Abstract
In this paper, a new proposal for the implementation of the well-known direct power control (DPC) technique in grid-connected photovoltaic (PV) systems is suggested. Normally, the DPC is executed using a look-up table procedure based on the error between the actual and reference values of the active and reactive power. Thus, the structure of the DPC is simple and results in a fast transient behavior of the inner current loop (injected currents). Therefore, in the current study, the DPC is reformulated using a dead-beat function. In this formulation, the reference voltage vector (RVV) is obtained in the - reference frame. Consequently, the switching states for the inverter can be obtained based on the sign of the components of the RVV. The suggested DPC is compared with the conventional one and other switching tables, which are intended for performance enhancement. Furthermore, an extended Kalman filter (EKF) is utilized to eliminate all grid-voltage sensors. Moreover, the switching frequency of the proposed technique is minimized without any need for weighting factors or cost function evaluation. The overall control technique is validated using a hardware-in-the-loop (HIL) experimental set-up and compared with other schemes under different operating conditions.
RENEWABLE energy sources (RESs) are becoming dominant in the energy market [
The RESs commonly use a two-stage structure, where the first stage is concerned with the maximum power point tracking (MPPT) technique. Popularly, this stage is dependent on the source of energy. For example, in a permanent-magnet synchronous generator based wind energy system, the first stage is a two-level converter. For PV sources, a boost converter is normally utilized to enable grid integration due to the voltage boosting capability. The second stage in different systems is usually a two-level inverter, and within this stage, the active and reactive power control is accomplished [
To regulate the active and reactive power in grid-connected applications, the most commonly utilized schemes are the voltage-oriented control (VOC) and direct power control (DPC) [
Recently, model predictive control techniques are getting more attention for different control objectives [
To this end,
Technique | Construction | Switching frequency | Flexibility | Tuning effort | Coordination transformation | Multi-variable | PWM requirement | Computational burden | Transient behavior | Steady-state response |
---|---|---|---|---|---|---|---|---|---|---|
VOC | Cascaded PI controllers, and pulse width modulation (PWM) | Fixed | Constraints and multi-objective are hard to include |
High (for PI controllers) | Yes | Coupled (active and reactive power decoupling is required) | Yes | Low | Slow | Excellent (small oscillations) |
FS-MPC | Discrete-time model of the system, and cost function design | Variable | Constraints and multi-objective can be incorporated in the cost function | Moderate (for weighting factors) | No | Decoupled | No | High | Fast | Good (moderate oscillations) |
DPC | Hysteresis controller, and look-up switching table | Variable |
Constraints and multi-objective are hard to include | Simple (for hysteresis bands) | No | Decoupled | No | Low | Fast | Bad (large oscillations) |
Various control techniques have been implemented in the literature to enhance the behavior of DPC. The main classification for such techniques is DPC with space vector modulation, DPC-based predictive control, and DPC with nonlinear controllers [
Recently, sensorless control techniques are gaining more interest due to several advantages not only in terms of cost reduction for low-power applications but also the ability to ensure continuous operation of the system in case of sensor failure. Furthermore, noise elimination and simplification of the hardware requirement are significant and major features of sensorless control techniques [
Considering the above, it is obvious that the DPC is simple without any tuning efforts. However, the conventional DPC suffers from high ripples in the steady-state, which deteriorate the quality of the injected currents. Therefore, we are motivated to sustain the simple principle of the DPC technique. In this regard, we propose a new formulation for the well-known DPC, where a dead-beat function is used to locate the optimal switching vector. In this function, the reference voltage is calculated in the - reference frame. Further on, the polarity of the two components of the reference voltage is used to set the switching actions without the need for hysteresis controllers or cost function evaluation. The grid-voltage sensors (3 sensors) are eliminated by utilizing an extended Kalman filter (EKF). This, in turn, reduces the cost and enhances the system reliability. The EKF is an efficient estimator in addition to its ability for noise rejection and filtering capability. Therefore, it is chosen for implementation in this paper. Furthermore, the reduction of the switching frequency is accomplished using weighting factorless technique. The main contributions of the current study are summarized as follows.
1) The DPC technique is novelly proposed to enhance the steady-state behavior of the conventional techniques.
2) Sensor reduction is accomplished by employing an EKF, which is considered an effective and reliable backup strategy in case of sensor failure. Furthermore, the filtering behavior of the EKF is investigated.
3) The switching frequency of the two-level inverter is reduced using a weighting factorless technique, which simplifies the overall control strategy without the need for tuning efforts.
4) Hardware-in-the-loop (HIL) of the suggested control technique is realized. Furthermore, the investigation and comparison with the conventional DPC and its enhanced versions are also conducted.
The remainder of this paper is organized as follows. Section II presents the mathematical model of the single-stage PV system. The proposed DPC without grid-voltage sensors is investigated in Section III. The experimental assessment using HIL set-up is given in Section IV. Finally, the paper is concluded in Section V.
The single-stage PV system is considered as an example of the RESs. Simply, this system is represented by a DC source, a two-level inverter, an RL filter, and a power grid [
(1) |

Fig. 1 Two-level inverter with grid integration.
where denotes the output voltage of the two-level inverter; denotes the grid voltage; denotes the flowing current; and and denote the filter parameters. This relation can be formulated in the - and - reference frames as [
(2) |
(3) |
where is the angular grid-frequency. Consequently, the expressions of active and reactive power at the same frames are:
(4) |
(5) |
Conventionally, the DPC implementation depends on dividing the - reference frame into 12 sectors. Based on this sector distribution, the optimal switching state can be located using a predefined switching table. The inputs for this table are the hysteresis commands and the grid-voltage position. The digitized commands produced from the hysteresis controller are based on the error (hysteresis band) between the reference values of the power (active and reactive) and actual values [
In the proposed DPC, a dead-beat function is used to govern which switching vector is applied. The principles of the dead-beat function are investigated in [
(6) |
where is the sampling time; and and are the future and present instants, respectively. According to dead-beat control [
(7) |
(8) |
where udref and uqref are the components of the RVV in the d-q reference frame, respectively; and idref and iqref are the components of the reference current in the d-q reference frame, respectively.
To this end, Park transformation is used to calculate the RVV in the - reference frame as:
(9) |
where is the grid-voltage angle. It is worth mentioning that we prefer to derive the control law of the proposed strategy in the - reference frame to simplify the implementation for the two-stage PV system, where commonly the DC-link voltage controller gives the reference d-axis current to the inner loop. However, the execution in the - reference frame is simply feasible in the proposed strategy by discretizing (2) directly. This, in turn, removes the step of coordinates transformation.
The possible voltage vectors of the two-level inverter are given in
Voltage vector | Switching state | Output voltages , | Output voltages , , |
---|---|---|---|
u0 | 0, 0 | 0, 0, 0 | |
u1 | , 0 | , , | |
u2 | , | , , | |
u3 | , | , , | |
u4 | , 0 | , , | |
u5 | , | , , | |
u6 | , | , , | |
u7 | 0, 0 | 0, 0, 0 |
1) Zero voltage vectors, which are notated by and .
2) Positive voltage vectors (, , and ), where the summation of the two components of the output voltage is greater than 0 ().
3) Negative voltage vectors (, , and ), for which .
As a result, the implementation of the DPC can be executed following this order:
1) If the calculated RVV equals zero, one of the zero voltage vectors is selected to be applied. In our design, u0 is selected. However, the other zero voltage vector u7 is used to minimize the switching frequency, which will be discussed in the following section.
2) If the computed RVV lies in the group of the positive voltage vectors, one vector from this group (u1, u2, and u3) will be adopted. Simply, if the two components of the RVV are positive, u2 is picked. However, if the component is negative and the component is positive, the switching state corresponding to u3 is chosen. Otherwise, u1 is nominated for application.
3) Similarly, u5 is applied for two negative components. u6 is enforced if is negative and is positive. Otherwise, u4 is placed in action.
As mentioned previously, in the present design, the voltage vector u0 is selected to be applied. However, if the previously switching state has two ones, i.e., the previous applied voltage vector is one of u2, u4, or u6, it is more convenient to consider the other zero voltage vector u7 for application. This reduces the number of commutations, and hence the switching frequency.

Fig. 2 Proposed algorithm for switching frequency minimization of proposed DPC.
In this subsection, the grid-voltage sensors are eliminated by utilizing an EKF, which is the nonlinear version of the Kalman filter [
(10) |
where is the state vector; is the input, and are the estimated grid voltages; is the measurement; w denote the system uncertainties with covariance matrix Q; and v is the measurement noise with covariance matrix R. The covariance matrices Q and R are represented as:
(11) |
Furthermore, A, B, C, and D are the system matrices, which can be expressed as (with reference to (2)):
(12) |
Therefore, the discrete model can be expressed as:
(13) |
where , and I is the identity matrix; ; ; and . Usually, the system uncertainty and measurement noise are not recognized, so the EKF is executed as:
(14) |
where is the Kalman gain; and and are the estimated values.
Finally, the implementation of the EKF can be carried out within two stages of prediction and modification. The prediction phase involves the state vector prediction and the covariance matrix error prediction as follows.
(15) |
(16) |
(17) |
where contains the partial derivatives of the state vector elements with respect to each other. In another context, it is defined as the Jacobian matrix and is expressed as:
(18) |
The modification or correction stage is formulated as:
(19) |
(20) |
(21) |
To this end, the grid voltages are replaced with their estimated values in (7) and (8). By doing so, a reduced sensor count is achieved (3 sensors are eliminated), which greatly reduces the cost and enhances the system reliability. The whole system setup and proposed DPC technique for single-stage PV system are illustrated in

Fig. 3 System set-up and proposed DPC technique for single-stage PV system.
The system under consideration consists of a DC source and a two-level inverter interfaced to the power grid via an RL filter. The system is built using HIL arrangement (RT Box CE). The real-time controller is implemented utilizing dSPACE MicroLabBox, where the voltage and current measurements are fed to the analog inputs of the controller. Furthermore, the switching actions are enforced to the digital inputs of the box. The HIL setup simplifies testing the system under different operating conditions. The configuration of the implemented system is shown in Appendix A Fig. A1.
Parameter | Value |
---|---|
DC input voltage | V |
Filter resistance | Ω |
Filter inductance | mH |
Grid-voltage (v) | V |
Grid-frequency | Hz |
Sampling time | µs |
Several attempts have been proposed to enhance the behavior of the conventional DPC by modifying the switching table. In this regard, the proposed method is compared with the conventional DPC, the first modified switching table [
The system response is investigated at step changes of the active power (), and the reference of the reactive power () is set to be zero to achieve unity power factor operation. The performance of the system is studied for three levels of active power variation, which are zero power level, 5 kW power level, and 10 kW power level.

Fig. 4 Transient behavior of different DPC techniques. (a) Conventional DPC. (b) Table . (c) Table . (d) Proposed DPC.

Fig. 5 Steady-state behavior of different DPC techniques. (a) Conventional DPC. (b) Table . (c) Table . (d) Proposed DPC.
Technique | Average active power (kW) | Average reactive power (var) |
---|---|---|
Conventional DPC | 9.52 | 317.67 |
Table | 9.52 | 378.17 |
Table | 9.23 | 188.80 |
Proposed DPC | 9.94 | -232.46 |
Regarding the steady-state behavior of the conventional DPC in
Moreover, the injected currents with the proposed DPC are more sinusoidal.
Technique | THD (%) |
---|---|
Conventional DPC | 9.62 |
Table | 9.37 |
Table | 8.28 |
Proposed DPC | 4.87 |
It is worth mentioning that the proposed DPC gives superior performance in all aspects compared with the other DPC techniques despite grid-voltage sensors elimination. Further insight is given to assess the performance of the DPC techniques, where the execution time and average switching frequency of all techniques are investigated in
Technique | Execution time (s) | (kHz) |
---|---|---|
Conventional DPC | 8.98 | 1.49 |
Table | 8.97 | 1.49 |
Table | 9.16 | 1.48 |
Proposed DPC | 18.19 | 1.44 |
To verify the outstanding performance of the proposed DPC, the conventional and modified DPC techniques are evaluated at a lower sampling time. To be specific, the sampling time is reduced to the half (50 ) and the response of the DPC techniques is revisited at the same previous step response.
In

Fig. 6 Transient behavior of DPC techniques under step change of active power at 50 μs sampling time. (a) Conventional DPC. (b) Table . (c) Table . (d) Proposed DPC.
Technique | THD (%) | (kHz) |
---|---|---|
Conventional DPC | 7.16 | 2.93 |
Table | 7.05 | 2.83 |
Table | 4.13 | 2.76 |
Proposed DPC | 2.95 | 2.65 |
In this subsection, the behavior of the proposed DPC without grid-voltage sensors is inspected.
(22) |

Fig. 7 Measured and estimated grid-voltages using EKF.

Fig. 8 Actual and estimated currents using EKF.

Fig. 9 Steady-state response of actual and estimated currents using EKF.
Case | THD (%) |
---|---|
Actual current | 4.87 |
Estimated current | 4.27 |
To verify the effectiveness of the EKF estimation, a case study is investigated, where a step-down change in the grid-voltage and grid-frequency is applied to the system. To be specific, the voltage and frequency are both decreased to 80% of their nominal values. The estimation of the voltage, in this case, is shown in

Fig. 10 Measured and estimated grid-voltages under step change of grid-voltage and grid-frequencies.
The average switching frequency of the proposed DPC with and without switching minimization is further investigated in
Technique | (kHz) |
---|---|
Proposed DPC without switching minimization | 1.72 |
Proposed DPC with switching minimization | 1.44 |
A new implementation for the DPC is suggested in this paper based on a dead-beat function, where the computed RVV is used as a guide to select the best switching state. The polarity of the components of the RVV in the - reference frame gives a simple directory to adopt the optimal switching vector. Unlike the conventional DPC, the proposed DPC can be executed without the need for a predefined switching table or hysteresis controller. Furthermore, switching frequency minimization is accomplished, in which no weighting factor is required. The grid-voltage sensors are eliminated by employing an EKF, where an accurate estimation of the voltages and currents is achieved. The comparative evaluation among the conventional DPC techniques and the proposed one udner different conditions indicates an elegant performance of the suggested methodology even when conventional techniques operate at lower sampling time. The proposed DPC achieves about 16.28% switching frequency reduction. Furthermore, the EKF is considered an effective backup strategy in case of sensor failure in addition to its filtering capability.
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