Integrating Power Quality Management with Photovoltaic Solar Inverters: A DG-FACTS Approach

The proliferation of distributed generation, particularly from photovoltaic (PV) sources, presents a dual-faceted opportunity for modern power distribution networks. While injecting clean energy, the inherent power electronic interfacing of these systems—primarily through solar inverters—offers a potential solution to the very power quality issues exacerbated by modern non-linear and unbalanced loads. Traditional mitigation devices like Active Power Filters (APFs) and Static Var Generators (SVGs), though effective, represent significant additional capital expenditure. This research explores and formalizes a control strategy to repurpose the existing and often underutilized capacity of distributed solar inverter systems, enabling them to perform comprehensive power quality compensation—acting as Distributed Grid-Friendly Advanced Flexible AC Transmission Systems (DG-FACTS)—without compromising their primary function of grid-tied power generation.

The core premise is based on the operational similarity between a grid-tied solar inverter and compensators like APFs/SVGs. Both are voltage-source converters connected to the grid via filters. The fundamental difference lies in their current reference: a PV inverter’s primary reference is a fundamental-frequency current in phase with the grid voltage for real power export, while an APF/SVG’s reference is composed of harmonic, reactive, or negative-sequence components. Given that a PV system rarely operates at its peak capacity continuously due to solar irradiance variations, a significant “redundant capacity” in terms of the solar inverter‘s current-carrying capability remains available. This capacity can be strategically deployed to absorb or inject specific current components, thereby cleaning the grid current at the point of common coupling (PCC). The technical challenge involves the seamless integration of multiple detection algorithms, a robust current reference synthesis strategy, and a precise current-tracking controller, all tailored for the hardware constraints of a typical PV system.

System Architecture and Operational Philosophy

The hardware configuration for a DG-FACTS-enabled solar inverter is largely identical to a standard three-phase, three-wire grid-tied system. The PV array feeds the DC-link, often through a DC-DC converter for Maximum Power Point Tracking (MPPT). The inverter bridge is connected to the grid via an LCL filter for harmonic attenuation. The augmentation is purely in the control software. The controller must simultaneously process inputs from the PV side (for MPPT and real power current reference generation) and from the grid/load side (for power quality disturbance extraction).

The operational states of such an enhanced solar inverter can be categorized as follows:

Pure Generation Mode: The inverter functions solely as a PV inverter, injecting real power corresponding to the available solar energy.
Integrated Generation and Compensation Mode: The inverter injects real power from the PV array while using its remaining current capacity to compensate for harmonics, reactive power, and/or imbalance present in the local network.
Dedicated Compensation Mode: During periods of no solar generation (night-time), if economically or technically justified, the inverter can function solely as a power quality compensator, utilizing its full rated capacity.

The overarching control objective is to synthesize a final current reference, $i_{ref}^*$, that is the sum of the real power current component, $i_p^*$, and the compensation current component, $i_c^*$, and to force the inverter output current to track this reference accurately.

Detection Algorithms for Compensation References

Accurate, fast, and digitally efficient extraction of disturbance components is critical. The chosen algorithms must be suitable for the typical harmonic spectrum and imbalance conditions found in distribution networks and implementable on standard digital signal processors (DSPs) used in solar inverter controllers.

Selective Harmonic Current Detection

Given that a solar inverter is primarily designed for fundamental frequency operation, its LCL filter and switching frequency may not be optimized for compensating very high-order harmonics. Therefore, a selective compensation strategy targeting dominant low-order harmonics (e.g., 5th, 7th, 11th, 13th) is prudent. A Sliding-Window Iterative Discrete Fourier Transform (DFT) algorithm is highly effective for this purpose. Unlike a full FFT performed on a data block, the iterative DFT updates the harmonic component calculation with each new sample, minimizing latency.

The fundamental principle involves calculating the in-phase and quadrature coefficients ($a_n$, $b_n$) for the $n^{th}$ harmonic from a moving window of the most recent $N$ samples (one fundamental cycle). For a sampled current signal $i_s(k)$, the coefficients for the $n^{th}$ harmonic are traditionally:
$$ a_n = \frac{2}{N} \sum_{k=0}^{N-1} i_s(k) \cos(n \omega_0 k T_s) $$
$$ b_n = \frac{2}{N} \sum_{k=0}^{N-1} i_s(k) \sin(n \omega_0 k T_s) $$
where $\omega_0$ is the fundamental angular frequency and $T_s$ is the sampling period.

The sliding-window iterative form dramatically reduces computation. Let $k_{\text{new}}$ be the index of the newest sample. The sum for $a_n$ is updated as:
$$ S_{a_n}(k_{\text{new}}) = S_{a_n}(k_{\text{new}}-1) – i_s(k_{\text{new}}-N) \cdot \cos(n \omega_0 (k_{\text{new}}-N) T_s) + i_s(k_{\text{new}}) \cdot \cos(n \omega_0 k_{\text{new}} T_s) $$
A similar update rule applies for $b_n$. The instantaneous value of the $n^{th}$ harmonic is then reconstructed as:
$$ i_{h_n}(k) = a_n(k) \cos(n \omega_0 k T_s) + b_n(k) \sin(n \omega_0 k T_s) $$
The total harmonic reference $i_h^*$ is the sum of selected harmonic orders. This method provides excellent selectivity and is easily implemented in a DSP with pre-calculated sine/cosine tables.

Reactive Current Detection

For reactive power compensation under potentially distorted grid voltages, the $i_p$-$i_q$ method based on instantaneous reactive power theory is robust and simple. It requires a Phase-Locked Loop (PLL) to generate sinusoidal signals synchronized with the fundamental positive-sequence of the grid voltage.

The three-phase load currents ($i_{La}, i_{Lb}, i_{Lc}$) are transformed via the Clarke transformation ($C_{32}$) and then into the synchronous rotating $dq$-frame aligned with the PLL output:
$$
\begin{bmatrix}
i_p \\
i_q
\end{bmatrix} = C_{pq} \cdot C_{32} \cdot
\begin{bmatrix}
i_{La} \\
i_{Lb} \\
i_{Lc}
\end{bmatrix}
$$
where
$$ C_{32} = \sqrt{\frac{2}{3}}
\begin{bmatrix}
1 & -\frac{1}{2} & -\frac{1}{2} \\
0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}
\end{bmatrix},
\quad
C_{pq} =
\begin{bmatrix}
\sin(\theta) & -\cos(\theta) \\
-\cos(\theta) & -\sin(\theta)
\end{bmatrix}
$$
and $\theta = \omega_0 t$ from the PLL.

In this frame, the fundamental positive-sequence active and reactive components appear as DC quantities. Low-pass filters (LPFs) extract these DC components, $\overline{i_p}$ and $\overline{i_q}$. The fundamental reactive current component in the $abc$ frame is obtained by the inverse transformation:
$$
\begin{bmatrix}
i_{qf}^* \\
i_{qf}^* \\
i_{qf}^*
\end{bmatrix} = C_{32}^T \cdot C_{pq}^{-1} \cdot
\begin{bmatrix}
0 \\
\overline{i_q}
\end{bmatrix}
$$
This $i_{qf}^*$ serves as the reactive compensation reference. The same PLL used for grid synchronization of the solar inverter can be shared here.

Negative-Sequence Current Detection

For three-wire systems, imbalance manifests as a negative-sequence current component. Extraction can be efficiently done in a double synchronous reference frame. The load current is first transformed into a positive-sequence synchronous $dq^+$ frame (rotating at $\omega_0$) and a negative-sequence $dq^-$ frame (rotating at $-\omega_0$).

In the positive-sequence frame, the positive-sequence component appears as DC, while the negative-sequence component appears as a $2\omega_0$ AC component. The converse is true in the negative-sequence frame. By applying a moving average or low-pass filter in the negative-sequence $dq^-$ frame, the DC part corresponding to the negative-sequence component is isolated. An inverse transformation then yields the negative-sequence compensation reference $i_{-}^*$ in the $abc$ domain.

Comparison of Detection Algorithms for DG-FACTS
Algorithm	Target	Key Advantage	Implementation Note
Sliding-Window Iterative DFT	Selective Harmonics	Low latency, selective filtering	Requires pre-stored sine/cosine tables; computational load scales with number of harmonics tracked.
$i_p$-$i_q$ Method	Reactive Power	Robust to voltage distortion, uses existing PLL	Simple; requires two LPFs for $\overline{i_p}$ and $\overline{i_q}$.
Double Synchronous Frame	Negative-Sequence	Accurate separation of sequence components	Requires two coordinate transformations and LPFs/moving averages.

Current Reference Synthesis and Priority-Based Management

The heart of the DG-FACTS strategy for a solar inverter lies in intelligently synthesizing the final current reference from multiple, potentially competing, demands. The available resource is the inverter’s current “headroom” or redundant capacity, $I_{\text{AMP}}^*$.

Let $I_n^*$ be the peak current rating of the inverter’s power semiconductors. Let $I_p^*$ be the magnitude of the real power current required for PV generation at any moment (derived from the MPPT and DC-link voltage control loop). The available compensation capacity is:
$$ I_{\text{AMP}}^* = I_n^* – I_p^* $$
Simultaneously, the compensation needs are quantified as the magnitudes of the detected references: reactive ($I_q^*$), harmonic ($I_h^*$), and negative-sequence ($I_{-}^*$). The total demanded compensation magnitude is $I_c^* = I_q^* + I_h^* + I_{-}^*$.

A critical decision logic is required:

If $I_c^* \leq I_{\text{AMP}}^*$, all compensation demands can be met. The compensation reference is simply the sum: $i_c^* = i_q^* + i_h^* + i_{-}^*$.
If $I_c^* > I_{\text{AMP}}^*$, the inverter’s capacity is insufficient to meet all demands. A user-configurable priority scheme must be invoked.

The proposed priority logic is as follows, assuming a user-set order where Compensation 1 (e.g., reactive) has highest priority, followed by Compensation 2 (e.g., harmonics), then Compensation 3 (e.g., imbalance):

Step 1: Check if Priority 1 demand, $I_1^*$, fits within total headroom.
$$ \text{If } I_1^* \leq I_{\text{AMP}}^*, \text{ assign } i_1^* \text{ fully.} $$
$$ \text{Remaining headroom: } I_{\text{AMP1}}^* = I_{\text{AMP}}^* – I_1^* $$
If $I_1^* > I_{\text{AMP}}^*$, apply an Amplitude Scaling Algorithm (ASA) to Priority 1 only, scaling it down to fit the entire available capacity: $i_c^* = (I_{\text{AMP}}^* / I_1^*) \cdot i_1^*$. Proceed no further.

Step 2: If Priority 1 was fully accommodated, check Priority 2 demand, $I_2^*$, against remaining headroom $I_{\text{AMP1}}^*$.
$$ \text{If } I_2^* \leq I_{\text{AMP1}}^*, \text{ assign } i_2^* \text{ fully.} $$
$$ \text{Remaining headroom: } I_{\text{AMP2}}^* = I_{\text{AMP1}}^* – I_2^* $$
If $I_2^* > I_{\text{AMP1}}^*$, assign a scaled version of Priority 2: $i_c^* = i_1^* + (I_{\text{AMP1}}^* / I_2^*) \cdot i_2^*$. Proceed no further.

Step 3: If both Priorities 1 and 2 were fully accommodated, assign Priority 3 current, $i_3^*$, scaled to fit the final remaining headroom $I_{\text{AMP2}}^*$:
$$ i_c^* = i_1^* + i_2^* + (I_{\text{AMP2}}^* / I_3^*) \cdot i_3^* $$

This logic ensures that the primary function of the solar inverter (injecting $i_p^*$) is never compromised, and the most critical power quality issue as defined by the operator is addressed first with any available remaining capacity. The final reference current for the inverter is:
$$ i_{ref}^* = i_p^* + i_c^* = i_p^* + k_1 i_1^* + k_2 i_2^* + k_3 i_3^* $$
where the coefficients $k_1, k_2, k_3$ are either 1 (full allocation) or a fractional scaling factor (partial allocation) as determined by the priority logic.

Current Tracking Control Strategy

Once the composite reference $i_{ref}^*$ is generated, the inverter’s power stage must track it with high fidelity. Given that the reference may contain fundamental frequency (for real/reactive power) and harmonic frequencies (for compensation), the controller requires a wide bandwidth and high gain at selected frequencies. A promising approach is a hybrid controller combining a proportional-resonant (PR) or a proportional-integral (PI) controller in the synchronous frame for the fundamental component, augmented with a Repetitive Controller (RC) or multiple resonant controllers for harmonics.

An improved RC scheme is particularly suitable for a solar inverter in DG-FACTS mode. The RC, based on the internal model principle, provides theoretically infinite gain at all integer multiples of the fundamental frequency, ensuring excellent tracking of periodic references and rejection of periodic disturbances. Its discrete-time transfer function in a positive-feedback structure is:
$$ G_{RC}(z) = \frac{k_r z^{-N} Q(z)}{1 – z^{-N} Q(z)} $$
where $N$ is the number of samples per fundamental period, $k_r$ is a gain factor for stability, and $Q(z)$ is typically a low-pass filter or a constant slightly less than 1 to enhance robustness against frequency variations. The $z^{-N}$ term represents a one-period delay, allowing the controller to “remember” and correct the error from the previous cycle. A typical implementation embeds the RC in parallel with a PI controller, where the PI handles transient response and the RC ensures steady-state accuracy for harmonic compensation.

Typical Control Parameters for a DG-FACTS Solar Inverter
Control Loop/Element	Parameter	Typical Value/Range	Purpose
DC-Link Voltage Control (Outer Loop)	PI Gains ($K_p, K_i$)	Application-specific	Regulates DC-link voltage, generates active current reference amplitude.
Current Control (Inner Loop) – PI in dq-frame	$K_p$, $K_i$	Designed for crossover ~1/10 of switching freq.	Provides fast transient response and fundamental current tracking.
Repetitive Controller	Gain $k_r$, Filter $Q(z)$	$k_r < 1$ (e.g., 0.95), $Q(z)=0.95$ or LPF	Ensures zero steady-state error for periodic harmonics up to high order.
LCL Filter	Inductances $L_1$, $L_2$, Capacitance $C_f$	Designed per inverter rating (e.g., $L_1=0.4mH$, $C_f=20\mu F$)	Attenuates switching frequency ripple; design must consider stability under compensation currents.
Priority Logic	Threshold $\epsilon$	Small value (e.g., 0.01-0.05 p.u.)	Prevents controller churn when compensation demands are negligible.

Simulation Analysis and Performance Validation

To validate the proposed DG-FACTS concept for a solar inverter, a comprehensive time-domain simulation model was developed. The system comprises a three-phase grid, mixed linear/non-linear/unbalanced loads, and the enhanced PV inverter system. Key simulation parameters mirror a practical low-voltage distribution system setup.

The simulation sequence was designed to demonstrate dynamic mode transitions:

t = 0.05s: The solar inverter is enabled, initially with no generation or compensation.
t = 0.14s: The imbalance compensation function is activated. The inverter begins compensating for negative-sequence currents from the unbalanced load, cleaning the grid currents even without generating real power.
t = 0.34s: The PV generation function is activated. The inverter starts injecting real power current $i_p^*$ corresponding to a simulated PV input, while continuing imbalance compensation.
t = 0.54s: Reactive power compensation is activated. The inverter now provides reactive current $i_q^*$ to correct the load’s lagging power factor.
t = 0.74s: Selective harmonic compensation is activated. The inverter begins injecting harmonic currents $i_h^*$ opposite to those drawn by a non-linear diode rectifier load.

The simulation results conclusively demonstrate the feasibility. Prior to compensation, the grid current is highly distorted, unbalanced, and lags the voltage. After the full DG-FACTS functionality is engaged, the grid current becomes perfectly sinusoidal, balanced, and in phase with the voltage. Key quantitative metrics show:

Total Harmonic Distortion (THD): Reduced from 24.12% to below 3%, well within standard limits (e.g., IEEE 519).
Power Factor: Corrected from approximately 0.7 lagging to unity.
Current Unbalance Factor: Effectively reduced to near zero.
Power Tracking: The inverter accurately delivers the commanded real (e.g., 35 kW) and reactive (e.g., 10.6 kVar) power, with tracking error less than 1%.

The dynamic response during mode transitions is stable, showing that the control strategy, including the priority-based reference synthesis, manages the switch between different compensation components effectively without causing instability or excessive overshoot in the solar inverter output.

Conclusion

The integration of comprehensive power quality management functions into distributed photovoltaic solar inverters represents a cost-effective and elegant solution to two pressing grid challenges: integrating intermittent renewables and maintaining high power quality. This DG-FACTS approach maximizes the utilization of existing power electronic infrastructure. The technical implementation hinges on three pillars: precise detection algorithms (iterative DFT for harmonics, $i_p$-$i_q$ for reactive power, double-frame for negative-sequence) tailored for digital control; an intelligent, priority-based current reference synthesis strategy that safeguards the primary generation function; and a robust current tracking controller capable of handling multi-frequency references. Simulation studies confirm that a standard three-phase solar inverter, with enhanced control software, can simultaneously deliver real power and provide significant harmonic filtering, reactive power support, and load balancing. This transforms the solar inverter from a simple power source into an active grid-supportive asset, enhancing the stability and power quality of the local distribution network without the need for additional dedicated compensation hardware.