A common feature of utility interactive inverters is an algorithm that seeks to .... The PLL frequency ÌÏ and phase Ï can track the utility frequency Ï and phase ...
Control of Utility Interactive Inverters Yilmaz Sozer
David A. Torrey
Advanced Energy Conversion, LLC 405 Front Street Schenectady, NY 12305, USA
1
Introduction
As the cost of conventional energy sources continues to increase, alternative energy sources continue to gain in popularity beyond those that see them as a way to reduce environmental pollution. The new technological developments in renewable energy systems make them commercially viable alternatives. Small hydro turbines, wind turbines and solar photovoltaics (PV) are the most common alternative energy sources currently. Solar electric energy usage has grown consistently at a rate of 20-25% annually over the last 20 years, and has accelerated to nearly 50% per annum in the last five years. In 2001, just under 350 MW of solar systems were installed. In 2005, 1.460 GW of PV systems were put into use. This number increased to 1.744 GW in 2006. On-grid installations (also known as utility-interactive) are being installed at almost twice the rate of off-grid installations for two reasons. First, most homes and businesses are connected to the utility grid. Second, most government incentive programs apply only to utility-interactive systems. The majority of the on-grid applications are “distributed,” namely installed at the point of use. According to the Global Wind Energy Council wind power plants generated 22,199 GWh in 2006, which is 6.48% higher than in 2005. This production represents a 9% coverage of demand. However, most alternative energy systems do not have constant energy sources. Wind speed, sun irradiance, and water flow rate might change quite a lot during the day. A stable grid interface is desired to filter the fluctuation in the renewable energy sources to provide reliable power to the user. As such, most of the renewable energy sources interface to the grid. The source side of the energy is mostly in DC form. Solar PV cells provide DC voltage, small and mid size wind generators output AC which is then rectified to DC voltage. The DC electric energy is usually converted into AC electric energy by use of an inverter. The control objective on the DC side is to capture maximum energy and deliver it to the utility grid. The resulting AC electric energy has to be compatible with the energy within the AC utility system at the point where the inverter is connected to the utility system. High penetration of so many distributed systems to the utility grid brings many issues with it. An unregulated interface to the utility grid affects the quality of the energy provided and safety of maintenance personnel or the system user. Standards have been developed to impose restrictions on connecting utility interactive inverters to the grid. A common feature of utility interactive inverters is an algorithm that seeks to maximize the energy extracted from the renewable resource. In solar PV, this is generally referred to as maximum power point tracking (MPPT). Wind turbines also seek to maximize energy capture, but this is typically accomplished by forcing the turbine to operate at maximum aerodynamic efficiency. Conceptually, this is a form of MPPT, but it involves more than the utility interactive inverter. This paper provides an overview of the challenges in modeling and control of the inverter interfaced to the utility grid. MPPT for solar pv implementation are explained in Section 2. Grid synchronization methods are
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discussed and details of the widely accepted phase-locked loop (PLL) algorithm is presented in Section 3. The islanding phenomenon and the vulnerability of the inverters to the phenomenon are discussed. Commonly used anti-islanding techniques with an emphasis on the Sandia voltage and frequency shift algorithm are given in Section 4. Current regulation algorithms are discussed and a linearized feedforward digital PI current regulator is developed in Section 5. PWM generation algorithms are presented for multilevel inverters, made generic to be implemented by an inverter with any number of levels in Section 6; both sine PWM and space vector techniques are discussed. Section 7 provides information about stand alone inverters that are not interfaced to the utility grid. Challenges for embedded control implementation of the inverter algorithms given is Section 8. Summary and conclusions are provided in Section 9.
2
Maximum Power Point Tracking for Solar PV Systems
A typical solar PV system is comprised of an array of solar photovoltaic panels that convert sunlight into DC electric energy that is proportional to the solar irradiance striking the panels. The DC electric energy is usually converted into AC electric energy by use of an inverter. The amount of solar energy available is subject to change with irradiance, temperature, and aging of the panels, so it is difficult to estimate it without the measurement of sun radiance and panel temperature. The sensing elements add extra costs. Even with the sensing elements estimation is not accurate. Shading happens quite frequently and affects the performance of the array. Also, the performance of the array degrades as the panels age. The inverter needs to automatically adjust the power output to draw maximum available power at any time. The algorithm to draw to maximum power available from the solar panel is called a maximum power point tracking algorithm (MPPT). Voltage and current characteristic of the solar arrays suggest that for any sun radiance and panel environment there is an optimum operating condition that processes maximum power from the array. The inverter need to actively search for the maximum power point. The desired MPPT algorithm quickly adjusts the inverter to a maximum power condition during transients and without oscillating at steady state conditions. Both slow acting and oscillating MPPT algorithms waste an opportunity to capture available power. Oscillating algorithms might also cause the array voltage to collapse. The stable and maximum power extraction from solar PV systems relies on accuracy and speed of the embedded processor capability to read, process, and respond to physical variables of the inverter.
3
Grid Synchronization
The phase tracking system is one important part of the control system. It affects power factor control of the inverter output as well as the harmonic content of the inverter output current. Ideally the phase tracking algorithm should respond quickly to changes in the utility phasing but it should reject the noise and higher harmonics in the utility voltage. Many algorithms have been proposed[1, 2, 3, 4]. The easiest phase tracking algorithm is based on zero crossing detection. The inverter output current is synchronized to the utility during zero crossings of the utility voltage. This algorithm suffers from noise and higher order harmonics in the utility voltage. Also, zero crossing detection suffers from speed as it adapts to utility phasing only twice in each utility cycle. Many filtering techniques have been used to estimate the phasing of the utility using open loop and closed loop techniques. Phase-locked loop (PLL) techniques have become something of an industry standard to estimate the phase of the utility [5]. Convergence speed and steady state noise and disturbance rejection performance can be adjusted through compensator design. The PLL performs quite well in tracking of the utility phase even in the presence of higher order harmonics in the utility voltage. On the other hand, PLL performance might deteriorate in the presence of unbalance in the utility voltage. Using pre- or post-filtering techniques, the effect of unbalance in the utility system can be rejected [6, 7, 8]. A time-varying three phase utility voltage is convenient for control purposes. To manipulate the natural
2
model we use transformations to move quantities from one reference frame to another. One transformation takes three coupled phase voltages (the abc frame) into two decoupled phase voltages (the αβ frame). A second transformation allows us to move quantities in one reference frame to a second reference frame that is displaced from the first by a phase angle (the dq frame). The purpose of the PLL is to estimate phase angle of the utility system. Combining the two transformations that converts three phase utility abc quantities into dq quantities gives ⎤ ⎡ cos θ 1 1 −√2 1 − 2 cos ϕ sin ϕ Vd √2 ⎣ cos θ − 2π ⎦ . (1) = 3 3 3 Vq 3 − sin ϕ cos ϕ 0 − 2 2 cos θ + 2π 3
After the transformations, the two phase decoupled utility voltages become vd (t) = cos (θ − ϕ) vq (t) = sin (θ − ϕ)
(2) .
(3)
As ϕ approaches θ, vd (t) goes to zero. We can linearize it for control purposes as vd (t) = (θ − ϕ)
.
(4)
The PLL frequency ω
and phase ϕ can track the utility frequency ω and phase angle θ respectively by the proper design of the loop filter. A proportional-integral (PI) type filter for the second order loop can be given as 1 + sτ . (5) Kf (s) = Kp sτ The transfer functions of the closed loop system are rewritten in the general form of second order system as H(s) = where ωn =
s2 s2 + 2ζωn + ωn2
,
(6)
Kp Vm /τ , and ζ = τ Kp Vm /2. A second order digital loop PI filter can be obtained as Kd (z) = Kp
z(z − α) (z − 1)2
,
(7)
where α = 1 − T /τ , and T is the sampling period. Figure 1 shows the block diagram of the PLL for a single phase inverter. The three phase PLL algorithm is shown in Figure 2.
4
Anti-islanding
For safety reasons, it is a requirement that utility interactive inverters disconnect themselves from the utility if the utility is interrupted for any reason. This will protect utility workers and equipment from energy being injected into the utility system that is not under the direct control of the utility. An inverter that feeds energy into the utility when the utility is not operating creates an islanding condition. All utility interactive inverters are required to have over/under frequency (OFP/UFP) and over/under voltage protection (OVP/UVP) methods that prevent the inverter from supplying power to the utility if the utility voltage or frequency is outside of an acceptable range. Figure 3 shows the typical connection of the inverter to the utility grid. The inverter outputs power P + jQ while local loads take Pld + jQld with the rest of power being supplied by the utility ΔP + jΔQ. The operation of the system after the utility disconnects depends on the amount of ΔP and ΔQ. If ΔP = 0 the amplitude of the utility voltage will change and OVP/UVP can detect the change and prevent islanding. If ΔQ = 0 the phase of the utility will 3
0+
Kf(s) Loop Filter
Ȉ
Tg
1/s
- V q
Vd
VDE toVdq VE
VD
Delay
Grid Voltage
Figure 1: The single phase PLL algorithm.
0+
Kf(s) Loop Filter
Ȉ
Tg
1/s
- V q
Vd
VDE toVdq VE
VD
Vabc to VDE Va
Vc
Vb
Grid Voltage
Figure 2: The three phase PLL algorithm.
suddenly shift and OFP/UFP will detect the change in frequency and detect the islanding condition. If the real and reactive power of the inverter is not matched closely to the loads or the resonant frequency of the load network is not close to the resonant frequency of the inverter OVP/UVP, then the OFP and UFP would be adequate to detect the islanding condition. However, when the load requirements are being satisfied by the inverter only, detection of an islanding condition becomes much more challenging. Certification test requirements for an inverter (such as IEEE1547) examine the response time of the inverter for the case where ΔP and ΔQ are near zero. The non-detection zone (NDZ) concept is developed to determine the effectiveness of the anti-islanding algorithm for a given ΔQ and ΔP [9, 10, 11]. The reaction time of the islanding detection is dependent on the NDZ. Calculation of the NDZ for ΔQ is given as ΔQN DZ =
V2 1 1 Xc − XL
,
(8)
√ where ω = 1/ LC. There are many active and passive methods that have been developed to detect an 4
Inverter
P+jQ
ǻP+jǻQ
S1
S2
DC
Grid AC
AC
Pld+jQld
R
L
C
Figure 3: An inverter interface to the utility grid.
islanding condition [12, 13, 14, 15]. Passive methods are either difficult to implement or have larger NDZs. Active methods require injecting disturbances into the utility. Those injections need to be controlled properly or harmonized with other inverters to avoid destabilization of the utility under normal operation. The Sandia frequency and voltage shift algorithms are very effective in detecting islanding if implemented at the same time [12]. The Sandia frequency shift is basically modification of frequency shift algorithm given as (9) cf = cf 0 + K(fa − fline ) , where K is an accelerator to destabilize the inverter output frequency when the utility is disconnected. The Sandia voltage shift algorithm is similar to the frequency shift algorithm. An additional term is added to the inverter output current based on the change in utility voltage as iout = iref + KΔV
.
(10)
Both of these methods cause the power quality of the inverter output waveform to deteriorate. The quality of the waveform and desired detection times are trade offs that can be adjusted through the value of K. The Sandia algorithm adds a small amount of positive feedback to both voltage and frequency regulation by the inverter, so the inverter is continuously trying to destabilize the utility. This works well if the utility is stiff; however, one can imagine what could happen with deep penetration of renewable resources.
5
Current Regulation
The amount of desired output power delivered to the utility is controlled through the current regulation algorithm. The accuracy of the current regulation algorithm is important for effective maximum power processing. The quality of the current regulation algorithm is also important to meet the total harmonic distortion restrictions imposed by the applicable standards. Many control algorithms have been proposed to control inverter output current for utility interactive operations. Hysteretic type controllers with different closed loop compensators have been used running at varying or constant switching frequencies [16, 17, 18, 19]. We present here an easily implementable and effective current regulation algorithm that works harmoniously with grid synchronization methods. It is also applicable to multilevel inverters.
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log |D(s)G(s)|
KI sR
KP R
KP sL
log Ȧ
Figure 4: The open-loop Bode plot asymptotes.
To control the sinusoidal inverter output current, it is advantageous to transform the dynamics into a reference frame where the desired waveform is a DC quantity rather than sinusoids of a given frequency. That is, we work in the dq reference frame. This allows the use of integral control action to remove steadystate error. The electrical dynamics of the inverter after transformation to the dq frame are given as vd (t) = Rid (t) + L vq (t) = Riq (t) + L
did − ωLiq (t) + ed (t) dt
diq + ωLid(t) + eq (t) dt
(11) .
(12)
The dynamics in one axis are dependent on the current state of the other axis. (This is analogous to the cross-coupling experienced in electric machines where direct axis flux produces quadrature axis back emf, and vice versa.) This introduces a coupled multi-input multi-output (MIMO) system that is dependent on the product of two states, current and frequency. The coupling term can be estimated by the measured currents and compensated. The utility voltage can be modeled as a disturbance to the system or can be compensated based on measurements. After feedforward compensation and decoupling, the linear model of the first order plant that we are trying to control is: G(s) =
1 1 = LR sL + R sR + 1
.
(13)
The structure of the controller was chosen to be a PI controller, which has the transfer function Kp
s +1 Kp s + KI = K I KI D(s) = s s
.
(14)
The frequency of the compensator zero is KI /KP , and is assumed to be lower in frequency than the pole of the plant at R/L. Therefore, the asymptotes of the Bode plot can be drawn as shown in Figure 4. Figure 5 shows the block diagram of the current regulation algorithm. The same algorithm can be used for both three-phase and single-phase systems once the dynamics are transferred into the rotating reference frame. Digital implementation of the PI controller can be realized with D(z) = KP
KI z − (1 − T K ) P
z−1
6
.
(15)
ed(k) id_ref(k) +
Ȉ
D(z)
+
+
Ȉ
-
Vd_ref(k)
-
id_act(k) iq_act(k)
L*Ȧe
eq(k) iq_ref(k) +
Ȉ
D(z)
+
+
Ȉ
-
Vq_ref(k)
+
iq_act(k) id_act(k)
L*Ȧe
Figure 5: The current regulation algorithm.
6
PWM Implementation
After calculating the reference voltages for the individual phases, the PWM generation algorithm produces the duty ratios for individual inverter switches [20]. The sine PWM technique is easy to implement and very effective. Sine PWM generation is modeled such that it can produce the switching positions for inverters of 2, 3, 4 and 5 levels. The current controller produces a reference voltage (Vref ) between −1 and 1. Vref is scaled based on the number of levels in the topology; m denotes the number of levels. A multilevel comparator produces the switch position output between 0 to m − 1. Sine PWM techniques provide independent control for each individual inverter phase leg. For three phase inverters it is possible to control all three inverter phase legs together to better use the available DC bus voltage. Space vector techniques provide three phase control with a centralized controller [21, 22]. Multilevel inverters generate their output voltage from three or more discrete voltage levels. For an m-level inverter the switching function for each phase takes on values between 0 to m − 1. The phase leg voltage is VAn0 =
Spos ∗ Vdc m−1
.
(16)
Each switching states produces uniquely defined three phase line voltages. If the switching positions for the three phases are i, j, and k, respectively, then the inverter output voltages can be represented by the switching vector as ⎡ ⎤ i−j V (ijk) = Vdc ⎣ j − k ⎦ . (17) k−i
7
h SECTOR B (-1,2)
(-2,2)
(0,2)
E
D
III
C
F
(0,1)
(-1,1)
(-2,1) G
B
(-2,0)
7 4
5
3 2
g
VII VI (1,-1)
(0,-1)
(-1,-1)
(2,0)
(1,0)
V
6
(0,-2)
IV
(0,0)
(-1,0) 8
SECTOR A
II I
A
H
(1,1)
(2,-1)
VIII 1 (2,-2)
(1,-2)
SECTOR C
Figure 6: Switching position vectors in coordinates for a three level inverter.
It is important to note that switching vectors can be produced by the different switching positions of the inverter. For balanced output voltages, the sum of the line-to-line voltages must be zero. That means switching vectors can be represented in two dimensions. The reference voltage can be realized by the application of the nearest three vectors with the appropriate duration times (duty cycles). That is, the reference voltage is created through a time-weighted combination of the nearest three vectors. The main objective of the modulator is to select the switching positions of the inverter and the duration of how long each switch position needs to be applied by the inverter in order to produce the reference voltage. According to [22] it is convenient to use non-orthogonal vectors as a new basis to represent the switching vectors. One base transformation would be (level − 1) 2 −1 −1 . (18) T = −1 2 −1 3 so V ref (g, h) = T V ref (a, b, c). After normalization to Vdc all the switching position vectors are integers. Switching position vectors in gh coordinates for a three level inverter are shown in Figure 6. Voltage Vref can be realized as an inverter output voltage by application of the three closest vectors consecutively during one switching cycle.
7
Standalone Control
In the absence of the utility grid, renewable energy systems could be used to provide energy to the local loads [22, 23, 24, 25] assuming an adequate supply of energy for the inverter to draw upon. The control structure on the DC and AC sides are changed to accommodate the needs of the local loads. Unless there is battery backup in the system, the system cannot work on the principle of maximum power extraction from the source since this would lead to a sustained power imbalance. In stand alone operation, power transfer is dictated primarily by the needs of the local loads and the losses within the inverter. If there is enough 8
Vdc(k)
Phase Vrms_ref(k) +
Ȉ
Switching PWM Generator Vcmd(k)
X
D(z)
Vrms_act(k)
Sine_ref
ș
Sin (ș)
Figure 7: RMS voltage control for standalone inverters.
Vdc(k)
Vph_ref(k) +
Ȉ
+
D(z)
-
+
Ȉ
Phase Switching PWM Generator Vcmd(k)
+
Vph_act(k) iph(k)
L*(iph(k)-iph(k-1))*1/Ts
Figure 8: Instantaneous voltage control for standalone inverters.
energy available at the source the local loads are fully supported by the inverter. If the demand from the loads is higher than the available energy at the source then lower priority loads are needed to be shed to make energy available for supporting the higher priority loads. The voltage and frequency of the AC side is set by the inverter. Similar voltage regulation algorithms can be used as in uninterruptable power supplies. Depending on the steady state and transient requirements on the voltage control different techniques can be used. One of the attractive methods used in UPS systems is RMS voltage control. The RMS voltage is controlled by a PI compensator. The output of the compensator adjusts modulation index of the 60Hz sine PWM. This type of control provides stable output in the steady state but transient performance may not be adequate for aggressive load transients [26], such as starting compressor-driven loads. Figure 7 shows the block diagram for the RMS voltage control of the stand alone inverters. Instantaneous voltage control provides more aggressive control during transients [27]. It is more difficult to design the compensator especially in the presence of noisy analog measurements. Figure 8 shows the block diagram for the instantaneous voltage control of the stand alone inverters. Multi-loop voltage control algorithms provide better results at both steady state and transient operations. The RMS voltage controller commands a 60 Hz reference current. An inner current regulator regulates the
9
current using an instantaneous current measurement.
8
Signal Processing Requirements
Almost all of the algorithms discussed in the previous sections are either developed in digital format or work best with the digital implementation. First, measured analog signals such as voltage, current, and temperatures are digitized through analog to digital converters, then the digital data are processed with control algorithms by the processor, and finally control actions are commanded to physical devices, usually in digital form. The analog signals to be digitized require high accuracy A/D converters; at least 10 usable bits of precision is important. In addition, the A/D converter must be fast or it will consume an unacceptable amount of each interrupt cycle. All of the control actions for the inverter require extensive processing. For example, a current regulator including grid synchronization requires 930 operations within the interrupt service routine. Beyond this, the MPPT algorithm may consume 410 operations, anti-islanding may consume 545 operations, etc. It quickly becomes clear that for 20 kHz PWM operation, the inverter needs a processor with a cycle rate in excess of 200 MHz. DSPs must also integrate key peripherals such as serial and parallel interfaces, PWM units, and a 12 bit analog to digital converter with true 12 bit resolution and tight integration to the processor. In addition, it is preferable that processors provide integrated flash memory for code execution to eliminate the need for external memory, thereby lowering overall system costs. The accuracy and speed of the processing affects the amount of power extraction from renewable energy sources, the quality of the power deployed to the utility grid, the safety of personnel in the case of the islanding conditions, and the ability to communicate performance to external devices. In addition to control actions, inverters need to communicate to the outside world for status and data reporting, harmonization for parallel units working together, and information sharing as a part of the smart grid. Figure 9 shows the overall block diagram of the single phase solar PV system. High performance processors can offer all of these capabilities in a single chip, as has been exemplified by Analog Devices’ new 400 MHz Blackfin BF50x series of processors for digital signal and control processing, which feature on-chip flash memory, integrated 12-bit A/D converters and a robust peripheral set. Processors with these capabilities are optimized to support many sophisticated control algorithms for maximum power extraction, high efficiency, reliable, and safe power processing.
9
Summary
Modeling and control of utility interactive inverters are presented in this paper. State of the art techniques on individual subjects are given and the most applicable techniques have been demonstrated in detail. The techniques presented are applicable to both single- and three-phase inverters and to any number of levels within the three-phase inverter. Grid synchronization, anti-islanding control, current regulation algorithm, PWM generation techniques and stand alone inverter controls are discussed. Control algorithms have been given in digital control format applicable to embedded control using digital signal processors.
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+ -
INVERTER
+
AC
-
INTERFACE CIRCUITRY
CONTROL & COMMUNICATION DSP ETHERNET COMMUNICATION
Figure 9: A block diagram of a single phase solar PV system.
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