Cross Reference to Related United States Applications

This application claims priority from "Maximum Power-Point Tracking Method With Dynamic Variable Step Size For Solar Photovoltaics", U.S. Provisional Application No. 61/696,853 of Xue, et ah, filed September 5, 2012, the contents of which are herein incorporated by reference in their entirety.

Technical Field

This application is directed to methods for searching for an optimum operating point for a solar photovoltaic (PV) array panel.

Discussion of the Related Art

Photovoltaic solar cells convert light energy directly into direct current electricity by the photoelectric effect, and have a complex relationship between solar irradiation, temperature and total resistance that produces a non-linear output efficiency which can be analyzed based on the I-V curve. A power inverter, or inverter, is an electrical power converter that can change the direct current (DC) to alternating current (AC). Maximum power-point tracking (MPPT) is a technique that can sample the output of the cells and apply the proper resistance (load) to obtain maximum power for any given environmental conditions. For any given set of operational conditions, cells have a single operating point where the values of the current / and voltage V of the cell result in a maximum power output. These values correspond to a particular load resistance, which by Ohm's Law is equal to VII. The power P is given by P=V*I. A photovoltaic cell, for the majority of its useful curve, acts as a constant current source. However, at a photovoltaic cell's maximum power point (MPP) region, its curve has an approximately inverse exponential relationship between current and voltage. The power delivered from or to a device is optimized where the derivative dl/dV of the I-V curve is equal to and opposite the I/V ratio where dP/dV=0. This is known as the maximum power point (MPP) and corresponds to the "knee" of the curve. A load with resistance R=V/I equal to the reciprocal of this value draws the maximum power from the device. If the resistance is lower or higher than this value, the power drawn will be less than the maximum available, and thus the cell will not be used as efficiently as it could be. The function of MPPT is to continually search for an optimum operating point at which a maximum possible power and energy available from the PV field inputs can be captured. The optimum operating point can be found by changing the direct current (DC) voltage set point in a direction towards the MPP over the entire MPP voltage range. The MPPT technique needs fast dynamics or tracking response time and a zero steady state error. Maximum power point trackers utilize different types of control circuit or logic to search for this point and thus to allow the converter circuit to extract the maximum power available from a cell.

A typical power characteristic curve for a PV array curve at a fixed irradiance and temperature is shown in FIG. 1. MPPT techniques can automatically find the voltage V _MPP or current I _MPP at the optimum operating point to obtain the maximum power P _MPP under different temperature and irradiance conditions.

Although many techniques have been proposed for MPPT, the widely used methods are Perturb & Observe and Incremental Conductance methods due to their easy implementation. Most PV inverters in the market use different variations of the P&O method. Some existing PV inverters use a fixed step size, perturb and observe (P&O) method. Other low power PV inverters have a front-end DC-DC converter, which performs MPPT by varying the duty cycle of power semiconductor switch and simultaneously creating a constant DC-link voltage. Other methods include incremental conductance (INC), fractional open-circuit voltage, fractional short-circuit current, fuzzy logic control (FLC), artificial neural networks (ANN), ripple correlation control (RCC), etc. However, these other methods are either too complicated to be used in practice, e.g. neural network, or incur more power loss, such as fractional open-circuit voltage and short-circuit current methods which require periodically measuring the open-circuit voltage short-circuit current for reference, resulting in more power loss.

Hill climbing/Perturb and Observe (P&O) methods are the most widely used in MPPT controllers. The differences are that hill-climbing methods introduce a perturbation in the duty ratio of the power converter, while P&O methods use a perturbation in the operating voltage of the PV array. Nevertheless, steady-state oscillations always exit in hill climbing/P&O methods as a result of the perturbation, which reduces the MPPT power efficiency. In general, these two methods demonstrate a trade-off between response time and accuracy. A large perturbation step can increase the tracking speed but will incur large steady state error, and vice versa.

Summary

Exemplary embodiments of the disclosure as described herein generally include systems and methods for a variable step-size incremental-conductance (INC) maximum power-point tracking (MPPT) for solar photovoltaic (PV) inverter systems with a wide MPP range. Systems and methods according to embodiments of the disclosure can realize a variable tracking step-size, a fast response time, and an accurate MPP tracking with automatic adaptation to different power and environment conditions, such as solar irradiance and temperature.

According to an aspect of the invention, there is provided a method for performing maximum power point tracking (MPPT) in a photovoltaic inverter system, including sampling a present value of a current / and a present value of a voltage V from a solar photovoltaic (PV) panel, determining a first step, a second step, and a third step from the present current value and the present voltage value, and setting a present reference voltage to a previous reference voltage, if the present voltage value equals a previous voltage value and the present current value equals a previous current value, or if the present voltage value does not equal the previous voltage value and a current- voltage derivative equals a current-voltage ratio.

According to a further aspect of the invention, the method includes setting the present reference voltage to a sum of the previous reference voltage and the third step, if the present voltage value equals the previous voltage value and a change in current is greater than zero, and setting the present reference voltage to a difference of the previous reference voltage and the third step, if the present voltage value equals the previous voltage value and a change in current is less than or equal to zero.

According to a further aspect of the invention, the method includes setting the present reference voltage to a sum of the previous reference voltage and the first step, if the present voltage value does not equal the previous voltage value and a sum of the current-voltage derivative and the current-voltage ratio is greater than zero, and setting the present reference voltage to a difference of the previous reference voltage and the second step, if the present voltage value does not equal the previous voltage value and a sum of the current-voltage derivative and the current- voltage ratio is less than or equal to zero.

According to a further aspect of the invention, the first step is defined as

* P ' ¥ I, the second step is defined as ^" \dv\, and the third step is defined as a V _ste p2, where P _mpp is a rated power of the photovoltaic inverter system, P is a power defined as the product of the present current value and the present voltage value, dP/dV is the power- voltage derivative, and N and a are predetermined design parameters.

According to a further aspect of the invention, ^ί d¥ , where Δ V _max is a maximum allowable step voltage, dV is defined as a difference of the present voltage value and the previous voltage value, and dP is defined as a difference of a product of the present voltage value and the present current value and a product of the previous voltage value and a previous current value.

According to a further aspect of the invention, the method includes updating the previous voltage value to be equal to the present voltage value, updating a previous current value to be equal to the present current value, and repeating the steps of sampling a present value of a current / and a present value of a voltage V from a solar photovoltaic (PV) panel, determining a first step, a second step, and a third step from the present current value and the present voltage value, and setting a present reference voltage.

According to another aspect of the invention, there is provided a non-transitory program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to perform the method steps for performing maximum power point tracking (MPPT) in a photovoltaic inverter system.

According to another aspect of the invention, there is provided a system for performing maximum power point tracking (MPPT) in a photovoltaic inverter system, including a computer processor; and a non-transitory program storage device, where the computer processor is configured to execute a program of instructions tangibly embodied in the non-transitory program storage device for performing maximum power point tracking (MPPT).

Brief Description of the Drawings

FIG. 1. depicts a typical PV array characteristic power curve at a fixed irradiance and temperature, according to an embodiment of the disclosure.

FIG. 2 depicts the slopes of various power versus voltage curves under different irradiation conditions, according to an embodiment of the disclosure.

FIG. 3. Is a flowchart of an MPPT algorithm according to an embodiment of the disclosure.

FIG. 4 illustrates an MPPT function in a PV inverter control system according to an embodiment of the disclosure

FIGS. 5(a)-(b) compare MPPT simulation results when PV maximum power is 500 kW, according to an embodiment of the disclosure.

FIGS. 6(a)-(b) compare MPPT simulation results when PV maximum power is 150 kW, according to an embodiment of the disclosure.

FIG. 7 is a block diagram of a system for searching for an optimum operating point for a solar photovoltaic (PV) cell, according to an embodiment of the disclosure.

Detailed Description of Exemplary Embodiments

Exemplary embodiments of the disclosure as described herein generally provide systems and methods for searching for an optimum operating point for a solar photovoltaic (PV) cell. While embodiments are susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the disclosure. Incremental-conductance (INC) methods may improve MPPT performance while being easily implemented in digital controls. INC methods are based on the fact that the slope of the PV array power curve versus voltage is zero at the MPP, as shown in EQ (1):

Since,

EQ (1) can be written as:

A trade-off between the dynamics and steady state accuracy still has to be addressed when a fixed step-size INC MPPT is designed. To address this situation, a variable step-size MPPT can be used as shown in EQ. (4), where N is a scaling factor which may be tuned at design time to adjust the step size:

The step-size N can be automatically adjusted to be proportional to the derivative of the power to voltage (dP/dV) of a PV array. A variable step-size INC MPPT has good accuracy at a steady state since dP/dV becomes very small around the MPP, while the step size increases when the operating point moves away from the MPP. FIG. 2 depicts the slopes of various power versus voltage curves under different irradiation conditions. However, as shown in FIG. 2, there may exist situations where a maximum power Pi is much larger than a maximum power P ₂ for different irradiances. In FIG. 2, AD _max is a largest step size for a fixed size MPPT operation, and N is a scaling factor. A scaling factor N tuned to realize a variable step-size MPPT for Pi will make the system converge much more slowly for P ₂ because \dP/dV\ is smaller for lower PV power, even when the operating point is far away from the MPP. On the other hand, if a large scaling factor N is chosen for a variable step size MPPT when the PV power is small, the maximum step change needed to ensure MPPT convergence when the MPPT operates at constant and fixed step size will reduce the system's tracking accuracy at a steady state. Thus, there is a "dead band" for the fixed scaling fact N from EQ. (4), and it is challenging for a variable step-size INC MPPT to find an optimal scaling factor that is suitable for both power curves P\ and P ₂ in the dead band simultaneously.

An improved variable step-size algorithm proposed for INC MPPT method switches the step-size modes by extreme values/points of a threshold function under different irradiation conditions. If the operating point is far from the MPP, the maximum step-size is maintained, which enables a fast tracking ability; if the operating point is close to the MPP, the step size may become very small according to a sinusoidal function (sin6 _k ) _? where the angle ¾ _: is correlated with dP/dl or dP/dV. However, second-order differentials are needed to find the threshold function for switching the step-size modes, which can introduce noise that can result in a wrong estimation. In addition, second-order or high-order differential computations are undesirable in actual implementation.

A method according to an embodiment of the disclosure can realize a variable step- size MPPT with essentially zero steady state error in all power conditions. In addition, a method according to an embodiment of the disclosure may be easy to implement, requires less computation effort, improves the tracking speed when the MPP is low, and may achieve fast dynamics over a wide range of MPP' s.

A conventional variable step-size INC MPPT can realize variable step-size in different power situations, however the settling time will be different for different MPP trackings. Because the variable step-size may be proportional to dP/dV ^' all situations, or in the neighborhood of MPPT, as shown in FIG. 2, the slope dP/dV of the PV power curve is greater when the PV power is high than when the PV power is low. Therefore, when the PV power is high, the tracking speed will be relatively fast; when the PV power is low, the tracking speed will be relatively slow. To achieve high speed tracking in all power conditions, the power should be considered when calculating the tracking step size.

According to an embodiment of the disclosure, the variable step size is not only determined by the slope of PV power versus voltage (dP/dV), but also the PV power, as shown in EQS. (5)-(6):

where n = 1 or 2, N is a design parameter, P _mpp is the inverter rated power, and Δ V _max is the maximum allowable step voltage. The absolute power is not considered to the right of MPP, that is, when dPIdV < 0, since the right-side slopes change little when the MPP changes from one point to another point.

A flowchart of an MPPT algorithm according to an embodiment of the disclosure is shown in FIG. 3. Referring now to the figure, a method according to an embodiment of the disclosure begins at step 310 by sampling values of the voltage V(k) and current I(k), where k is a counter. At step 312, values of dV, dl, dP and P are defined in terms of the current and previous samples, and the step sizes are defined, according to the following expressions: dV = V(k) - V(k-1);

dl = I(k) = I(k-l)

dP = V(k)I(k) - V(k-l)I(k-l);

= V(k)I(k);

Vstep3— CI X V _s tep2-

An exemplary, non-limiting value for the constant a is 0.10. If, at step 314, dV = 0, and, at step 316, if dl = 0, then V _re k) is set to V _re k-l) at step 318. Otherwise, if dl≠0 at step 316, then if dl > 0 at step 320, V _re k) is set to V _re k-l) + V _step 3 at step 322, and if dl < 0, V _re j(k) is set to Vre k-l) - V _s tep3 at step 324. On the other hand, if dV≠ 0 at step 314, and if dl/dV + l/V= 0 at step 326, then V _reJ (k) is set to V _reJ (k-l) at step 328. Otherwise, iidl/dV + l/V≠ 0 at step 326, then iidl/dV + l/V > 0 at step 330, V _reJ (k) is set to V _reJ (k-l) + V _step i at step 334, and if dl/dV + l/V < 0, Vrefk) is set to V _re (k-l) - V _siep2 at step 332. Then at step 336, V(k-l) and l(k-l) are respectively updated to be V(k) and l(k), and the method returns to step 310 to obtain new samples of V(k+1) and l(k+l), and to repeat steps 312 to 336.

At certain solar irradiance and temperature conditions, an MPPT algorithm according to an embodiment of the disclosure can find the optimum PV operating voltage where the MPP can be achieved. Then the PV inverter will typically use two control loops, a DC voltage control in an outer loop and an AC current control in an inner loop, to maintain system operation at the optimum point. FIG. 4 is a block diagram of a system control of a PV inverter, according to an embodiment of the disclosure. Referring now to the figure, item 41 represents a variable step MPPT algorithm according to an embodiment of the disclosure, which takes as input voltage v _pv and current i _pv samples from the solar photovoltaic array pane, and outputs the DC reference voltage Vdc * which is the V _re f calculated above in FIG. 3. Items 42, 44, and 45 are subtract operators. The difference of the DC reference voltage Vdc * and a DC feedback voltage Vdc from subtractor 42 is regulated by the voltage controller 43, and its output is considered is the active reference current Id*. The difference of the active reference current Id* and an active feedback current Id from subtractor 44 as well as the difference of reactive reference current I _q * and reactive feedback current I _q from subtractor 45 are transferred to active power and reactive power decoupling current control block 46 in direct- quadrature coordinate, followed by the pulse-width modulation (PWM) unit 47, which generates the pulse signals to drive the semiconductor switches of a power inverter with an additional drive circuit, not shown in the figure. An MPPT method according to an embodiment of the disclosure has been simulated using MatLab/Simulink and compared with a method proposed by Liu, et al., "A Variable Step Size INC MPPT Method for PV Systems," IEEE Trans. Ind. Electron., Vol. 55, No. 7, pp. 2622-2628, Jul. 2008, the contents of which are herein incorporated by reference in their entirety. In the simulations, the maximum allowed voltage tracking step size is chosen to be 50 V, and the design parameter N is chosen to be 0.005 based on EQ. (7), which satisfies EQ. (6). FIGS. 5(a)-(b) and 6(a)-(b) compares MPPT simulation results when PV maximum power is 500 kW and 150 kW, respectively, for a method according to an embodiment of the disclosure and the method of Liu, et al. FIGS. 5(a) and 6(a) depict voltage and power results as functions of time for an algorithm according to an embodiment of the disclosure for different solar power values, while FIGS. 5(b) and 6(b) show the simulation results using the method of Liu, et al. It can be observed that when the PV power is high, e.g. 500 kW, as shown in FIGS. 5(a)-(b), the tracking speeds of both methods are roughly the same. But when the PV power is small, e.g. 150 kW, the tracking speed of t a method according to an embodiment of the disclosure is faster than that of the method in Liu, et al. A method according to an embodiment of the disclosure can reach maximum power within 0.35 seconds, while the method of Liu, et al. has not settled down.

(?)

It is to be understood that the embodiments of the present disclosure can be implemented in various forms of hardware, software, firmware, special purpose processes, or a combination thereof. In one embodiment, the present disclosure can be implemented in software as an application program tangible embodied on a computer readable program storage device. The application program can be uploaded to, and executed by, a machine comprising any suitable architecture.

FIG. 7 is a block diagram of an exemplary computer system for implementing a method for searching for an optimum operating point for a solar photovoltaic (PV) cell according to an embodiment of the disclosure. Referring now to FIG. 7, a computer system 71 for implementing the present disclosure can comprise, inter alia, a central processing unit (CPU) 72, a memory 73 and an input/output (I/O) interface 74. The computer system 71 is generally coupled through the I/O interface 74 to a display 75 and various input devices 76 such as a mouse and a keyboard. The support circuits can include circuits such as cache, power supplies, clock circuits, and a communication bus. The memory 73 can include random access memory (RAM), read only memory (ROM), disk drive, tape drive, etc., or a combinations thereof. The present disclosure can be implemented as a routine 77 that is stored in memory 73 and executed by the CPU 72 to process the signal from the signal source 78. As such, the computer system 71 is a general purpose computer system that becomes a specific purpose computer system when executing the routine 77 of the present disclosure.

The computer system 71 also includes an operating system and micro instruction code. The various processes and functions described herein can either be part of the micro instruction code or part of the application program (or combination thereof) which is executed via the operating system. In addition, various other peripheral devices can be connected to the computer platform such as an additional data storage device and a printing device.

It is to be further understood that, because some of the constituent system components and method steps depicted in the accompanying figures can be implemented in software, the actual connections between the systems components (or the process steps) may differ depending upon the manner in which the present disclosure is programmed. Given the teachings of the present disclosure provided herein, one of ordinary skill in the related art will be able to contemplate these and similar implementations or configurations of the present disclosure.

While the present disclosure has been described in detail with reference to exemplary embodiments, those skilled in the art will appreciate that various modifications and substitutions can be made thereto without departing from the spirit and scope of the disclosure as set forth in the appended claims.