A self-replicating rapid prototyper (RepRap) is a type of 3-D printer capable of printing many of its own components in addition to a wide assortment of products from high-value scientific or medical tools to household products and toys. There is some evidence that these printers could provide low-cost distributed manufacturing in underprivileged rural areas. For the most isolated communities without access to the electric grid, a low-cost alternative energy is needed. Solar energy can be harvested through a stand-alone photovoltaic (PV ) power system specifically designed to match the needs of the RepRap. The voltage and current requirement for the printer demands the use of buck along with a bidirectional DC converters to ensure proper operation. This paper provides the design for a stand-alone PV—lithium ion battery power system with an efficient controller. Robust and agile PI controller schemes are utilized to efficiently maintain the distribution of energy through the power system. The system was defined with ordinary differential equations, simulated and tested for two operational conditions in MATLAB/Simulink. The results showed that the controller developed operates the system in a stable condition and the simulation shows steady acceptable behavior that makes this system highly suitable for hardware implementation. Keywords: Solar energy, Photovoltaic, Distributed manufacturing, Appropriate technology, Open source hardware, 3-D printing, Off-grid, Distributed power, Electrical storage Introduction industrialization is economically challenging (Canessa 3-D printing using fused filament fabrication (FFF) is et al. 2013; Pearce et al. 2010; Hurst and Kane 2013; the process of producing a solid object by accumulating Lotz et al. 2013; De Maria et al. 2014; Gwamuri and successive layer of normally polymer-based materials fol- Pearce 2017; Savonen et al. 2018). Simultaneous devel- lowing a digital CAD model. Historically, 3-D printing opment and wide adoption of information technologies was limited to rapid prototyping in well-funded labora- have enabled a commons-based open design or open tories and large manufacturing firms. The designs for source method to accelerate development of appropri- the RepRap (short for self-replicating rapid prototyper) ate technology (AT) (Buitenhuis and Pearce 2012; Pearce were released under open hardware licenses and a com- and Mushtaq 2009; Pearce 2012a, b). Such open source bination of rapid innovation and competition between appropriate technology (OSAT) follows the free and open now many 3-D printing firms rapidly reduced the cost source (FOSS) model that allows technology users to be of 3-D printing below $1000 (Sells et al. 2010; Jones developers and share the open source code of their physi- et al. 2011; Wittbrodt et al. 2013). These cost declines cal AT designs (Pearce 2009; Korukonda 2011; Louie permit rapid distributed manufacturing of high-value 2011) and to use this ability as a science and engineering products in underprivileged areas of the world where education aide (Kentzer et al. 2011; Pearce 2007, 2012b, 2013). Thus, in this context, the “source code” for the OSAT are 3-D CAD designs, which enable anyone with *Correspondence: email@example.com access to a 3-D printer and electricity to fabricate them. Department of Electrical and Computer Engineering, Michigan Unfortunately, 1.4 billion people lack access to electric- Technological University, 1400 Townsend Drive, Houghton, MI ity (Birol 2010; van der Hoeven 2013) and despite rural 49931-1295, USA Full list of author information is available at the end of the article electrification projects (Zomers 2003; Barnes 2011) the © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Khan et al. Renewables (2018) 5:5 Page 2 of 14 problem persists as the International Energy Agency esti- resistance placed in series with the batteries. The previ - mates that at the present rate, electricity access will only ous designs had efficiency losses from the use of a resis - keep pace with population growth until 2030 (Birol 2010; tive element to limit the charging and discharging current van der Hoeven 2013). To enable rural isolated commu- of the battery from PV module. Secondly, this circuit is nities without access to the grid to leverage the power of charging a pack of lithium ion batteries, which requires a 3-D printing for development, solar photovoltaic (PV)- specific CC and CV charging method or they suffer from powered RepRaps with battery storage have been devel- capacity fading, swelling and even explosion, creating a oped (King et al. 2014). The electrical designs and the potentially hazardous situation. An improved electrical performance of such systems have not been optimized. design is simulated here for a MOST delta RepRap. The In order to improve the electrical design of such sys- MOST Delta RepRap printer (Irwin et al. 2014; Anzalone tems, this study provides a detailed simulation of a PV et al. 2015) is a conglomeration of 4 stepper motor con- power system for stand-alone 3-D printing with a con- trolled by a motor drive controller based on the Arduino troller using a buck and a bidirectional DC converter architecture and a resistively heated hot end with tem- used to charge and discharge the batteries with minimum perature feedback and position feedback from end stop energy loss. These converters utilize MOSFET switch - mechanical switches. ing that disconnects the PV or the battery autonomously The new electrical design is due to improvements in when not required. Each of the converters is controlled knowledge of 3-D printing materials and in the evolu- by their own PI controller, which ensures the constant tionary nature of the RepRap itself. Improvements in sur- current (CC) and constant voltage (CV) charging pat- face treatments have enabled elimination of the heated tern of the lithium ion battery and provides the output bed, radically reducing power consumption (130–140 W voltage with a small band of oscillation. Finally, the sys- down to 45 W), which reduces the storage requirements tem is designed in a way that the load always receives and PV size. For example, polylactic acid (PLA), the most power (e.g. either from the PV module or from the popular 3-D printing polymer, can be printed directly on battery), which enables the system to be able to print Kapton tape as shown in Fig. 1 or can be printed directly anytime there is sufficient power. The entire system on glass after pre-treatment with common glue sticks. simulation is designed using ordinary differential equa - tions to have the maximum flexibility while observing the required dynamic behavior. The simulated controllers are tested for stability in different steps to make sure that the designed controller for the linear approximation of the system also can operate properly for the actual nonlin- ear design. The entire system simulation is tested for two different operating conditions, charging and discharg - ing. In the first, the PV module is able to provide enough power to the 3-D printer and charge the battery and then in the second, during reduced simulated solar irradiance the battery acts as the source for the 3-D printer. Results of the simulations are discussed and conclusions are drawn about the efficacy of such designs for off-grid 3-D printing. Methods Delta RepRap Previously designed systems powered more energy-inten- sive Cartesian-based RepRap 3-D printers (King et al. 2014). The Cartesian RepRap power systems use only two operational amplifier comparator circuits named as over-charge and over-discharge protection to control two MOSFET devices. The over-charge protection circuit allows the battery to be charged up to a specific voltage Fig. 1 MOST delta RepRap 3-D printer. The polymer components where the over-discharge protection cuts off the batteries visible (yellow and black) have been printed on the same type of 3-D when the state of charge of the battery is too low. Moreo- printer ver, the only current limiter used in this schematic is a Khan et al. Renewables (2018) 5:5 Page 3 of 14 The new delta-style of RepRap design has also decreased 5. When the PV does not have enough power, the bat- the number of stepper motors further reducing power tery should step in as the sole power supplier and run use as shown in Fig. 1. Three for the motion control the printers until depleted. (located under the columns in Fig. 1) and one for the fila - ment driver (located on the column to the right in Fig. 1). To meet all of these standards, the system depicted in Polymer filament is fed by the filament driver through a Fig. 2 is designed. It can be seen that the PV module is Bowden sheath to the hot end located on the end effector connected with the buck converter, which is operated (yellow component with fan in middle of Fig. 1). by a voltage PI controller providing a duty cycle signal to a pulse width modulator. The output of the buck con - Modeling the stand‑alone PV power system verter is connected with the load of the 3-D printer. The The system is designed with the following operating con - lower-voltage side of the bidirectional converter is con- ditions and dispatch strategy: nected to the 3-D printer. Thus, the low-voltage side of the buck converter, the 3-D printer and low-voltage side 1. During the day, the PV should be able to power the of the bidirectional converter are connected in paral- printer provided 800 W/m (0.8 sun) AM1.5 illumi- lel. The high-voltage side of the bidirectional converter nation is available. is connected to the battery. Like the buck converter, 2. While PV-powered printing, the system should be the PI controller, the controller for bidirectional con- able to route the power toward charging the battery verter, is connected through a pulse width modulator. whenever there is a positive difference between avail - Both of these converters are of non-isolated topology. able power and the load of the 3-D printer. The transformer isolated converter topologies have the 3. If the battery is fully charged and the PV power can advantage of separating the ground of the two side of the still support the printer, then the battery will remain converter (Sira-Ramírez and Silva-Ortigoza 2006), but as reserve for low-light/nighttime usage, while the it also requires more switching devices compared to the PV continues to provide the printers. non-isolated topology converters (Jain et al. 2000; Duarte 4. Whenever the PV power is insufficient to run the et al. 2007; Inoue and Akagi 2007; Li et al. 2011; Wu et al. 3-D printer, the battery converter changes mode of 2012). Moreover, soft-switching is implemented for these operation from charge to discharge to fulfill the lack - converters in most cases to reduce switching losses with ing, provided the battery has enough power to dis- an objective of improving efficiency (Xie et al. 2010; Jain tribute. This is the mixed mode of operation where and Ayyanar 2011; Oggier et al. 2011; Krismer and Kolar both the PV and the battery are sharing the load 2012). Thus, the complexity of the system increases along requirements. with the cost (Fardoun et al. 2014). One of the purposes Fig. 2 Schematic of stand-alone PV system for RepRap 3-D printing Khan et al. Renewables (2018) 5:5 Page 4 of 14 of this paper is to minimize cost; thus, this paper concen- to 12.6 V, which necessitates a buck-boost converter trates on non-isolated topologies only. with the 12 V load, which will create unnecessary com- Testing with a MOST Delta RepRap printing PLA plications in controlling schemes. Thus, a 4S battery revealed the voltage and maximum power require- pack is considered, which has a usual operation range ments of 12 V and 48 W, respectively. It should be noted from 14.8 to 16.8 V. The entire operating region of the that the standard printing power requirements for the battery pack is higher than the load requirement. Thus, MOST Delta RepRap are 37 W. The converter connected a converter with bidirectional current flow (Drolia et al. between the solar module and the 3-D printer has to 2003), a bidirectional converter, is used where the high regulate its output voltage to match the measured printer side is connected to the lithium ion battery. Similar to requirement. Since the system should be able to print the buck converter, an extra inductor is used to limit while being charged, the PV modules should be rated at current ripples. The PI controller of the bidirectional least 48 W to meet the requirement of the printer and converter forces the entire system to operate at two dif- provide the remaining to the battery when the printer ferent operating conditions. When the PV has enough will not operate at maximum rating. A market analysis power, then i input of this controller is set to a Ref revealed that PV modules with more than 50 W power negative value, which denotes a safe charging current rating have a voltage rating higher than 12 V. This obvi - for the battery. Moreover, this safe charging current ated the use of the buck converter. Power converters in should be less than the difference between maximum a hybrid system where a source requires a bidirectional current output of the module and the printer require- flow like in Jung et al. (2014) a bidirectional converter ment. This prevents the battery from sinking too much would be preferable, but here the major source is a PV current that may prevent a proper 3-D printer opera- module. Power flowing back can be fatal for the PV mod - tion. The required current input changes according to ule. A buck converter has a unidirectional flow of power the power provided from the PV to ensure an uninter- (Sira-Ramírez and Silva-Ortigoza 2006), which prevents rupted printing process. In Karunarathne et al. (2011), any power feedback toward the PV module also elimi- this type of different operation of a same controller is nates the need for a protection diode. This is a norm for a used. Such operation of the controller fulfills the design hybrid system like (Li et al. 2015) to connect the primary requirement statement of 2, 3, 4 and 5. Thus, it can source with a unidirectional converter. An extra induc- be considered that the designed system fulfills all the tor is used with the buck converter to reduce the cur- aimed goals. rent ripple and protect the 3-D printer. The PI controllers are used because these can eliminate the error with least overshoot percentage, peak time and steady-state error. Simulating the designed system During the day when the illumination requirements are The system was simulated in MATLAB/Simulink met, the PI controller of the buck converter produces a 2014. The operating condition requires that the system duty cycle, which results in a good regulated 12 V supply. should be able to provide power from the battery if the On the other side, the battery needs to be charged PV is incapable to run the 3-D printer. This handover and discharged. The control system provides the from PV to the battery has to occur in a very short time required duty cycle when there is excess power pro- frame to carry out an uninterrupted 3-D printing. Thus, duction from the PV module. The duty cycle changes the simulation needs to be defined by the differential when the PV modules cannot produce enough power to equation representation of the system to observe the supply power from the battery to the load. This type of dynamic responses. The ordinary differential equations architecture is called active hybrids (Blackwelder and (ODE) associated with the model are shown in Fig. 2 Dougal 2004). A semi-active hybrid structure is more and the list of variables are: economically viable as explained in Song et al. (2015), Variable Description but a more precise control strategy can only be adopted in the active hybrid as explained in Zhang et al. (2014). i Current flowing through the inductor L Current in this converter should be able to reverse to V Voltage across the capacitor C C S achieve this feat. There are several converter options i Current flowing through the inductor L L SL SL that meet this requirement, but the selection of bidi- D Duty cycle of the buck converter rectional converter is governed by the battery property. i Current flowing through the inductor L L HB HB The battery of choice is lithium ion due to its highest V Voltage across the capacitor C C HB HB energy density among the currently available battery i Current flowing through the inductor L L B technologies (ICCNEXERGY 2015). A lithium ion 3S V Voltage across the capacitor C C B battery pack usually has an operating range from 11.1 Khan et al. Renewables (2018) 5:5 Page 5 of 14 Variable Description derri = V − V (10) C C S S i Current flowing through the inductor L L BL Ref BL dt D Duty cycle of the bidirectional converter V Voltage across the capacitor C or the load voltage C Load Load V Input voltage from the PV module derri in = i − i (11) L L B B V Battery terminal voltage Ref bat dt R Load resistance of the 3-D printer Load i Reference current for PI controller of bidirectional converter Ref Here, Eqs. (1) and (2) belong to the buck converter. The V Reference voltage for PI controller of buck converter Ref PI controller of the buck converter takes the feedback of erri Integral of error signal in PI controller for buck converter V to control the output of the buck converter. Equa- erri Integral of error signal in PI controller for bidirectional con- tions (3)–(6) are from the bidirectional converter. i HB verter and V represent the actual terminal voltage, the cur- HB kp Proportional gain for buck converter rent flowing in and out of the battery. The PI controller of ki Integral gain for buck converter the bidirectional converter controls i to determine how kp Proportional gain for bidirectional converter much current is withdrawn from or supplied to the sys- ki Integral gain for bidirectional converter tem. Equations (7) and (8) belong to the inductor outside the converter toward the load which act to limit the cur- Each of the inductor and capacitor delivers an ODE rent ripple of the system. The method of developing these from Fig. 2. The obtained ODE’s are: ODEs is explained in detail in Karunarathne et al. (2011). di The current across the load is designed as an algebraic L × = D × V − V (1) S 1 in C dt equation with Eq. (9). Equations (10) and (11) define the PI controllers. Since the system has been defined using the differen - dV tial equation, the next step in simulating the system is C × = i − i (2) S L L S SL dt to determine the operating points and linearize the sys- tem around a specific operating point. Linearization is required in order to produce the eigenvalues for specific di controller parameters. The eigenvalues reveal the stabil - HB L × = V − V (3) HB C bat HB dt ity of the system for the selected parameters. The system will have two different set of parameters because of the distinct charging and discharging states. Some values are dV needed to be assumed to set up the simulation to depict HB C × = i − D × i (4) HB L 2 L HB B dt these two operating points. The assumed parameters are listed in Table 1. The threshold for V is set to 12 V because the output in di of the buck converter has to be 12 V. If the input from L × = D × V − V (5) B 2 C C HB B dt the PV module is at least 12 V, then the buck converter can maintain an output of 12 V, theoretically. However, practically the voltage output will be less than 12 V dV because of the internal losses in the buck converter. C × = i − i (6) B L L B BL dt Charging current of − 1 A is set as an acceptable value because a market analysis revealed that 4S lithium ion batteries can withstand 4 A of charging current. Dis- di charging current of 4 A is set to make sure the load SL L × = V − V (7) SL C C S Load dt Table 1 The assumed values to define the systems point di BL of operation (1) L × = V − V (8) BL C C B Load dt Parameters State If V ≥ 12 V Then, i =−1A Charging in L Ref dV V C C If V < 12 V Then, i = 4A Discharging Load Load in L Ref C × = i + i − L L (9) Load BL SL dt R Load Khan et al. Renewables (2018) 5:5 Page 6 of 14 Table 2 The assumed values to define the systems point of operation (2) L = 2 mH L = 2 mH L = 2 mH L = 3 mH C = 10 μF V = 16.8 V S HB B SL Load bat C = 10 μF C = 100 μF C = 10 μF L = 3 mH V = 20 V R = 3 S HB B BL in Load Table 3 The assumed gain values kp ki kp ki S S B B 0.02 20 0.1 20 receives 12 V because at maximum load the resistance of the printer is 3 Ω. The other parameters required for the simulation are shown in Table 2. The value of the inductors and capacitors are selected from an array of available products. The input of PV is set to 20 V for the charging state of the system. The Fig. 3 The pole–zero plot for the charging state maximum battery voltage is considered for a 4S lithium ion battery. Using these values and the ODEs, the oper- ating point of the system is generated. Particulars of controller for this system. For the determined A matrix the operating points listed below are generated using is given below by Table 3. Mathematica 10. The determined respective eigenvalues are depicted using a pole–zero plot in Figs. 3 and 4. Figures 3 and 4 i → 5 i → 0 L L s s V → 12 V → 12 C C show eigenvalues for the assumed gains during charg- S S i →−0.7142857142857142 i → 2.8571428571428568 L L hB hB ing and discharging state, respectively. In both cases, it V → 16.8 V → 16.8 C C HB HB can be observed that all the poles are on the left of the i →−1 i → 4 L L B B imaginary axis. This proves that for the assumed gain, all V → 12 V → 12 C C B B i → 5 i → 0 L L of the eigenvalues are negative. Negative coefficient on SL SL i →−1 i → 4 L L BL BL all eigenvalues verifies stability of the system (Eren and V → 12 V → 12 C C L L Liptak 2016). Thus, this system along with its assumed 3 3 erri → erri → S S 5∗ki 5∗ki S S parameter is stable and can be implemented both in sim- 0.7142857142857142 0.7142857142857142 erri → erri → B B ki ki B B ulation and in physical domain. Now, an average mode simulation is carried out in Simulink using the ODE equations defined earlier. A self-improvised model of a battery is utilized in the sim- Here it can be observed that in both conditions, the ulation. A detailed battery model is ignored to reduce values of the variable are reasonable considering practi- complexity of the simulation. The simulation is run for cal applications. This means that this system is practical 0.2 s of operation to depict the dynamic response of the and can be simulated or implemented in the physical system. At the start, the PV input is kept at 20 V. After domain. This also proves that assumed values of dif - 0.1 s, the PV input is simulated to fall to 10 V to initiate ferent components can also be used in the simulation. the switching from the charging to the discharging state Now the system is linearized on these two points of of operation. The results of the simulation are provided in operation using Mathematica. The A and B matrices the next section. from the linearization process produce the equation of eigenvalues. The controller gains are assumed as below. Results Both of these points are the desired point of opera- To test the designed system, the simulation was run for tion and there is no need to change the assumed values. 0.2 s. The PV supply is a step signal going from 20 to 10 V. Now the system is linearized using Mathematica. The This would cause the system to switch from charging to dis - most significant matrix during linearization is matrix charge operating condition. The battery capacity and initial A. This matrix is required in order to determine the state of charge (SOC) are selected as 20 Ah and 0.9998% to eigenvalues. The eigenvalues are required to design the Khan et al. Renewables (2018) 5:5 Page 7 of 14 It can be observed from Fig. 5a that the source is stepped down from 20 to 10 V. As a result, the buck con- verter output voltage initially was set to 12 V by 0.08 s in Fig. 5c. When the supply voltage is reduced below zero, the PV module cannot sustain the printer output of 12 V. So there is a dip in buck converter output voltage in Fig. 5c as the battery on the other side is switched from being a sink to a source. It takes about 0.05 s to recover from the change of sources. This is what it would take for an actual battery to recover from such a change. In Fig. 5d, buck converter output current was supplying the load as long as it had enough power from the PV. Initially Fig. 4 The pole–zero plot for the discharging state there were some transients in Fig. 5c, d due to the induc- tor and the capacitor charging. Soon by 0.08 s the current output settled to 5 A which is the sum of requirement of properly display the effect of charging and discharging. The the load and the battery charging current requirement. source converter responses are shown in Fig. 5a–d. The characteristics of the battery parameters are shown in Fig. 6a–d. Fig. 5 a PV output voltage. b Buck converter duty cycle. c Buck converter output voltage. d Buck converter output current Khan et al. Renewables (2018) 5:5 Page 8 of 14 Fig. 6 a Battery current input during charging (negative) and output while discharging (positive). b Battery SOC during charging (rising) and discharging (falling). c Battery open circuit voltage during charging (rising) and discharging (falling). d Battery terminal voltage After some initial transients due to charging of a large battery is being charged. Since the design of the battery capacitor on the high side of the bidirectional converter is linear, the SOC increases with a linear pattern. In real (BDC), the battery current in Fig. 6a settles slightly less life for lithium ion batteries, the SOC is linear. But the than − 1 A. This is the charging state of the battery and it terminal voltage are highly nonlinear especially near the continues until 0.1 s as the PV provides the battery. The high and the low end of the SOC level due to the effects charging current demanded from the PV is 1 A, but due of activation overpotentials and concentration overpo- to the duty cycle the voltage increased on the high side of tentials (Broadhead and Kuo 2001). When the battery is the BDC converter and the current decreased. The cur - discharged, the SOC falls linearly. The open circuit volt - rent is almost − 0.7 A which corresponds to a duty cycle age (OCV) in Fig. 6c increases while being charged and of 0.7 (= 12/16.8). After the PV is disconnected from the decreases while being discharged. Battery terminal volt- system, the battery starts discharging by reversing the age in Fig. 6d is a bit more interesting even with a linear flow of current to almost 3 A. This is also less than the design. The terminal voltage is slightly higher than the printer requirement of 4 A. The duty cycle reduces the rated voltage of the battery. This is expected of a real bat - voltage on the lower side of the convert and increases tery. While charging the battery, the terminals account the current by the order of duty cycle of 0.7 (= 12/16.8). for all the internal losses due to overpotentials (Broad- In Fig. 6b, SOC of the battery increases as long as the head and Kuo 2001) (manifested in the design by a simple Khan et al. Renewables (2018) 5:5 Page 9 of 14 resistor) and the rated open circuit OCV. Thus, during BDC converter output is now operated by the battery. the charging state, the V is higher than 16.8 V. While The voltage on lower side in Fig. 7c settles within 0.05 s bat being discharged in Fig. 6d, the battery has to overcome of the switching of the sources. During the switching, its internal losses. Thus, the V during discharge is less the min and max voltages are 10 and 22 V, respectively. bat than 16.8 V and decaying as SOC of battery is dropping The converter current through the lower side is shown as shown in Fig. 6d. The simulated performance of the in Fig. 7d. Initially when the PV was supplying, the ini- bidirectional converter is shown in Fig. 7a–d. tial condition of the converter was trying to charge the Figure 7b shows the plot of voltage across the capaci- battery with all the current supplied by PV. However, as tor on the high side of the converter. Since the capaci- shown in Fig. 7d, the controller soon takes action and tor is of a higher size, there is higher oscillation while reduces the charging current to − 1 A by 0.06 s. When charging it initially. Then by 0.08 s it settles down to the PV is detached by 0.1 s, the current in the inductor the battery terminal voltage which is slightly higher reverses by the action of the controller and reaches 4 A than 16.8 V. The voltage on the lower side in Fig. 7c of by 0.15, 0.05 s after the switching. Figure 8a, b shows the converter supplies the battery as it is initially being the output voltage and current across the 3-D printer. controlled by the PV supply. After some initial oscilla- Figure 8c shows a zoomed in Fig. 8a to properly dem- tion, the voltage settles to 12 V by 0.06 s. The battery onstrate the dynamic behavior of the system. acts as the source as the PV module is detached. The Fig. 7 a BDC high side current input during charging (negative) and output while discharging (positive). b BDC high side voltage. c BDC low side voltage. d BDC low side current input during charging (negative) and output while discharging (positive) Khan et al. Renewables (2018) 5:5 Page 10 of 14 Fig. 8 a Voltage across the RepRap. b Current through the RepRap. c Zoomed in on voltage across RepRap during the transition from PV to battery Khan et al. Renewables (2018) 5:5 Page 11 of 14 The load output voltage is then obtained from a state is a maximum speed for a given quality/resolution of equation. However, the current in Fig. 8b is just an print obtainable. This limitation can be offset in part by algebraic equation as the load is considered to be just a increasing the nozzle size of the hot end, which allows resistor. It can be clearly seen in Fig. 8a that the output more material to be deposited in each layer. Although voltage has much lesser ripple in the voltage as well as the the positional accuracy remains the same, both the line current. This is due to the fact that the output is sepa - width and the roundness of corners increase to the size rated from both the converter with two inductors. This of the nozzle. This is a fundamental limitation of FFF 3-D approach caused the currents to be filtered through the printing and can only be further increased by increasing two inductors. Moreover, the voltage across the load is the number of print heads and either chain ganging verti- also filtered by the presence of the capacitor. The param - cally or horizontally to increase throughput of identical eter of the system was perfectly chosen to provide these parts. Finally, the power system can support improved results. The output voltage settles by 0.06 s to 12 V. Dur - accuracy by changing the nozzle size, which provides ing the switching, the min and max are 11.4–14.8 V, tighter corners and smaller line widths, but comes at the respectively. The system returns to 12 V by 0.17 s (0.07 s penalty of increasing print time. In addition, resolution later switching). This can be perceived better in Fig. 8c, can be improved by using a smaller drive gear or using which shows the ripples in the output voltage during the a geared drive, which although requiring redesigning handover from the PV to the battery source. The perfor - the extruder drive body could be printed on the MOST mance of the system was observed in this section while delta itself, thus enabling self-upgrading. This improve - being operated in both charging and discharging state. ment again would be accommodated by the power sys- tem described here. The print resolution in the x–y Discussion and future work plane is complex for a delta as it improves when closer As the results show, a new system for PV-powered to an apex for that apex. So, for example, when moving RepRaps has been successfully designed. Such a system toward the W apex (positive y direction), the resolution is relevant to any rural isolated off-grid community that in x (controlled by U and V) degrades, but resolution in y wants digital distributed manufacturing of OSAT or improves. For the optimal resolution for both x–y dimen- possibly export items to sell (Laplume et al. 2016). It is sions, the optimal print location is the center of the print important to note the self-upgrading and open source bed. If the object has high-resolution bottom features, nature of the RepRap 3-D printer. RepRaps are capable of printing on a raft can help preserve the dimensionality of printing their own components for replacement and are those features and only has a small penalty in energy con- able to upgrade themselves as the global RepRap commu- sumption for the first layer raft printing. The z resolution nity iterates on the design. This effectively extends the life is equivalent to the resolution of moving the carriages cycle of the device and enables it to be considered appro- and is independent of the location. The MOST Delta (12 priate technology for most communities as it is both tooth T5 belt), which operates at 53.33 steps/mm, pro- economically viable (Wittbrodt et al. 2013) and there are vides a z-precision of about 19 μm. This can be improved also substantial reductions in the environmental impact to 10 μm by changing to a 16 tooth GT2 belt, which oper- of manufacturing using this process rather than standard ates at 100 steps/mm. manufacturing (Kreiger and Pearce 2013a, b). The final requirement for appropriate technology status The system as described here will support upgrades is access to the raw materials to print with. Fortunately, to improve RepRap 3-D printer size, speed and accu- recyclebot technology has been developed that enables racy. First, the power requirements do not change if users to turn plastic waste into 3-D printing filament the RepRap build volume is enhanced by increasing the with lower costs and less environmental impact (Bae- z-height with greater vertical lengths of the smooth guide chler et al. 2013; Kreiger et al. 2013, 2014; Zhong et al. rods, the support structure/frame and the belts. Similarly 2017; Woern et al. 2018). Polymer waste, often from the x–y area can be expanded by changing the size of the food and drink containers, is common in many develop- base plate, the tie rods and the linking boards without ing communities (Muttamara et al. 1994) and e-waste is impacting the power system. These approaches can be becoming more predominant that can also be used as a combined to increase the build volume as needed. Sec- feedstock (Zhong and Pearce 2018). Informal waste recy- ondly, the power system provided here can support faster cling is already conducted as an economic activity (Zia print speeds as the print speed is not limited in this case et al. 2008) and now recyclebot technology enables the by the power system. The MOST delta can be acceler - potential for fair trade filament or social plastic (Feeley ated further by adjusting the slicing settings. As the print et al. 2014). Already the non-profit Plastic Bank in South speed increases, however, there are materials deposition America and business Protoprint in India are using waste limitations and depending on the type of filament there pickers to recycle plastic into 3-D filament, and there is Khan et al. Renewables (2018) 5:5 Page 12 of 14 significant interest in the technical development com - ensuring a constant supply of scarce products for iso- munity (Birtchnell and Hoyle 2014). Preliminary work lated communities such as in rural clinics (Savonen et al. has already begun to determine the number of cycles 2018). Further work is needed in biopolymer reactors to a polymer can withstand the print, recycle, filament produce PLA from agricultural waste for regions, with no extrude loop (Sanchez et al. 2015, 2017). Advanced flex - access to waste plastic. In addition, continual reductions ible materials (Woern and Pearce 2017) as well as waste on the energy consumption of RepRaps by, for example, composites (Pringle et al. 2018) have also been recycled improving hot end geometry will also help reduce the size successfully following this approach, and an untethered and cost of the PV and battery storage systems. Finally, in solar-powered recyclebots have been developed (Zhong order to absolutely minimize costs while ensuring opti- et al. 2017). As expanded resin identification codes are mized designs, all of the components of the system need adopted, this activity can expand (Hunt et al. 2015). It to be completely open source and 3-D printable. There should be noted that this design focused on PLA-based have already been some substantial improvements in printing, and that the overall print time of the device the capabilities of such 3-D printers to either mill their will be limited by the polymer selected. High tempera- own PCBs or print electronic materials (Andersson 2015; ture polymer feedstocks will entail some redesign of the Anzalone et al. 2015; Krassenstein 2015). RepRap. For example, nylon is a strong, durable, and ver- For the electric system itself, there is still future work satile 3-D printing material, which is both flexible when needed. First, multi-level PI controllers can be imple- thin, but has high inter-layer adhesion, which enables it mented that take in separate gains for charging and dis- to be used for functional parts such as those needed in charging operating point to make the system more agile. a bicycle. However, nylon requires temperatures above Secondly, other controlling schemes should be simulated 240 °C to extrude. To handle these higher temperatures, and tested to further improve the response of the sys- the MOST delta RepRaps can be upgraded with an all- tem. Thirdly, a simulation with a switching model can be metal hot end, and the end effector would need to be implemented to observe more dynamic behavior. Finally, redesigned in order to print with materials such as nylon. it is clear from the promising nature of the results that In addition, with some materials, a heated printer bed is a hardware prototype can be made and tested with the recommended and can be accommodated by the exist- delta RepRap to validate the simulations and test its ing Melzi Arduino-based microcontroller. However, this effectiveness. upgrade comes with significant energy penalties as the recommended printer settings for nylon involve extruder Conclusions temperature from 240 to 260 °C, hot bed temperatures This study simulated a new design of a stand-alone PV 70–80 °C with a PVA-based glue on glass, print speeds of power system for RepRap 3-D printing. A schematic of 30–60 mm/s and 0.2–0.4 mm layer heights (Taylor 2014). the electric system was developed, which lead to the dif- Such relatively slow print speeds, with a high tempera- ferential equations that were analyzed and a controller ture hot end and a heated bed will significantly increase for the system was developed. The results showed that energy consumption and thus decrease print time with the controller developed operates the system in a stable the system developed here. Future work is needed to condition and the simulation shows steady acceptable improve the size of PV and storage system to accom- behavior that makes this system highly suitable for hard- modate this more energy-intensive type of printing with ware implementation. comparable print volumes/times. Building upon the simulations detailed here, Gwa- Authors’ contributions JMP conceived of the study, KK performed the simulations, KK, LG and JMP muri et al. (2016) fabricated and tested a PV-powered analyzed the data and wrote the paper. All authors read and approved the 3-D printer that performed as required under all condi- final manuscript. tions including: charging the battery and running the 3-D Author details printer, printing under low-solar-insolation conditions, Department of Electrical and Computer Engineering, Michigan Techno- battery powered 3-D printing, PV charging the battery logical University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA. only and battery fully charged with PV-powered 3-D Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Houghton, USA. Department of Materials Science printing. The results show the promise of solar-powered and Engineering, Michigan Technological University, Houghton, USA. 3-D printing systems providing feasibility for adoption in off-grid rural communities (Gwamuri et al. 2016). Thus, Acknowledgements Not applicable. the technology has the potential to help reduce poverty through employment creation (e.g., for recyclebot opera- Competing interests tors or 3-D printing operators as well as the associated The authors declare that they have no competing interests. positions). In addition, it provides some promise for Khan et al. Renewables (2018) 5:5 Page 13 of 14 Availability of data and materials Hunt, E. J., Zhang, C., Anzalone, N., & Pearce, J. M. (2015). Polymer recycling Data is available by request. codes for distributed manufacturing with 3-D printers. Resources, Conser- vation and Recycling, 97, 24–30. Ethics approval and consent to participate Hurst, A., & Kane, S. (2013). Making making accessible. In Proceedings of the Not applicable. 12th international conference on interaction design and children (pp. 635–638). ACM. ICCNEXERGY. (2015). 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