Detailed explanation of the circuit design of inverters connected to the public grid in terms of modeling and control

This article introduces the modeling and control of grid-connected inverters, discusses the state-of-the-art in each area, and details the most applicable techniques. The techniques mentioned in this article can be used for both single-phase and three-phase inverters, as well as for any number of stages in a three-phase inverter. Grid synchronization, anti-islanding control, current regulation algorithms, PWM generation techniques, and independent inverter control are discussed, and the control algorithms are presented in a digital control format suitable for embedded control using digital signal processors.

According to the Global Wind Energy Association, the total power generation of wind power plants in the world reached 22,199 GWh in 2006, an increase of 6.48% over 2005. This means that wind power generation can meet 9% of the total power demand. However, most alternative energy systems cannot provide stable energy. Wind speed, solar radiation, and water flow speed may vary greatly within a day. A stable grid interface is needed to filter the fluctuations of renewable energy and provide users with reliable power. Most renewable energy sources are connected to the grid, and the source of energy is mostly in the form of direct current. Solar photovoltaic cells can provide direct current voltage, and small and medium-sized wind turbines can output alternating current, which can then be converted into direct current. With the help of inverters, direct current can be converted into alternating current. The control goal of the DC end is to capture the maximum energy and transmit it to the public grid. The generated alternating current must be compatible with the power at the point where the inverter connects to the public grid in the AC public grid.

The widespread penetration of so many distributed systems into the public power grid has brought many problems. If they are connected to the public power grid in an irregular manner, the quality of the power may be affected and the safety of maintenance personnel or system users may be threatened. At present, relevant parties have formulated a number of standards to restrict the connection of grid-connected inverters to the grid.

A common feature of grid-tied inverters is that they have a specific algorithm that maximizes the amount of electrical energy extracted from renewable energy sources. In solar PV systems, this is usually referred to as maximum power point tracking (MPPT). Wind turbines similarly seek to maximize energy capture, but this is usually achieved by forcing the turbine to operate at maximum aerodynamic efficiency. In theory, this is an MPPT technique, but it involves more than just grid-tied inverters. Maximum Power Point Tracking for Solar PV Systems

A typical solar photovoltaic system consists of an array of solar photovoltaic panels. Solar photovoltaic panels can convert sunlight into DC power; the strength of DC power is proportional to the solar irradiance reaching the solar photovoltaic panel. With the help of an inverter, DC power can be converted into AC power. The amount of solar energy available depends on the irradiance, temperature and the age of the photovoltaic panel. Therefore, it is difficult to estimate the amount of solar energy available without measuring the solar irradiance and the temperature of the photovoltaic panel. Sensor components add additional costs. Even if sensors are applied, the estimated values ​​are not accurate. Sunlight is often blocked, which affects the performance of the photovoltaic panel array. In addition, the age of the photovoltaic panel will also affect its performance. The inverter needs to automatically adjust the power output to capture the maximum available power at any time. This algorithm for capturing the maximum available power from the solar photovoltaic panel is called MPPT. The voltage and current characteristics of the solar panel array require that the best operating conditions for obtaining the maximum power from the array must be provided under any solar irradiance and panel environment. The inverter needs to actively search for the maximum power point. When the inverter is in a transient state and not oscillating in steady-state conditions, an ideal MPPT algorithm should be able to quickly adjust the inverter to a state where maximum power can be obtained. Slow-acting, oscillating MPPT algorithms waste opportunities to capture available power. Oscillating algorithms can also cause array voltage collapse. Getting stable maximum power from a solar PV system depends on the accuracy and speed with which the embedded processor can read, process, and respond to the physical variables of the inverter.

Grid synchronization

The phase tracking system is an important part of the control system. It affects both the power factor control of the inverter output and the harmonic content of the inverter output current. Ideally, the phase tracking algorithm should be able to respond quickly to changes in grid phasing and shield noise and higher harmonics in the grid voltage. Many algorithms have been proposed. The earliest phase tracking algorithm is based on zero crossing detection. When the grid voltage crosses zero, the inverter output current will be synchronized with the grid. This algorithm may be affected by noise and higher harmonics in the grid voltage. In addition, there is a speed problem with zero crossing detection, which can only respond to grid phasing twice in each grid cycle. With the help of open and closed loop techniques, many filtering techniques can achieve grid phasing estimation.

Phase-locked loop (PLL) technology has become an industry standard for estimating the phase of the power grid. Through compensator design, the convergence speed, steady-state noise and anti-interference performance can be adjusted. PLL performs well in tracking the phase of the power grid, even when high-order harmonics are present in the power grid voltage. However, the performance of PLL may deteriorate when the power grid voltage is unbalanced. Using pre-filter technology or post-filter technology, imbalance in the utility grid system can be avoided.

The time-varying three-phase grid voltage facilitates control purposes. To manipulate the natural model, we use the conversion function to convert the quantity of one reference coordinate system to the quantity of another reference coordinate system. Through one conversion, the three-phase coupled voltage (abc coordinate system) can be converted to a two-phase decoupled voltage (αβ coordinate system). The second conversion converts the quantity in one reference coordinate system to the quantity of the second reference coordinate system (dq coordinate system, which differs from the first coordinate system by a phase angle). The purpose of the PLL is to estimate the phase angle of the utility grid system. Combining the above two conversion processes of converting the abc quantity of the three-phase grid into the dq quantity, it can be known that:

After the conversion is completed, the two-phase decoupled grid voltage becomes:

When φ approaches θ, vd (t) becomes 0. For control purposes, it is linearized to: vd (t) = (θ − φ)

With proper loop filter design, ŵ (PLL frequency) and ϕ (phase) can be used to track ω (grid frequency) and θ (phase angle), respectively. The proportional-integral (PI) filter used in the second-order loop is calculated as follows:

Where α = 1 − T/τ and T is the sampling period. Figure 1 shows the functional block diagram of a single-phase inverter PLL. Figure 2 shows the three-phase PLL algorithm.

Anti-islanding effect

For safety reasons, when the public grid is interrupted for some reason, the grid-connected inverter must be disconnected from the public grid. In this way, when the grid system is not directly controlled by the power company, it can prevent the power injected into the grid system from causing harm to the power supply personnel and equipment. When the grid is not operating, if the inverter injects power into the grid, an island effect will occur.

All grid-connected inverters must have over-frequency/under-frequency (OFP/UFP) and over-voltage/under-voltage (OVP/UVP) protection methods to prevent the inverter from supplying power to the grid when the grid voltage or frequency is outside the acceptable range. Figure 3 shows a typical connection of the inverter to the utility grid. The output power of the inverter is P +jQ, the local load is Pld +jQld, and the remaining power is provided by the grid ΔP +jΔQ. After the grid is disconnected, whether the system operates depends on the values ​​of ΔP and ΔQ. If ΔP≠0, the amplitude of the grid voltage will change, and OVP/UVP can detect this change and prevent the islanding effect. If ΔQ≠0, the phase of the grid will suddenly shift, and OFP/UFP will detect the change in frequency and the islanding condition. OFP and UFP can be used to detect the islanding condition when the inverter real power and reactive power do not match the load, or when there is a large gap between the resonant frequency value of the load network and the resonant frequency value of the inverter OVP/UVP. However, when the load requirement is met by the inverter alone, it is much more difficult to detect the islanding condition. The inverter certification test requirements (such as IEEE1547) are designed to examine the inverter response time when the values ​​of ΔP and ΔQ are close to zero.

Figure 3: Inverter-to-utility grid interface

The concept of non-detectable zone (NDZ) is used to determine the effectiveness of the anti-islanding algorithm under given ΔQ and ΔP values. The reaction time of islanding detection depends on the NDZ. The calculation formula for the NDZ value of ΔQ is as follows:

There are many active and passive methods to detect islanding conditions. Passive methods are either difficult to implement or have large undetectable zones. Active methods require the addition of interference signals to the grid. To prevent the grid from becoming unstable during normal operation, the addition of interference signals must be properly controlled or coordinated with other inverters. If the Sandia Frequency Shift Algorithm and the Sandia Voltage Shift Algorithm can be implemented simultaneously, it will be very effective in detecting islanding effects. The Sandia Frequency Shift Algorithm is basically a modification of the Frequency Shift Algorithm, as shown in the following formula:

cf = cf 0 + K(fa − fline)，

Among them, K is an accelerator, which can make the inverter output frequency unstable when the grid is disconnected.

The Sandia voltage shift algorithm is similar to the frequency shift algorithm. An additional term is added to the inverter output current according to the change in grid voltage, as shown in the following formula:

iout = iref + KΔV。

Both of these methods result in poor power quality at the inverter output waveform. The quality of the waveform can be traded off against the expected detection time via the value of K. The Sandia algorithm adds a small amount of positive feedback to the voltage and frequency regulation via the inverter, so the inverter will continually try to destabilize the grid. This algorithm works very well when the grid is stable, but imagine what would happen if renewable resources were further penetrated.

Current Regulation

The current regulation algorithm is used to control the amount of output power that needs to be transferred to the grid. The accuracy of the current regulation algorithm is critical to effectively process the maximum power. The quality of the current regulation algorithm is also important to meet the total harmonic distortion limits of the applicable standards.

Many control algorithms have been proposed to control the output current of inverters when they are connected to the grid. Hysteretic controllers with various closed-loop compensators operate at variable or constant switching frequencies. Here, an easy-to-implement effective current regulation algorithm is introduced that can be used with various grid synchronization methods and is also applicable to multi-level inverters.

 To control the output current of a sinusoidal inverter, the dynamic coordinate system can be converted into a reference coordinate system, in which the expected waveform is a DC quantity rather than a sinusoidal curve of a specific frequency. In other words, this is a dq reference coordinate system. In this way, the steady-state error can be eliminated by using integral control operation. After completing the dq coordinate system conversion, the electrical dynamic characteristics of the inverter are as follows:

The dynamic value on one axis depends on the current state on the other axis (this is like the cross coupling in a motor, where the direct axis flux generates the orthogonal axis back EMF, or vice versa). Here, a coupled multiple-input multiple-output (MIMO) system is described, which is determined by the product of two states (current and frequency). The coupling terms can be estimated by measuring the current and compensating the current. The grid voltage can be represented as a disturbance to the system; the system can also compensate for the grid voltage based on the voltage measurement results. After feedforward compensation and decoupling, the linear model of the first-order power plant to be controlled is as follows:

The selected controller structure is a PI controller with a transfer function.

The frequency of the compensator zero is KI/KP, which is assumed to be lower than the frequency of the plant R/L pole. Therefore, the asymptotes of the Bode plot are shown in Figure 4.

Figure 4: Open-loop Bode plot asymptotes

Figure 5 shows the block diagram of the current regulation algorithm. This algorithm can be used for both three-phase and single-phase systems when the dynamic coordinate system is transformed into a rotating reference coordinate system. The digital implementation of the PI controller is as follows:

Figure 5: Current regulation algorithm PWM implementation

After the reference voltage is calculated for a single phase, the PWM generation algorithm generates the duty cycle for each inverter switch. The sinusoidal PWM technique is easy to implement and very effective. The sinusoidal PWM generation has been modeled so that it can generate switch positions for 2-, 3-, 4-, and 5-level inverters. The current controller generates a reference voltage value (Vref) between -1 and 1. Vref varies in proportion to the number of levels in the topology; m represents the number of levels. The multi-level comparator generates a switch position output value ranging from 0 to m-1.

Using sinusoidal PWM technology, each phase of the inverter can be controlled individually. Taking a three-phase inverter as an example, using sinusoidal PWM technology, the three phases of the inverter can be controlled together, thereby making better use of the available DC bus voltage. Space vector technology provides a centralized controller for three-phase control.

Multilevel inverters can generate output voltages from three or more discrete voltage levels. For an m-level inverter, the switching function value for each phase is 0 to m-1. The phase leg voltage is:

Each switching state can produce a uniquely defined three-phase line voltage. When the switch positions of the three phases are i, j, and k, respectively, the inverter output voltage can be represented by the switching vector as:

Note: Different switch positions of the inverter can produce different switching vectors. For a balanced output voltage, the sum of the line-to-line voltages must be 0. That is, the switching vector can be represented in a two-dimensional manner. The reference voltage can be achieved using the closest three vectors with appropriate duration (duty cycle). That is, the reference voltage can be generated by the time-weighted combination of the closest three vectors. The main purpose of the modulator is to select the switch position of the inverter and how long each switch position needs to last in order to generate the reference voltage. Non-orthogonal vectors can be conveniently used as a new way to represent the switching vector. A single basic conversion is as follows:

Therefore, . After normalization to Vdc, all switch position phasors are integers. Figure 6 shows the switch position vectors of the three-level inverter in gh coordinates. In one switching cycle, if the three closest vectors are continuously used, the voltage Vref can be realized in the form of the inverter output voltage.

Figure 6: Switch position vectors of a three-level inverter in coordinates

Independent control

In the absence of a utility grid, a renewable energy system can provide energy for local loads (assuming that the inverter can obtain sufficient power). The control structure on both the DC and AC sides can be adjusted according to the needs of the local loads. Without a backup battery in the system, the system will not be able to operate at maximum power, as this may result in continuous unbalanced power generation. When working independently, the power conversion depends mainly on the required local load and the internal losses of the inverter. If there is enough energy, the local load can be fully powered by the inverter. If the load demand is higher than the available power, it is necessary to disconnect the low priority loads to ensure that power is provided to the high priority loads.

The voltage and frequency at the AC side are controlled by the inverter. The same voltage regulation algorithm can also be used for uninterruptible power supplies. Different techniques can be used depending on the steady-state and transient requirements for voltage control. An attractive method used in UPS systems is RMS voltage control. A PI compensator can control the RMS voltage. The output of the compensator can adjust the modulation index of the 60Hz sinusoidal PWM. This type of control can provide a stable output in the steady state, but the transient performance may not meet the needs of strong load transients, such as starting a compressor driven load. Figure 7 shows the RMS voltage control block diagram of a standalone inverter.

Figure 7: RMS voltage control in a stand-alone inverter During transients, transient voltage control provides a higher level of control. Designing the compensator is particularly difficult when performing noise simulation measurements. Figure 8 shows the transient voltage control block diagram for a stand-alone inverter.

Figure 8: Instantaneous voltage control in a standalone inverter

The multi-loop voltage control algorithm provides better results in both steady-state and transient operations. The RMS voltage controller requires a 60 Hz reference current. The internal current regulator can regulate the current by measuring the instantaneous current.

Signal processing requirements

Almost all algorithms discussed in the previous sections are either developed in digital format or implemented digitally for best results. First, an analog-to-digital converter converts the measured analog signals (such as voltage, current, and temperature) into digital signals; then, the processor processes the digital data using the control algorithm; and finally, commands are issued to the physical devices to perform the control operations (usually in digital form). The analog signals that need to be digitized require high-precision analog-to-digital converters; the accuracy should be at least 10 usable bits. In addition, the conversion speed of the analog-to-digital converter must be fast enough, otherwise the length of each interrupt cycle will be unacceptable to the system.

All control actions of the inverter require a lot of processing. For example, the current regulator with grid synchronization requires 930 operations in the interrupt service routine. In addition to this, the MPPT algorithm may require 410 operations, anti-islanding control may require 545 operations, and so on. Obviously, for 20kHz PWM operation, the inverter needs a processor with a cycle rate higher than 200MHz.

In addition, the DSP must integrate key peripherals such as serial/parallel interfaces, PWM units, and a true 12-bit resolution, 12-bit analog-to-digital converter tightly integrated into the processor. The processor should also integrate flash memory for executing code to reduce the need for external memory, thereby reducing the cost of the entire system. The accuracy and speed of processing affect the energy obtained from renewable energy, the quality of power deployed to the utility grid, personal safety when islanding occurs, and the ability to communicate with external devices. In addition to control operations, the inverter needs to communicate with the outside world to obtain status and data reports, ensure that parallel units work effectively together, and achieve information sharing in the smart grid. Figure 9 shows the overall block diagram of a single-phase solar photovoltaic power generation system. High-performance processors can provide all of the above functions in a single chip, such as the new 400 MHz Blackfin BF50x series processors from Analog Devices, which can be used for digital signal processing and control processing, with on-chip flash memory, integrated 12-bit digital-to-analog converters, and a stable combination of peripherals. Processors with these functions are optimized to support a variety of complex control algorithms to ensure maximum power is obtained and efficient, reliable, and safe power processing is achieved.

Figure 9: Block diagram of a single-phase solar photovoltaic power generation system

Summarize

This paper briefly introduces the challenges of modeling and controlling inverters connected to the utility grid. Section 2 introduces MPPT techniques for solar PV. Section 3 discusses grid synchronization methods, details the well-established phase-locked loop (PLL) algorithms, and discusses islanding phenomena and the weaknesses of inverters in this regard. Section 4 introduces common anti-islanding techniques, with a focus on the Sandia voltage shift and frequency shift algorithms. Section 5 discusses current regulation algorithms and linear feedforward digital PI current regulators. Section 6 introduces PWM generation algorithms for multi-level inverters. This general algorithm can be implemented with any number of inverter stages, and sine wave PWM and space vector techniques are also discussed. Section 7 introduces stand-alone inverters that are not connected to the utility grid. Section 8 explains the challenges of implementing embedded control of inverter algorithms. Section 9 summarizes the paper and provides conclusions.