# Compressor Scheduling and Pressure Control for an Alternating Aeration Activated Sludge Process—A Simulation Study Validated on Plant Data

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. The Aeration Process

#### 1.2. State-of-the-Art

#### 1.3. Objectives & Contribution

## 2. Case Plant: Grindsted Wastewater Treatment Plant

**Algorithm****1**- A relational operator determines which compressor to activate depending on the number of completely open valves.
**Algorithm****2**- The DO controller is a relational operator between DO feedback and set-point, meaning the valves are either set completely open or closed.

## 3. Modelling of the Airflow Distribution Network

#### 3.1. Mass Balances

#### 3.2. Pipe Friction Losses

#### 3.3. Diffuser Model

#### 3.4. Valve and Flow Sensor Models

**Assumption****1**- The gas is an ideal gas and the flow through the orifice is steady.
**Assumption****2**- Flow through the orifice is an adiabatic process; there is no heat exchange with the surroundings.
**Assumption****3**- The upstream flow velocity (inlet) is much smaller than the downstream flow velocity.
**Assumption****4**- The discharge coefficient, ${C}_{d}$, is constant.

#### 3.5. Combined Model

**Step****1**- Calculate ${P}_{B}$, ${\mathit{P}}_{C}$, ${\rho}_{B}$ and ${\rho}_{C}$ from Equation (3). Note the bold notation where ${\mathbf{P}}_{C}=\left[{P}_{C,1},\cdots ,{P}_{C,4}\right]$ and ${\rho}_{C}=\left[{\rho}_{C,1},\cdots ,{\rho}_{C,4}\right]$
**Step****2****Step****3****Step****4**- Calculate ${\mathbf{Q}}_{d}$ using Equation (8). Note that ${\mathbf{Q}}_{d}=\left[{Q}_{d,1},\cdots ,{Q}_{d,4}\right]$.
**Step****5**

#### 3.6. Parameter Identification

#### 3.7. System Curves

## 4. Pressure Control

#### 4.1. Benchmark PID Controller (Benchmark PID)

#### 4.2. LUT-Feedforward Controller (LUT-FF)

#### 4.3. LUT-Feedforward-Feedback Controller (LUT-FF-FB)

## 5. Compressor Scheduling

#### 5.1. Static Power Model

**Assumption****1**- The transient dynamics of the compressors are assumed fast enough to be neglected, meaning that static models are adequate to describe the system.
**Assumption****2**- The efficiency of the motor and motor driver is constant. This implies that the system efficiency, $\eta $, can be defined as the ratio of hydraulic power to electric power [65].

#### 5.2. Compressor Load Sharing

#### 5.3. Scheduling Algorithm

**Constraint****1**- The solution should be within the flow and pressure ranges defined in Equation (17). This constraint ensures that the air supply system never exceeds the physical limitations in pressure drop across the diffusers or approaches the limits of operation (surge/stall) for the compressors.
**Constraint****2**- To facilitate biochemical treatment a minimum airflow supply for each reactor is required (${Q}_{min}$), therefore, the air supply is subject to: $Q\ge {\sum}_{i}^{4}{u}_{v,i}{Q}_{min}$

Algorithm 1: Compressor scheduling algorithm pseudo code. |

## 6. Results

**Control Rule****1**- one valve is completely open → start C1
**Control Rule****2**- two valves are completely open → start C2

## 7. Discussion

**Flow sensor dynamics**are approximated assuming a first-order filter, resulting in the model being fitted to the damped sensor measurements rather than the actual flows. This is however a necessity as there is no other option for validating the airflow distribution model without changing the system setup and implementing another sensor. Should another, faster sensor (like a pressure transmitter) be implemented, the sensor dynamics should still be modelled despite the faster dynamics, as these dynamics most likely would contribute to the over-all system dynamics.**Valve discharge coefficients**which are estimated using a numerical method minimizing a cost function. By using this approach, the estimated parameters are not identified to fit the actual discharge coefficients of the valves alone, but instead an estimate of a general “loss coefficient” for the entire system, compensating for and eliminating many of the uncertainties introduced when modelling other flow elements.

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Symbol | Description | Value | Unit |
---|---|---|---|

D | Main pipe diameter | 460 | mm |

L | Main pipe length | 16.5 | m |

${A}_{m}$ | Main pipe cross-sectional area | 0.1662 | ${\mathrm{m}}^{2}$ |

${V}_{A}$ | Volume in $C{V}_{A}$ | 4.00 | ${\mathrm{m}}^{3}$ |

${V}_{B}$ | Volume in $C{V}_{B}$ | 12.00 | ${\mathrm{m}}^{3}$ |

${V}_{C,i}$ | Volume in $C{V}_{C,i}$ | 4.00 | ${\mathrm{m}}^{3}$ |

${P}_{h}$ | Pressure at diffusers | 149.9 | kPa |

${C}_{L}$ | Leakage flow coefficient | $4.00\xb7{10}^{-6}$ | ${\mathrm{m}}^{3}/\mathrm{s}\xb7\mathrm{Pa}$ |

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**Figure 1.**Sketch of an activated sludge process. Note that the anoxic/aerobic treatment is executed alternately in the same tank.

**Figure 2.**Block diagram of the aeration system. The notation presented in this figure is used repeatedly throughout this work and is described in Table 1.

**Figure 3.**Simplified sketch of the case plant aeration system with a pressure transmitter (PT), flow transmitter (FT) and flow valve (FV).

**Figure 5.**Sketch of the airflow distribution network with control volumes marked. Airflows are noted in blue and flow regulating actuators in green.

**Figure 6.**Data points for the specific diffuser installation (from manufacturer datasheets), and the corresponding polynomial fit (2nd order) with saturations.

**Figure 8.**Numerical estimation of the discharge coefficients with different NM coefficients. Left axis: normalized value of the cost function. Right axis: value of the discharge coefficients. The stippled line indicates the iteration where the solver is within $<1\%$ of the final cost.

**Figure 9.**Comparison of model output and measured airflow to each branch (subset of validation data).

**Figure 10.**System curves for the airflow model at different valve openings. The legend denotes the sum of open valves for each configuration. The black lines denote the estimated models (using Equation (12)).

**Figure 14.**Steady-state power data, $W(P,Q)$, from the two compressors (black dots) and the fitted maps.

**Figure 16.**Selection of operation point based on valve openings. (

**a**–

**c**) shows the selected operating point with 1, 2 and 4 completely open valves, respectively.

**Figure 17.**Firstcomparison of aeration efficiency. The efficiency for the current configuration is compared to a simulation with the proposed compressor scheduling and pressure control; (

**a**) shows the compressor efficiency for case plant and simulation, (

**b**) shows which compressors are running, and (

**c**) shows the sum of open valves.

**Figure 18.**Second comparison of aeration efficiency. The efficiency for the current configuration is compared to a simulation with the proposed compressor scheduling and pressure control; (

**a**) shows the compressor efficiency for case plant and simulation, (

**b**) shows which compressors are running, and (

**c**) shows the sum of open valves.

**Table 1.**Explanation of notation used in Figure 2.

Symbol | Description | Unit |
---|---|---|

$\chi $ | Compressor load percentage | % |

${Q}_{in}$ | Airflow delivered by compressors | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${Q}_{eq}$ | Airflow through airflow distribution network | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${Q}_{v}$ | Valve airflow | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${Q}_{d}$ | Diffuser airflow | ${\mathrm{m}}^{3}/\mathrm{s}$ |

$DO$ | Dissolved oxygen | mg/L |

$N{O}_{3}^{-}$ | Nitrate concentration | mg/L |

$N{H}_{4}^{+}$ | Ammonium concentration | mg/L |

Symbol | Description | Unit |
---|---|---|

${P}_{in}$ | Upstream supply pipe pressure | kPa |

${u}_{v}$ | Valve state | % |

${Q}_{v}$ | Valve airflow | ${\mathrm{m}}^{3}$/h |

$DO$ | Dissolved oxygen | mg/L |

$D{O}_{SP}$ | Dissolved oxygen setpoint | mg/L |

$N{H}_{4}^{+}$ | Ammonium concentration | mg/L |

$N{H}_{4,SP}^{+}$ | Ammonium concentration setpoint | mg/L |

**Table 3.**Symbolic notation for the airflow model. Subscript i and j denotes the tank and compressor number, respectively. The subscript n denote a control volume given as A, B, ${C}_{i}$.

Symbol | Description | Unit |
---|---|---|

${Q}_{in,j}$ | Airflow from compressor j | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${Q}_{eq}$ | Total airflow through the supply pipe | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${Q}_{v,i}$ | Airflow through a control valve | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${Q}_{d,i}$ | Airflow through diffusers | ${\mathrm{m}}^{3}/\mathrm{s}$ |

${P}_{n}$ | Pressure (absolute) in control volume n | $\mathrm{Pa}$ |

${\rho}_{n}$ | Air density in control volume n | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

${u}_{v,i}$ | State of flow regulating valve | % |

${C}_{d}$ | Valve discharge coefficient | − |

NM Coefficient | Original NM | Fan and Zahara [63] | Wang and Shoup [64] |
---|---|---|---|

Setup 1 | Setup 2 | Setup 3 | |

Reflection (${\rho}_{NM3pt}$) | 1.00 | 1.50 | 1.29 |

Expansion (${\chi}_{NM3pt}$) | 2.00 | 2.75 | 2.29 |

Contraction (${\gamma}_{NM3pt}$) | 0.50 | 0.75 | 0.47 |

Simplex size (${\sigma}_{NM3pt}$) | 0.50 | 0.50 | 0.57 |

Final cost (normalized) | $8.8196\xb7{10}^{-2}$ | $8.8246\xb7{10}^{-2}$ | $8.9214\xb7{10}^{-2}$ |

Final ${C}_{d}$ values | $[0.178,0.116,0.117,0.131]$ | $[0.179,0.114,0.114,0.130]$ | $[0.181,0.119,0.118,0.127]$ |

Tank | 1 | 2 | 3 | 4 | Mean GOF |
---|---|---|---|---|---|

Identification Data (16 h) [GOF] | 60.29 | 64.46 | 69.08 | 79.60 | 68.63 |

Validation Data (9 days) [GOF] | 58.17 | 63.69 | 72.73 | 77.29 | 67.97 |

**Table 6.**Efficiency given for 1–4 completely open valves (higher is better), and number of compressor restart cycles (smaller is better).

Efficiency [%] | Restarts pr. Day | ||||
---|---|---|---|---|---|

1 Valve | 2 Valves | 3 Valves | 4 Valves | ||

Current | 69.7 | 77.3 | 71.6 | 61.4 | 93.4 |

Proposed | 74.8 | 78.8 | 78.2 | 76.4 | 65.8 |

Difference | 5.1 | 1.6 | 6.6 | 15.0 | −27.6 |

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**MDPI and ACS Style**

Hansen, L.D.; Veng, M.; Durdevic, P. Compressor Scheduling and Pressure Control for an Alternating Aeration Activated Sludge Process—A Simulation Study Validated on Plant Data. *Water* **2021**, *13*, 1037.
https://doi.org/10.3390/w13081037

**AMA Style**

Hansen LD, Veng M, Durdevic P. Compressor Scheduling and Pressure Control for an Alternating Aeration Activated Sludge Process—A Simulation Study Validated on Plant Data. *Water*. 2021; 13(8):1037.
https://doi.org/10.3390/w13081037

**Chicago/Turabian Style**

Hansen, Laura Debel, Morten Veng, and Petar Durdevic. 2021. "Compressor Scheduling and Pressure Control for an Alternating Aeration Activated Sludge Process—A Simulation Study Validated on Plant Data" *Water* 13, no. 8: 1037.
https://doi.org/10.3390/w13081037