the element thermal model and the element power loss, junction temperature of the element can be obtained, a fault rate model of the power conversion device IGBT and the diode is established, and the fault rate models of the inverter, the boost converter and the photoelectric conversion system are obtained;
S2.4: embedding a fault rate model of the photoelectric conversion system into the temperature-irradiation Markov chain in the step 1 to obtain the fault rate Markov chain of the photoelectric conversion system;
in the step 2.2, the power loss of the Boost converter under the specific temperature-irradiation state The method comprises the following steps:；
wherein: And/> The power losses of the IGBT and the diode in the Boost converter are respectively;；
wherein: And/> IGBT conduction loss and switching loss in Boost converter respectively,/>The output current is the output current of the photovoltaic array; /(I)The turn-on threshold voltage of the IGBT; /(I)The IGBT on-resistance is adopted; /(I)Is the duty cycle of the converter; Switching frequency for Boost converter;
And/> The energy consumption of each turn-on and turn-off of the IGBT is respectively; /(I)Outputting a voltage for the Boost converter;
And/> The rated voltage and the current value of the IGBT in the Boost converter are respectively;
；
wherein: is the diode on-resistance; /(I) Energy consumption for each turn-off of the diode; /(I)And/>Respectively the rated voltage and the current value of the diode;
the inverter power loss is: ，
wherein: And/> The power losses of the IGBT and the diode in the inverter are respectively;
The power loss of the diodes in the inverter is calculated as follows:
；
wherein M is the modulation factor of the inverter; θ is the included angle between the output voltage and the current of the inverter; Is the diode on-resistance; Is the peak current of the inverter; /(I) FO is the diode turn-on threshold voltage; /(I)Switching frequency for the inverter; /(I)Energy consumption for each turn-off of the diode; /(I)Outputting current for the inverter; /(I)And/>The rated voltage and the current value of the diode are respectively;
the power loss of the IGBTs in the inverter is calculated as follows:
wherein: the turn-on threshold voltage of the IGBT; /(I) And/>The energy consumption of each turn-on and turn-off of the IGBT is respectively,And/>The rated voltage and the current value of the IGBT are respectively;
In the step 2.3, the junction temperature of the element is: ；
Wherein: t a、Rha and R jh are respectively the ambient temperature, the thermal resistance of the radiator to the environment, and the thermal resistance of the junction to the radiator;
P diode/igbt is the loss of a single diode or IGBT; p total is the total loss of the converter; the obtained IGBT and diode fault rate is as follows:
；
，
Wherein: And/> The basic failure rates of the IGBT and the diode are respectively, pi Q is the quality factor of the element, pi A is the application factor, pi E is the environmental factor of each part quantification in the failure rate model, pi C is the related structural factor, pi S is the stress factor, pi T is the thermal factor, and the environmental temperature and the junction temperature are dependent, as shown in the formula:
，
Wherein: And/> Thermal factors of the IGBT and the diode respectively;
And/> Junction temperatures of the IGBT and the diode respectively;
the failure rates of the boost converter and the inverter under the single temperature-irradiation state are respectively as follows:
、/>；
Wherein: And/> The failure rates of the IGBT and the diode in the Boost converter are respectively;
And/> The failure rates of the IGBT and the diode in the inverter are respectively;
The failure rate of the system is as follows: ；
The step 3 includes the following steps:
s3.1: all states are divided into four parts:
The failure rate of the low-temperature scale (1-5) and low-irradiation scale (1-11) set state is low, and the low-temperature scale and the low-irradiation scale are marked as a low failure rate state lambda L;
The failure rate of the high temperature scale (6-10) and the high irradiation scale (8-13) in the aggregate state is higher, and the failure rate is marked as a high failure rate state lambda H;
The failure rate of the low temperature scale (1-5), the high irradiation scale (8-13), the high temperature scale (6-10) and the low irradiation scale (1-7) are in the two states, and the partial state is divided into a medium failure rate set lambda M;
The reliability of the photoelectric conversion system is evaluated by calculating probability indexes and frequency indexes of high, medium and low fault rate states;
S3.2: solving a photoelectric conversion system fault rate Markov chain to obtain probability P= [ P (1,1),p(1,2),…, p(j,k)…,p(10,13) ] of each fault rate state, wherein: p (j,k) is the occurrence probability of the failure rate state lambda (j,k), and j and k respectively represent a temperature state and an irradiation state;
From the above steps, the average failure rate of the converter and the system can be calculated; .
The average failure rate of the system is as follows:；
Wherein: n t is the temperature state number; n r is the number of irradiation states; is the failure rate state/>, of the photoelectric conversion system Probability of occurrence,/>Is a system failure rate state at temperature-irradiance state (i, j);
Similarly, it will Replaced by/>And/>The average failure rate/>, of the inverter and Boost converter can be calculatedAndThe method comprises the following steps of:
；/>；
Wherein, And/>Average failure rates of Boost converter and inverter under respective states (i, j);
The occurrence probability of three types of fault rate levels of the photoelectric conversion system is represented by the sum of all state probabilities respectively belonging to respective sets, and the low fault rate probability is as follows: ；
Wherein: the subscript L is a low failure rate set, Probability of belonging to a failure rate state (s, m) in the low failure rate set; similarly, the high failure rate probability p H and the medium failure rate probability p M can be calculated as:
And/> ；
Wherein, subscripts M and H represent a medium failure rate set and a high failure rate set;
the occurrence frequency of three types of fault rate levels of the photoelectric conversion system can be obtained by combining the fault rate frequencies, and the low fault rate frequency is that ；
Wherein: probability of being a state (u, k) in the low failure rate set L; /(I) Is a high and medium failure rate set; is the transition rate of state (u, k) to state (x, y); /(I) For the transition rate of state (i, j) to state (m, n) within set L,/>Probability of being state (i, j);
The same method can calculate that the high fault rate frequency f H and the medium fault rate frequency f M of the photoelectric conversion system are respectively
；
；
Wherein: m and H respectively represent a medium failure rate set and a high failure rate set;
S3.3: defining that the value of a scaling coefficient beta t,βt of temperature is in a [0.1,2] interval, multiplying the scaling coefficient beta t of temperature by all measured temperature data, multiplying temperature irradiation data (t 1, r1), (t2, r2), …, (tN, rN) by the scaling coefficient beta t to obtain new temperature irradiation data (βtt1, r1), (βtt2, r2), …, (βttN, rN),, then re-evaluating the fault rate of the regional system based on a Markov chain model of the fault rate of the photoelectric conversion system, and comparing the fault rates before and after the scaling coefficient is applied;
the temperature elastic coefficient defining the average failure rate of the photoelectric conversion system is as follows: ；
In the method, in the process of the invention, Is the elastic coefficient of the failure rate of the photoelectric conversion system when the temperature changes,/>The average failure rate of the photoelectric conversion system after the actual temperature data is integrally changed by beta T;
Defining that the value of a scaling coefficient beta r,βr of irradiation is in a [0.1,2] interval, multiplying beta r by all measured irradiation data, multiplying temperature irradiation data (t 1, r1), (t2, r2), …, (tN, rN) of a certain region by the scaling coefficient beta r to obtain new temperature irradiation data (t1, βrr1), (t2, βrr2), …, (tN, βrrN),, then re-evaluating the fault rate of the system of the region based on a Markov chain model of the fault rate of a photoelectric conversion system, and comparing the fault rates before and after the application of the scaling coefficient; the temperature elastic coefficient defining the average failure rate of the photoelectric conversion system is as follows: ；
Wherein: Is the elastic coefficient generated when the failure rate of the photoelectric conversion system changes due to irradiation,/> For the average failure rate of the photoelectric conversion system after the actual irradiation data is integrally changed by beta R, beta R is an irradiation scaling factor, and the value is 0.1 and 2;
and calculating the index, and establishing a program for influencing the reliability of the photoelectric conversion system by temperature irradiation, so that the reliability of the photoelectric conversion system can be evaluated.
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