Power control strategy of wave energy converter with a hybrid double-machine hydraulic energy storage and generating system

Wave energy converters (WEC) with the increasing capacity, which has reached a level of hundreds of kilowatts, would play a role in the connected microgrid. Due to the inherent fluctuation and randomness of wave energy, the unstable output power of WEC is a threat to the power balance of the microgrid. Machines start and stop periodically and the output power changes continuously and significantly. The previous study focused little on the power control of grid-connected WECs. In this paper, a power control strategy is proposed for WECs to achieve stable power output and regulation in various wave conditions. The power control strategy is based on a hybrid double-machine hydraulic energy storage and generating system composed of a controlled unit and an uncontrolled unit. The control strategy enables the stability control and the controllable regulation of power of WEC in various wave conditions. Simulation results of several wave conditions have validated the effect of the power control strategy. The power control strategy would contribute to the extensive deployment of WECs.


Introduction
Wave energy received much concentration in the past decades for its cleanness, sustainability and immense utilization potential [1] .Wave energy converter (WEC) has experienced great development and appears to be various in concepts and shapes [2] .In early research, the capacity of WEC is small, and only a few converters are connected to the grid.With the improvement of technology, the capacity of WECs is increasing to a hundreds-kilowatts level and a considerable number of WECs are involved in the power grid.The rated power of Wave Dragon, Pelamis, British LIMPET, OCEANTEC, and WaveStar are multi-MW, 750 kW, 500 kW, 500 kW and 600 kW [3][4][5] .Located in a remote sea area with abundant wave energy sources, the power produced by WECs is imported into the nearby island microgrid of little capacity.WECs have a significant influence on the stability of the microgrid.While, due to the randomness and volatility inherent to wave energy, the output power of WECs is fluctuating and introduces instability to the power balance of the island microgrid [6] .Suppression of power oscillation and regulation of power amplitude are necessary.Previous research on the control of WECs aimed at the promotion of efficiency [7] .The power control of WEC relies on the energy storage system such as the battery and flywheel [8] .There is still a lack of study on the intrinsic stability and controllability control of the power of WEC.
Hydraulic energy storage and generating system (HESGS) is widely used and can partly smooth the output power [9,10] , which has been validated in many cases [11,12] .However, limited by the space and cost of WEC, the accumulator capacity is far from big enough to eliminate power fluctuation.To solve the instability of output power, this paper proposed a power control strategy based on a hybrid doublemachine hydraulic energy storage and generating system.The strategy can realize long-term stable generation and adjustment of power and pressure of accumulator in various wave conditions.The effects have been verified in several wave conditions by simulation.
2. The hybrid double-machine HESGS 2.1.Sturcture of hybrid double-machine HESGS HESGS involves the absorber, the hydraulic ram, the accumulator, the hydraulic motor, the waves and the permanent magnet generator.The hybrid double-machine HESGS is composed of a controlled unit and an uncontrolled unit that shares the accumulator.The structure of the hybrid double-machine HESGS is shown in Figure 1.The floating body moves up and down forced by waves and drives the piston.The oil is pumped into the accumulator from the tank.Energy is stored in the accumulator.The motor transforms hydraulic energy into rotor kinetic energy.The generator and motor are synchronous.The generator is connected to the direct current bus through a rectifier.The controlled unit is a unit with a variable rotor speed.The regulation of rotor speed is easily achieved by voltage control equipment, such as a controlled rectifier or boost circuit.The uncontrolled unit is a unit with a fixed rated speed.The mathematical models of HESGS are described by: where QC is the flow rate of the hydraulic ram and the inflow of the accumulator, v is the speed of piston, S is the area of the piston, Va is the volume of the accumulator, P0 is the pre-charge pressure, Vf is the volume of oil, Pa is the pressure of oil in the accumulator, Qm1 and Qm2 are the flow rate of motors of unit 1 and 2, Q is the displacement of motor, n is the motor speed, ηm is the mechanical efficiency of motor, Pe is electric output power of generator, ηe is efficiency of generator, and ηm and ηe are considered as a constant.To complete the generation orderly, the start and stop of motors are affected by the accumulator pressure Pa and are realized by the control valve.The opening pressure POpen and the closing pressure PClose are settable.

Analysis of power instability
The power performance of WEC with HESGS shows significant instability during actual operation.Analysis of the power instability is conducted based on the mathematical models.Assuming the oil volume is Vf-t0 in time t0, the electric power Pe in time t1 is calculated by Equations ( 2)-( 6): where Vf-t0, QC and n are the status parameters which determine the value of Pe, Vf-t0 is the initial status parameter, n is fixed or controlled, QC is mainly determined by wave condition.During operation, Vf-t0 and n are invariant.The fluctuation of power comes from the term: When ΔVf is not 0, Pe changes during operation.The accumulator pressure Pa would increase or decrease over time with the fluctuation of ΔVf.When Pa crosses the working pressure boundary of units, units would start and shut down periodically.The fluctuation of ΔVf is caused by the fluctuation of QC.
To take a further study of the power instability and power control strategy, simulations of hybrid double-machine HESGS without power control strategy are conducted and have validated the theoretical analysis of power instability.In the simulation, the start and stop of the motor are decided by the accumulator pressure Pa.The rotor speeds of two units are the rated speed nr.The parameters of hybrid double-machine HESGS are shown in Table 1.Four common wave conditions in The South China Sea are chosen as simulation wave conditions [13] .The parameters of waves are given in Table 2.The performance of double-machine HESGS is shown in Figure 2 and Figure 3.
Table 1.Parameters of hybrid double-machine HESGS.Simulation results demonstrated serious fluctuations of output power.The output power and pressure of the accumulator are periodical.The difference between the maximum and minimum output power reached 24%-28% of the average power.With the minutes, strong fluctuation of the output power of WEC would result in power imbalance frequently in the connected island microgrid.

Power control strategy
To achieve the stable operation and regulation of output power, a power control strategy of the doublemachine HESGS is proposed in this paper.The power control strategy includes power-stability control and power/pressure-amplitude control.The former is to realize a long-term stable operation.The latter is to realize the adjustment of power and pressure.

Power-stability control strategy
According to Equations ( 7) and ( 8), Pe is stable when ΔVf is 0. Adjusting n to make Qn/60 equal to QC, ΔVf is 0. However, QC is oscillating with a period of 5-7s and a relatively large amplitude.It is difficult to keep Qn/60 always equal to QC.A feasible method is keeping Qn/60 equal to the average value of QC.Then the control speed nC is calculated by: where QCT is average value of QC.
When nC is defined according to Equation ( 9), Equation ( 7) can be written as: where Pe is a relatively stable value.It is noted that the Pe in Equation ( 10) is a mean value.Small oscillation of Pe is inevitable due to the fluctuation of QC.
According to Equation ( 9), the corresponding nC is calculated for different QCT.The value of QCT is obtained according to Equation (1).The speed v in Equation ( 1) comes from the sensors in the hydraulic ram.The value of QCT is also available by flow measurement.QCT is the sum of the flow of two units.With the power control strategy, the speed and flow rate of unit 1# is a controllable value and may be different from unit 2#.To deal with the various wave condition, unit 1# is set as the first priority.A working range of unit 1# is necessary for the safe operation and the coordinated operation of two units.The range of working speed of unit 1# is 0 to nmax.When QCT≤Qnmax/60, unit 1# is open and unit 2# is closed.When QCT > Qnmax/60, unit 1# and unit 2# are open.The value of nmax depends on the parameters of HESGS.Under the power-stability control strategy, the running status of unit 2# is decided by QC, rather than the accumulator pressure.The flow rates of two units are calculated by:  =  =   ≤  =  +  = ( +  )  > . (11)

Power/Pressure-amplitude control strategy
The power-stability control strategy in Section 3.1 realizes the stability of power.Aiming at the regulation of the amplitude of power or pressure, the power/pressure-amplitude control is based on the power-stability control.The regulation of power amplitude is limited by the wave power and the energy conversion efficiency of WEC.In a certain condition, there is a maximum output of electrical power.The regulation of power amplitude is in a limited scope.
According to Equation ( 7), the amplitude of power Pe is influenced by the status parameters Vf-t0 and n.Essentially, the influence of Vf-t0 on power is from the accumulator pressure Pa which is related to Vf-t0.Pe is proportional to Pa.Based on Equation ( 4), Equation ( 7) can be written as: Pe is affected by Pa and QCT.It must be noted that the value of QCT is related to Pa.The resistance on the hydraulic piston, which influences the damping force of the power take-off system, is proportional to the pressure.Thus, the change of Pa would result in the change of motion mode of the floating body and finally lead to the change of QCT.QCT and nC are the functions of Pa.The function expression can be obtained through several methods.After building the expression, the power Pe is completely determined by Pa.
Given a target power, the corresponding target pressure Pa is obtained according to Equation ( 12) when the wave condition remains unchanged.The regulation of power is equivalent to the regulation of pressure.Similarly, precise control of pressure and power is impossible.The control objective is the mean pressure and mean power.The power/pressure-amplitude control strategy helps the achievement of the farthest energy absorption and conversion.
Based on Equations ( 4)-( 6), the adjustment of Pa is also completed by adding a deviation speed ΔnC on nC.While the regulation of nC is temporary.Once the pressure or the power reaches the target value, ΔnC is 0. The adjustment time depends on the change range of Vf and nC.Supposing that the adjusting time is t, the added speed ΔnC is calculated as follows: where Pa-t0 is the initial status parameter, and Pa-t is the target pressure.
For the safe and stable operation in transient progress, the adjusting time t and ΔnC should be subject to limitations.t should be greater than a minimum value tmin.The absolute value of ΔnC should be less than a maximum Δnmax.The bounds are determined by the parameters of HESGS.The calculation process of ΔnC is shown in Figure 4.

Integrated control strategy
The control of power is the integration of stability control and amplitude control.The integrated control speed nCS is the sum of nC and ΔnC.The algorithm of nCS is shown in Figure 5. Figure 5. Calculation process of nCS.

Simulation verification
4.1.Verification of power-stability control strategy Simulations of power-stability control in four cases in Table 2 are conducted.Simulation results are shown in Figures 6 and 7.The simulation time is 200 s.In the 0-100 s, the control strategy is not conducted and the performance of power and pressure is the same as that in Figure 2 and 3.The powerstability control strategy is adopted after 100 s.As observed from Figure 6 and 7, the power-stability control strategy works well.In the 100-200 s, the power and pressure are basically unchanged after the control strategy was applied.The volatility of power is 0.6%-3.0%.The volatility of pressure is 0.6%-3.0%.The volatility is consistent with wave amplitudes.4.2 Verification of power/pressure-amplitude control strategy Simulation of power/pressure-amplitude control strategy is conducted on the fundament of powerstability control.The adjustment of pressure is suggested greater than 1 MPa because little adjustment would be covered by the inherent fluctuation.The simulation results of power and pressure are shown in Figure 8 and 9.The simulation time is 120 s.In the 0-20 s, the power-stability control strategy is adopted.The power/pressure-amplitude control strategy is conducted in 20 s.In Case 1 and 4, the added speed ΔnC is greater than nmax.The adjusting time of Case 1 and 4 are 44.3 s and 60.1 s.In cases 2 and 3, the added speed ΔnC calculated is less than nmax.Then the adjusting time t is the minimum value, 40 s.The adjustment of power and pressure in simulation is about 6%, 5.4%, 5.1% and 10% of mean value in Case 1, 2, 3 and 4. The adjustment range is big enough to play a role in the power balance control of the connected island power grid.

Discussion
Simulation results in Section 4.1 and 4.2 proved the effectiveness of the power-stability control strategy and power/pressure-amplitude control strategy.The power-stability control strategy enables the output power and pressure stays around a fixed value.The power/pressure-amplitude control strategy realizes the appreciable regulation of output power and pressure and may help improve the efficiency of WEC.
Integrating two control strategy, the output power and pressure has become stable and controllable parameters.It enormously improves the power performance of WEC.

Conclusion
A power control strategy of WEC based on a hybrid double-machine HESGS is proposed in this paper.
The power-stability control strategy avoids the repetitive startup and shutdown of units and ensures the long-term stability of output power.It reduces the threat of WEC on the stable operation of the microgrid.
The power/pressure-amplitude control strategy makes the power and pressure controllable within a certain range.WEC processes the ability of active regulation of power.The strategy allows WEC to participate in the power balance regulation of microgrids.Besides, the controllability of pressure benefits the energy absorption of WEC.Simulation of different cases is conducted.Simulation results proved that the control strategy is effective.The application of the proposed power control strategy is easy and cheap.With the power control strategy, WEC would be more friendly for the connected grids.
The power control strategy would contribute to the wide deployment and application of WEC.

Figure 2 .
Figure 2. Performance of output power in different wave conditions.

Figure 3 .
Figure 3. Performance of pressure of accumulator in different wave conditions.

Figure 6 .
Figure 6.Performance of output power under power-stability control.

Figure 7 .
Figure 7. Performance of accumulator pressure under power-stability control.

Figure 8 .
Figure 8. Performance of output power under power/pressure-amplitude control.

Figure 9 .
Figure 9. Performance of output power under power/pressure-amplitude control.