Modelling Photovoltaic Systems Using PSpice - 45271 07

Modelling Photovoltaic Systems Using PSpice - 45271 07

(Parte 1 de 4)

7 Standalone PV Systems


Standalone photovoltaic systems are described and PSpice models developed to ill-e the Wc concepts of energy balance, energy mismatch, loss of load probability and short and Img-tmm simulations and cornparison with measured waveforms. Analytical and simple sizing ~XQC&URS ip~e described and combined with long-term simulations using synthetic solar radiation time series.

7. I Standalone Photovoltaic Systems

Standalone PV systems are the most popular systems used worldwide despite the rrme recent interest of the market in grid-connected systems. A standalone PV system shauld provide enough energy to a totally mains-isolated application. The standard configuration of this system is depicted in Figure 7.1, where it can be seen that the PV generator is connected to the storage battery (this connection may include protection and power-conditiming devices), and to the load. In some specific cases, such as water pumping, the generator can be connected directly to the motor.

We have described in previous chapters, the models available for the various elements encountered in PV applications, such as the PV modules, power-conditioning devices, inverters and batteries and specific operating properties. This chapter describes simple pro- cedures to size a PV system for a given application and illustrates several important concepts:

0 Equivalent length of a standard day or peak solar hours (PSH) concept. 0 Generation and load energy mismatch. 0 Energy balance in a PV system. 0 Loss of load probability (LLP).

0 System-level simulation and comparison with monitoring data. 0 Long-term simulation using stochastically generated radiation and temperature series.


PV modules hod d

Figure 7.1 Standalone PV system

7.2 The Concept of the Equivalent Peak Solar Hours (PSH)

It is useful to introduce the concept of the equivalent peak solar hours (PSH) defined as the length of an equivalent day in which the irradiance is 1000 W/m2, Tcell = 25 "C, in such a way that the radiation (time integral of the irradiance over the day) is the same in one sun- equivalent day as in a real day.

Let us consider that the real irradiance profile in a given day is G(t) and that the irradiance of the equivalent day is by definition 1 kW/m2 during a time of length PSH hours. If we write that the total daily radiation in the real day has the same value as in the equivalent day, then

G(r)dt = 1 . PSH day

As can be seen, if the units of the irradiance are kW/m2, then the numerical value of the daily sun radiation equals the numerical value of the parameter PSH.

The definition of PSH is further illustrated in the following example.

Example ZI

Consider the average irradiance data for a given location, namely Barcelona (41.318' North, Spain), 16 January. (a) Write a PSpice .cir file to calculate the total radiation received that day.

We first write a subcircuit containing the hourly radiation data for that day [7.1], arranged as a PWL source 'virradiance' in the file 'irradjan-16' as follows,

*irrad-jan-l6.lib .subcktirrad-jan-l61210 virradiance1210pw10uO11u0,2u0,3u O,4uO,5uO,6uO,7uO +8uO,9u76,1Ou191,11u317,12u418,13u469,14u469,15u418,16u317

+17u191,18u76,19u0,20u0,21u0,22u0,23u0,24u0 .ends irrad-jan-16

These irradiance values are available at the subcircuit node (12).

THE CONCEPT OF THE EQUIVALENT PEAK SOLAR HOURS (FsH1p B(yi A .cir file is written to compute the lime integral as:

*irrad-jan-l6.cir xrad 72 0 irrad-Jan-16 .includeirrad-jan-16.lib erad 70 0 value= {sdt (v(72)*le6) } vpsh73Opulse (0100011u002.941u24u) epsh 74Ovalue={sdt(v(63)*le6)} .tranO.O01u24u .probe .end where node (70) returns the value of the daily radiation.

The result is shown in Figure 7.2 where it can be seen that the time integral gives a r&Eue of the total daily radiation of 2.94 kWh/m’day. According to equation (7.1) this means thap the value of the parameter PSH is 2.94 hours.

., ,-.............. ..................... ............... _._._ I Janbary/IGth’radia!ion [Wh ,,,
#I/ >!I ,.. 2.OKV I,, 1,....,.... .... .................... ...-..............
I,,SEL>> ........ ....,.............. ........i.........,..... ............-,.

I, ov7 ‘ ’ ’ ‘ ’ 0s 4PS 8 PS 12ps 16ps 20ps 24ps

Time 0 V(60)

Figure 7.2 (a) Irradiance profile in Barcelona, 16 January inclination 40”. Warning: y-axis is the irradiance in W/m’. (b) Time integral of irradiance. Warning: y-axis is the radiation in kWh/m’. In botyl graphs, the x-axis internal PSpice unit is a microsecond and real unit is time in hours (1 ps = I h)

(b) Plot the irradiance profile and radiation of the equivalent day. According to the definition we choose a 2.94 hour day length at 1 kW/m2 (as the definition is independent of the initial and final time values of the irradiance pulse, we choose 1190 as the initial time of the equivalent day and 13.94 hours the final time). This is shown in Figure 7.3.

The source ‘vpsh’ is a pulse-type voltage source simulating the equivalent one sun day. The time integral is available at node (74).

The utility of the PSH concept comes from the fact that the technical information usually available on PV commercial modules only includes standard characteristics. Even though these can be translated into arbitrary irradiance and temperature conditions as described in Chapter 4, in order to have a first-order hand calculation model of the energy potential of a


0s 12ps 24ps Time V( 40)

Figure 7.3 (top) Equivalent one sun irradiance profile in Barcelona, 16 Jarmery inclination 4W. Warning: y-axis is the irradiance in W/m2. (bottom) Time integral of equivalent one sun irradimm. Warning: y-axis is the radiation in kWNm2. In both graphs, the x-axis intd PSpice unit is a microsecond and real unit is time in hours (1 ps = 1 hour) given PV plant, the PSH concept allows us to work with the values of the stamdad characteristics if the equivalent length of one-sun day (PSH) is used.

This approximation is, of course, subject to some inaccuracy in the evaltlatim af the energy produced by a given PV generator due to the fact that effects of temperature ae not taken into account. An assessment of the accuracy of the PSH concep is iIlustrated in Example 7.2. We will consider in the next examples and subsections a PV system as depicted in Figure 7.4, which shows a block diagram of a PV module driven by irmdiamrce d temperature profiles connected to an ideal battery Vbat and a resistive 104 in series wirh a switch. As we will consider three cases of load, this switch allows an easy modifidon of the load connection schedule.

Figure 7.4 Block diagram for the circuit used to show power mismatch, night-time load arwl day-time load


Example Z2

Consider a simple installation such as the one depicted in Figure 7.4 where the switch is open and the battery voltage is set to zero. We will use the two outputs of the maximum power point coordinates in this example.

Consider the irradiance of 16 January used in Example 7.1, and the temperame pfile given in Annex 7 by the file ‘tempjan-l6.lib’. Calculate the total energy generated at the maximum power point by this PV module.


We have to use the time integral of the values of the maximum power delivered by the PV module over that day to compute the total energy supplied by running the following Pspice file ‘psh.cir’:

*psh. c ir

.include irrad-jan-16. lib .includetemp-jan-16.lib .includemodule-beh.lib xternp 73 Otemp-jan-16 xirrad 72 0 irrad-]an-16 xrnoduleO72 73 747576777879rnodule~behparams:iscmr=5,coef~iscm=9.94e-6, +vocmr = 2.3, coef-vocm= - 0.0828, pmaxmr = 85,noct = 47, immr = 4.726. vmmr = 17.89,

+tr=25, ns=36, np=l vaux 74Odc 0

.tranO.O1u24u .probe .end

As v(78) and v(79) are the values of the current and of the voltage respectively at the maximum power point, the energy generated that day is given by after running the ‘psh.cir’ file.

standard characteristics provide 85 W at 1 sun) during a day length of PSH, is The value of the equivalent-day total energy delivered by this same module (note that the

85 W x PSH = 85 W x 2.94 h = 249.9 Wh-day (7-3) where the value of PSH = 2.94 is the value of the total radiation received on 16 January in Barcelona at a 40” tilted surface expressed in kWh/m2 as calculated in Example 7.1.


Comparing the results obtained in equations (7.2) and (7.3) in Example 7.2, it becomes clear that the PSH concept underestimates the total energy delivered by the PV module in a January day by approximately 5%. This is due to the fact that the ambient temperature data in January at that location takes an average value close to 10 "C and as the irradiance values are also low, the cell operating temperature is lower than the value of the reference standard temperature leading to larger power generated by the PV module. Problem 7.1 addresses the same issue in June where both irradiance and temperature are higher, leading to a different conclusion.

7.3 Energy Balance in a PV System: Simplified PV Array Sizing Procedure

Sizing standalone PV systems is not an easy task due to the random nature of the sun's radiation at a particular place, the effects of the horizon, the albedo reflection of the surroundings, the orientation of the collecting surface (both azimuth and inclination) and to the unreliable data on the energy demand by the user.

All sizing methods are then subject to the same inaccuracy as the method we are describing here, which is a simple procedure that considers the energy balance of the photovoltaic system and the PSH concept. This procedure allows a clear description of how the different parameters enter the problem. It has also been shown [7.2] that the method has practical value by comparing the results of more rigorous procedures 17.31.

The energy balance in a PV system is established by a general equation stating that the energy consumed in a given period of time equals the energy generated by the PV system in the same period of time. This general equation in practical terms has to be established for the most suitable period of time for a given application. For example, if the application is a summer water pumping system, we are interested in the energy balance in the summer season, whereas if the application is a year-round standalone plant, we will write the energy balance for a period of one year. In any of these cases, the most conservative criteria usually considers, for the period of time analysed, the month having less solar radiation (worst-case design), while another, less conservative approach considers the average monthly radiation value (average design).

This energy balance method uses the peak solar hours (PSH) concept to write the energy balance equation in a given day, as:

where Pmax~r is the nominal output power of the PV generator at standard conditions (1 sun AMI.5 and 25 "C operating temperature), PSH is the value of the peak solar hours (which is numerically equal to the global in-plane radiation in kWh/m2day), and L is the energy consumed by the load over this average (or worst) day.

(a) Worst-case design: Equation (7.4) can now be written for the two design scenarios:

where (PSrnmi, is the value of PSH in the worst month.


- where (PSH) is the average value of the 12 monthly PSH values.

generator by its value: We continue using an average design. Replacing the nominal maximum powa af ERE PV

Considering that a PV generator is composed of Ns~ series string of N@ paraflef FV modules, it follows where Vm~,. and ImMr are the voltage and current coordinates of the maximum power point of one PV module under standard lSun AM1.5. From equation (7.8) the basic design equation can be drawn:

Usually the loads in a standalone PV system are connected to a DC voltage, namely Ves,,. The load L can now be written as:

L = 24Vcc Ieq (7.10) where Ipq is the equivalent DC current drawn by the load over the whole day. Replacing in equation (7.9):

There are a number of reasons why the real energy generation of the PV system might be different than the value given by the left-hand side in equation (7.1). One of them, as has been mentioned earlier, is that the peak solar hour concept underestimates or overestimates the energy generation. The other reasons are related to the energy efficiency of the several interfaces between the PV generator and the load, as for example, the efficiency of the MPP tracker, the efficiency of the charge4ischarge cycle of the battery itself, wiring losses, and DC/AC converter efficiency to supply AC loads. This means that the design process has to be deliberately oversized to account for these energy losses. It is very useful to introduce here an engineering oversizing factor or ‘safety factor’ (SF) in such a way that equation (7.1) becomes:

186 STANDALONE PV SYSTEMS Finally equation (7.12) can be split in two,

(7.13) 47. €4) where independent equations are found to size the number of PV modules in sezies (7-13) and in parallel (7.14). As can be seen the array oversize safety factor (SF) has &so Been divided into a voltage safety factor (VSF) and a current safety factor (CSF). In PV literature the PV generator size is often normalized to the daily load L as;

(7.15) NsG x NpG x PmaxGr (m) L c, =

Example Z3

Calculate the values of Ns~ and Npc for a PV system having to supply a DC load of

2000 WWday at 24 V in Sacramento (USA). The PV surface is tilted 40" and faces south. The solar radiation data available for Sacramento [7.4] are shown in Table 7.1 in kWWm2 month. The PV modules which will be used in the system have the following characteristies at standard conditions (1000 W/m2, AM1.5, 25 "C):

P,,, = 85 W, V,,, = 2.3 V, I,,, = 5 A, Idr = 4.72 A, Vd,. = I8 V We first compute the value of Ieq

L = 241,,VCc = 2000 Wh/day

Ieq = - - 24 x 24- 3'46 A

Table 7.1 Radiation data for Sacramento (CA)


Monthly radiation (kWh/m' month)

Jan Feb Ma

APr May


SeP Oct



Jun Jul

(7.116) (7.17)


The value of PSH is now required and it is computed by calculating the av- daiIy radiation value from Table 7.1, taking into account that January, March, hy, .hi&- August, October and December have 3 1 days each; that April, June, September and NQ- have 30 and that February has 29 days. The daily radiation values for mery mon& am given in Table 7.2.

Table 7.2 Daily radiation


Daily radiatkm (kWh/m' day)

2.83 3.89 5.12 6.16 6.70 6.93

6.63 5.4s 3.56 2.67

The average value of the average monthly daily radiation data in Table 7.2 is 5-35 kWh/

Considering the values of the parameters of a single PV mod& in equatiam (7-13) and m2 day.

(7.14) and assuming that the safety factors are unity, it follows,

Ns~ = 1.3 Np~ = 3.28

The recommended size of the PV array will be 4 x 2 which is the closest practical value.

As can be seen in practice the system becomes oversized by the factors: VSF = 1.5 and CSF = 1.21 due to rounding to the closest higher integer.

7.4 Daily Energy Balance in a PV System

The procedure described in Section 7.3 to size the PV array for a given application can be extended to calculate the size of the battery required. In a standalone PV system, the battery has in general to fulfil several tasks, among them:

(Parte 1 de 4)