Digital System Performance Enhancement of a Tent Map-Based ADC for Monitoring Photovoltaic Systems
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Compensation Algorithm
- Determine the sign for difference measure (SDM) to establish the direction of difference between the ideal output and that due to the non-ideal gain for each TM stage.
- Calculate the difference measure (DM) to determine the magnitude of difference between the ideal output and that due to the non-ideal gain for each TM stage.
- Compute the difference value (DV), which provides the overall magnitude and direction of the cumulative difference between the non-ideal gain of the TM based ADC output and the ideal.
- Compensate the ADC output.
2.2. Methodology
2.2.1. Analysis of the Algorithm
2.2.2. FPGA Implementation
2.2.3. Comparison with Basu et al.’s Method
2.2.4. Approximation of Difference Values
2.2.5. Sensitivity Analysis of Algorithm
3. Results
3.1. Analysis of the Algorithm
3.2. FPGA Implementation
3.3. Comparison with Basu et al.’s Method
3.4. Approximation of Difference Values.
3.5. Sensitivity Analysis of Algorithm
4. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. List of Acronyms and Symbols
Acronyms and Symbols | Meaning |
---|---|
ADC | Analogue-to-Digital Converter. A device that samples an analogue signal and digitizes the acquired data [23]. |
BESS | Battery Energy Storage System. Enables excess electrical energy from a PV system to be stored. When the PV system is unable to generate enough energy to supply connected loads, then the stored energy can be released to meet the demand [3]. |
CBC | Compensated Binary Code. |
DAQ | Data Acquisition. This is a process where electrical signals, representing real world physical phenomena, are measured and digitize for further processing [24]. |
DM | Difference Measure |
DV | Difference Value |
FPGA | Field Programmable Gate Array. A two-dimensional array of logic cells which can be configured to produce highly complex digital electronic circuits [25]. |
GCO | Gray Code Output. |
LSB | Least Significant Bit [26]. |
MSB | Most Significant Bit [26]. |
n stage | Number of TM stages employed. |
PV | Photovoltaic [27]. |
SDM | Sign for Difference Measure. |
SoC | State of Charge. The percentage of charge being stored by a battery relative to its capacity [4]. |
TM | Tent Map. A type of one-dimensional, discrete chaotic map [9]. |
UBC | Uncompensated Binary Code. |
Vcc | In the context of this paper, it is the maximum of the valid input voltage range for the TM-based ADC. |
Vee | In the context of this paper, it is the minimum of the valid input voltage range for the TM-based ADC. |
VHDL | Very high speed integrated circuits Hardware Description Language. This language enables digital electronic systems to be described [28]. |
xn | In the context of this paper, it is the input value supplied to a TM. |
xn+1 | In the context of this paper, it is the output value given by a TM. |
µ | In the context of this paper, it is the TM gain. |
µADC | The TM gain of the TM-based ADC. |
µc | Referring to the Scalar Approximation Method (Section 2.2.4), it is the actual TM gain of the TM circuit. |
µo | Referring to the Scalar Approximation Method (Section 2.2.4), it is the TM gain used to calculate the DM values suing Equation (2). |
Term | Meaning |
---|---|
Initial Conditions | The initial state of a chaotic system (e.g., control parameters and input values) [9]. |
Straight-Line and Error Approximation Method | A method proposed (see Section 2.2.4) in this paper to approximate the DM values employed by the algorithm. |
Scalar Approximation Method | A method proposed (see Section 2.2.4) in this paper to approximate the DM values employed by the algorithm. |
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TM Gain | Difference (Step-Size 1) | Effective Resolution (Nearest Bit) |
---|---|---|
1.9 | ±1543 | 4 |
1.99 | ±162 | 7 |
2 | ±1 | 15 |
TM Gain = 2 | TM Gain = 1.8 | |||||
---|---|---|---|---|---|---|
x | b2 | b1 | b0 | b2 | b1 | b0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.1 | 0 | 0 | 0 | 0 | 0 | 0 |
0.2 | 0 | 0 | 1 | 0 | 0 | 1 |
0.3 | 0 | 1 | 1 | 0 | 1 | 1 |
0.4 | 0 | 1 | 0 | 0 | 1 | 1 |
0.5 | 1 | 1 | 0 | 1 | 1 | 0 |
0.6 | 1 | 1 | 0 | 1 | 1 | 1 |
0.7 | 1 | 1 | 1 | 1 | 1 | 1 |
0.8 | 1 | 0 | 1 | 1 | 0 | 1 |
0.9 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 |
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Hazell, P.; Mather, P.; Longstaff, A.; Fletcher, S. Digital System Performance Enhancement of a Tent Map-Based ADC for Monitoring Photovoltaic Systems. Electronics 2020, 9, 1554. https://doi.org/10.3390/electronics9091554
Hazell P, Mather P, Longstaff A, Fletcher S. Digital System Performance Enhancement of a Tent Map-Based ADC for Monitoring Photovoltaic Systems. Electronics. 2020; 9(9):1554. https://doi.org/10.3390/electronics9091554
Chicago/Turabian StyleHazell, Philippa, Peter Mather, Andrew Longstaff, and Simon Fletcher. 2020. "Digital System Performance Enhancement of a Tent Map-Based ADC for Monitoring Photovoltaic Systems" Electronics 9, no. 9: 1554. https://doi.org/10.3390/electronics9091554