District Heating: Finland Case Study

• District Heating (DH) is widespread in Europe since the early 20th century.
• In Finland, DH covered about half the heating market by 2011.
• Real-time monitoring of water flows, temperatures, and heat losses improves DH network management.
• Automated remote meter reading, applied since 2005, will expand across Helsinki within a decade.
• Automated meter reading allows more precise heat loss calculation.
• A new model estimates water flows, temperatures, and heat losses using automated hourly customer meter readings.
• Flow equations form a determined, potentially nonlinear system, solved iteratively assuming a connected graph topology.
• Water temperature and heat loss in each pipe are expressed as an over-determined linear system.
• A least squares (LSQ) solution ensures the smallest 2-norm error vector and applies to arbitrary DH networks.
• A real DH network illustrates the method using hourly temperature and flow data for one week.

Introduction

• The first DH network was established in Lockport, New York, in 1877.
• DH is common in European countries like Germany, Denmark, and Finland since the 20th century.
• In most large Finnish cities, DH covers over 90% of the heating market.
• Approximately 74% of DH is produced in combined heat and power (CHP) plants.
• DH advantages include high energy efficiency, low emissions, fuel flexibility, and heat storage utilization.
• DH systems can utilize renewable energy and regulate emissions in centralized plants.
• High energy efficiency in DH systems is advantageous.
• Surplus heat from industrial processes can also be utilized in DH systems.
• DH enables more efficient resource usage but has challenges like high investment costs and heat losses.
• The Finnish DH network is a dual-pipe system using heated water.
• Water is circulated by pumps at the heating plant, sometimes along the DH network.
• Network construction pressure is typically 1.6 MPa.
• Customers connect with indirect connections, transferring heat through exchangers.
• Heat loss in DH systems is primarily from conduction into the ground.
• A small fraction of heat also occurs from the supply pipe into the return pipe
• Studies estimate heat losses in heat distribution networks at 8-10%.
• Heat loss can be 10-20% in small networks (50 mm inner diameter average).
• Heat loss is around 4-10% in large networks (150 mm inner diameter average), due to surface area compared to transferred heat.
• It is impractical to measure the heat losses of each pipe manually in large networks.
• Estimates of heat losses in different network parts are desirable, using available measurements.
• Three main measurements are taken to compute heat consumption: volume flow rate, supply water temperatures, and return water temperatures.
• Customers send heat meter readings regularly to the energy company.
• Drawbacks included incomplete readings, distribution of consumed heat energy could not be resolved.
• Automated remote meter reading for all customers is a recent trend in DH technology.
• EU legislation will require upgraded measurement and management of DH, district cooling, and gas/electricity distribution.
• Companies are adopting remote meter reading for automated data collection of consumed heat
• It was only previously possible to measure only annual heat losses, remote meter allows for accurate, real-time energy consumption data.
• Remote meter reading enables more accurate heat loss calculation using remote meter reading since 2005.
• It is expected to be applied Helsinki-wide within the next 10 years.
• Remote reading increases DH network costs in the short term, costs will be saved long run.
• Remote meter readings are mainly used for billing at the moment, but not monitored consecutively
• Remote meter reading data from customers allows computation of hourly heat losses for each pipe.
• The energy companies can identify faults in the network and identify inefficient heat usage of customers.
• Importantly, measurement data is needed to forecast demand more accurately.
• Existing DH network calculation software systems do not compute DH network using measurements
• A new model will compute the optimal least squares (LSQ) estimate for the state of the DH network based on hourly customer consumption measurements
• The model outputs the volume flow rate and based on the input measurements, heat loss in each pipe along with supply and return temperature at each node.
• With the models output, the network state can be monitored more accurately and in real-time.
• The state information is useful for managing and operating the network more efficiently and planning DH production optimally.
• An earlier version of state estimation was presented for small cycle-free networks.
• This study extends the model using a part of a real-life network of a Finnish municipal DH company

Network Representation

• A node is the junction of two or more branches.

Definitions

• A branch is an element of the network connecting two nodes, consisting of supply and return pipes.
• A branching node is the junction of three or more branches.
• A intermediate node is the junction of any two or more than two branches, branching nodes are subset of intermediate nodes.
• A cycle is a closed circuit of consecutive branches.
• A customer node is typically a leaf node in the network.
• DH network forms a connected graph
• DH networks are mostly tree-like, can contains small number of cycles.
• Cycles make the network more robust by providing alternative routes.
• The network contains 14 customer nodes that are located as leaf nodes.
• The nominal water flow directions are shown in supply pipes, the water direction can sometimes be reversed.
• Input data includes hourly water demands and temperatures at customer one week (168 h), the known quantities consist of pipe data.
• As the water supply should equal the demand, d₁ can be computed by summing all the customer demands.
• The demand variation of different customers is to some extent coincident due to space heating depending on outdoor temperature and non-coincident use of the hot tap water.
• Due to heat consumption, the return water is about 40° Celsius cooler than the supply water.

Estimation Based on Customer Measurements

• The state estimation is implemented by the following three steps:
• First identify the topology of the network to verify that it is connected and to locate the existence of the cycle.
• Second comes the estimation of the volume flow rate for each pipe, based on measurements at measured nodes.
• Estimate the temperatures at each computed node as well as the heat loss for each pipe, based on measured temps.
• The computations in steps 2 and 3 have been implemented in Matlab.

Estimation of Water Flows

• First consider the estimation of water flows in a network without cycles and then with cycles.

Volume Flow in a Tree-like Network

• In a tree-structured network without loss of water, the volume flow in each supply pipe is identical to the corresponding return
• For each node in the network, incoming water discounted for out-going water must equal to the water consumption.
• At customer nodes, there will be a positive non-negative demand volume and in intermediate nodes, the consumption will be zero.
• The water supply at the power plant can be considered as a negative consumption,
• Matrix form is as equation matrix F times Volume = Demand Volume.
• A tree (connected, non-cyclic) with set size n contains volume size n, with the system equations consisting of n equations and n-1 variables.
• One is redundant, as the supply sums the demands and removing such equation yields a fully determined linear equation system, creating a unique solution.
• The same can be obtained without matrix computations, it can be obtained by summing up recursively along branches to Node 1.
• If there flow the supply node is known, it becomes an over-determined volume, which matlab can only compute with the LQS.

Volume Flow in a Network with Cycles

• Focus is on traditional DH networks with cycles.
• Cycles make the flow system more complicated to solve, as water can take multiple paths between nodes. In this case solving the volume flows requires flow dynamic modelling.
• A cyclic network can be created within a tree-line network by adding between nodes, which creates multiple paths
• Cycle added to the tree creates a addition variable to the network
• Creating an under-determined system, but system is under-determined both in presence and absence of the nth measurement of the supply node.
• As such, eliminating one eliminates that relationship, with with a constant value, it can now be re-solved
• Additional constrains are needed to uniquely solve all flows in a cyclic network, we write a balance equation

Solving the Volume Flow System

• The sample network contains one cycle, which which can find in Ref [24]
• At which point, P is the pressure balance equation, stops then 2 consecutive runs are smaller then Delta,
• The iteration with each cycle
• Can use Newtonian-Rampson method for computing viscosity

Estimation

Temperature Equations

• Heat loss from DH pipes is proportional to the temperature difference between the surrounding ground and the water in the pipes.
• As the water travels at constant speed in the pipe, the temperature will exponentially as a function.
• One expression the energy balance with the time for traveling the pipe length, giving to two different expression. with the temp at end.
• When the node is the destination multiple, we must introduced temp
• To consider that expression includes incoming volume

Heat Loss Equations

• Can be obtained per methods of analytical chemistry
• It broken down equation to find relationship of loss

Solving the Temp equation

• Each branch contributes Temp equation/Heat loss equations ( 4 )
• Target Nodes are in the form of more expressions
• We use matrix form
• Form right/left handed side based on network.
• Acyclic are easy. supplyside is determine. - Both fully
• Cyclistic - Over determined.
• Using 218 / 204 - To compute the heat
• Form Coefficient with right hand side with vector programming.
• Can solve independently due to matrix of program

Computational results

• 103/51 - Not going to show off of the info
• Shows two types of temps. Show cases - Good steady temp over heat. over heat.

Conclusion and Discussion

• An estimation model was developed to estimate DH networks.
• Aid and solve is rapid solving. - Prerquisite- and management. - Best satisfy demand.